TY - JOUR
TI - Filtering and portfolio optimization with stochastic unobserved drift in asset returns
AU - Fouque, Jean-Pierre
AU - Papanicolaou, Andrew
AU - Sircar, Ronnie
T2 - Communications in Mathematical Sciences
AB - We consider the problem of ltering and control in the setting of portfolio optimization in nancial markets with random factors that are not directly observable. The example that we present is a commodities portfolio where yields on futures contracts are observed with some noise. Through the use of perturbation methods, we are able to show that the solution to the full problem can be approximated by the solution of a solvable HJB equation plus an explicit correction term.
DA - 2015///
PY - 2015///
DO - 10.4310/cms.2015.v13.n4.a5
VL - 13
IS - 4
SP - 935-953
LA - en
OP -
SN - 1539-6746 1945-0796
UR - http://dx.doi.org/10.4310/CMS.2015.v13.n4.a5
DB - Crossref
KW - Portfolio optimization
KW - filtering
KW - Hamilton-Jacobi-Bellman equation
KW - asymptotic approximations
ER -
TY - JOUR
TI - Coxeter-biCatalan combinatorics
AU - Barnard, Emily
AU - Reading, Nathan
T2 - Discrete Mathematics & Theoretical Computer Science
AB - We consider several counting problems related to Coxeter-Catalan combinatorics and conjecture that the problems all have the same answer, which we call the $W$ -biCatalan number. We prove the conjecture in many cases. Nous considérons des problèmes énumératifs liés à la combinatoire de Coxeter-Catalan et conjecturons que tous les problèmes ont la même solution, que nous appelons le nombre $W$ -biCatalan. Nous prouvons la conjecture dans de nombreux cas.
DA - 2015/1/1/
PY - 2015/1/1/
DO - 10.46298/dmtcs.2519
UR - https://doi.org/10.46298/dmtcs.2519
ER -
TY - JOUR
TI - S4_Video.avi
AU - Bokka, Kishore K
AU - Lozoya, Oswaldo A
AU - Lubkin, Sharon R
AU - Jesudason, Edwin C
AU - Warburton, David
AU - Guilak, Farshid
T2 - Figshare
DA - 2015///
PY - 2015///
DO - 10.1371/journal.pone.0132015.s005
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=DRCI_CEL&KeyUT=DRCI:DATA2016078008585319&KeyUID=DRCI:DATA2016078008585319
ER -
TY - JOUR
TI - S3_Video.avi
AU - Bokka, Kishore K
AU - Lozoya, Oswaldo A
AU - Lubkin, Sharon R
AU - Jesudason, Edwin C
AU - Warburton, David
AU - Guilak, Farshid
T2 - Figshare
DA - 2015///
PY - 2015///
DO - 10.1371/journal.pone.0132015.s004
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=DRCI_CEL&KeyUT=DRCI:DATA2016078008585317&KeyUID=DRCI:DATA2016078008585317
ER -
TY - JOUR
TI - S2_Video.avi
AU - Bokka, Kishore K
AU - Lozoya, Oswaldo A
AU - Lubkin, Sharon R
AU - Jesudason, Edwin C
AU - Warburton, David
AU - Guilak, Farshid
T2 - Figshare
DA - 2015///
PY - 2015///
DO - 10.1371/journal.pone.0132015.s003
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=DRCI_CEL&KeyUT=DRCI:DATA2016078008585314&KeyUID=DRCI:DATA2016078008585314
ER -
TY - JOUR
TI - S1_Video.avi
AU - Bokka, Kishore K
AU - Lozoya, Oswaldo A
AU - Lubkin, Sharon R
AU - Jesudason, Edwin C
AU - Warburton, David
AU - Guilak, Farshid
T2 - Figshare
DA - 2015///
PY - 2015///
DO - 10.1371/journal.pone.0132015.s002
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=DRCI_CEL&KeyUT=DRCI:DATA2016078008585311&KeyUID=DRCI:DATA2016078008585311
ER -
TY - JOUR
TI - S1_File.rar
AU - Bokka, Kishore K
AU - Lozoya, Oswaldo A
AU - Lubkin, Sharon R
AU - Jesudason, Edwin C
AU - Warburton, David
AU - Guilak, Farshid
T2 - Figshare
DA - 2015///
PY - 2015///
DO - 10.1371/journal.pone.0132015.s001
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=DRCI_CEL&KeyUT=DRCI:DATA2016078008585309&KeyUID=DRCI:DATA2016078008585309
ER -
TY - JOUR
TI - Parameters and variables used in estimates and computational model.
AU - Bokka, Kishore K
AU - Lozoya, Oswaldo A
AU - Lubkin, Sharon R
AU - Jesudason, Edwin C
AU - Warburton, David
AU - Guilak, Farshid
T2 - Figshare
DA - 2015///
PY - 2015///
DO - 10.1371/journal.pone.0132015.t002
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=DRCI_CEL&KeyUT=DRCI:DATA2016036008304545&KeyUID=DRCI:DATA2016036008304545
ER -
TY - JOUR
TI - Morphogenetic Implications of Peristalsis-Driven Fluid Flow in the Embryonic Lung
AU - Bokka, Kishore K
AU - Lozoya, Oswaldo A
AU - Lubkin, Sharon R
AU - Jesudason, Edwin C
AU - Warburton, David
AU - Guilak, Farshid
T2 - Figshare
DA - 2015///
PY - 2015///
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=DRCI_CEL&KeyUT=DRCI:DATA2016074008585305&KeyUID=DRCI:DATA2016074008585305
ER -
TY - JOUR
TI - Morphogenetic Implications of Peristalsis-Driven Fluid Flow in the Embryonic Lung
AU - Bokka, Kishore K.
AU - Jesudason, Edwin C.
AU - Lozoya, Oswaldo A.
AU - Guilak, Farshid
AU - Warburton, David
AU - Lubkin, Sharon R.
T2 - Plos One
AB - Epithelial organs are almost universally secretory. The lung secretes mucus of extremely variable consistency. In the early prenatal period, the secretions are of largely unknown composition, consistency, and flow rates. In addition to net outflow from secretion, the embryonic lung exhibits transient reversing flows from peristalsis. Airway peristalsis (AP) begins as soon as the smooth muscle forms, and persists until birth. Since the prenatal lung is liquid-filled, smooth muscle action can transport fluid far from the immediately adjacent tissues. The sensation of internal fluid flows has been shown to have potent morphogenetic effects, as has the transport of morphogens. We hypothesize that these effects play an important role in lung morphogenesis. To test these hypotheses in a quantitative framework, we analyzed the fluid-structure interactions between embryonic tissues and lumen fluid resulting from peristaltic waves that partially occlude the airway. We found that if the airway is closed, fluid transport is minimal; by contrast, if the trachea is open, shear rates can be very high, particularly at the stenosis. We performed a parametric analysis of flow characteristics' dependence on tissue stiffnesses, smooth muscle force, geometry, and fluid viscosity, and found that most of these relationships are governed by simple ratios. We measured the viscosity of prenatal lung fluid with passive bead microrheology. This paper reports the first measurements of the viscosity of embryonic lung lumen fluid. In the range tested, lumen fluid can be considered Newtonian, with a viscosity of 0.016 ± 0.008 Pa-s. We analyzed the interaction between the internal flows and diffusion and conclude that AP has a strong effect on flow sensing away from the tip and on transport of morphogens. These effects may be the intermediate mechanisms for the enhancement of branching seen in occluded embryonic lungs.
DA - 2015///
PY - 2015///
DO - 10.1371/journal.pone.0132015
VL - 10
IS - 7
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000358157600180&KeyUID=WOS:000358157600180
ER -
TY - JOUR
TI - Diffusion coefficients (mum2/s) of various molecules in various fluids.
AU - Bokka, Kishore K
AU - Lozoya, Oswaldo A
AU - Lubkin, Sharon R
AU - Jesudason, Edwin C
AU - Warburton, David
AU - Guilak, Farshid
T2 - Figshare
DA - 2015///
PY - 2015///
DO - 10.1371/journal.pone.0132015.t001
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=DRCI_CEL&KeyUT=DRCI:DATA2016036008304544&KeyUID=DRCI:DATA2016036008304544
ER -
TY - JOUR
TI - A topological approach for protein classification
AU - Cang, Zixuan
AU - Mu, Lin
AU - Wu, Kedi
AU - Opron, Kristopher
AU - Xia, Kelin
AU - Wei, Guo-Wei
T2 - Computational and Mathematical Biophysics
AB - Abstract Protein function and dynamics are closely related to its sequence and structure.However, prediction of protein function and dynamics from its sequence and structure is still a fundamental challenge in molecular biology. Protein classification, which is typically done through measuring the similarity between proteins based on protein sequence or physical information, serves as a crucial step toward the understanding of protein function and dynamics. Persistent homology is a new branch of algebraic topology that has found its success in the topological data analysis in a variety of disciplines, including molecular biology. The present work explores the potential of using persistent homology as an independent tool for protein classification. To this end, we propose a molecular topological fingerprint based support vector machine (MTF-SVM) classifier. Specifically,we construct machine learning feature vectors solely fromprotein topological fingerprints,which are topological invariants generated during the filtration process. To validate the presentMTF-SVMapproach, we consider four types of problems. First, we study protein-drug binding by using the M2 channel protein of influenza A virus. We achieve 96% accuracy in discriminating drug bound and unbound M2 channels. Secondly, we examine the use of MTF-SVM for the classification of hemoglobin molecules in their relaxed and taut forms and obtain about 80% accuracy. Thirdly, the identification of all alpha, all beta, and alpha-beta protein domains is carried out using 900 proteins.We have found a 85% success in this identification. Finally, we apply the present technique to 55 classification tasks of protein superfamilies over 1357 samples and 246 tasks over 11944 samples. Average accuracies of 82% and 73% are attained. The present study establishes computational topology as an independent and effective alternative for protein classification.
DA - 2015/11/30/
PY - 2015/11/30/
DO - 10.1515/mlbmb-2015-0009
VL - 3
IS - 1
UR - http://dx.doi.org/10.1515/mlbmb-2015-0009
ER -
TY - BOOK
TI - PASCO '15 Proceedings of the 2015 International Workshop on Parallel Symbolic Computation
A3 - Dumas, Jean-Guillaume
A3 - Kaltofen, Erich L.
A3 - Pernet, Clément
DA - 2015///
PY - 2015///
PB - Association for Computing Machinery
ER -
TY - CONF
TI - A Categorification of One-Variable Polynomials
AU - Khovanov, M.
AU - Sazdanovic, R.
T2 - 27th International Conference on Formal Power Series and Algebraic Combinatorics
C2 - 2015///
C3 - Discrete Mathematics and Theoretical Computer Science
CY - Daejeon, South Korea
DA - 2015///
PY - 2015/7//
SP - 937–948
ER -
TY - CONF
TI - A categorification of the chromatic symmetric polynomial
AU - Sazdanovic, R.
AU - Yip, M.
T2 - 27th International Conference on Formal Power Series and Algebraic Combinatorics
C2 - 2015///
C3 - Discrete Mathematics and Theoretical Computer Science
CY - Daejeon, South Korea
DA - 2015///
PY - 2015/7//
SP - 631–642
ER -
TY - JOUR
TI - Imaginary Verma modules and Kashiwara algebras for Uq(gˆ)
AU - Cox, Ben
AU - Futorny, Vyacheslav
AU - Misra, Kailash C.
T2 - Journal of Algebra
AB - We consider imaginary Verma modules for quantum affine algebra Uq(gˆ), where gˆ has Coxeter–Dynkin diagram of ADE type, and construct Kashiwara type operators and the Kashiwara algebra Kq. We show that a certain quotient Nq− of Uq(gˆ) is a simple Kq-module.
DA - 2015/2//
PY - 2015/2//
DO - 10.1016/J.JALGEBRA.2014.09.025
VL - 424
SP - 390-415
J2 - Journal of Algebra
LA - en
OP -
SN - 0021-8693
UR - http://dx.doi.org/10.1016/J.JALGEBRA.2014.09.025
DB - Crossref
KW - Quantum affine algebras
KW - Imaginary Verma modules
KW - Kashiwara algebras
KW - Simple modules
ER -
TY - CONF
TI - Real-Time Implementation of a Power Series Based Nonlinear Controller for the Balance of a Single Inverted Pendulum
T2 - IMECS 2015
C2 - 2015///
C3 - International MultiConference of Engineers and Computer Scientists : IMECS 2015 : 18-20 March, 2015, the Royal Garden Hotel, Kowloon, Hong Kong
CY - Hong Kong
DA - 2015///
PY - 2015/3/18/
VL - 1
SP - 237–241
PB - Newswood Limited, International Association of Engineers
SN - 978-988-19253-2-9
ER -
TY - JOUR
TI - Hyperbolic polynomials, interlacers, and sums of squares
AU - Kummer, Mario
AU - Plaumann, Daniel
AU - Vinzant, Cynthia
T2 - Mathematical Programming
AB - Hyperbolic polynomials are real polynomials whose real hypersurfaces are maximally nested ovaloids, the innermost of which is convex. These polynomials appear in many areas of mathematics, including optimization, combinatorics and differential equations. Here we investigate the special connection between a hyperbolic polynomial and the set of polynomials that interlace it. This set of interlacers is a convex cone, which we write as a linear slice of the cone of nonnegative polynomials. In particular, this allows us to realize any hyperbolicity cone as a slice of the cone of nonnegative polynomials. Using a sums of squares relaxation, we then approximate a hyperbolicity cone by the projection of a spectrahedron. A multiaffine example coming from the Vámos matroid shows that this relaxation is not always exact. Using this theory, we characterize the real stable multiaffine polynomials that have a definite determinantal representation and construct one when it exists.
DA - 2015/10//
PY - 2015/10//
DO - 10.1007/S10107-013-0736-Y
VL - 153
IS - 1
SP - 223–245
SN - 0025-5610 1436-4646
UR - http://dx.doi.org/10.1007/S10107-013-0736-Y
ER -
TY - CONF
TI - Certifying Isolated Singular Points and their Multiplicity Structure
AU - Hauenstein, Jonathan D.
AU - Mourrain, Bernard
AU - Szanto, Agnes
AB - This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion uses a single linear differential form defined from the Jacobian matrix of the input, and defines the deflated system by applying this differential form to the original system. The advantages of this new deflation is that it does not introduce new variables and the increase in the number of equations is linear instead of the quadratic increase of previous methods. The second construction gives the coefficients of the so-called inverse system or dual basis, which defines the multiplicity structure at the singular root. We present a system of equations in the original variables plus a relatively small number of new vari-ables. We show that the roots of this new system include the original singular root but now with multiplicity one, and the new variables uniquely determine the multiplicity structure. Both constructions are "exact", meaning that they permit one to treat all conjugate roots simultaneously and can be used in certification procedures for singular roots and their multiplicity structure with respect to an exact rational polynomial system.
C2 - 2015///
C3 - Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '15
DA - 2015///
DO - 10.1145/2755996.2756645
PB - ACM Press
UR - http://dx.doi.org/10.1145/2755996.2756645
KW - isolated point
KW - root deflation
KW - dual space
KW - multiplicity structure
KW - inverse system
KW - local algebra
KW - multiplication operator
ER -
TY - JOUR
TI - Viktor Solomonovich Ryaben'kii and his school (on his 90th birthday)
AU - Godunov, S K
AU - Zhukov, V T
AU - Lazarev, M I
AU - Sofronov, I L
AU - Turchaninov, V I
AU - Kholodov, A S
AU - Tsynkov, S V
AU - Chetverushkin, B N
AU - Epshteyn, Ye Yu
T2 - Russian Mathematical Surveys
DA - 2015/12/31/
PY - 2015/12/31/
DO - 10.1070/RM2015V070N06ABEH004981
VL - 70
IS - 6
SP - 1183-1210
J2 - Russ. Math. Surv.
OP -
SN - 0036-0279 1468-4829
UR - http://dx.doi.org/10.1070/RM2015V070N06ABEH004981
DB - Crossref
ER -
TY - BOOK
TI - Reversible logic circuits
DA - 2015///
PY - 2015///
ER -
TY - JOUR
TI - On finite-dimensional representations of two-parameter quantum affine algebras
AU - Jing, Naihuan
AU - Zhang, H.
T2 - Journal of Algebra and its Applications
AB - We introduce the notion of Drinfeld polynomials of two-parameter quantum affine algebras and establish a one-to-one correspondence between finite-dimensional irreducible representations and sets of [Formula: see text]-tuples of pairs of polynomials with certain conditions.
DA - 2015///
PY - 2015///
DO - 10.1142/S0219498816500547
VL - 15
IS - 3
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84940849711&partnerID=MN8TOARS
KW - Two-parameter quantum affine algebra
KW - Drinfeld realization
KW - evaluation representation
KW - finite-dimensional representation
ER -
TY - JOUR
TI - Modules for double affine Lie algebras
AU - Jing, Naihuan
AU - Wang, C.
T2 - Frontiers of Mathematics in China
AB - Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.
DA - 2015///
PY - 2015///
DO - 10.1007/s11464-015-0447-1
VL - 11
IS - 1
SP - 89–108
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84937065004&partnerID=MN8TOARS
KW - Double affine Lie algebra
KW - Verma module
KW - irreducibility
KW - Weyl module
ER -
TY - JOUR
TI - Compactness estimates for Hamilton-Jacobi equations depending on space
DA - 2015/4/13/
PY - 2015/4/13/
ER -
TY - JOUR
TI - On compactness estimates for hyperbolic systems of conservation laws
AU - Ancona, Fabio
AU - Glass, Olivier
AU - Nguyen, Khai T.
T2 - Annales de l'Institut Henri Poincare (C) Non Linear Analysis
AB - We study the compactness in $L^{1}_{loc}$ of the semigroup mapping $(S_t)_{t > 0}$ defining entropy weak solutions of general hyperbolic systems of conservation laws in one space dimension. We establish a lower estimate for the Kolmogorov $\varepsilon$-entropy of the image through the mapping $S_t$ of bounded sets in $L^{1}\cap L^\infty$, which is of the same order $1/\varepsilon$ as the ones established by the authors for scalar conservation laws. We also provide an upper estimate of order $1/\varepsilon$ for the Kolmogorov $\varepsilon$-entropy of such sets in the case of Temple systems with genuinely nonlinear characteristic families, that extends the same type of estimate derived by De Lellis and Golse for scalar conservation laws with convex flux. As suggested by Lax, these quantitative compactness estimates could provide a measure of the order of "resolution" of the numerical methods implemented for these equations.
DA - 2015/11//
PY - 2015/11//
DO - 10.1016/j.anihpc.2014.09.002
VL - 32
IS - 6
SP - 1229-1257
J2 - Annales de l'Institut Henri Poincare (C) Non Linear Analysis
LA - en
OP -
SN - 0294-1449
UR - http://dx.doi.org/10.1016/J.ANIHPC.2014.09.002
DB - Crossref
KW - Hyperbolic systems of conservation laws
KW - Temple systems
KW - Compactness estimates
KW - Kolmogorov entropy
ER -
TY - JOUR
TI - Modeling infectious disease dynamics in the complex landscape of global health
AU - Heesterbeek, Hans
AU - Anderson, Roy M.
AU - Andreasen, Viggo
AU - Bansal, Shweta
AU - De Angelis, Daniela
AU - Dye, Chris
AU - Eames, Ken T.D.
AU - Edmunds, W. John
AU - Frost, Simon D.W.
AU - Funk, Sebastian
AU - others
T2 - Science
AB - Despite some notable successes in the control of infectious diseases, transmissible pathogens still pose an enormous threat to human and animal health. The ecological and evolutionary dynamics of infections play out on a wide range of interconnected temporal, organizational, and spatial scales, which span hours to months, cells to ecosystems, and local to global spread. Moreover, some pathogens are directly transmitted between individuals of a single species, whereas others circulate among multiple hosts, need arthropod vectors, or can survive in environmental reservoirs. Many factors, including increasing antimicrobial resistance, increased human connectivity and changeable human behavior, elevate prevention and control from matters of national policy to international challenge. In the face of this complexity, mathematical models offer valuable tools for synthesizing information to understand epidemiological patterns, and for developing quantitative evidence for decision-making in global health.
DA - 2015///
PY - 2015///
DO - 10.1126/science.aaa4339
VL - 347
IS - 6227
SP - aaa4339
UR - http://dx.doi.org/10.1126/science.aaa4339
ER -
TY - JOUR
TI - An algebraic characterization of injectivity in phase retrieval
AU - Conca, Aldo
AU - Edidin, Dan
AU - Hering, Milena
AU - Vinzant, Cynthia
T2 - Applied and Computational Harmonic Analysis
AB - A complex frame is a collection of vectors that span $\mathbb{C}^M$ and define measurements, called intensity measurements, on vectors in $\mathbb{C}^M$. In purely mathematical terms, the problem of phase retrieval is to recover a complex vector from its intensity measurements, namely the modulus of its inner product with these frame vectors. We show that any vector is uniquely determined (up to a global phase factor) from $4M-4$ generic measurements. To prove this, we identify the set of frames defining non-injective measurements with the projection of a real variety and bound its dimension.
DA - 2015/3//
PY - 2015/3//
DO - 10.1016/J.ACHA.2014.06.005
VL - 38
IS - 2
SP - 346-356
J2 - Applied and Computational Harmonic Analysis
LA - en
OP -
SN - 1063-5203
UR - http://dx.doi.org/10.1016/J.ACHA.2014.06.005
DB - Crossref
KW - Phase retrieval
KW - Algebraic geometry
ER -
TY - CHAP
TI - Response-Guided Community Detection: Application to Climate Index Discovery
AU - Bello, Gonzalo A.
AU - Angus, Michael
AU - Pedemane, Navya
AU - Harlalka, Jitendra K.
AU - Semazzi, Fredrick H. M.
AU - Kumar, Vipin
AU - Samatova, Nagiza F.
T2 - Machine Learning and Knowledge Discovery in Databases
AB - Discovering climate indices–time series that summarize spatiotemporal climate patterns–is a key task in the climate science domain. In this work, we approach this task as a problem of response-guided community detection; that is, identifying communities in a graph associated with a response variable of interest. To this end, we propose a general strategy for response-guided community detection that explicitly incorporates information of the response variable during the community detection process, and introduce a graph representation of spatiotemporal data that leverages information from multiple variables. We apply our proposed methodology to the discovery of climate indices associated with seasonal rainfall variability. Our results suggest that our methodology is able to capture the underlying patterns known to be associated with the response variable of interest and to improve its predictability compared to existing methodologies for data-driven climate index discovery and official forecasts.
PY - 2015///
DO - 10.1007/978-3-319-23525-7_45
SP - 736-751
OP -
PB - Springer International Publishing
SN - 9783319235240 9783319235257
UR - http://dx.doi.org/10.1007/978-3-319-23525-7_45
DB - Crossref
KW - Community detection
KW - Spatiotemporal data
KW - Climate index discovery
KW - Seasonal rainfall prediction
ER -
TY - JOUR
TI - Attraction-based computation of hyperbolic Lagrangian coherent structures
AU - Karrasch, Daniel
AU - Farazmand, Mohammad
AU - Haller, George
T2 - Journal of Computational Dynamics
AB - Recent advances enable the simultaneous computation of both attracting and repelling families of Lagrangian Coherent Structures (LCS) at the same initial or final time of interest. Obtaining LCS positions at intermediate times, however, has been problematic, because either the repelling or the attracting family is unstable with respect to numerical advection in a given time direction. Here we develop a new approach to compute arbitrary positions of hyperbolic LCS in a numerically robust fashion. Our approach only involves the advection of attracting material surfaces, thereby providing accurate LCS tracking at low computational cost. We illustrate the advantages of this approach on a simple model and on a turbulent velocity data set.
DA - 2015/8//
PY - 2015/8//
DO - 10.3934/jcd.2015.2.83
VL - 2
IS - 1
SP - 83-93
J2 - JCD
LA - en
OP -
SN - 2158-2491
UR - http://dx.doi.org/10.3934/jcd.2015.2.83
DB - Crossref
ER -
TY - JOUR
TI - Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
AU - Beron-Vera, Francisco J.
AU - Olascoaga, María J.
AU - Haller, George
AU - Farazmand, Mohammad
AU - Triñanes, Joaquín
AU - Wang, Yan
T2 - Chaos: An Interdisciplinary Journal of Nonlinear Science
AB - Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.
DA - 2015/8//
PY - 2015/8//
DO - 10.1063/1.4928693
VL - 25
IS - 8
SP - 087412
J2 - Chaos
LA - en
OP -
SN - 1054-1500 1089-7682
UR - http://dx.doi.org/10.1063/1.4928693
DB - Crossref
ER -
TY - JOUR
TI - Asymptotic Dynamics of Inertial Particles with Memory
AU - Langlois, Gabriel Provencher
AU - Farazmand, Mohammad
AU - Haller, George
T2 - Journal of Nonlinear Science
AB - Recent experimental and numerical observations have shown the significance of the Basset–Boussinesq memory term on the dynamics of small spherical rigid particles (or inertial particles) suspended in an ambient fluid flow. These observations suggest an algebraic decay to an asymptotic state, as opposed to the exponential convergence in the absence of the memory term. Here, we prove that the observed algebraic decay is a universal property of the Maxey–Riley equation. Specifically, the particle velocity decays algebraically in time to a limit that is $$\mathcal {O}(\epsilon )$$ -close to the fluid velocity, where $$0<\epsilon \ll 1$$ is proportional to the square of the ratio of the particle radius to the fluid characteristic length scale. These results follow from a sharp analytic upper bound that we derive for the particle velocity. For completeness, we also present a first proof of the global existence and uniqueness of mild solutions to the Maxey–Riley equation, a nonlinear system of fractional differential equations.
DA - 2015/5/1/
PY - 2015/5/1/
DO - 10.1007/s00332-015-9250-0
VL - 25
IS - 6
SP - 1225-1255
J2 - J Nonlinear Sci
LA - en
OP -
SN - 0938-8974 1432-1467
UR - http://dx.doi.org/10.1007/s00332-015-9250-0
DB - Crossref
KW - Inertial particles
KW - Fractional calculus
KW - Integro-differential equations
KW - Maxey-Riley equation
KW - Solid-fluid interaction
ER -
TY - CONF
TI - Analysis of Anderson acceleration on a simplified neutronics/thermal hydraulics system
AU - Toth, A.
AU - Kelley, C.T.
AU - Slattery, S.
AU - Hamilton, S.
AU - Clarno, K.
AU - Pawlowski, R.
C2 - 2015///
C3 - Joint International Conference on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method
DA - 2015///
ER -
TY - JOUR
TI - Second-Order Γ-limit for the Cahn–Hilliard Functional
AU - Leoni, Giovanni
AU - Murray, Ryan
T2 - Archive for Rational Mechanics and Analysis
AB - The goal of this paper is to solve a long standing open problem, namely, the asymptotic development of order 2 by Γ-convergence of the mass-constrained Cahn–Hilliard functional.
DA - 2015/9/5/
PY - 2015/9/5/
DO - 10.1007/s00205-015-0924-4
VL - 219
IS - 3
SP - 1383-1451
ER -
TY - JOUR
TI - Stochastic nonlinear mixed effects: a metformin case study
AU - Matzuka, Brett
AU - Chittenden, Jason
AU - Monteleone, Jonathan
AU - Tran, Hien
T2 - Journal of Pharmacokinetics and Pharmacodynamics
DA - 2015/11/19/
PY - 2015/11/19/
DO - 10.1007/s10928-015-9456-7
VL - 43
IS - 1
SP - 85-98
J2 - J Pharmacokinet Pharmacodyn
LA - en
OP -
SN - 1567-567X 1573-8744
UR - http://dx.doi.org/10.1007/s10928-015-9456-7
DB - Crossref
KW - Population pharmacokinetics
KW - Kalman filter
KW - tochastic differential equations
KW - Model development
KW - Parameter estimation
KW - Nonlinear mixed effects
ER -
TY - CHAP
TI - Transmission and Scattering of Waves by General Shapes with High Order Accuracy
Using the Difference Potentials Method
AU - Medvinsky, M.
AU - Turkel, E.
AU - Tsynkov, S.
T2 - Book of Abstracts, The 12th International Conference on
Mathematical and Numerical Aspects of Wave Propagation, WAVES 2015,
Karlsruhe, Germany, July 20--24, 2015
PY - 2015///
SP - 256-257
UR - https://stsynkov.math.ncsu.edu/publications/Waves2015-book-of-abstracts.pdf
ER -
TY - JOUR
TI - Reaction Path Following with Sparse Interpolation
AU - Nance, James
AU - Jakubikova, Elena
AU - Kelley, C T
T2 - J.Chem.Th. Comp.
AB - Computing the potential energy of an N-atom molecule is an expensive optimization process of 3N – 6 molecular coordinates, so following reaction pathways as a function of all 3N – 6 coordinates is unfeasible for large molecules. In this paper, we present a method that isolates d < 3N – 6 molecular coordinates and continuously follows reaction paths on d-dimensional potential energy surfaces approximated by a Smolyak’s sparse grid interpolation algorithm.1 Compared to dense grids, sparse grids efficiently improve the ratio of invested storage and computing time to approximation accuracy and thus allow one to increase the number of coordinates d in molecular reaction path following simulations. Furthermore, evaluation of the interpolant is much less expensive than the evaluation of the actual energy function, so our technique offers a computationally efficient way to simulate reaction paths on ground and excited state potential energy surfaces. To demonstrate the capabilities of our method, we present simulation results for the isomerization of 2-butene with two, three, and six degrees of freedom.
DA - 2015///
PY - 2015///
DO - 10.1021/ct5004669
VL - 10
IS - 2
SP - 2942-2949
ER -
TY - JOUR
TI - Optimization with hidden constraints and embedded Monte Carlo computations
AU - Chen, Xiaojun
AU - Kelley, C. T.
T2 - Optimization and Engineering
AB - In this paper we explore the convergence properties of deterministic direct search methods when the objective function contains a stochastic or Monte Carlo simulation. We present new results for the case where the objective is only defined on a set with certain minimal regularity properties. We present two numerical examples to illustrate the ideas.
DA - 2015/12/22/
PY - 2015/12/22/
DO - 10.1007/s11081-015-9302-1
VL - 17
IS - 1
SP - 157-175
J2 - Optim Eng
LA - en
OP -
SN - 1389-4420 1573-2924
UR - http://dx.doi.org/10.1007/s11081-015-9302-1
DB - Crossref
KW - Sampling methods
KW - Monte Carlo simulation
KW - Water resource policy
KW - Hidden constraints
ER -
TY - JOUR
TI - Preface
AU - Barlow, J.L.
AU - Drma?, Z.
AU - Ipsen, I.
AU - Moro, J.
T2 - Linear Algebra and Its Applications
DA - 2015///
PY - 2015///
DO - 10.1016/j.laa.2014.10.006
VL - 464
SP - 1-2
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84908326625&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Correlation of parameter estimators for models admitting multiple parametrizations
AU - Adoteye, K
AU - Baraldi, R
AU - Flores, K
AU - Nardini, J
AU - Banks, HT
AU - Thompson, WC
T2 - International Journal of Pure and Applied Mathematics
DA - 2015/12/15/
PY - 2015/12/15/
DO - 10.12732/ijpam.v105i3.16
VL - 105
IS - 3
SP - 497-522
SN - 1311-8080 1314-3395
UR - http://dx.doi.org/10.12732/ijpam.v105i3.16
ER -
TY - JOUR
TI - The complex-step method for sensitivity analysis of non-smooth problems arising in biology
AU - Bociu, Lorena
AU - Banks, H.T.
AU - Bekele-Maxwell, K.
AU - Noorman, M.
AU - Tillman, K.
T2 - Eurasian Journal of Mathematical and Computer Applications
DA - 2015///
PY - 2015///
VL - 3
IS - 3
SP - 16–68
SN - 2306-6172
ER -
TY - JOUR
TI - Universal geometric coefficients for the once-punctured torus
AU - Reading, Nathan
T2 - Séminaire Lotharingien de Combinatoire
DA - 2015///
PY - 2015///
VL - B71e
SP - Art. B71e, 29
UR - http://math.univ-lyon1.fr/~slc/wpapers/s71reading.html
ER -
TY - JOUR
TI - On compactness estimates for general nonlinear system hyperbolic systems
AU - Nguyen, Tien Khai
AU - Ancona, F.
AU - Glass, O.
T2 - Annales de l'Institut Henri Poincaré, Analyse non Linéaire
DA - 2015///
PY - 2015///
VL - 32
IS - 6
SP - 1229–1257
ER -
TY - JOUR
TI - GARCH Models for Credit Risk and Market Risk of Relative Returns
AU - Pang, T.
AU - Yang, S.
T2 - Journal of Finance and Management Research
DA - 2015///
PY - 2015///
VL - 1
IS - 1
SP - 19–38
ER -
TY - JOUR
TI - CVA Wrong Way Risk Multiplier Decomposition and Efficient CVA Curve
AU - Pang, T.
AU - Chen, W.
AU - Li, L.
T2 - Journal of Risk Management in Financial Institutions
DA - 2015///
PY - 2015///
VL - 8
IS - 4
SP - 390–404
ER -
TY - CONF
TI - Optimal control in a free boundary fluid-elasticity interaction
AU - Toundykov, Daniel
AU - Martin, Kristina
AU - Castle, Lucas
AU - Bociu, Lorena
T2 - The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain)
AB - We establish existence of an optimal control for the problem of minimizing flow turbulence in the case of a nonlinear fluid-structure interaction model in the framework of the known local well-posedness theory. If the initial configuration is regular, in an appropriate sense, then a class of sufficiently smooth control inputs contains an element that minimizes, within the control class, the vorticity of the fluid flow around a moving and deforming elastic solid.
C2 - 2015/11//
C3 - Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain)
DA - 2015/11//
DO - 10.3934/proc.2015.0122
PB - American Institute of Mathematical Sciences
SN - 1601330189
UR - http://dx.doi.org/10.3934/proc.2015.0122
DB - Crossref
ER -
TY - CHAP
TI - On the Solution of the Elliptic Interface Problems by Difference Potentials Method
AU - Epshteyn, Yekaterina
AU - Medvinsky, Michael
T2 - Lecture Notes in Computational Science and Engineering
AB - Designing numerical methods with high-order accuracy for problems in irregular domains and/or with interfaces is crucial for the accurate solution of many problems with physical and biological applications. The major challenge here is to design an efficient and accurate numerical method that can capture certain properties of analytical solutions in different domains/subdomains while handling arbitrary geometries and complex structures of the domains. Moreover, in general, any standard method (finite-difference, finite-element, etc.) will fail to produce accurate solutions to interface problems due to discontinuities in the model’s parameters/solutions. In this work, we consider Difference Potentials Method (DPM) as an efficient and accurate solver for the variable coefficient elliptic interface problems.
PY - 2015///
DO - 10.1007/978-3-319-19800-2_16
SP - 197-205
OP -
PB - Springer International Publishing
SN - 9783319197999 9783319198002
UR - http://dx.doi.org/10.1007/978-3-319-19800-2_16
DB - Crossref
ER -
TY - CHAP
TI - An Application of Functional Ito's Formula to Stochastic Portfolio Optimization with Bounded Memory
AU - Pang, Tao
AU - Hussain, Azmat
T2 - 2015 Proceedings of the Conference on Control and its Applications
AB - We consider a stochastic portfolio optimization model in which the returns of risky asset depend on its past performance. The price of the risky asset is described by a stochastic delay differential equation. The investor's goal is to maximize the expected discounted utility by choosing optimal investment and consumption as controls. We use the functional Ito's formula to derive the associated Hamilton-Jacobi-Bellman equation. For logarithmic and exponential utility functions, we can obtain explicit solutions in a finite dimensional space.
PY - 2015/7//
DO - 10.1137/1.9781611974072.23
SP - 159-166
OP -
PB - Society for Industrial and Applied Mathematics
SN - 9781611974072
UR - http://dx.doi.org/10.1137/1.9781611974072.23
DB - Crossref
ER -
TY - JOUR
TI - Convergence Studies on Monte Carlo Methods for Pricing Mortgage-Backed Securities
AU - Pang, Tao
AU - Yang, Yipeng
AU - Zhao, Dai
T2 - International Journal of Financial Studies
AB - Monte Carlo methods are widely-used simulation tools for market practitioners from trading to risk management. When pricing complex instruments, like mortgage-backed securities (MBS), strong path-dependency and high dimensionality make the Monte Carlo method the most suitable, if not the only, numerical method. In practice, while simulation processes in option-adjusted valuation can be relatively easy to implement, it is a well-known challenge that the convergence and the desired accuracy can only be achieved at the cost of lengthy computational times. In this paper, we study the convergence of Monte Carlo methods in calculating the option-adjusted spread (OAS), effective duration (DUR) and effective convexity (CNVX) of MBS instruments. We further define two new concepts, absolute convergence and relative convergence, and show that while the convergence of OAS requires thousands of simulation paths (absolute convergence), only hundreds of paths may be needed to obtain the desired accuracy for effective duration and effective convexity (relative convergence). These results suggest that practitioners can reduce the computational time substantially without sacrificing simulation accuracy.
DA - 2015/5/5/
PY - 2015/5/5/
DO - 10.3390/ijfs3020136
VL - 3
IS - 2
SP - 136-150
J2 - IJFS
LA - en
OP -
SN - 2227-7072
UR - http://dx.doi.org/10.3390/ijfs3020136
DB - Crossref
KW - Monte Carlo method
KW - mortgage-backed securities (MBS)
KW - coefficient of variation (CV)
KW - absolute convergence
KW - relative convergence
KW - option-adjusted spread (OAS)
KW - effective duration (DUR)
KW - effective convexity (CNVX)
KW - Greeks
ER -
TY - CONF
TI - Error-Correcting Sparse Interpolation in the Chebyshev Basis
AU - Arnold, Andrew
AU - Kaltofen, Erich L.
T2 - the 2015 ACM
AB - We present an error-correcting interpolation algorithm for a univariate black-box polynomial that has a sparse representation using Chebyshev polynomials as a term basis. Our algorithm assumes that an upper bound on the number of erroneous evaluations is given as input, and is a generalization of the algorithm by Lakshman and Saunder [SIAM J. Comput., vol. 24 (1995)] for interpolating sparse Chebyshev polynomials and the techniques in error-correcting sparse interpolation in the usual basis of consecutive powers of the variable due to Comer, Kaltofen, and Pernet [Proc. ISSAC 2012 and 2014]. We prove the correctness of our list-decoder-based algorithm with a Descartes-rule-of-signs-like property for sparse polynomials in Chebyshev basis. We also give a new algorithm that reduces the sparse interpolation in Chebyshev basis to that in power basis, thus making the many techniques for the sparse interpolation in power basis, for instance, supersparse (lacunary) interpolation over large finite fields, available to interpolation in Chebyshev basis. Furthermore, we can customize the randomized early termination algorithms from Kaltofen and Lee [J. Symb. Comput., vol. 36 (2003)] to our new approach.
C2 - 2015///
C3 - Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '15
DA - 2015///
DO - 10.1145/2755996.2756652
PB - ACM Press
SN - 9781450334358
UR - http://dx.doi.org/10.1145/2755996.2756652
DB - Crossref
KW - sparse polynomial interpolation
KW - Prony's algorithm
KW - Chebyshev polynomials
KW - Descartes' rule of signs
KW - orthogonal basis
KW - error-correcting code
ER -
TY - CHAP
TI - The Flexibility of DAE Formulations
AU - Campbell, Stephen L.
T2 - Surveys in Differential-Algebraic Equations III
AB - There has been extensive research on DAEs and their applications. One major reason given for the usefulness of DAEs is that they are the initial way that many complex systems are most naturally modeled. But there are other ways that DAE formulations are useful. This survey focuses on a number of problems where the extra flexibility of a DAE formulation permits the solution of a problem that would be hard to solve otherwise.
PY - 2015///
DO - 10.1007/978-3-319-22428-2_1
SP - 1-59
OP -
PB - Springer International Publishing
SN - 9783319224275 9783319224282
UR - http://dx.doi.org/10.1007/978-3-319-22428-2_1
DB - Crossref
ER -
TY - JOUR
TI - A strongly convergent primal–dual method for nonoverlapping domain decomposition
AU - Attouch, Hédy
AU - Briceño-Arias, Luis M.
AU - Combettes, Patrick L.
T2 - Numerische Mathematik
AB - We propose a primal–dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling constraints which model various properties of the solution at the interfaces. The proposed method can handle a wide range of linear and nonlinear problems, with flexible, possibly nonlinear, transmission conditions across the interfaces. Strong convergence in the energy spaces is established in this general setting, and without any additional assumption on the energy functions or the geometry of the problem. Several examples are presented.
DA - 2015/7/10/
PY - 2015/7/10/
DO - 10.1007/s00211-015-0751-4
VL - 133
IS - 3
SP - 443-470
J2 - Numer. Math.
LA - en
OP -
SN - 0029-599X 0945-3245
UR - http://dx.doi.org/10.1007/s00211-015-0751-4
DB - Crossref
ER -
TY - JOUR
TI - Kolmogorov n-Widths of Function Classes Induced by a Non-Degenerate Differential Operator: A Convex Duality Approach
AU - Combettes, Patrick L.
AU - Dũng, Dinh
T2 - Set-Valued and Variational Analysis
AB - The problem of computing the asymptotic order of the Kolmogorov n-width of the unit ball of the space of multivariate periodic functions induced by a differential operator associated with a polynomial in the general case when the ball is compactly embedded into L 2 has been open for a long time. In the present paper, we use convex analytical tools to solve it in the case when the differential operator is non-degenerate.
DA - 2015/8/8/
PY - 2015/8/8/
DO - 10.1007/s11228-015-0338-3
VL - 24
IS - 1
SP - 83-99
J2 - Set-Valued Var. Anal
LA - en
OP -
SN - 1877-0533 1877-0541
UR - http://dx.doi.org/10.1007/s11228-015-0338-3
DB - Crossref
KW - Asymptotic order
KW - Kolmogorov n-widths
KW - Non-degenerate differential operator
KW - Convex duality
ER -
TY - JOUR
TI - Best Approximation from the Kuhn-Tucker Set of Composite Monotone Inclusions
AU - Alotaibi, Abdullah
AU - Combettes, Patrick L.
AU - Shahzad, Naseer
T2 - Numerical Functional Analysis and Optimization
AB - Kuhn-Tucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for constructing the best approximation to a reference point from the set of Kuhn-Tucker points of a general Hilbertian composite monotone inclusion problem. Applications to systems of coupled monotone inclusions are presented. Our framework does not impose additional assumptions on the operators present in the formulation, and it does not require knowledge of the norm of the linear operators involved in the compositions or the inversion of linear operators.
DA - 2015/12/2/
PY - 2015/12/2/
DO - 10.1080/01630563.2015.1077864
VL - 36
IS - 12
SP - 1513-1532
J2 - Numerical Functional Analysis and Optimization
LA - en
OP -
SN - 0163-0563 1532-2467
UR - http://dx.doi.org/10.1080/01630563.2015.1077864
DB - Crossref
KW - Best approximation
KW - Duality
KW - Haugazeau
KW - Monotone operator
KW - Primal-dual algorithm
KW - Splitting algorithm
KW - Strong convergence
ER -
TY - JOUR
TI - Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping
AU - Combettes, Patrick L.
AU - Pesquet, Jean-Christophe
T2 - SIAM Journal on Optimization
AB - This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces. The asymptotic analysis relies on a notion of stochastic quasi-Fejér monotonicity, which is thoroughly investigated. The iterative methods under consideration feature random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and they allow for stochastic errors in the evaluation of the operators. Algorithms using quasi-nonexpansive operators or compositions of averaged nonexpansive operators are constructed, and weak and strong convergence results are established for the sequences they generate. As a by-product, novel block-coordinate operator splitting methods are obtained for solving structured monotone inclusion and convex minimization problems. In particular, the proposed framework leads to random block-coordinate versions of the Douglas--Rachford and forward-backward algorithms and of some of their variants. In the standard case of m=1 block, our results remain new as they incorporate stochastic perturbations.
DA - 2015/1//
PY - 2015/1//
DO - 10.1137/140971233
VL - 25
IS - 2
SP - 1221-1248
J2 - SIAM J. Optim.
LA - en
OP -
SN - 1052-6234 1095-7189
UR - http://dx.doi.org/10.1137/140971233
DB - Crossref
KW - arbitrary sampling
KW - block-coordinate algorithm
KW - fixed-point algorithm
KW - monotone operator splitting
KW - primal-dual algorithm
KW - stochastic quasi-Fejer sequence
KW - stochastic algorithm
KW - structured convex minimization problem
ER -
TY - JOUR
TI - Compositions and convex combinations of averaged nonexpansive operators
AU - Combettes, Patrick L.
AU - Yamada, Isao
T2 - Journal of Mathematical Analysis and Applications
AB - Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward–backward splitting algorithm for finding a zero of the sum of two monotone operators is obtained.
DA - 2015/5//
PY - 2015/5//
DO - 10.1016/j.jmaa.2014.11.044
VL - 425
IS - 1
SP - 55-70
J2 - Journal of Mathematical Analysis and Applications
LA - en
OP -
SN - 0022-247X
UR - http://dx.doi.org/10.1016/j.jmaa.2014.11.044
DB - Crossref
KW - Averaged operator
KW - Fixed-point algorithm
KW - Forward-backward splitting
KW - Monotone operator
KW - Nonexpansive operator
ER -
TY - JOUR
TI - Invariants of objects and their images under surjective maps
AU - Kogan, I. A.
AU - Olver, P. J.
T2 - Lobachevskii Journal of Mathematics
AB - We examine the relationships between the differential invariants of objects and of their images under a surjective maps. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the image, and the case when only a proper subgroup of the entire group acts projectably. In the former case, we establish a constructible isomorphism between the algebra of differential invariants of the images and the algebra of fiber-wise constant (gauge) differential invariants of the objects. In the latter case, we describe residual effects of the full transformation group on the image invariants. Our motivation comes from the problem of reconstruction of an object from multiple-view images, with central and parallel projections of curves from three-dimensional space to the two-dimensional plane serving as our main examples.
DA - 2015/7//
PY - 2015/7//
DO - 10.1134/s1995080215030063
VL - 36
IS - 3
SP - 260-285
J2 - Lobachevskii J Math
LA - en
OP -
SN - 1995-0802 1818-9962
UR - http://dx.doi.org/10.1134/s1995080215030063
DB - Crossref
KW - invariant
KW - surjective map
KW - curve
KW - centro-affine
KW - affine
KW - projective actions
KW - image processing
ER -
TY - JOUR
TI - The emergence of nonuniform spatiotemporal fractionation schemes within the standard BED model
AU - Unkelbach, Jan
AU - Papp, Dávid
T2 - Medical Physics
AB - Nonuniform spatiotemporal radiotherapy fractionation schemes, i.e., delivering distinct dose distributions in different fractions can potentially improve the therapeutic ratio. This is possible if the dose distributions are designed such that similar doses are delivered to normal tissues (exploit the fractionation effect) while hypofractionating subregions of the tumor. In this paper, the authors develop methodology for treatment planning with nonuniform fractions and demonstrate this concept in the context of intensity-modulated proton therapy (IMPT).Treatment planning is performed by simultaneously optimizing (possibly distinct) IMPT dose distributions for multiple fractions. This is achieved using objective and constraint functions evaluated for the cumulative biologically equivalent dose (BED) delivered at the end of treatment. BED based treatment planning formulations lead to nonconvex optimization problems, such that local gradient based algorithms require adequate starting positions to find good local optima. To that end, the authors develop a combinatorial algorithm to initialize the pencil beam intensities.The concept of nonuniform spatiotemporal fractionation schemes is demonstrated for a spinal metastasis patient treated in two fractions using stereotactic body radiation therapy. The patient is treated with posterior oblique beams with the kidneys being located in the entrance region of the beam. It is shown that a nonuniform fractionation scheme that hypofractionates the central part of the tumor allows for a skin and kidney BED reduction of approximately 10%-20%.Nonuniform spatiotemporal fractionation schemes represent a novel approach to exploit fractionation effects that deserves further exploration for selected disease sites.
DA - 2015/4/13/
PY - 2015/4/13/
DO - 10.1118/1.4916684
VL - 42
IS - 5
SP - 2234-2241
J2 - Med. Phys.
LA - en
OP -
SN - 0094-2405
UR - http://dx.doi.org/10.1118/1.4916684
DB - Crossref
KW - intensity-modulated proton therapy (IMPT)
KW - nonuniform fractionation
KW - biologically equivalent dose (BED)
ER -
TY - JOUR
TI - Optimal Investment and Consumption for Portfolios with Stochastic Dividends
AU - Pang, T.
AU - Varga, K.
T2 - Journal of Finance and Management Research
DA - 2015///
PY - 2015///
VL - 1
IS - 2
SP - 1–22
ER -
TY - JOUR
TI - Optimal design for minimizing uncertainty in dynamic equilibrium systems
AU - Banks, H.T.
AU - Baraldi, R.
AU - Flores, K.B.
T2 - Eurasian Journal of Mathematical and Computer Applications
DA - 2015///
PY - 2015///
VL - 3
IS - 1
SP - 23-47
ER -
TY - JOUR
TI - Виктор Соломонович Рябенький и его школа (к девяностолетию со дня рождения)
AU - Годунов, Сергей Константинович
AU - Godunov, Sergei Konstantinovich
AU - Жуков, Виктор Тимофеевич
AU - Zhukov, Victor Timofeevich
AU - Лазарев, М И
AU - Lazarev, M I
AU - Софронов, Иван Львович
AU - Sofronov, Ivan L'vovich
AU - Турчанинов, Виктор Игоревич
AU - Turchaninov, Viktor Igorevich
AU - Холодов, Александр Сергеевич
AU - Kholodov, Aleksandr Sergeevich
AU - Цынков, С В
AU - Tsynkov, Semyon
AU - Четверушкин, Борис Николаевич
AU - Chetverushkin, Boris Nikolaevich
AU - Эпштейн, Екатерина Ю
AU - Epshteyn, Yekaterina
T2 - Uspekhi Matematicheskikh Nauk
DA - 2015///
PY - 2015///
DO - 10.4213/rm9676
VL - 70
IS - 6(426)
SP - 213-236
J2 - Uspekhi Mat. Nauk
LA - ru
OP -
SN - 0042-1316 2305-2872
UR - http://dx.doi.org/10.4213/rm9676
DB - Crossref
N1 - [in Russian]
RN - [in Russian]
ER -
TY - JOUR
TI - Professor V.S. Ryaben'kii. On the occasion of the 90-th birthday
AU - Epshteyn, Yekaterina
AU - Sofronov, Ivan
AU - Tsynkov, Semyon
T2 - Applied Numerical Mathematics
AB - Numerical approximations and computational modeling of problems from Biology and Materials Science often deal with partial differential equations with varying coefficients and domains with irregular geometry. The challenge here is to design an efficient and accurate numerical method that can resolve properties of solutions in different domains/subdomains, while handling the arbitrary geometries of the domains. In this work, we consider 2D elliptic models with material interfaces and develop efficient high-order accurate methods based on Difference Potentials for such problems.
DA - 2015/7//
PY - 2015/7//
DO - 10.1016/j.apnum.2015.02.001
VL - 93
SP - 1-2
J2 - Applied Numerical Mathematics
LA - en
OP -
SN - 0168-9274
UR - http://dx.doi.org/10.1016/j.apnum.2015.02.001
DB - Crossref
ER -
TY - JOUR
TI - Reducible surgeries and Heegaard Floer homology
AU - Hom, Jennifer
AU - Lidman, Tye
AU - Zufelt, Nicholas
T2 - Mathematical Research Letters
AB - In this paper, we use Heegaard Floer homology to study reducible surgeries. In particular, suppose K is a non-cable knot in the three-sphere with an L-space surgery. If p-surgery on K is reducible, we show that p equals 2g(K)-1. This implies that any knot with an L-space surgery has at most one reducible surgery, a fact that we show additionally for any knot of genus at most two.
DA - 2015///
PY - 2015///
DO - 10.4310/mrl.2015.v22.n3.a8
VL - 22
IS - 3
SP - 763-788
LA - en
OP -
SN - 1073-2780 1945-001X
UR - http://dx.doi.org/10.4310/mrl.2015.v22.n3.a8
DB - Crossref
ER -
TY - JOUR
TI - Contact structures and reducible surgeries
AU - Lidman, Tye
AU - Sivek, Steven
T2 - Compositio Mathematica
AB - We apply results from both contact topology and exceptional surgery theory to study when Legendrian surgery on a knot yields a reducible manifold. As an application, we show that a reducible surgery on a non-cabled positive knot of genus $g$ must have slope $2g-1$ , leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum Thurston–Bennequin numbers of cables.
DA - 2015/9/24/
PY - 2015/9/24/
DO - 10.1112/s0010437x15007599
VL - 152
IS - 1
SP - 152-186
J2 - Compositio Math.
LA - en
OP -
SN - 0010-437X 1570-5846
UR - http://dx.doi.org/10.1112/s0010437x15007599
DB - Crossref
KW - cabling conjecture
KW - Dehn surgery
KW - contact structures
KW - Stein fillings
ER -
TY - JOUR
TI - Optima and equilibria for traffic flow on networks with backward propagating queues
AU - Bressan, Alberto
AU - Nguyen, Khai T.
T2 - Networks and Heterogeneous Media
AB - This paper studies an optimal decision problem for severalgroups of drivers on a network of roads. Drivers have differentorigins and destinations,and different costs, related to their departure and arrival time.On each road the flow is governed by a conservation law, while intersectionsare modeled using buffers of limited capacity, so that queues can spill backwardalong roads leading to a crowded intersection.Two main results are proved: (i)the existence of a globally optimal solution, minimizing the sum of the coststo all drivers, and (ii) the existence ofa Nash equilibrium solution, where no driver can lower his own cost by changinghis departure time or the route taken to reach destination.
DA - 2015/10//
PY - 2015/10//
DO - 10.3934/nhm.2015.10.717
VL - 10
IS - 4
SP - 717-748
J2 - NHM
LA - en
OP -
SN - 1556-1801
UR - http://dx.doi.org/10.3934/nhm.2015.10.717
DB - Crossref
KW - Traffic flows
KW - network of roads
KW - scalar conservation laws
KW - global optima
KW - Nash equilibria
ER -
TY - JOUR
TI - Optimality conditions and regularity results for time optimal control problems with differential inclusions
AU - Cannarsa, Piermarco
AU - Marigonda, Antonio
AU - Nguyen, Khai T.
T2 - Journal of Mathematical Analysis and Applications
AB - We study the time optimal control problem with a general target S for a class of differential inclusions that satisfy mild smoothness and controllability assumptions. In particular, we do not require Petrov's condition at the boundary of S. Consequently, the minimum time function T(⋅) fails to be locally Lipschitz—never mind semiconcave—near S. Instead of such a regularity, we use an exterior sphere condition for the hypograph of T(⋅) to develop the analysis. In this way, we obtain dual arc inclusions which we apply to show the constancy of the Hamiltonian along optimal trajectories and other optimality conditions in Hamiltonian form. We also prove an upper bound for the Hausdorff measure of the set of all non-Lipschitz points of T(⋅) which implies that the minimum time function is of special bounded variation (SBV).
DA - 2015/7//
PY - 2015/7//
DO - 10.1016/j.jmaa.2015.02.027
VL - 427
IS - 1
SP - 202-228
J2 - Journal of Mathematical Analysis and Applications
LA - en
OP -
SN - 0022-247X
UR - http://dx.doi.org/10.1016/j.jmaa.2015.02.027
DB - Crossref
KW - Proximal normal vectors
KW - Differential inclusions
KW - Time optimal control
KW - Semiconcave functions
ER -
TY - JOUR
TI - Conservation law models for traffic flow on a network of roads
AU - Bressan, Alberto
AU - Nguyen, Khai T.
T2 - Networks and Heterogeneous Media
AB - The paper develops a model of traffic flow near an intersection,where drivers seeking to enter a congested road wait in abuffer of limited capacity. Initial data comprise the vehicle density on each road,together with the percentage of drivers approaching the intersectionwho wish to turn into each of the outgoing roads. If the queue sizeswithin the buffer are known, then the initial-boundary valueproblems become decoupled and can be independently solvedalong each incoming road.Three variational problems are introduced, related to different kind ofboundary conditions. From thevalue functions, one recovers the traffic densityalong each incoming or outgoing road by a Lax type formula. Conversely,if these value functions are known, then the queue sizes can be determinedby balancing the boundary fluxes of all incoming and outgoing roads.In this way one obtains a contractive transformation, whose fixed point yields the unique solution of the Cauchy problemfor traffic flow in an neighborhood of the intersection. The present model accounts for backward propagation of queues along roads leading to a crowded intersection,it achieves well-posedness for general $L^\infty $ data, and continuity w.r.t. weak convergence of the initial densities.
DA - 2015/4//
PY - 2015/4//
DO - 10.3934/nhm.2015.10.255
VL - 10
IS - 2
SP - 255-293
J2 - NHM
LA - en
OP -
SN - 1556-1801
UR - http://dx.doi.org/10.3934/nhm.2015.10.255
DB - Crossref
KW - Traffic flows
KW - network of roads
KW - scalar conservation laws
KW - Hamilton Jacobi equations
KW - Lax type formula
ER -
TY - JOUR
TI - Quantitative Compactness Estimates for Hamilton–Jacobi Equations
AU - Ancona, Fabio
AU - Cannarsa, Piermarco
AU - Nguyen, Khai T.
T2 - Archive for Rational Mechanics and Analysis
AB - We study quantitative compactness estimates in $\mathbf{W}^{1,1}_{loc}$ for the map $S_t$, $t>0$ that associates to every given initial data $u_0\in Lip(\mathbb{R}^N)$ the corresponding solution $S_t u_0$ of a Hamilton-Jacobi equation $$ u_t+H\big(\nabla_{/!x} u\big)=0\,, \qquad t\geq 0,\quad x\in \mathbb{R}^N, $$ with a uniformly convex Hamiltonian $H=H(p)$. We provide upper and lower estimates of order $1/\varepsilon^N$ on the the Kolmogorov $\varepsilon$-entropy in $\mathbf{W}^{1,1}$ of the image through the map $S_t$ of sets of bounded, compactly supported initial data. Estimates of this type are inspired by a question posed by P.D. Lax within the context of conservation laws, andcould provide a measure of the order of "resolution" of a numerical method implemented for this equation.
DA - 2015/7/24/
PY - 2015/7/24/
DO - 10.1007/s00205-015-0907-5
VL - 219
IS - 2
SP - 793-828
J2 - Arch Rational Mech Anal
LA - en
OP -
SN - 0003-9527 1432-0673
UR - http://dx.doi.org/10.1007/s00205-015-0907-5
DB - Crossref
ER -
TY - JOUR
TI - Randomized algorithms for generalized Hermitian eigenvalue problems with application to computing Karhunen-Loève expansion
AU - Saibaba, Arvind K.
AU - Lee, Jonghyun
AU - Kitanidis, Peter K.
T2 - Numerical Linear Algebra with Applications
AB - Summary We describe randomized algorithms for computing the dominant eigenmodes of the generalized Hermitian eigenvalue problem A x = λ B x , with A Hermitian and B Hermitian and positive definite. The algorithms we describe only require forming operations A x , B x and B −1 x and avoid forming square roots of B (or operations of the form, B 1/2 x or B −1/2 x ). We provide a convergence analysis and a posteriori error bounds and derive some new results that provide insight into the accuracy of the eigenvalue calculations. The error analysis shows that the randomized algorithm is most accurate when the generalized singular values of B −1 A decay rapidly. A randomized algorithm for the generalized singular value decomposition is also provided. Finally, we demonstrate the performance of our algorithm on computing an approximation to the Karhunen–Loève expansion, which involves a computationally intensive generalized Hermitian eigenvalue problem with rapidly decaying eigenvalues. Copyright © 2015 John Wiley & Sons, Ltd.
DA - 2015/11/13/
PY - 2015/11/13/
DO - 10.1002/nla.2026
VL - 23
IS - 2
SP - 314-339
J2 - Numer. Linear Algebra Appl.
LA - en
OP -
SN - 1070-5325
UR - http://dx.doi.org/10.1002/nla.2026
DB - Crossref
KW - randomized algorithms
KW - generalized Hermitian eigenvalue problems
KW - Karhunen-Loeve expansion
ER -
TY - JOUR
TI - Fast computation of uncertainty quantification measures in the geostatistical approach to solve inverse problems
AU - Saibaba, A.K.
AU - Kitanidis, P.K.
T2 - Advances in Water Resources
AB - We consider the computational challenges associated with uncertainty quantification involved in parameter estimation such as seismic slowness and hydraulic transmissivity fields. The reconstruction of these parameters can be mathematically described as Inverse Problems which we tackle using the Geostatistical approach. The quantification of uncertainty in the Geostatistical approach involves computing the posterior covariance matrix which is prohibitively expensive to fully compute and store. We consider an efficient representation of the posterior covariance matrix at the maximum a posteriori (MAP) point as the sum of the prior covariance matrix and a low-rank update that contains information from the dominant generalized eigenmodes of the data misfit part of the Hessian and the inverse covariance matrix. The rank of the low-rank update is typically independent of the dimension of the unknown parameter. The cost of our method scales as $\bigO(m\log m)$ where $m $ dimension of unknown parameter vector space. Furthermore, we show how to efficiently compute measures of uncertainty that are based on scalar functions of the posterior covariance matrix. The performance of our algorithms is demonstrated by application to model problems in synthetic travel-time tomography and steady-state hydraulic tomography. We explore the accuracy of the posterior covariance on different experimental parameters and show that the cost of approximating the posterior covariance matrix depends on the problem size and is not sensitive to other experimental parameters.
DA - 2015///
PY - 2015///
DO - 10.1016/j.advwatres.2015.04.012
VL - 82
SP - 124-138
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84929572878&partnerID=MN8TOARS
KW - Inverse problems
KW - Geostatistical approach
KW - Uncertainty quantification
KW - Seismic tomography
KW - Hydraulic tomography
ER -
TY - JOUR
TI - Fast algorithms for hyperspectral diffuse optical tomography
AU - Saibaba, A.K.
AU - Kilmer, M.
AU - Miller, E.L.
AU - Fantini, S.
T2 - SIAM Journal on Scientific Computing
AB - The image reconstruction of chromophore concentrations using diffuse optical tomography (DOT) data can be described mathematically as an ill-posed inverse problem. Recent work has shown that the use of hyperspectral DOT data, as opposed to data sets comprising a single or, at most, a dozen wavelengths, has the potential for improving the quality of the reconstructions. The use of hyperspectral diffuse optical data in the formulation and solution of the inverse problem poses a significant computational burden. The forward operator is, in actuality, nonlinear. However, under certain assumptions, a linear approximation, called the Born approximation, provides a suitable surrogate for the forward operator, and we assume this to be true in the present work. Computation of the Born matrix requires the solution of thousands of large scale discrete PDEs and the reconstruction problem requires matrix-vector products with the (dense) Born matrix. In this paper, we address both of these difficulties, thus making the Born approach a computational viable approach for hyperspectral DOT reconstruction. In this paper, we assume that the images we wish to reconstruct are anomalies of unknown shape and constant value, described using a parametric level set approach [A. Aghasi, M. Kilmer, and E. L. Miller, SIAM J. Imaging Sci., 4 (2011), pp. 618--650] on a constant background. Specifically, to address the issue of the PDE solves, we develop a novel recycling-based Krylov subspace approach that leverages certain system similarities across wavelengths. To address the expense of using the Born operator in the inversion, we present a fast algorithm for compressing the Born operator that locally compresses across wavelengths for a given source-detector set and then recursively combines the low-rank factors to provide a global low-rank approximation. This low-rank approximation can be used implicitly to speed up the recovery of the shape parameters and the chromophore concentrations. We provide a detailed analysis of the accuracy and computational costs of the resulting algorithms and demonstrate the validity of our approach by detailed numerical experiments on a realistic geometry for breast imaging.
DA - 2015///
PY - 2015///
DO - 10.1137/140990073
VL - 37
IS - 5
SP - B712-B743
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84945917007&partnerID=MN8TOARS
KW - diffuse optical tomography
KW - inverse problems
KW - recycling Krylov subspaces
KW - parametric level set
KW - recursive SVD
ER -
TY - JOUR
TI - Fast Kalman filter using hierarchical matrices and a low-rank perturbative approach
AU - Saibaba, A.K.
AU - Miller, E.L.
AU - Kitanidis, P.K.
T2 - Inverse Problems
AB - We develop a fast algorithm for a Kalman filter applied to the random walk forecast model. The key idea is an efficient representation of the estimate covariance matrix at each time step as a weighted sum of two contributions—the process noise covariance matrix and a low-rank term computed from a generalized eigenvalue problem, which combines information from the noise covariance matrix and the data. We describe an efficient algorithm to update the weights of the preceding terms and the computation of eigenmodes of the generalized eigenvalue problem. The resulting algorithm for the Kalman filter with a random walk forecast model scales as in memory and in computational cost, where N is the number of grid points. We show how to efficiently compute measures of uncertainty and conditional realizations from the state distribution at each time step. An extension to the case with nonlinear measurement operators is also discussed. Numerical experiments demonstrate the performance of our algorithms, which are applied to a synthetic example from monitoring CO2 in the subsurface using travel-time tomography.
DA - 2015///
PY - 2015///
DO - 10.1088/0266-5611/31/1/015009
VL - 31
IS - 1
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84920486586&partnerID=MN8TOARS
KW - Kalman filter
KW - hierarchical matrices
KW - uncertainty quantification
KW - random walk forecast model
ER -
TY - JOUR
TI - A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers
AU - Bakhos, T.
AU - Saibaba, A.K.
AU - Kitanidis, P.K.
T2 - Journal of Computational Physics
AB - We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.
DA - 2015///
PY - 2015///
DO - 10.1016/j.jcp.2015.07.007
VL - 299
SP - 940-954
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84938709974&partnerID=MN8TOARS
KW - Inverse problems
KW - Krylov solvers
KW - Hydraulic tomography
KW - Laplace transforms
ER -
TY - CONF
TI - 3D parameter reconstruction in hyperspectral diffuse optical tomography
AU - Saibaba, A.K.
AU - Krishnamurthy, N.
AU - Anderson, P.G.
AU - Kainerstorfer, J.M.
AU - Sassaroli, A.
AU - Miller, E.L.
AU - Fantini, S.
AU - Kilmer, M.E.
AB - The imaging of shape perturbation and chromophore concentration using Diffuse Optical Tomography (DOT) data can be mathematically described as an ill-posed and non-linear inverse problem. The reconstruction algorithm for hyperspectral data using a linearized Born model is prohibitively expensive, both in terms of computation and memory. We model the shape of the perturbation using parametric level-set approach (PaLS). We discuss novel computational strategies for reducing the computational cost based on a Krylov subspace approach for parameteric linear systems and a compression strategy for the parameter-to-observation map. We will demonstrate the validity of our approach by comparison with experiments.
C2 - 2015///
C3 - Progress in Biomedical Optics and Imaging - Proceedings of SPIE
DA - 2015///
DO - 10.1117/12.2079775
VL - 9319
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84928719400&partnerID=MN8TOARS
KW - Hyperspectral Imaging
KW - Diffuse Optical Tomography
KW - Born approximation
KW - Fast algorithms
ER -
TY - JOUR
TI - Two evolving social network models
AU - Magura, S. R.
AU - Pong, V. H.
AU - Durrett, R.
AU - Sivakoff, D.
T2 - Alea-Latin American Journal of Probability and Mathematical Statistics
DA - 2015///
PY - 2015///
VL - 12
IS - 2
SP - 699-715
ER -
TY - CONF
TI - A small frame and a certificate of its injectivity
AU - Vinzant, C.
AB - We present a complex frame of eleven vectors in 4-space and prove that it defines injective measurements. That is, any rank-one 4 × 4 Hermitian matrix is uniquely determined by its values as a Hermitian form on this collection of eleven vectors. This disproves a recent conjecture of Bandeira, Cahill, Mixon, and Nelson. We use algebraic computations and certificates in order to prove injectivity.
C2 - 2015///
C3 - 2015 International Conference on Sampling Theory and Applications (SAMPTA)
DA - 2015///
DO - 10.1109/sampta.2015.7148879
SP - 197-200
ER -
TY - JOUR
TI - The Helmholtz Conditions and the Method of Controlled Lagrangians
AU - Bloch, Anthony M.
AU - Krupka, Demeter
AU - Zenkov, Dmitry V.
T2 - INVERSE PROBLEM OF THE CALCULUS OF VARIATIONS: LOCAL AND GLOBAL THEORY
AB - In this chapter we consider the relationship between the classical inverse problem of the calculus of variations and the method of controlled Lagrangians. The latter is a technique for deriving stabilizing feedback controls for nonlinear controlled mechanical systems. It relies on deriving a Lagrangian which describes the feedback controlled dynamics. This is a nontrivial extension to the theory of the inverse problem as it involves controls. We discuss various aspects of both subjects and illustrate the theory with examples.
DA - 2015///
PY - 2015///
DO - 10.2991/978-94-6239-109-3_1
SP - 1-29
ER -
TY - CONF
TI - Recent advances in beam optics analyzer
AU - Bui, T.
AU - Read, M.
AU - Lin, M. C.
AU - Ives, R. L.
AU - Tallis, B.
AU - Tran, Hien
AB - Beam Optics Analyzer (BOA) is a finite element, particle-in-cell, charged particle code. We will present its recent advances including methodologies and numerical results to simulate a gridded magnetron, study surface coating by investigating backscattered electron penetration depth, and use permanent magnets to focus doubly converged electron beams.
C2 - 2015///
C3 - 2015 ieee international vacuum electronics conference (ivec)
DA - 2015///
DO - 10.1109/ivec.2015.7223806
ER -
TY - CONF
TI - The nonnegative matrix factorization and atomic deconvolution
AU - Ito, K.
AU - Landi, A. K.
AB - The Nonnegative Matrix Factorization is an unsupervised maching learning technique that finds a representation of measured data in terms of two low-rank factors. It has recently gained popularity in various applications as a feature selection and dimension reduction tool, e.g. text mining, signal processing, and image processing. Thus, the nonnegative matrix factorization is an increasingly important tool in big data analysis as data continues to grow not only in size but also in complexity. In this paper, we advance the NMF analysis in the case of the convolution. That is, the two factors have the clear roles of convolution kernel and signal. Specifically, for the case of the point-spread function, atoms are the weights that describe the kernel. Using proper atoms, we develop a method for the blind deconvolution based on an NMF representation so that we obtain an estimate of the signal and the kernel. In addition, with Magnetic Resonance Imaging (MRI). Specifically, we extend the idea of the two factors to the Fourier transform and develop a coordinate-descent method in order to determine phases.
C2 - 2015///
C3 - Proceedings 2015 ieee international conference on bioinformatics and biomedicine
DA - 2015///
DO - 10.1109/bibm.2015.7359923
SP - 1650-1657
ER -
TY - CONF
TI - Robust finite-time filtering for singular discrete-time stochastic systems
AU - Zhang, A. Q.
AU - Campbell, Stephen
AB - This paper addresses the problem of singular stochastic finite-time filter design for uncertain discrete-time singular stochastic systems. The stochastic Lyapunov function method is adopted to design a filter such that for all admissible uncertainties, the filtering error system is singular stochastic finite-time stable (SSFTS) and preserves a prescribed performance level. A sufficient condition for the existence of a filter for the system under consideration is developed and the corresponding filter parameters can be calculated by solving a sequence of linear matrix inequalities (LMI). Finally, a numerical example is given to illustrate the design procedure and the effectiveness of the proposed method.
C2 - 2015///
C3 - 2015 27th chinese control and decision conference (ccdc)
DA - 2015///
DO - 10.1109/ccdc.2015.7162049
SP - 913–918
ER -
TY - JOUR
TI - Bayesian uncertainty analysis of finite deformation viscoelasticity
AU - Miles, Paul
AU - Hays, Michael
AU - Smith, Ralph
AU - Oates, William
T2 - MECHANICS OF MATERIALS
AB - The viscoelasticity of the dielectric elastomer, VHB 4910, is experimentally characterized, modeled, and analyzed using Bayesian uncertainty analysis. Whereas these materials are known for their large-field induced deformation and broad applications in smart structures, the rate-dependent viscoelastic effects are not well understood. To address this issue, we quantify both the hyperelastic and viscoelastic constitutive behavior and use Bayesian uncertainty analysis to assess several key modeling attributes. Specifically, we compare an Ogden-based phenomenological model to a nonaffine hyperelastic model and couple hyperelasticity to both linear and nonlinear viscoelasticity. The utilization of Bayesian statistics is shown to provide insight into quantifying nonlinear viscoelasticity behavior as a function of internal state variables. The results are validated experimentally in the finite deformation regime over a range of stretch rates spanning four orders of magnitude (6.7×10-5–0.67 Hz). A unique set of hyperelastic parameters are identified, independent of the stretch rate. In addition, comparisons of the linear and nonlinear viscoelastic models demonstrate a reduction in modeling error by approximately a factor of three. Finally, the viscoelastic time constant is shown to produce an inverse stretch rate power law dependence regardless of which hyperelastic model is used.
DA - 2015/12//
PY - 2015/12//
DO - 10.1016/j.mechmat.2015.07.002
VL - 91
SP - 35-49
SN - 1872-7743
KW - Viscoelasticity
KW - Uncertainty
KW - Dielectric elastomers
KW - Bayesian statistics
ER -
TY - BOOK
TI - The inverse problem of the calculus of variations: Local and global theory
DA - 2015///
PY - 2015///
DO - 10.2991/978-94-6239-109-3
PB - Amsterdam: Atlantis Press
SN - 9789462391086
ER -
TY - JOUR
TI - Some new analysis results for a class of interface problems
AU - Li, Zhilin
AU - Wang, Li
AU - Aspinwall, Eric
AU - Cooper, Racheal
AU - Kuberry, Paul
AU - Sanders, Ashley
AU - Zeng, Ke
T2 - MATHEMATICAL METHODS IN THE APPLIED SCIENCES
AB - Interface problems modeled by differential equations have many applications in mathematical biology, fluid mechanics, material sciences, and many other areas. Typically, interface problems are characterized by discontinuities in the coefficients and/or the Dirac delta function singularities in the source term. Because of these irregularities, solutions to the differential equations are not smooth or discontinuous. In this paper, some new results on the jump conditions of the solution across the interface are derived using the distribution theory and the theory of weak solutions. Some theoretical results on the boundary singularity in which the singular delta function is at the boundary are obtained. Finally, the proof of the convergency of the immersed boundary (IB) method is presented. The IB method is shown to be first‐order convergent in L ∞ norm. Copyright © 2013 John Wiley & Sons, Ltd.
DA - 2015/12//
PY - 2015/12//
DO - 10.1002/mma.2865
VL - 38
IS - 18
SP - 4530-4539
SN - 1099-1476
KW - immersed boundary (IB) method
KW - immersed interface method (IIM)
KW - jump conditions
KW - discontinuous coefficient
KW - Dirac delta function
KW - weak solution
KW - boundary singularity
KW - convergence of IB method
KW - equivalent boundary conditions
ER -
TY - JOUR
TI - Insights into the Spin-State Transitions in [Fe(tpy)2]2+: Importance of the Terpyridine Rocking Motion
AU - Nance, James
AU - Bowman, David N.
AU - Mukherjee, Sriparna
AU - Kelley, C. T.
AU - Jakubikova, Elena
T2 - Inorganic Chemistry
AB - Iron(II) polypyridine complexes have the potential for numerous applications on a global scale, such as sensitizers, sensors, and molecular memory. The excited-state properties of these systems, particularly the intersystem crossing (ISC) rates, are sensitive to the choice of ligands and can be significantly altered depending on the coordination environment. We employ density functional theory and Smolyak's sparse grid interpolation algorithm to construct potential energy surfaces (PESs) for the photophysically relevant states ((1)A, (3,5)MC, and (1,3)MLCT) of the [Fe(tpy)2](2+) (tpy = 2,2':6',2"-terpyridine) complex, with the goal of obtaining a deeper understanding of the ground- and excited-state electronic structure of this system. The three dimensions that define our adiabatic PESs consist of equatorial and axial metal-ligand bond length distortions and a terpyridine ligand "rocking angle", which has not previously been investigated. The intersection crossing seams and minimum energy crossing points (MECPs) between surfaces are also determined. Overall, we find that the PESs of all electronic excited states investigated are characterized by low-energy valleys along the tpy rocking-angle coordinate. This results in the presence of large low-energy areas around the MECPs on the intersection seams of different electronic states and indicates that inclusion of this third coordinate is crucial for an adequate description of the PESs and surface crossing seams of the [Fe(tpy)2](2+) complex. Finally, we suggest that tuning the energetics of the tpy ligand rocking motion could provide a way to control the ISC process in this complex.
DA - 2015/11/16/
PY - 2015/11/16/
DO - 10.1021/acs.inorgchem.5b01747
VL - 54
IS - 23
SP - 11259-11268
J2 - Inorg. Chem.
LA - en
OP -
SN - 0020-1669 1520-510X
UR - http://dx.doi.org/10.1021/acs.inorgchem.5b01747
DB - Crossref
ER -
TY - JOUR
TI - In Memoriam: Slavik Jablan 1952-2015 Obituary
AU - Crowe, Donald
AU - Darvas, Gyoergy
AU - Huylebrouck, Dirk
AU - Kappraff, Jay
AU - Kauffman, Louis
AU - Lambropoulou, Sofia
AU - Przytycki, Jozef
AU - Radovic, Ljiljana
AU - Sazdanovic, Radmila
AU - Spinadel, Vera W.
AU - Zekovic, Ana
T2 - SYMMETRY-BASEL
AB - first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing: Column Width: Background: Open AccessObituary In Memoriam: Slavik Jablan 1952–2015 by Donald Crowe 1, György Darvas 2, Dirk Huylebrouck 3, Jay Kappraff 4, Louis Kauffman 5, Sofia Lambropoulou 6, Jozef Przytycki 7, Ljiljana Radović 8, Radmila Sazdanovic 9,*, Vera W. De Spinadel 10, Ana Zeković 11 and Symmetry Editorial Office 12 1 Department of Mathematics, University of Wisconsin-Madison, Madison WI 53706, USA 2 Symmetrion, 29 Eötvös St., Budapest H-1067, Hungary 3 Faculty of Architecture, KU Leuven, Hoogstraat 51, 9000 Gent, Belgium 4 Department of Mathematical Sciences, New Jersey Institute of Technology University Heights, Newark, NJ 07102, USA 5 Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA 6 Department of Applied Mathematics, National Technical University of Athens, Athens 15780, Greece 7 Departments of Mathematics, The George Washington University, Monroe Hall, Room 240, 2115 G St. NW., Washington, DC 20052, USA 8 Faculty of Mechanical Engineering, Aleksandra Medvedeva, Niš 18000, Serbia 9 Department of Mathematics, North Carolina State University, PO Box 8205, Raleigh, NC 27695, USA 10 Jose M. Paz 1131 Florida (1602) Provincia de Buenos Aires, Argentina 11 Department of Mathematical Sciences, Faculty of Technology and Metallurgy, Karnegijeva 4, Belgrade 11000, Serbia 12 Klybeckstrasse 64, Basel 4057, Switzerland add Show full affiliation list remove Hide full affiliation list * Author to whom correspondence should be addressed. Symmetry 2015, 7(3), 1261-1274; https://doi.org/10.3390/sym7031261 Received: 29 May 2015 / Revised: 29 May 2015 / Accepted: 1 June 2015 / Published: 15 July 2015 Download Download PDF Download PDF with Cover Download XML Download Epub Browse Figures Versions Notes Graphical Abstract 1. In Memory of Slavik Jablan by Ljiljana Radovic and Radmila SazdanovicAfter a long and brave battle with a serious illness, our dear friend and colleague Slavik Jablan passed away on 26 February 2015. The world is deprived of a remarkable mathematician, a great artist, a wonderful man and a dear friend. He made significant contributions to many areas of mathematics: geometry, group theory, mathematical crystallography, the theory of symmetry, antisymmetry, colored symmetry, combinatorial geometry, knot theory, visual mathematics and mathematical art.Slavik Jablan was born on 10 June 1952 in Sarajevo, Yugoslavia (now in Bosnia-Herzegovina). He grew up in Sarajevo, Dubrovnik and Belgrade. He studied at the University of Belgrade and graduated in 1977 in theoretical mathematics from the Faculty of Mathematics, University of Belgrade, where he also obtained his MA in 1981 and PhD in 1984, with a thesis entitled Theory of Simple and Multiple Antisymmetry in E 2 and E 2 ∖ { O } . In 1985 and 1988, he pursued an advanced scientific program in colored symmetry at the University of Kishinev in the former USSR (now Chişinău, Republic of Moldova). He also held numerous visiting positions, including in the USA and Canada (1990): the University of Wisconsin-Madison; Indiana University Bloomington, Department of Anthropology; Tsukuba University, Tsukuba, Science City, Japan (1999); Fulbright Scholar, USA (2003–2004); and many others.Slavik Jablan started his career at the PTT School center and at the Pedagogical Academy for Teacher Training in Belgrade, where he worked until 1984. He moved to the Faculty of Philosophy, Department of Mathematics at the University of Niš in southern Serbia, where he was a professor of geometry. In 1999, he returned to Belgrade, to work at the College of Information and Communication Technology. He designed and taught a visual mathematics course for designers at the Metropolitan University in Belgrade. Over the years, he was a Researchmember of the Mathematical Institute of the Serbian Academy of Science and Arts, the Editor of the VisMath electronic journal (http://www.mi.sanu.ac.rs/vismath) and the Editor in Chief of Symmetry. He was a member of the Advisory Board of The International Society for the Interdisciplinary Study of Symmetry, as well as a member of many other math societies.His scientific roots lie in deriving and cataloging groups of simple and multiple antisymmetry based on an antisymmetry characteristic (AC) method that he developed in his PhD thesis. Using AC methods, it was possible to derive and to distinguish different antisymmetry groups based on their antisymmetry characteristic. He was also interested in enantiomorphism forms and chirality. His first PhD student Ljiljana Radovic continued this work and implemented the method of antisymmetry characteristic in the computation of multiplied antisymmetry groups by computer. He published more than 30 scientific papers on this topic, as well as several monographs: Theory of Symmetry and Ornament, APXAIA, Belgrade, 1984 (in Serbo-Croatian); Geometry in Pre-Scientific Period & Ornament Today, Math. Inst., History of Math. and Mech. Sci., 3, Belgrade, 1989; Theory of Symmetry and Ornament, Math. Inst., Belgrade, 1995 (http://www.mi.sanu.ac.rs/jablans/mon.htm); Symmetry, Ornament and Modularity, World Scientific, New York, 2002.Starting in the mid-1990s, Slavik Jablan expanded his interests to knot theory, an area of low-dimensional topology. His unique background enabled Slavik to discover various patterns in the world of knots and their invariants. In 1995, he proposed the so-called Bernhard–Jablan conjecture about an invariant called the unknotting number. His idea of utilizing Conway notation as well as knot and link families is the core of the knot theory software package LinKnot that he developed together with Radmila Sazdanovic. They also published a book titled LinKnot: Knot Theory by Computer (World Scientific, Singapore, 2007) along with a webMathematica version of LinKnot (http://math.ict.edu.rs/). Slavik published many significant scientific papers with theoretical and experimental results, and influenced the area of knot theory through collaborations and inspiring students to take up this field of study. Till the very end, Slavik was working with his last PhD student, Ana Zekovic, who defended her PhD thesis “Conway notation and its appliance in knot distance determination methods, in knot theory” on the same day when Slavik Jablan passed away.Slavik Jablan was one of the leading experts in visual mathematics. All his life, he was building bridges between science and art. He was interested in the history of ornamental art, patterns, modularity, visual perception, Celtic art, ornamental design, key-patterns, Roman mazes and labyrinths, Paleolithic ornaments and op art puzzles. His contribution to the symmetry approach of ornamental design by SpaceTiles, KnotTiles and especially OpTiles based on modularity will be remembered by all. Slavik was an accomplished painter and math artist with more than 15 solo exhibitions, and his work on Two-Colored Ornamental Tilings based on modularity and Mathematics and Design (1998) winning one of the awards at the International Competition of Industrial Design and New Technology CEVISAMA1987 (Valencia, Spain).He was an avid promoter of the concept of visual geometry and visual mathematics, with emphasis on symmetry in visual and ornamental art, at numerous conferences, such as ISIS-Symmetry, BRIDGES, Gathering for Gardner, as well as in the series of lectures all around the world: at the University of Wisconsin (Madison, Department of Mathematics), Indiana University (Bloomington, Department of Anthropology), Technische Universität (Vienna, Austria, Department of Geometry), Symmetry and Visual Perception at Faculty of Philosophy (Belgrade, Department of Experimental Psychology), Symmetry and Visual Arts at the National Museum (Belgrade), Classification of Ornaments at the Museum of Contemporary Art (Belgrade). His love and passion for ornamental art lasted all his life. He was one of the founders of the Experience Workshop Math-Art Movement and creator of the course “Visual Mathematics and Design” at the Faculty of Information Technologies (Belgrade), and his ideas and contributions were essential for the success of the Tempus Project on Visual Mathematics. He was invited to give the contribution “Classification of Ornaments” for the catalog of the exhibition “Memory Update: Ornaments of Serbian Medieval Frescoes”, held at the Museum of Applied Arts, Belgrade, November 2013–March 2014. In November 2014, he had his last solo exhibition, “Do you like Paleolithic ornamental art?” in the Radio Television of Serbia Gallery in Belgrade. Figure 1. Slavik’s lecture at the Summer Institute in Eger, Hungary, July 2013. Figure 1. Slavik’s lecture at the Summer Institute in Eger, Hungary, July 2013. Figure 2. Knot-2013 ICTS, Tata Institute for Fundamental Research, India, December 2013. Figure 2. Knot-2013 ICTS, Tata Institute for Fundamental Research, India, December 2013. Slavik Jablan was a brilliant mathematician, artist and, above all, a wonderful man and a devoted friend, and he will be missed and remembered by all. 2. Donald Crowe, Professor Emeritus, University of Wisconsin-Madison, WI, USASlavik Jablan was born 1952 in Sarajevo at a time midway between the two dramatic events by which Sarajevo is otherwise known to the outside world: the assassination of Archduke Ferdinand, which set off World War I, and the siege of Sarajevo, which marked the disintegration of modern Yugoslavia. Slavik emerged from this second event to become a prominent spokesman and practitioner for symmetry in its mathematical and artistic forms. In the early 1990s, he received a grant to travel to America to become acquainted with prominent figures, such as H.S.M. Coxeter (who had recently helped organize an Escher conference in Rome) and Arthur Loeb, whose book on color symmetry dealt with a topic much like Slavik’s own 1984 Belgrade thesis (published in English as Theory of Symmetry and Ornament, 1995).Growing out of this trip, he received a Fulbright scholarship to return to America to work with me and others on real-world symmetry. However, this was suspended when the war in Yugoslavia intervened. For the next few years, he made many contacts in Europe, especially via the ISIS-Symmetry organization of Georgy Darvas and Denes Nagy. By 1998, he founded the electronic journal VisMath, where “visual mathematics” came to include not only traditional geometric topics, but decorative art (at which Slavik was an expert) and symmetries of primitive and ethnographic art (providing an outlet, for example, for the work of Paulus Gerdes, who sadly died a few months before Slavik). I was honored to have him accept a small paper of mine to be the first paper in the first issue, and as editor, he enlivened the paper, so that it lights up like a shopping mall. Slavik’s own art can be seen in several papers in the MathArt section of VisMath. The Bridges organization was founded in America about the same time, and Slavik became an early participant in its annual conferences, including editing one of the proceedings. At the Bridges conference that year, he entertained some of the participants by producing almost instant watercolors, including marine scenes from the Adriatic coast of his homeland. Each New Years, he produced modular or op art calendars. Not until 2004 was he able to get his 1992 Fulbright reinstated, and he used the time in Wisconsin to complete his knot theory book (published with Radmila Sazdanovic) and work with Jay Kappraff in New Jersey.At the time of his death, Slavik was the editor not only of VisMath, but of the electronic journal Symmetry published in Switzerland. It will be hard to fill his niche in the world of mathematics and art, impossible to fill it in the memories of those who were his friends. 3. György Darvas, Editor of Symmetry: Culture and Science, Budapest, HungaryI had known Slavik since 1988, and we met in the following year. Twenty seven years is a long time: uncountable correspondence, several common projects, many personal meetings. Our relation was not restricted to collaboration in science. We visited each other, and when his home country was the subject of bombing by foreign armed forces, my wife and I invited him and his kind wife Jadranka to survive the hard period in our home in Budapest. Although they did not want to leave their apartment unattended in that period, they did not forget it, even until our last meeting last autumn. Of course, there were less and more intensive periods in the contact over such a long time, but we could recover our collaboration when our mutually beloved common theme, symmetry, demanded it. The last few years belonged again to collaborative periods, and we had further plans that, unfortunately, will never be realized. I appreciated greatly his scholarly intellect, his wide knowledge both in the sciences and the arts and his smart attitude. Figure 3. Slavik Jablan at the Bridges Conference in Pecs, Hungary, 2010. Figure 3. Slavik Jablan at the Bridges Conference in Pecs, Hungary, 2010. 4. Dirk Huylebrouck, Faculty of Architecture, KU Leuven, Gent, BelgiumI first met Slavik Jablan somewhere in the middle of the 1990s during a mathematics and design conference in San Sebastian, Spain, where his lecture was elected “best lecture of the meeting”. We would keep in touch, through many conferences and uncountable emails during the years. Slavik came to Belgium several times, and I always programmed him as the first speaker of my conferences on “Mathematics and Art”, to make sure to have a good start.As a foremost member of many mathematics and art societies, he started the very first “Visual Mathematics” website, at times when making and spreading Internet sites was not as evident as it is now. It became a top virtual library on mathematics and art. I stand behind the point of view that it was Slavik who coined the term “visual mathematics”, though I know he found this statement exaggerated. In 2012, he gave me a copy of a chapter of an unusual course, entitled “visual mathematics”, which he was teaching to graphical designers at the Belgrade Metropolitan University. I tried to teach that chapter to my own architecture students in Belgium and I can confirm firsthand that it would be a pity if this course were to not be published nor taught in the future. It was Slavik’s opinion that designers and artists have the obligation and right to know mathematics, and that was right.Over the years, we discussed many times how to find some support for those visual mathematics activities. Several draft project versions were written, rejected for all kinds of reasons, sometimes related to the political situation of Serbia. However, Slavik persisted, and in the end, we got a Tempus project approved on visual mathematics. Symbolically, the project finished in 2014, as if he had waited for it to be completed. We will not forget how much he enjoyed the attention of the general public for mathematics, during the “Belgrade Summer School on Visual Mathematics”, in 2014, at the shores of the River Danube. Slavik was the foremost mathematician in the group, and that was right. Figure 4. At the Math and Art meeting in Ghent, Belgium, 20–21 May 2011. Figure 4. At the Math and Art meeting in Ghent, Belgium, 20–21 May 2011. After a talk of mine in Israel somewhere in 1998 about the oldest mathematical object, the Congolese Ishango rod, we engaged in a discussion about this object. We did not entirely agree, but on the contrary, that was not a problem. Later, in 2007, he would even come to my conference “Ishango, 22000 and 50 years later: the cradle of mathematics?” at the Flemish Royal Academy of Belgium. Additionally, in 2013, a contribution by his hand, entitled “A Second Opinion on the Ishango Rod”, would be a part of a chapter in my book “Belgium + Mathematics”. This genuine interest he had for Africa was also confirmed in a kind of expedition we held in Buenos Aires, Argentina. Someone informed us that an Argentine citizen had a large collection of Congolese fabrics that he did not exactly know what to do with and how they should be grouped together, and for some reason, he did not want to follow the official steps. Yet, we went to visit him, took numerous pictures and crowned the expedition with a paper on a group theory classification of Congolese fabrics in Buenos Aires. Mathematics combined with adventure, and that was fun.Because of that Tempus project, I finally had an official reason to visit Slavik in Belgrade, in April 2013. I thought it would be awkward, since, after all, his Serbia had been heavily bombed by NATO, in 1999. He reported about the bombing to me from his side, while I was e-mailing from Brussels, the city of NATO’s head quarters. Still, the welcome in Belgrade could not be better, and I have hardly ever been in a country as hospitable as Serbia. Additionally, even posthumously, he continues to spread the message about the mathematical beauty of Serbia, through the exhibition “Memory Update: Ornaments of Serbian Medieval Frescoes”. This exhibition, to which he contributed the mathematical aspects, is starting a tour around the world. His spirit will travel with it. 5. Jay Kappraff, New Jersey Institute of Technology, Newark, NJ, USASlavik was a prince among mathematicians. I had a long and fruitful history with him and also with his wonderful wife Jadranka and son Ivan. In 2005, he got a Fulbright, and we spent three months together at NJIT with Slavik living in my town of South Orange. During this time, we wrote a couple of papers together and had many adventures. When it came time to part, he told me that he wanted to give me a gift. At the end of the weekend, he presented me with two large watercolor paintings. Being overwhelmed by my own work, I put them in my attic. It was three years later that I took a careful look at them. They were masterpieces, and they now adorn my apartment. One in particular is priceless. It keeps another of his still life paintings company in a place of honor in my living room. For this past year, we have been working on a book to help faculty who wish to teach a course in Math of Design for which we have contracted with World Scientific. Although he cannot complete this task, he has bequeathed it to two former students of his, Ljiljana Radovic and Radmila Sazdanovic. They will carry on this work, which will be a fitting tribute to Slavik. In 2008, I paid a visit to Slavik in Belgrade. Ivan, Slavik’s son, who is an archivist of Serbian history and culture, took me on a historical tour of Belgrade, while Jadranka shared her novel approach to musical theory with me. Ivan is a fine chorale singer in the Serbian choral tradition. It so happened that in 2012, my daughter-in-law was visiting Belgrade as a choral conductor during which Slavik showed her great hospitality. Slavik was broad gauged in his approach to art and life with strong interests in both music, art and design. He also had a passion for the history of design going back as far as 23,000 BC to the Mezin culture. He collected designs through all of Europe, but particularly in Eastern Europe. His essay on mathematics in the art of Salvador Dali, never published, is a masterpiece. In recent years, he became one of the world’s authorities on knot theory, establishing a fruitful collaboration with Prof. Louis Kauffman, the leading authority on this subject, and he continued, almost single-handedly, to publish the on-line Journal of Visual Mathematics. In fact, he did all of this in a lifetime full of physical challenges. There was nothing that could deter him and disturb his laser beam concentration and focus. However, with all of his adversities, he never once complained. It all became part of his special dance through life. Even through his final disease, his focus was more on sharing yet more of his extensive oeuvre than on the excruciating pain he was enduring. This world is richer for his presence and poorer now that he has departed. 6. Louis H. Kauffman, University of Illinois at Chicago, Chicago, IL, USAI first met Slavik Jablan in the 1990s, and it was clear from the start that he had a new and different point of view about knot theory and indeed a different and artistic view of mathematics in general. He had worked in symmetry, ornaments, painting and design before coming to knot theory, and his vision of knot theory was suffused with the rich appearance of knotting and weaving in tapestry, painting and design, the use of knots both practical and decorative in rope-work and for ships and construction that extended back into antiquity. While for the rest of us, knot theory was a modern phenomenon that began in the 19th century, for Slavik, it was a mathematical phenomenon that had begun in the roots of civilization. I say a mathematical phenomenon, because it was mathematics in the patterns and calculations of weaving and painting and design. Knot theory became a chapter of systematized, algebraic and abstract mathematics only recently, but it had been part of a tradition that respected pattern and craft and practical calculation for long before that. This meant that Slavik’s view of knot theory was wider, more artistic and, at the same time, more computational than the rest of us. He was genuinely interested in how knots and links could fall into visual and recursively generated families. He was sensitive to the extraordinary combination of calculation and topological patterning that lay behind the abstract definitions that most of us explore. Consequently, he was willing to enter into computational investigations and conjectures about knots and links from all areas of the theory. He never stopped examining, from his point of view, any statement of relationships. This led him to make very fine conjectures (such as the Bernhard–Jablan conjecture about the unknotting number), and it made him an absolutely extraordinary collaborator. One could invent or discover some combinatorial property of knots and, the next day, send Slavik an account of the definition and ask some question about generating examples of a type or whether such and such a phenomenon might occur. He would immediately understand and put the matter to his computing system (LinKnot) and generate many examples, and the work and the conjecturing would go forward. He had a completely open mind, full creativity, devotion to art and mathematics, love of collaboration and love of friends and humanity. He was a person of value beyond words. We are going to miss him more and more as time goes on. Figure 5. Advanced School and Conference on Knot Theory and its Applications to Physics and Biology, International Centre for Theoretical Physics (ICTP), Trieste, Italy, 11–29 May 2009. Figure 5. Advanced School and Conference on Knot Theory and its Applications to Physics and Biology, International Centre for Theoretical Physics (ICTP), Trieste, Italy, 11–29 May 2009. 7. Sofia Lambropoulou, National Technical University of Athens, Athens, GreeceI first talked with Slavik Jablan at the International Centre for Theoretical Physics (ICTP) in Trieste in May 2009, where we co-organized, together with Louis Kauffman and Jozef Przytycki, the “Advanced School and Conference on Knot Theory and its Applications to Physics and Biology”. In the period prior to the meeting, we had discussed, over email, being the two local organizers. However, I had already, long before, heard of him and his ability to do programming and computations with knots, which would lead him to formulating deep conjectures.At the ICTP, every evening of the meeting, we would sit with the four organizers at the terrace of the dinning cafeteria over a pitcher of wine, and we would see to organizational matters that needed attention. One evening, many of us played, on the spot, as actors at the improvised play “Dehn’s dilemma”. This was an idea I had been amusing myself with for a while, imagining topological surgery as medical surgery, of which I talked to Cameron Gordon early that evening with the pressing request that we do some kind of play. Cameron soon started forming a scenario in his mind, involving rational and irrational surgery and Dr. Dehn being an absurd doctor, which evolved into a superb, unforgettable comedy in the mind and hands of Colin Adams: “Unhappy solid torus wishes to become lens space, consults mad doctor who performs irrational surgery. The love interest of the torus falls for the figure 8 knot complement, and high drama occurs.” From YouTube: https://www.youtube.com/watch?v=UM-U5RE2mN0. I recall that Slavik enjoyed his role enormously, I think, being the solid torus, as well as the whole event. In September 2010, we co-organized the same team “Knots in Chicago”. Figure 6. Slavik Jablan and Jesus Juyumaya in Ancient Olympia, Greece, 2013. Figure 6. Slavik Jablan and Jesus Juyumaya in Ancient Olympia, Greece, 2013. Two years later, I was asking him if he would be willing to help with a puzzling problem: with my collaborator Jesus Juyumaya from Chile, we had constructed an infinitum of knot and link invariants via the Yokonuma–Hecke algebras, which are quotients of the framed braid group over a complex quadratic relation. These invariants needed to be compared with known ones, especially with the Homflypt polynomial, but a direct comparison was not obvious. My student Konstantinos Karvounis and Michael Chmutov had created computational packages, so we started making computations (together with Sergei Chmutov). Slavik provided us immediately with several pairs of knots and links in braid form sharing the same Homflypt polynomial. We could quickly come to the idea that our invariants were no stronger than the Homflypt polynomial, but a theoretical proof was not in sight.In April 2013, I visited him in Belgrade in order to look at the problem more systematically. There, I had the opportunity to meet his wife Jadranka, a music teacher, a wonderful person and a great cook. Their apartment, which had an artistic bohemian air, was full of Slavik’s amazing oil paintings and several rare and interesting artistic objects.We started skyping with Konstantinos and making testing computations on knot and link families that Slavik had indicated. Soon, he was able to figure out some pattern. In September 2013, Slavik and Jadranka visited me in Athens, where, together with Konstantinos and Jesus, we managed to formulate our main conjecture: on knots, our invariants are topologically equivalent to the Homflypt polynomial. This was proven recently and will appear in a joint paper with his name on it. The conjecture was proven recently, and we even showed that on links, the behavior is different.Slavik has been an excellent, tireless researcher and highly intelligent, with his own unique taste for mathematics and art; a good friend, a person with broad and deep human awareness, honest, open-minded and non-judgmental, in the company of whom one would feel a warm and calm light. 8. Jozef Przytycki, George Washington University, Washington, DC, USAI first met Slavik at Knots in Hellas, Greece 1998. I remember him mostly as a strong proponent of the conjecture about the unknotting number, stating that under certain conditions, the unknotting number can be obtained from a minimal diagram, now known as the Bernhard –Jablan conjecture. The next time we met at Knots in Washington XVII in 2003, when he brought with him his student collaborator Radmila Sazdanovic. Radmila soon became my student, so following the example of Hugo Steinhaus, I can say that “Radmila was one of Slavik’s biggest mathematical discoveries”. One of Slavik’s greatest gifts was his passion of relating mathematics and art. This he advocated whenever I met him: in Trieste in May 2009 or, the last time, in India in December 2013. For all of this, he will be remembered! 9. Ljiljana Radovic, Faculty of Mechanical Engineering, Niš, SerbiaI had the pleasure of being a student of Professor Slavik Jablan at the Faculty of Philosophy, Department of Mathematics at the University of Niš in 1990. Prof. Slavik Jablan also was my mentor for my Masters and PhD theses. During 25 years of collaborations, he became my dear friend. It was a great privilege to learn from him, not only mathematics and geometry, not only about symmetry and knots, but also about arts and artists, paintings and painters, about anthropology, archeology, architecture, ethnology, about movies, music and windsurfing.Slavik Jablan was a brilliant mathematician and artist and, above all, a wonderful man, unselfish in shearing ideas, information, knowledge, books and graphics. It was not always easy to follow his quick mind nor keep track of his numerous ideas, amazing creativity and great intelligence, but it was a great honor to work with him and to be his friend. He always had new ideas about what we could do next and what we should write about and prepared new materials, workshops and projects. During all of these years, we worked on many papers and projects together. In the last two years, we were working on several projects. Our work on the paper “Classification of ornaments based on Serbian fresco medieval art” is especially precious for me, but also our work on the book Visual mathematics with Jay Kapraff, education material for the teachers included in the Tempus project “Visuality & Mathematics: Experimental Education of Mathematics through Visual Arts, Sciences and Playful Activities”, workshops and lectures.We all were able to learn how to live and fight in sp
DA - 2015/9//
PY - 2015/9//
DO - 10.3390/sym7031261
VL - 7
IS - 3
SP - 1261-1274
SN - 2073-8994
KW - symmetry
KW - multiple antisymmetry
KW - ethnomathematics
KW - knot theory
KW - Conway notation
KW - link families
KW - visual mathematics
KW - modularity
KW - unknotting number
ER -
TY - JOUR
TI - A Cambrian framework for the oriented cycle
AU - Reading, Nathan
AU - Speyer, David E.
T2 - Electron. J. Combin.
DA - 2015///
PY - 2015///
VL - 22
IS - 4
SP - Paper 4.46, 21
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84951847857&partnerID=MN8TOARS
ER -
TY - BOOK
TI - Partial differential equations: An introduction to theory and applications
AU - Shearer, M.
AU - Levy, R.
DA - 2015///
PY - 2015///
PB - Princeton: Princeton University Press
SN - 9780691161297
ER -
TY - JOUR
TI - Multiple transverse homoclinic solutions near a degenerate homoclinic orbit (vol 259, pg 1, 2015)
AU - Lin, Xiao-Biao
AU - Long, Bin
AU - Zhu, Changrong
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - The authors sincerely apologize for the error in counting the codimension of bifurcations in the above published paper, which will be called [LLZ] for short. First, to fix the paper [LLZ], we look for bifurcations of heteroclinic solutions x(t) = γμ, rather than the homoclinic solutions as in [LLZ]. And the bifurcated heteroclinic solutions x(t) are close to γ (t) as a function to another function, without a phase shift. That is x(t) = γ (t) +z(t) where z(0) ⊥ γ (0). Second, we assume the heteroclinic solution connects two hyperbolic equilibria u = 0 to u = A, i.e., γ (−∞) = 0, γ (∞) = A, with Re{σ(Df (0))} = 0, Re{σ(Df (A))} = 0. Let Lu := u′ −Df (γ (t))u. Let N(L) and N(L∗) be the null spaces of L and its adjoint operator L∗. If d is the dimension of N(L) and d∗ is the dimension of N(L∗), then the index of the Fredholm operator L is I (L) := d − d∗. The basic change in this corrigendum is the following hypothesis: (H) d = 3, d∗ = 2, and I (L) = 1. Let N(L) be spanned by (u1, u2, u3) with u3 = γ (t), and N(L∗) be spanned by (ψ1, ψ2). Let K : R(L) → N(L)⊥ be a particular solution map to the equation L(z) = h, where h ∈ R(L). With the phase condition z(0) ⊥ γ (0), the general solution to L(z) = h, h ∈ R(L) is z=∑p=1,2 βpup +Kh.
DA - 2015/12/5/
PY - 2015/12/5/
DO - 10.1016/j.jde.2015.07.032
VL - 259
IS - 11
SP - 6885-6886
SN - 1090-2732
ER -
TY - JOUR
TI - A pseudo-extractor approach to hidden boundary regularity for the wave equation with mixed boundary conditions
AU - Bociu, Lorena
AU - Zolesio, Jean-Paul
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - In this paper we introduce a new approach to “hidden” boundary regularity for the linear wave equation with mixed Dirichlet–Neumann boundary conditions, where the Neumann data is non-smooth. First, we obtain existence and uniqueness of solution by Galerkin estimates. Then we use a new, pseudo-extractor technique (based on the Fourier transform and shape and tangential calculus) in order to provide sharp regularity for the solution at the boundary.
DA - 2015/12/5/
PY - 2015/12/5/
DO - 10.1016/j.jde.2015.07.006
VL - 259
IS - 11
SP - 5688-5708
SN - 1090-2732
KW - Wave equation
KW - Neumann boundary conditions
KW - Pseudo-extractor
KW - Boundary regularity
ER -
TY - CONF
TI - A Dynamic Feature Selection Based LDA Approach to Baseball Pitch Prediction
AU - Hoang, P.
AU - Hamilton, M.
AU - Murray, J.
AU - Stafford, C.
AU - Tran, H.
T2 - PAKDD 2015 Workshops: BigPMA, VLSP, QIMIE, DAEBH
A2 - Li, Xiao-Li
A2 - Cao, Tru
A2 - Lim, Ee-Peng
A2 - Zhou, Zhi-Hua
A2 - Ho, Tu-Bao
A2 - Cheung, David
T3 - Lecture Notes in Computer Science
AB - Baseball, which is one of the most popular sports in the world, has a uniquely discrete gameplay structure. This stop-and-go style of play creates a natural ability for fans and observers to record information about the game in progress, resulting in a wealth of data that is available for analysis. Major League Baseball (MLB), the professional baseball league in the US and Canada, uses a system known as PITCHf/x to record information about every individual pitch that is thrown in league play. We extend the classification to pitch prediction (fastball or nonfastball) by restricting our analysis to pre-pitch features. By performing significant feature analysis and introducing a novel approach for feature selection, moderate improvement over published results is achieved.
C2 - 2015///
C3 - Trends and Applications in Knowledge Discovery and Data Mining
CY - Ho Chi Minh City, Vietnam
DA - 2015///
PY - 2015/5/19/
DO - 10.1007/978-3-319-25660-3_11
VL - 9441
SP - 125–137
PB - Springer
SN - 978-3-319-25659-7
KW - Machine learning
KW - Hypothesis testing
KW - Feature selection
KW - Pitch prediction
KW - PITCHf/x
KW - MLB
KW - LDA
KW - ROC
ER -
TY - JOUR
TI - Tying up loose strands: Defining equations of the strand symmetric model
AU - Long, C.
AU - Sullivant, S.
T2 - Journal of Algebraic Statistics
AB - The strand symmetric model is a phylogenetic model designed to reflect the symmetry inherent in the double-stranded structure of DNA. We show that the set of known phylogenetic invariants for the general strand symmetric model of the three leaf claw tree entirely defines the ideal. This knowledge allows one to determine the vanishing ideal of the general strand symmetric model of any trivalent tree. Our proof of the main result is computational. We use the fact that the Zariski closure of the strand symmetric model is the secant variety of a toric variety to compute the dimension of the variety. We then show that the known equations generate a prime ideal of the correct dimension using elimination theory.
DA - 2015///
PY - 2015///
DO - 10.18409/jas.v6i1.34
VL - 6
IS - 1
SP - 17-23
ER -
TY - JOUR
TI - Computing Hermitian determinantal representations of hyperbolic curves
AU - Plaumann, Daniel
AU - Sinn, Rainer
AU - Speyer, David E.
AU - Vinzant, Cynthia
T2 - INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
AB - Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the polynomial and their existence has been proved in several different ways. However, the resulting algorithms for computing determinantal representations are computationally intensive. In this note, we present an algorithm that reduces a large part of the problem to linear algebra and discuss its numerical implementation.
DA - 2015/12//
PY - 2015/12//
DO - 10.1142/s0218196715500435
VL - 25
IS - 8
SP - 1327-1336
SN - 1793-6500
KW - Hyperbolic polynomials
KW - determinantal representations
KW - interlacing
KW - Hermitian matrices of linear forms
ER -
TY - JOUR
TI - BOUNDS ON THE EXPECTED SIZE OF THE MAXIMUM AGREEMENT SUBTREE
AU - Bernstein, Daniel Irving
AU - Ho, Lam Si Tung
AU - Long, Colby
AU - Steel, Mike
AU - St John, Katherine
AU - Sullivant, Seth
T2 - SIAM JOURNAL ON DISCRETE MATHEMATICS
AB - We prove lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and the Yule--Harding distribution and prove upper bounds under the Yule--Harding distribution. This positively answers a question posed in earlier work. Determining tight upper and lower bounds remains an open problem.
DA - 2015///
PY - 2015///
DO - 10.1137/140997750
VL - 29
IS - 4
SP - 2065-2074
SN - 1095-7146
KW - random trees
KW - agreement subtrees
KW - Yule-Harding distribution
ER -
TY - JOUR
TI - Tribological properties of nanodiamonds in aqueous suspensions: effect of the surface charge
AU - Liu, Zijian
AU - Leininger, Dustin
AU - Koolivand, Amir
AU - Smirnov, Alex I.
AU - Shenderova, Olga
AU - Brenner, Donald W.
AU - Krim, Jacqueline
T2 - RSC ADVANCES
AB - The sign of nanodiamond surface charge is discovered to profoundly impact friction at both nanometer and macroscopic scales.
DA - 2015///
PY - 2015///
DO - 10.1039/c5ra14151f
VL - 5
IS - 96
SP - 78933-78940
SN - 2046-2069
ER -
TY - JOUR
TI - The linearized Boltzmann equation with Cercignani-Lampis boundary conditions: Heat transfer in a gas confined by two plane-parallel surfaces
AU - Garcia, R. D. M.
AU - Siewert, C. E.
T2 - ANNALS OF NUCLEAR ENERGY
AB - The analytical discrete-ordinates method is used to solve the problem of heat transfer for a single-species gas confined by two plane-parallel surfaces. The formulation of the problem is based on the linearized Boltzmann equation for rigid-sphere interactions between gas particles and the Cercignani–Lampis kernel for gas–surface interactions. Accurate numerical results are reported for the density, temperature, and heat-flow perturbations from a reference (equilibrium) state and are compared with similar results from five kinetic models. An interesting finding of this work is that there are combinations of the four numerical values of the accommodation coefficients used to define the Cercignani–Lampis boundary conditions that give rise to heat flows that are larger for the transition regime than for the free-molecular regime, an effect not observed when the standard (Maxwell) boundary conditions are used.
DA - 2015/12//
PY - 2015/12//
DO - 10.1016/j.anucene.2015.01.013
VL - 86
SP - 45-54
SN - 0306-4549
KW - Rarefied gas dynamics
KW - Linearized Boltzmann equation
KW - Cercignani-Lampis kernel
KW - Heat transfer
ER -
TY - JOUR
TI - Surfactant spreading on a thin liquid film: reconciling models and experiments
AU - Swanson, Ellen R.
AU - Strickland, Stephen L.
AU - Shearer, Michael
AU - Daniels, Karen E.
T2 - JOURNAL OF ENGINEERING MATHEMATICS
AB - The spreading dynamics of surfactant molecules on a thin fluid layer is of both fundamental and practical interest. A mathematical model formulated by Gaver and Grotberg [J Fluid Mech 235:399–414, 1992] describing the spreading of a single layer of insoluble surfactant has become widely accepted, and several experiments on axisymmetric spreading have confirmed its predictions for both the height profile of the free surface and the spreading exponent (the radius of the circular area covered by surfactant grows as $$t^{1/4}$$ ). However, these prior experiments utilized primarily surfactant quantities exceeding (sometimes far exceeding) a monolayer. In this paper, we report that this regime is characterized by a mismatch between the timescales of the experiment and model and, additionally, find that the spatial distribution of surfactant molecules differs substantially from the model prediction. For experiments performed in the monolayer regime for which the model was developed, the surfactant layer is observed to have a spreading exponent of less than $$1/10$$ , far below the predicted value, and the surfactant distribution is also in disagreement. These findings suggest that the model is inadequate for describing the spreading of insoluble surfactants on thin fluid layers.
DA - 2015/10//
PY - 2015/10//
DO - 10.1007/s10665-014-9735-0
VL - 94
IS - 1
SP - 63-79
SN - 1573-2703
KW - Experiment
KW - Model
KW - Surfactant
KW - Thin liquid film
ER -
TY - JOUR
TI - Steady State and Sign Preserving Semi-Implicit Runge--Kutta Methods for ODEs with Stiff Damping Term
AU - Chertock, Alina
AU - Cui, Shumo
AU - Kurganov, Alexander
AU - Wu, Tong
T2 - SIAM Journal on Numerical Analysis
AB - In this paper, we develop a family of second-order semi-implicit time integration methods for systems of ordinary differential equations (ODEs) with stiff damping term. The important feature of the new methods resides in the fact that they are capable of exactly preserving the steady states as well as maintaining the sign of the computed solution under the time step restriction determined by the nonstiff part of the system only. The new semi-implicit methods are based on the modification of explicit strong stability preserving Runge--Kutta (SSP-RK) methods and are proven to have a formal second order of accuracy, $A(\alpha)$-stability, and stiff decay. We illustrate the performance of the proposed SSP-RK based semi-implicit methods on both a scalar ODE example and a system of ODEs arising from the semi-discretization of the shallow water equations with stiff friction term. The obtained numerical results clearly demonstrate that the ability of the introduced ODE solver to exactly preserve equilibria plays an important role in achieving high resolution when a coarse grid is used.
DA - 2015/1//
PY - 2015/1//
DO - 10.1137/151005798
VL - 53
IS - 4
SP - 2008-2029
J2 - SIAM J. Numer. Anal.
LA - en
OP -
SN - 0036-1429 1095-7170
UR - http://dx.doi.org/10.1137/151005798
DB - Crossref
KW - ordinary differential equations with stiff damping terms
KW - semi-implicit methods
KW - strong stability preserving Runge-Kutta methods
KW - implicit-explicit methods
KW - shallow water equations with friction terms
ER -
TY - JOUR
TI - Scenario generation for stochastic optimization problems via the sparse grid method
AU - Chen, Michael
AU - Mehrotra, Sanjay
AU - Papp, David
T2 - COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
AB - We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid method can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. It is indicated that the method scales well with the dimension of the distribution—especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.
DA - 2015/12//
PY - 2015/12//
DO - 10.1007/s10589-015-9751-7
VL - 62
IS - 3
SP - 669-692
SN - 1573-2894
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84948380676&partnerID=MN8TOARS
KW - Scenario generation
KW - Stochastic optimization
KW - Discretization
KW - Sparse grid
ER -
TY - JOUR
TI - Positive expressions for skew divided difference operators
AU - Liu, Ricky Ini
T2 - JOURNAL OF ALGEBRAIC COMBINATORICS
AB - For permutations $$v,w \in \mathfrak S_n$$ , Macdonald defines the skew divided difference operators $$\partial _{w/v}$$ as the unique linear operators satisfying $$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ$$ for all polynomials $$P$$ and $$Q$$ . We prove that $$\partial _{w/v}$$ has a positive expression in terms of divided difference operators $$\partial _{ij}$$ for $$i II ≈ III > IV. These bandgap sizes are smaller by ∼0.1-0.4 eV in comparison to related vanadate hybrids, owing to the addition of the higher-energy 3d orbital contributions from the Mn(II) cations. Each compound also exhibits temperature-dependent photocatalytic activities for hydrogen production under visible-light irradiation in 20% methanol solutions, with threshold temperatures of ∼30 °C for III, ∼36 °C for I, and ∼40 °C for II, IV, and V4O10(o-phen)2. Hydrogen production rates are ∼142 μmol H2 g(-1)·h(-1), ∼673 μmol H2 g(-1)·h(-1), ∼91 μmol H2 g(-1)·h(-1), and ∼218 μmol H2 g(-1)·h(-1) at 40 °C, for I, II, III, and IV, respectively, increasing with the oxide/organic network connectivity. In contrast, the related V4O10(o-phen)2 exhibits a much lower photocatalytic rate of ∼36 H2 g(-1)·h(-1). Electronic structure calculations based on density-functional theory methods show that the valence band edges are primarily derived from the half-filled Mn 3d(5) orbitals in each, while the conduction band edges are primarily comprised of contributions from the empty V 3d(0) orbitals in I and II and from ligand π* orbitals in III. Thus, the coordinating organic ligands are shown to significantly affect the local and extended structural features, which has elucidated the underlying relationships to their photocatalytic activities, visible-light bandgap sizes, electronic structures, and thermal stabilities.
DA - 2015/8/3/
PY - 2015/8/3/
DO - 10.1021/acs.inorgchem.5b00931
VL - 54
IS - 15
SP - 7388-7401
SN - 1520-510X
ER -
TY - JOUR
TI - EXPOSITORY PAPER: A PRIMER ON HOMOGENIZATION OF ELLIPTIC PDES WITH STATIONARY AND ERGODIC RANDOM COEFFICIENT FUNCTIONS
AU - Alexanderian, Alen
T2 - ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
AB - We study the problem of characterizing the effective (homogenized) properties of materials whose diffusive properties are modeled with random fields. Focusing on elliptic PDEs with stationary and ergodic random coefficient functions, we provide a gentle introduction to the mathematical theory of homogenization of random media. We also present numerical examples to elucidate the theoretical concepts and results.
DA - 2015///
PY - 2015///
DO - 10.1216/rmj-2015-45-3-703
VL - 45
IS - 3
SP - 703-735
SN - 1945-3795
KW - Homogenization
KW - random media
KW - ergodic dynamical system
KW - stationary random field
KW - diffusion in random media
ER -
TY - JOUR
TI - Characterisation of Elastic and Acoustic Properties of an Agar-Based Tissue Mimicking Material
AU - Brewin, M. P.
AU - Birch, M. J.
AU - Mehta, D. J.
AU - Reeves, J. W.
AU - Shaw, S.
AU - Kruse, C.
AU - Whiteman, J. R.
AU - Hu, S.
AU - Kenz, Z. R.
AU - Banks, H. T.
AU - Greenwald, S. E.
T2 - ANNALS OF BIOMEDICAL ENGINEERING
AB - As a first step towards an acoustic localisation device for coronary stenosis to provide a non-invasive means of diagnosing arterial disease, measurements are reported for an agar-based tissue mimicking material (TMM) of the shear wave propagation velocity, attenuation and viscoelastic constants, together with one dimensional quasi-static elastic moduli and Poisson’s ratio. Phase velocity and attenuation coefficients, determined by generating and detecting shear waves piezo-electrically in the range 300 Hz–2 kHz, were 3.2–7.5 ms−1 and 320 dBm−1. Quasi-static Young’s modulus, shear modulus and Poisson’s ratio, obtained by compressive or shear loading of cylindrical specimens were 150–160 kPa; 54–56 kPa and 0.37–0.44. The dynamic Young’s and shear moduli, derived from fitting viscoelastic internal variables by an iterative statistical inverse solver to freely oscillating specimens were 230 and 33 kPa and the corresponding relaxation times, 0.046 and 0.036 s. The results were self-consistent, repeatable and provide baseline data required for the computational modelling of wave propagation in a phantom.
DA - 2015/10//
PY - 2015/10//
DO - 10.1007/s10439-015-1294-7
VL - 43
IS - 10
SP - 2587-2596
SN - 1573-9686
KW - Acoustic properties
KW - Acoustic localisation
KW - Coronary artery
KW - Elastic moduli
KW - Poisson's ratio
KW - Shear modulus
KW - Shear wave
KW - Stenosis
KW - Tissue mimicking material
KW - Viscoelasticity
ER -
TY - JOUR
TI - Relative Quantification and Higher-Order Modeling of the Plasma Glycan Cancer Burden Ratio in Ovarian Cancer Case-Control Samples
AU - Hecht, Elizabeth S.
AU - Scholl, Elizabeth H.
AU - Walker, S. Hunter
AU - Taylor, Amber D.
AU - Cliby, William A.
AU - Motsinger-Reif, Alison A.
AU - Muddiman, David C.
T2 - JOURNAL OF PROTEOME RESEARCH
AB - An early-stage, population-wide biomarker for ovarian cancer (OVC) is essential to reverse its high mortality rate. Aberrant glycosylation by OVC has been reported, but studies have yet to identify an N-glycan with sufficiently high specificity. We curated a human biorepository of 82 case-control plasma samples, with 27%, 12%, 46%, and 15% falling across stages I-IV, respectively. For relative quantitation, glycans were analyzed by the individuality normalization when labeling with glycan hydrazide tags (INLIGHT) strategy for enhanced electrospray ionization, MS/MS analysis. Sixty-three glycan cancer burden ratios (GBRs), defined as the log10 ratio of the case-control extracted ion chromatogram abundances, were calculated above the limit of detection. The final GBR models, built using stepwise forward regression, included three significant terms: OVC stage, normalized mean GBR, and tag chemical purity; glycan class, fucosylation, or sialylation were not significant variables. After Bonferroni correction, seven N-glycans were identified as significant (p < 0.05), and after false discovery rate correction, an additional four glycans were determined to be significant (p < 0.05), with one borderline (p = 0.05). For all N-glycans, the vectors of the effects from stages II-IV were sequentially reversed, suggesting potential biological changes in OVC morphology or in host response.
DA - 2015/10//
PY - 2015/10//
DO - 10.1021/acs.jproteome.5b00703
VL - 14
IS - 10
SP - 4394-4401
SN - 1535-3907
KW - N-linked glycosylation
KW - INLIGHT
KW - ovarian cancer
KW - relative quantification
KW - cancer biomarker
KW - human plasma
ER -
TY - JOUR
TI - Orbifolds of lattice vertex algebras under an isometry of order two
AU - Bakalov, Bojko
AU - Elsinger, Jason
T2 - JOURNAL OF ALGEBRA
AB - Every isometry $\sigma$ of a positive-definite even lattice $Q$ can be lifted to an automorphism of the lattice vertex algebra $V_Q$. An important problem in vertex algebra theory and conformal field theory is to classify the representations of the $\sigma$-invariant subalgebra $V_Q^\sigma$ of $V_Q$, known as an orbifold. In the case when $\sigma$ is an isometry of $Q$ of order two, we classify the irreducible modules of the orbifold vertex algebra $V_Q^\sigma$ and identify them as submodules of twisted or untwisted $V_Q$-modules. The examples where $Q$ is a root lattice and $\sigma$ is a Dynkin diagram automorphism are presented in detail.
DA - 2015/11/1/
PY - 2015/11/1/
DO - 10.1016/j.jalgebra.2015.06.028
VL - 441
SP - 57-83
SN - 1090-266X
KW - Lattice vertex algebra
KW - Orbifold algebra
KW - Twisted module
KW - Intertwining operator
KW - Dynkin diagram automorphism
ER -
TY - JOUR
TI - Morphogenetic implications of peristaltic fluid-tissue dynamics in the embryonic lung
AU - Bokka, Kishore K.
AU - Jesudason, Edwin C.
AU - Warburton, David
AU - Lubkin, Sharon R.
T2 - JOURNAL OF THEORETICAL BIOLOGY
AB - Peristalsis begins in the lung as soon as the smooth muscle forms, and persists until birth. Since the prenatal lung is liquid-filled, smooth muscle action can deform tissues and transport fluid far from the immediately adjacent tissues. Stretching of embryonic tissues and sensation of internal fluid flows have been shown to have potent morphogenetic effects. We hypothesize that these effects are at work in lung morphogenesis. To place that hypothesis in a quantitative framework, we analyze a model of the fluid-structure interactions between embryonic tissues and lumen fluid resulting from peristaltic waves that partially occlude the airway. We find that if the airway is closed, deformations are synchronized; by contrast, if the trachea is open, maximal occlusion precedes maximal pressure. We perform a parametric analysis of how occlusion, stretch, and flow depend on tissue stiffnesses, smooth muscle force, tissue shape and size, and fluid viscosity. We find that most of these relationships are governed by simple ratios.
DA - 2015/10/7/
PY - 2015/10/7/
DO - 10.1016/j.jtbi.2015.06.022
VL - 382
SP - 378-385
SN - 1095-8541
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000361085200037&KeyUID=WOS:000361085200037
KW - Airway
KW - Peristalsis
KW - Fluid-structure interaction
KW - Pressure
KW - Morphogenesis
ER -
TY - JOUR
TI - Identifiability Results for Several Classes of Linear Compartment Models
AU - Meshkat, Nicolette
AU - Sullivant, Seth
AU - Eisenberg, Marisa
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
AB - Identifiability concerns finding which unknown parameters of a model can be estimated, uniquely or otherwise, from given input–output data. If some subset of the parameters of a model cannot be determined given input–output data, then we say the model is unidentifiable. In this work, we study linear compartment models, which are a class of biological models commonly used in pharmacokinetics, physiology, and ecology. In past work, we used commutative algebra and graph theory to identify a class of linear compartment models that we call identifiable cycle models, which are unidentifiable but have the simplest possible identifiable functions (so-called monomial cycles). Here we show how to modify identifiable cycle models by adding inputs, adding outputs, or removing leaks, in such a way that we obtain an identifiable model. We also prove a constructive result on how to combine identifiable models, each corresponding to strongly connected graphs, into a larger identifiable model. We apply these theoretical results to several real-world biological models from physiology, cell biology, and ecology.
DA - 2015/8//
PY - 2015/8//
DO - 10.1007/s11538-015-0098-0
VL - 77
IS - 8
SP - 1620-1651
SN - 1522-9602
KW - Identifiability
KW - Linear compartment models
KW - Identifiable functions
KW - Differential algebra
ER -
TY - JOUR
TI - Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance
AU - Banks, H. T.
AU - Catenacci, J.
AU - Hu, S. H.
T2 - Journal of Inverse and Ill-Posed Problems
DA - 2015///
PY - 2015///
VL - 23
IS - 5
SP - 491-509
ER -
TY - JOUR
TI - DIRECT SAMPLING METHOD FOR DIFFUSIVE OPTICAL TOMOGRAPHY
AU - Chow, Yat Tin
AU - Ito, Kazufumi
AU - Liu, Keji
AU - Zou, Jun
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - In this work, we are concerned with the diffusive optical tomography (DOT) problem in the case when only one or two pairs of Cauchy data are available. We propose a simple and efficient direct sampling method to locate inhomogeneities inside a homogeneous background and solve the DOT problem in both full and limited aperture cases. This new method is easy to implement and less expensive computationally. Numerical experiments demonstrate its effectiveness and robustness against noise in the data. This provides a new promising numerical strategy for the DOT problem.
DA - 2015///
PY - 2015///
DO - 10.1137/14097519x
VL - 37
IS - 4
SP - A1658-A1684
SN - 1095-7197
KW - direct sampling method
KW - diffusive optical tomography
ER -
TY - JOUR
TI - CONDITIONING OF LEVERAGE SCORES AND COMPUTATION BY QR DECOMPOSITION
AU - Holodnak, John T.
AU - Ipsen, Ilse C. F.
AU - Wentworth, Thomas
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - The leverage scores of a full-column rank matrix $A$ are the squared row norms of any orthonormal basis for $\mathrm{range}\,(A)$. We show that corresponding leverage scores of two matrices $A$ and $A+\Delta A$ are close in the relative sense if they have large magnitude and if all principal angles between the column spaces of $A$ and $A+\Delta A$ are small. We also show three classes of bounds that are based on perturbation results of QR decompositions. They demonstrate that relative differences between individual leverage scores strongly depend on the particular type of perturbation $\Delta A$. The bounds imply that the relative accuracy of an individual leverage score depends on its magnitude and the two-norm condition of $A$ if $\Delta A$ is a general perturbation; the two-norm condition number of $A$ if $\Delta A$ is a perturbation with the same normwise row-scaling as $A$; (to first order) neither condition number nor leverage score magnitude if $\Delta A$ is a componentwise row-scaled perturbation. Numerical experiments confirm the qualitative and quantitative accuracy of our bounds.
DA - 2015///
PY - 2015///
DO - 10.1137/140988541
VL - 36
IS - 3
SP - 1143-1163
SN - 1095-7162
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84944583307&partnerID=MN8TOARS
KW - principal angles
KW - stable rank
KW - condition number
KW - row-scaling
KW - componentwise perturbations
ER -
TY - JOUR
TI - A Sparse Interpolation Algorithm for Dynamical Simulations in Computational Chemistry
AU - Nance, J.
AU - Kelley, C. T.
T2 - SIAM Journal on Scientific Computing
AB - In this paper we present a new implementation of Smolyak's sparse grid interpolation algorithm designed for dynamical simulations. The implementation is motivated by an application to quantum chemistry where the goal is to simulate photo-induced molecular transformations. A molecule conforms to a geometry that minimizes its potential energy, and many molecules have multiple potential energy minima. These geometries correspond to local minima of the molecule's potential energy surface, and one can simulate how a molecule transitions from one geometry to another by following the steepest descent path, or reaction path, on potential energy surfaces. Molecular vibrations and thermal fluctuations cause randomness in dynamics, so one must follow several paths simultaneously to more accurately simulate possible reaction paths. Current algorithms for reaction path following are too computationally burdensome for molecules of moderate size, but Smolyak's interpolation algorithm offers a cheap surrogate for potential energy surfaces. While current implementations of Smolyak's algorithm are not designed to simultaneously follow multiple reaction paths efficiently, our implementation of Smolyak's algorithm achieves this efficiency by recursively defining Lagrange basis polynomials and making use of an efficient reformulation of Smolyak's algorithm. In this paper we describe our new implementation of Smolyak's algorithm and compare performance times to MATLAB's Sparse Grid Interpolation Toolbox to demonstrate its computational savings. We also present dynamical simulations for the photoisomerization of 2-butene as an example of our reaction path following method.
DA - 2015/1//
PY - 2015/1//
DO - 10.1137/140965284
VL - 37
IS - 5
SP - S137-S156
J2 - SIAM J. Sci. Comput.
LA - en
OP -
SN - 1064-8275 1095-7197
UR - http://dx.doi.org/10.1137/140965284
DB - Crossref
KW - sparse interpolation
KW - sparse grids
KW - Smolyak's algorithm
KW - dynamics
KW - reaction path following
ER -
TY - JOUR
TI - Well-balanced positivity preserving central-upwind scheme for the shallow water system with friction terms
AU - Chertock, A.
AU - Cui, S.
AU - Kurganov, A.
AU - Wu, T.
T2 - INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
AB - Summary Shallow water models are widely used to describe and study free‐surface water flow. While in some practical applications the bottom friction does not have much influence on the solutions, there are still many applications, where the bottom friction is important. In particular, the friction terms will play a significant role when the depth of the water is very small. In this paper, we study shallow water equations with friction terms and develop a semi‐discrete second‐order central‐upwind scheme that is capable of exactly preserving physically relevant steady states and maintaining the positivity of the water depth. The presence of the friction terms increases the level of complexity in numerical simulations as the underlying semi‐discrete system becomes stiff when the water depth is small. We therefore implement an efficient semi‐implicit Runge‐Kutta time integration method that sustains the well‐balanced and sign preserving properties of the semi‐discrete scheme. We test the designed method on a number of one‐dimensional and two‐dimensional examples that demonstrate robustness and high resolution of the proposed numerical approach. The data in the last numerical example correspond to the laboratory experiments reported in [L. Cea, M. Garrido, and J. Puertas, Journal of Hydrology, 382 (2010), pp. 88–102], designed to mimic the rain water drainage in urban areas containing houses. Since the rain water depth is typically several orders of magnitude smaller than the height of the houses, we develop a special technique, which helps to achieve a remarkable agreement between the numerical and experimental results. Copyright © 2015 John Wiley & Sons, Ltd.
DA - 2015/6/30/
PY - 2015/6/30/
DO - 10.1002/fld.4023
VL - 78
IS - 6
SP - 355-383
SN - 1097-0363
UR - https://doi-org.prox.lib.ncsu.edu/10.1002/fld.4023
KW - shallow water equations with friction terms
KW - central-upwind scheme
KW - well-balanced scheme
ER -
TY - JOUR
TI - Unitary and orthogonal equivalence of sets of matrices
AU - Jing, Naihuan
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - Two matrices $A$ and $B$ are called unitary (resp. orthogonal) equivalent if $AU=VB$ for two unitary (resp. orthogonal) matrices $U$ and $V$. Using trace identities, criteria are given for simultaneous unitary, orthogonal or complex orthogonal equivalence between two sets of matrices.
DA - 2015/9/15/
PY - 2015/9/15/
DO - 10.1016/j.laa.2015.04.036
VL - 481
SP - 235-242
SN - 1873-1856
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84929179522&partnerID=MN8TOARS
KW - Simultaneous unitary equivalence
KW - Simultaneous similarity
KW - Simultaneous orthogonal equivalence
KW - Congruence
ER -
TY - JOUR
TI - Two Fluid Flow in a Capillary Tube
AU - Strait, Melissa
AU - Shearer, Michael
AU - Levy, Rachel
AU - Cueto-Felgueroso, Luis
AU - Juanes, Ruben
T2 - COLLABORATIVE MATHEMATICS AND STATISTICS RESEARCH
DA - 2015///
PY - 2015///
DO - 10.1007/978-3-319-11125-4_14
VL - 109
SP - 149-161
SN - 2194-1009
ER -
TY - JOUR
TI - The immersed interface method for axis-symmetric problems and application to the Hele-Shaw flow
AU - Ruiz Alvarez, Juan
AU - Li, Zhilin
T2 - APPLIED MATHEMATICS AND COMPUTATION
AB - Many physical application problems are axis-symmetric. Using axis-symmetric properties, many three dimensional problems can be solved efficiently using two dimensional axis-symmetric coordinates. In this paper, the immersed interface method (IIM) in axis-symmetric coordinates is developed for elliptic interface problems that have a discontinuous coefficient, solution or flux. A staggered grid is used to overcome the pole singularity. Other challenges include deriving the jump relations in axis-symmetric coordinates, designing the numerical algorithm when the interface is close to the pole (r = 0); computing interface quantities such as the normal and tangential directions, surface derivatives, curvature information, etc. The numerical algorithm is based on a finite difference discretization and uniform grid in the axis-symmetric coordinates. The finite difference scheme is the standard one away from the interface but is modified at grid points near and on the interface. The method is shown to be second order accurate in the infinity norm. The developed new IIM is applied to the Hele-Shaw flow and compared with the results from the literature.
DA - 2015/8/1/
PY - 2015/8/1/
DO - 10.1016/j.amc.2015.03.131
VL - 264
SP - 179-197
SN - 1873-5649
KW - Immersed interface method
KW - Axis-symmetric interface problem
KW - Discontinuous coefficients
KW - Finite difference method
KW - Level set method
KW - Hele-Shaw flow
ER -
TY - JOUR
TI - Special algorithm for stability analysis of multistable biological regulatory systems
AU - Hong, Hoon
AU - Tang, Xiaoxian
AU - Xia, Bican
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We consider the problem of counting (stable) equilibriums of an important family of algebraic differential equations modeling multistable biological regulatory systems. The problem can be solved, in principle, using real quantifier elimination algorithms, in particular real root classification algorithms. However, it is well known that they can handle only very small cases due to the enormous computing time requirements. In this paper, we present a special algorithm which is much more efficient than the general methods. Its efficiency comes from the exploitation of certain interesting structures of the family of differential equations.
DA - 2015///
PY - 2015///
DO - 10.1016/j.jsc.2014.09.039
VL - 70
SP - 112-135
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2014.09.039
KW - Quantifier elimination
KW - Root classification
KW - Biological regulation system
KW - Stability
ER -
TY - CONF
TI - RFI modeling and prediction approach for SATOPS applications
AU - Nguyen, Tien M.
AU - Tran, Hien T.
AU - Wang, Zhonghai
AU - Coons, Amanda
AU - Nguyen, Charles C.
AU - Lane, Steven A.
AU - Pham, Khanh D.
AU - Chen, Genshe
AU - Wang, Gang
T2 - SPIE Defense + Security
A2 - Pham, Khanh D.
A2 - Chen, Genshe
AB - This paper describes innovative frameworks to develop RFI modeling and prediction models for (i) estimating the RFI characteristics, (ii) evaluating effectiveness of the existing Unified S-Band (USB) command waveforms employed by civil, commercial and military SATOPS ground stations, and (iii) predicting the impacts of RFI on USB command systems. The approach presented here will allow the communications designer to characterize both friendly and unfriendly RFI sources, and evaluate the impacts of RFI on civil, commercial and military USB SATOPS systems. In addition, the proposed frameworks allow the designer to estimate the optimum transmitted signal power to maintain a required USB SATOPS Quality-of-Service (QoS) in the presence of both friendly and unfriendly RFI sources.
C2 - 2015/5/22/
C3 - Sensors and Systems for Space Applications VIII
DA - 2015/5/22/
DO - 10.1117/12.2177955
VL - 9469
SP -
PB - SPIE
UR - http://dx.doi.org/10.1117/12.2177955
DB - Crossref
KW - Friendly RFI
KW - Unfriendly RFI
KW - Detection
KW - Prediction
KW - Satellite Operations
KW - Command
KW - Quality-of-Service
KW - Bit Error Rate
KW - Synchronization
KW - Unified-S-Band
KW - Satellite Control Network
KW - Interference Protection Criteria
ER -
TY - JOUR
TI - Quantifying uncertainty and variable sensitivity within the US billion-dollar weather and climate disaster cost estimates
AU - Smith, Adam B.
AU - Matthews, Jessica L.
T2 - NATURAL HAZARDS
DA - 2015/7//
PY - 2015/7//
DO - 10.1007/s11069-015-1678-x
VL - 77
IS - 3
SP - 1829-1851
SN - 1573-0840
KW - Natural disasters
KW - Costs
KW - Losses
KW - Uncertainty
KW - Statistics of extreme events
KW - Sensitivity
ER -
TY - JOUR
TI - On the sectorial property of the Caputo derivative operator
AU - Ito, Kazufumi
AU - Jin, Bangti
AU - Takeuchi, Tomoya
T2 - APPLIED MATHEMATICS LETTERS
AB - In this note, we establish the sectorial property of the Caputo fractional derivative operator of order α∈(1,2) with a zero Dirichlet boundary condition.
DA - 2015/9//
PY - 2015/9//
DO - 10.1016/j.aml.2015.03.001
VL - 47
SP - 43-46
SN - 0893-9659
KW - Caputo fractional derivative
KW - Sectorial property
ER -
TY - JOUR
TI - Lobatto IIIA methods, direct transcription, and DAEs with delays
AU - Betts, John T.
AU - Campbell, Stephen L.
AU - Thompson, Karmethia
T2 - NUMERICAL ALGORITHMS
DA - 2015/6//
PY - 2015/6//
DO - 10.1007/s11075-014-9896-y
VL - 69
IS - 2
SP - 291-300
SN - 1572-9265
KW - Optimal control
KW - Delays
KW - Direct transcription
KW - Numerical discretizations
KW - Stability
ER -
TY - CONF
TI - Identification of thermal degradation using probabilistic models in reflectance spectroscopy
AU - Criner, A. K.
AU - Cherry, A. J.
AU - Cooney, A. T.
AU - Katter, T. D.
AU - Banks, H. T.
AU - Hu, Shuhua
AU - Catenacci, Jared
T2 - 41ST ANNUAL REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION: Volume 34
AB - Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation A. K. Criner, A. J. Cherry, A. T. Cooney, T. D. Katter, H. T. Banks, Shuhua Hu, Jared Catenacci; Identification of thermal degradation using probabilistic models in reflectance spectroscopy. AIP Conference Proceedings 31 March 2015; 1650 (1): 1898–1906. https://doi.org/10.1063/1.4914816 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search
C2 - 2015///
C3 -
DA - 2015///
DO - 10.1063/1.4914816
VL - 1650
SP - 1898-1906
PB - AIP Publishing LLC
UR - http://dx.doi.org/10.1063/1.4914816
DB - Crossref
ER -
TY - JOUR
TI - Elastic collisions among peakon solutions for the Camassa-Holm equation
AU - Chertock, Alina
AU - Liu, Jian-Guo
AU - Pendleton, Terrance
T2 - APPLIED NUMERICAL MATHEMATICS
AB - The purpose of this paper is to study the dynamics of the interaction among a special class of solutions of the one-dimensional Camassa–Holm equation. The equation yields soliton solutions whose identity is preserved through nonlinear interactions. These solutions are characterized by a discontinuity at the peak in the wave shape and are thus called peakon solutions. We apply a particle method to the Camassa–Holm equation and show that the nonlinear interaction among the peakon solutions resembles an elastic collision, i.e., the total energy and momentum of the system before the peakon interaction is equal to the total energy and momentum of the system after the collision. From this result, we provide several numerical illustrations which support the analytical study, as well as showcase the merits of using a particle method to simulate solutions to the Camassa–Holm equation under a wide class of initial data.
DA - 2015/7//
PY - 2015/7//
DO - 10.1016/j.apnum.2014.01.001
VL - 93
SP - 30-46
SN - 1873-5460
UR - https://doi-org.prox.lib.ncsu.edu/10.1016/j.apnum.2014.01.001
KW - Camassa-Holm equation
KW - Particle method
KW - Peakon solutions
KW - Elastic collisions
KW - Conservation laws
KW - Completely integrable systems
ER -
TY - JOUR
TI - Computation of singular solutions to the Helmholtz equation with high order accuracy
AU - Britt, S.
AU - Petropavlovsky, S.
AU - Tsynkov, S.
AU - Turkel, E.
T2 - Applied Numerical Mathematics
AB - Solutions to elliptic PDEs, in particular to the Helmholtz equation, become singular near the boundary if the boundary data do not possess sufficient regularity. In that case, the convergence of standard numerical approximations may slow down or cease altogether. We propose a method that maintains a high order of grid convergence even in the presence of singularities. This is accomplished by an asymptotic expansion that removes the singularities up to several leading orders, and the remaining regularized part of the solution can then be computed on the grid with the expected accuracy. The computation on the grid is rendered by a compact finite difference scheme combined with the method of difference potentials. The scheme enables fourth order accuracy on a narrow 3×3 stencil: it uses only one unknown variable per grid node and requires only as many boundary conditions as needed for the underlying differential equation itself. The method of difference potentials enables treatment of non-conforming boundaries on regular structured grids with no deterioration of accuracy, while the computational complexity remains comparable to that of a conventional finite difference scheme on the same grid. The method of difference potentials can be considered a generalization of the method of Calderon's operators in PDE theory. In the paper, we provide a theoretical analysis of our combined methodology and demonstrate its numerical performance on a series of tests that involve Dirichlet and Neumann boundary data with various degrees of “non-regularity”: an actual jump discontinuity, a discontinuity in the first derivative, a discontinuity in the second derivative, etc. All computations are performed on a Cartesian grid, whereas the boundary of the domain is a circle, chosen as a simple but non-conforming shape. In all cases, the proposed methodology restores the design rate of grid convergence, which is fourth order, in spite of the singularities and regardless of the fact that the boundary is not aligned with the discretization grid. Moreover, as long as the location of the singularities is known and remains fixed, a broad spectrum of problems involving different boundary conditions and/or data on “smooth” segments of the boundary can be solved economically since the discrete counterparts of Calderon's projections need to be calculated only once and then can be applied to each individual formulation at very little additional cost.
DA - 2015/7//
PY - 2015/7//
DO - 10.1016/j.apnum.2014.10.006
VL - 93
SP - 215-241
J2 - Applied Numerical Mathematics
LA - en
OP -
SN - 0168-9274
UR - http://dx.doi.org/10.1016/j.apnum.2014.10.006
DB - Crossref
KW - Difference potentials
KW - Boundary projections
KW - Calderon's operators
KW - Regular grids
KW - Curvilinear boundaries
KW - Non-conforming boundaries
KW - Solutions with singularities
KW - Singularity subtraction
KW - Discontinuous boundary data
KW - Asymptotic expansion near singularity
KW - Compact differencing
KW - High order accuracy
ER -
TY - JOUR
TI - Comparative Genomic Analysis Identifies Divergent Genomic Features of Pathogenic Enterococcus cecorum Including a Type IC CRISPR-Cas System, a Capsule Locus, an epa-Like Locus, and Putative Host Tissue Binding Proteins
AU - Borst, Luke B.
AU - Suyemoto, M. Mitsu
AU - Scholl, Elizabeth H.
AU - Fuller, Fredrick J.
AU - Barnes, H. John
T2 - PLOS ONE
AB - Enterococcus cecorum (EC) is the dominant enteric commensal of adult chickens and contributes to the gut consortia of many avian and mammalian species. While EC infection is an uncommon zoonosis, like other enterococcal species it can cause life-threating nosocomial infection in people. In contrast to other enterococci which are considered opportunistic pathogens, emerging pathogenic strains of EC cause outbreaks of musculoskeletal disease in broiler chickens. Typical morbidity and mortality is comparable to other important infectious diseases of poultry. In molecular epidemiologic studies, pathogenic EC strains were found to be genetically clonal. These findings suggested acquisition of specific virulence determinants by pathogenic EC. To identify divergent genomic features and acquired virulence determinants in pathogenic EC; comparative genomic analysis was performed on genomes of 3 pathogenic and 3 commensal strains of EC. Pathogenic isolates had smaller genomes with a higher GC content, and they demonstrated large regions of synteny compared to commensal isolates. A molecular phylogenetic analysis demonstrated sequence divergence in pathogenic EC genomes. At a threshold of 98% identity, 414 predicted proteins were identified that were highly conserved in pathogenic EC but not in commensal EC. Among these, divergent CRISPR-cas defense loci were observed. In commensal EC, the type IIA arrangement typical for enterococci was present; however, pathogenic EC had a type IC locus, which is novel in enterococci but commonly observed in streptococci. Potential mediators of virulence identified in this analysis included a polysaccharide capsular locus similar to that recently described for E. faecium, an epa-like locus, and cell wall associated proteins which may bind host extracellular matrix. This analysis identified specific genomic regions, coding sequences, and predicted proteins which may be related to the divergent evolution and increased virulence of emerging pathogenic strains of EC.
DA - 2015/4/10/
PY - 2015/4/10/
DO - 10.1371/journal.pone.0121294
VL - 10
IS - 4
SP -
SN - 1932-6203
ER -
TY - JOUR
TI - Vertex Representations of Toroidal Special Linear Lie Superalgebras
AU - Jing, Naihuan
AU - Xu, Chongbin
T2 - CHINESE ANNALS OF MATHEMATICS SERIES B
AB - Based on the loop-algebraic presentation of 2-toroidal Lie superalgebras, free field representation of toroidal Lie superalgebras of type $A(m, n)$ is constructed using both vertex operators and bosonic fields.
DA - 2015/5//
PY - 2015/5//
DO - 10.1007/s11401-015-0921-9
VL - 36
IS - 3
SP - 427-436
SN - 1860-6261
KW - Toroidal Lie superalgebras
KW - Vertex operators
KW - Free fields
ER -
TY - JOUR
TI - Traveling waves for conservation laws with cubic nonlinearity and BBM type dispersion
AU - Shearer, Michael
AU - Spayd, Kimberly R.
AU - Swanson, Ellen R.
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - Scalar conservation laws with non-convex fluxes have shock wave solutions that violate the Lax entropy condition. In this paper, such solutions are selected by showing that some of them have corresponding traveling waves for the equation supplemented with dissipative and dispersive higher-order terms. For a cubic flux, traveling waves can be calculated explicitly for linear dissipative and dispersive terms. Information about their existence can be used to solve the Riemann problem, in which we find solutions for some data that are different from the classical Lax–Oleinik construction. We consider dispersive terms of a BBM type and show that the calculation of traveling waves is somewhat more intricate than for a KdV-type dispersion. The explicit calculation is based upon the calculation of parabolic invariant manifolds for the associated ODE describing traveling waves. The results extend to the p-system of one-dimensional elasticity with a cubic stress–strain law.
DA - 2015/10/5/
PY - 2015/10/5/
DO - 10.1016/j.jde.2015.04.019
VL - 259
IS - 7
SP - 3216-3232
SN - 1090-2732
ER -
TY - JOUR
TI - The Development of a Customization Framework for the WRF Model over the Lake Victoria Basin, Eastern Africa on Seasonal Timescales
AU - Argent, R.
AU - Sun, X.
AU - Semazzi, F.
AU - Xie, L.
AU - Liu, B.
T2 - ADVANCES IN METEOROLOGY
AB - Lake Victoria, Africa, supports millions of people. To produce reliable climate projections, it is desirable to successfully model the rainfall over the lake accurately. An initial step is taken here with customization of the Weather, Research, and Forecast (WRF) model. Of particular interest is an asymmetrical rainfall pattern across the lake basin, due to a diurnal land-lake breeze. The main aim is to present a customization framework for use over the lake. This framework is developed by conducting several series of model runs to investigate aspects of the customization. The runs are analyzed using Tropical Rainfall Measuring Mission rainfall data and Climatic Research Unit temperature data. The study shows that the choice of parameters and lake surface temperature initialization can significantly alter the results. Also, the optimal physics combinations for the climatology may not necessarily be suitable for all circumstances, such as extreme years. The study concludes that WRF is unable to reproduce the pattern across the lake. The temperature of the lake is too cold and this prevents the diurnal land-lake breeze reversal. Overall, this study highlights the importance of customizing a model to the region of research and presents a framework through which this may be achieved.
DA - 2015///
PY - 2015///
DO - 10.1155/2015/653473
VL - 2015
SP -
SN - 1687-9317
ER -
TY - JOUR
TI - THE CHARACTERISTIC IMSET POLYTOPE OF BAYESIAN NETWORKS WITH ORDERED NODES
AU - Xi, Jing
AU - Yoshida, Ruriko
T2 - SIAM JOURNAL ON DISCRETE MATHEMATICS
AB - In 2010, M. Studený, R. Hemmecke, and S. Lindner explored a new algebraic description of graphical models, called characteristic imsets. Compared with standard imsets, characteristic imsets have several advantages: they are still unique vector representatives of conditional independence structures, 0-1 vectors, and more intuitive in terms of graphs than standard imsets. After defining a characteristic imset polytope (cim-polytope) as the convex hull of all characteristic imsets with a given set of nodes, they also showed that a model selection in graphical models, which maximizes a quality criterion, can be converted into a linear programming problem over the cim-polytope. However, in general, for a fixed set of nodes, the cim-polytope can have exponentially many vertices over an exponentially high dimension. Therefore, in this paper, we focus on the family of directed acyclic graphs whose nodes have a fixed order. This family includes diagnosis models described by bipartite graphs with a set of $m$ nodes and a set of $n$ nodes for any $m, n \in \mathbb{Z}_+$. We first consider cim-polytopes for all diagnosis models and show that these polytopes are direct products of simplices. Then we give a combinatorial description of all edges and all facets of these polytopes. Finally, we generalize these results to the cim-polytopes for all Bayesian networks with a fixed underlying ordering of nodes with or without fixed (or forbidden) edges.
DA - 2015///
PY - 2015///
DO - 10.1137/130933848
VL - 29
IS - 2
SP - 697-715
SN - 1095-7146
KW - graphical model
KW - characteristic imset polytope
KW - diagnosis model
KW - bipartite graph
KW - directed acyclic graphs
ER -
TY - JOUR
TI - Stability of concatenated traveling waves: Alternate approaches
AU - Lin, Xiao-Biao
AU - Schecter, Stephen
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - We consider a reaction–diffusion equation in one space dimension whose initial condition is approximately a sequence of widely separated traveling waves with increasing velocity, each of which is asymptotically stable. As in [14], [24], [25], we show that the sequence of traveling waves is itself asymptotically stable: as t→∞, the solution approaches the concatenated wave pattern, with different shifts of each wave allowed. Our proof is similar to that of [14] in that it is based on spatial dynamics, Laplace transform, and exponential dichotomies, but it incorporates a number of modifications.
DA - 2015/10/5/
PY - 2015/10/5/
DO - 10.1016/j.jde.2015.04.015
VL - 259
IS - 7
SP - 3144-3177
SN - 1090-2732
KW - Traveling wave
KW - Stability
KW - Spatial dynamics
KW - Laplace transform
KW - Exponential dichotomy
ER -
TY - JOUR
TI - Seven challenges for modelling indirect transmission: Vector-borne diseases, macroparasites and neglected tropical diseases
AU - Hollingsworth, T. Déirdre
AU - Pulliam, Juliet R.C.
AU - Funk, Sebastian
AU - Truscott, James E.
AU - Isham, Valerie
AU - Lloyd, Alun L.
T2 - Epidemics
AB - Many of the challenges which face modellers of directly transmitted pathogens also arise when modelling the epidemiology of pathogens with indirect transmission – whether through environmental stages, vectors, intermediate hosts or multiple hosts. In particular, understanding the roles of different hosts, how to measure contact and infection patterns, heterogeneities in contact rates, and the dynamics close to elimination are all relevant challenges, regardless of the mode of transmission. However, there remain a number of challenges that are specific and unique to modelling vector-borne diseases and macroparasites. Moreover, many of the neglected tropical diseases which are currently targeted for control and elimination are vector-borne, macroparasitic, or both, and so this article includes challenges which will assist in accelerating the control of these high-burden diseases. Here, we discuss the challenges of indirect measures of infection in humans, whether through vectors or transmission life stages and in estimating the contribution of different host groups to transmission. We also discuss the issues of “evolution-proof” interventions against vector-borne disease.
DA - 2015/3//
PY - 2015/3//
DO - 10.1016/j.epidem.2014.08.007
VL - 10
SP - 16-20
J2 - Epidemics
LA - en
OP -
SN - 1755-4365
UR - http://dx.doi.org/10.1016/j.epidem.2014.08.007
DB - Crossref
KW - Vector-borne disease
KW - Macroparasites
KW - Neglected tropical diseases
KW - Helminths
KW - Vectors
ER -
TY - JOUR
TI - Seven challenges for model-driven data collection in experimental and observational studies
AU - Lessler, J.
AU - Edmunds, W.J.
AU - Halloran, M.E.
AU - Hollingsworth, T.D.
AU - Lloyd, A.L.
T2 - Epidemics
AB - Infectious disease models are both concise statements of hypotheses and powerful techniques for creating tools from hypotheses and theories. As such, they have tremendous potential for guiding data collection in experimental and observational studies, leading to more efficient testing of hypotheses and more robust study designs. In numerous instances, infectious disease models have played a key role in informing data collection, including the Garki project studying malaria, the response to the 2009 pandemic of H1N1 influenza in the United Kingdom and studies of T-cell immunodynamics in mammals. However, such synergies remain the exception rather than the rule; and a close marriage of dynamic modeling and empirical data collection is far from the norm in infectious disease research. Overcoming the challenges to using models to inform data collection has the potential to accelerate innovation and to improve practice in how we deal with infectious disease threats.
DA - 2015/3//
PY - 2015/3//
DO - 10.1016/j.epidem.2014.12.002
VL - 10
SP - 78-82
J2 - Epidemics
LA - en
OP -
SN - 1755-4365
UR - http://dx.doi.org/10.1016/j.epidem.2014.12.002
DB - Crossref
KW - Modeling
KW - Data collection
KW - Observational studies
KW - Experimental studies
ER -
TY - JOUR
TI - Regional Climate Change: Downscaling, Prediction, and Impact Assessment
AU - Xie, Lian
AU - Semazzi, Fredrick
AU - Hanna, Adel
AU - Anyah, Richard
AU - Gao, Huiwang
AU - He, Yijun
T2 - ADVANCES IN METEOROLOGY
AB - Although the issue of climate change is often dealt with in global perspective, the impact of climate change must be assessed at regional scales. While global climate models can provide projections of the average state of large-scale circulation of future climate, the downscaling of such projections to regional scale with improved spatial and temporal resolution for both the forcing fields and the climatic responses is the basis for assessing the societal impacts of climate change. Therefore, it is important to not only study climate change at the global scale but also study the regional manifestations of the climate system at spatial scales ranging from less than a hundred kilometers to thousands of kilometers with time scales from months to years to decades. This special issue publishes a collection of articles covering a wide range of topics of our understanding of “regional climate” from downscaling the variability of extreme rainfall over the Yangtze River basin (T. Gao and L. Xie) and assessing the water resources in the Yellow River region (Z. Wu et al.) in China to forecasting the precipitation and water resources in the Lake Victoria region in East Africa (X. Sun et al., R. Argent et al., and K. A. Smith and F. H. M. Semazzi), from downscaling wind energy resources in the contiguous United States (B. Liu et al.) to characterizing the precipitation extremes in the Carpathian region in central and southern Europe (L. Gaal et al.), and from analyzing the energy balance in semiarid grasslands in China (Q. Jiang et al.) to detecting future climate change signals in central and eastern Europe from numerical model simulations (M. Belda et al.). This special issue also includes articles addressing the impacts of regional climate change on tropical cyclones over the Atlantic Ocean (K. Xie and B. Liu), on crop yields in North China (H. Liu et al.), and on litter production and nutrient dynamics in a plantation in China (X. Ge et al.), as well as rainfall and drought in Eastern Kenya (M. O. Kisaka et al.). Additionally, several articles with focus on regional climate downscaling methodologies are also included. S. Kim et al. studied the effects of geographic features in a mountainous area on the downscaling of global climate model data; T. R. Lee et al. demonstrated the feasibility of using PRISM (parameterelevation regression on independent slope model) to downscale maximum temperature to subkilometer scale; L. Gao et al. applied the LASSO algorithm to statistically downscale the ERA-interim precipitation forecast over complex terrain; and K.-H. Min and W.-Y. Sun explored the application of an atmosphere-cryosphere coupledmodel in regional climate applications. These articles reflect the recent advances and applications in “regional climate downscaling, prediction, and impact assessment” from a set of unique angles. We hope they are of interest to peers.
DA - 2015///
PY - 2015///
DO - 10.1155/2015/290281
VL - 2015
SP -
SN - 1687-9317
ER -
TY - JOUR
TI - Reductive Linear Differential Algebraic Groups and the Galois Groups of Parameterized Linear Differential Equations
AU - Minchenko, Andrey
AU - Ovchinnikov, Alexey
AU - Singer, Michael F.
T2 - INTERNATIONAL MATHEMATICS RESEARCH NOTICES
AB - We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives in differential representations of reductive LDAGs, extending existing results, which were obtained for SL2 in the case of just one derivation. As an application of the above bound, we develop an algorithm that tests whether the parameterized differential Galois group of a system of linear differential equations is reductive and, if it is, calculates it.
DA - 2015///
PY - 2015///
DO - 10.1093/imrn/rnt344
VL - 2015
IS - 7
SP - 1733-1793
SN - 1687-0247
ER -
TY - JOUR
TI - RANDOMIZED APPROXIMATION OF THE GRAM MATRIX: EXACT COMPUTATION AND PROBABILISTIC BOUNDS
AU - Holodnak, John T.
AU - Ipsen, Ilse C. F.
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - Given a real matrix $\mathbf{A}$ with $n$ columns, the problem is to approximate the Gram product $\mathbf{A}\mathbf{A}^T$ by $c\ll n$ weighted outer products of columns of $\mathbf{A}$. Necessary and sufficient conditions for the exact computation of $\mathbf{A}\mathbf{A}^T$ (in exact arithmetic) from $c\geq \mathrm{rank}(\mathbf{A})$ columns depend on the right singular vector matrix of $\mathbf{A}$. For a Monte Carlo matrix multiplication algorithm by Drineas et al. that samples outer products, we present probabilistic bounds for the two-norm relative error due to randomization. The bounds depend on the stable rank or the rank of $\mathbf{A}$, but not on the matrix dimensions. Numerical experiments illustrate that the bounds are informative, even for stringent success probabilities and matrices of small dimension. We also derive bounds for the smallest singular value and the condition number of matrices obtained by sampling rows from orthonormal matrices.
DA - 2015///
PY - 2015///
DO - 10.1137/130940116
VL - 36
IS - 1
SP - 110-137
SN - 1095-7162
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84925298413&partnerID=MN8TOARS
KW - leverage scores
KW - singular value decomposition
KW - stable rank
KW - coherence
KW - matrix concentration inequalities
KW - unbiased estimator
ER -
TY - JOUR
TI - Quartic spectrahedra
AU - Ottem, John Christian
AU - Ranestad, Kristian
AU - Sturmfels, Bernd
AU - Vinzant, Cynthia
T2 - MATHEMATICAL PROGRAMMING
AB - Quartic spectrahedra in 3-space form a semialgebraic set of dimension 24. This set is stratified by the location of the ten nodes of the corresponding real quartic surface. There are twenty maximal strata, identified recently by Degtyarev and Itenberg, via the global Torelli Theorem for real K3 surfaces. We here give a new proof that is self-contained and algorithmic. This involves extending Cayley’s characterization of quartic symmetroids, by the property that the branch locus of the projection from a node consists of two cubic curves. This paper represents a first step towards the classification of all spectrahedra of a given degree and dimension.
DA - 2015/7//
PY - 2015/7//
DO - 10.1007/s10107-014-0844-3
VL - 151
IS - 2
SP - 585-612
SN - 1436-4646
ER -
TY - JOUR
TI - ORTHOGONAL LOW RANK TENSOR APPROXIMATION: ALTERNATING LEAST SQUARES METHOD AND ITS GLOBAL CONVERGENCE
AU - Wang, Liqi
AU - Chu, Moody T.
AU - Yu, Bo
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - With the notable exceptions of two cases---that tensors of order 2, namely, matrices, always have best approximations of arbitrary low ranks and that tensors of any order always have the best rank-1 approximation, it is known that high-order tensors may fail to have best low rank approximations. When the condition of orthogonality is imposed, even under the modest assumption of semiorthogonality where only one set of components in the decomposed rank-1 tensors is required to be mutually perpendicular, the situation is changed completely---orthogonal low rank approximations always exist. The purpose of this paper is to discuss the best low rank approximation subject to semiorthogonality. The conventional high-order power method is modified to address the desirable orthogonality via the polar decomposition. Algebraic geometry technique is employed to show that for almost all tensors the orthogonal alternating least squares method converges globally.
DA - 2015///
PY - 2015///
DO - 10.1137/130943133
VL - 36
IS - 1
SP - 1-19
SN - 1095-7162
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84925305684&partnerID=MN8TOARS
KW - orthogonal tensor decomposition
KW - low rank approximation
KW - alternating least squares
KW - high-order power method
KW - polar decomposition
KW - global convergence
KW - Zariski topology
ER -
TY - JOUR
TI - OPTIMAL DESIGN FOR PARAMETER ESTIMATION IN EEG PROBLEMS IN A 3D MULTILAYERED DOMAIN
AU - Banks, H. T.
AU - Rubio, D.
AU - Saintier, N.
AU - Troparevsky, M. I.
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - The fundamental problem of collecting data in the ``best way'' in order to assure statistically efficient estimation of parameters is known as Optimal Experimental Design. Many inverse problems consist in selecting best parameter values of a given mathematical model based on fits to measured data. These are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data. We consider an electromagnetic interrogation problem, specifically one arising in an electroencephalography (EEG) problem, of finding optimal number and locations for sensors for source identification in a 3D unit sphere from data on its boundary. In this effort we compare the use of the classical D-optimal criterion for observation points as opposed to that for a uniform observation mesh. We consider location and best number of sensors and report results based on statistical uncertainty analysis of the resulting estimated parameters.
DA - 2015/8//
PY - 2015/8//
DO - 10.3934/mbe.2015.12.739
VL - 12
IS - 4
SP - 739-760
SN - 1551-0018
KW - Electromagnetic inverse problems
KW - optimal design in 3D EEG analysis
KW - parameter estimation
KW - asymptotic error analysis
ER -
TY - JOUR
TI - Nine challenges for deterministic epidemic models
AU - Roberts, Mick
AU - Andreasen, Viggo
AU - Lloyd, Alun
AU - Pellis, Lorenzo
T2 - Epidemics
AB - Deterministic models have a long history of being applied to the study of infectious disease epidemiology. We highlight and discuss nine challenges in this area. The first two concern the endemic equilibrium and its stability. We indicate the need for models that describe multi-strain infections, infections with time-varying infectivity, and those where superinfection is possible. We then consider the need for advances in spatial epidemic models, and draw attention to the lack of models that explore the relationship between communicable and non-communicable diseases. The final two challenges concern the uses and limitations of deterministic models as approximations to stochastic systems.
DA - 2015/3//
PY - 2015/3//
DO - 10.1016/j.epidem.2014.09.006
VL - 10
SP - 49-53
J2 - Epidemics
LA - en
OP -
SN - 1755-4365
UR - http://dx.doi.org/10.1016/j.epidem.2014.09.006
DB - Crossref
KW - Deterministic models
KW - Endemic equilibrium
KW - Multi-strain systems
KW - Spatial models
KW - Non-communicable diseases
ER -
TY - JOUR
TI - NONCROSSING ARC DIAGRAMS AND CANONICAL JOIN REPRESENTATIONS
AU - Reading, Nathan
T2 - SIAM JOURNAL ON DISCRETE MATHEMATICS
AB - We consider two problems that appear at first sight to be unrelated. The first problem is to count certain diagrams consisting of noncrossing arcs in the plane. The second problem concerns the weak order on the symmetric group. Each permutation $x$ has a canonical join representation: a unique lowest set of permutations joining to $x$. The second problem is to determine which sets of permutations appear as canonical join representations. The two problems turn out to be closely related because the noncrossing arc diagrams provide a combinatorial model for canonical join representations. The same considerations apply more generally to lattice quotients of the weak order. Considering quotients produces, for example, a new combinatorial object counted by the Baxter numbers and an analogous new object in bijection with generic rectangulations.
DA - 2015///
PY - 2015///
DO - 10.1137/140972391
VL - 29
IS - 2
SP - 736-750
SN - 1095-7146
UR - https://doi.org/10.1137/140972391
KW - canonical join representation
KW - lattice congruence
KW - noncrossing arc diagram
KW - permutation
KW - weak order
ER -
TY - JOUR
TI - Five challenges for stochastic epidemic models involving global transmission
AU - Britton, Tom
AU - House, Thomas
AU - Lloyd, Alun L.
AU - Mollison, Denis
AU - Riley, Steven
AU - Trapman, Pieter
T2 - EPIDEMICS
AB - The most basic stochastic epidemic models are those involving global transmission, meaning that infection rates depend only on the type and state of the individuals involved, and not on their location in the population. Simple as they are, there are still several open problems for such models. For example, when will such an epidemic go extinct and with what probability (questions depending on the population being fixed, changing or growing)? How can a model be defined explaining the sometimes observed scenario of frequent mid-sized epidemic outbreaks? How can evolution of the infectious agent transmission rates be modelled and fitted to data in a robust way?
DA - 2015/3//
PY - 2015/3//
DO - 10.1016/j.epidem.2014.05.002
VL - 10
SP - 54-57
SN - 1755-4365
KW - Stochastic epidemics
KW - Global transmission
KW - Extinction
KW - Genetic evolution
KW - Endemicity
ER -
TY - JOUR
TI - Effect of Lake Surface Temperature on the Spatial Distribution and Intensity of the Precipitation over the Lake Victoria Basin
AU - Sun, Xia
AU - Xie, Lian
AU - Semazzi, Fredrick
AU - Liu, Bin
T2 - MONTHLY WEATHER REVIEW
AB - Abstract A series of sensitivity experiments are performed to investigate the response of precipitation over the Lake Victoria basin (LVB) to the changes of lake surface temperature (LST) using the Weather Research and Forecasting (WRF) Model. It is shown that the default LST initialized from NCEP FNL (Final) Operational Global Analysis is deficient for simulating the rainfall over the LVB. Comparative experiments demonstrate the unambiguous impact of LST on the intensity and pattern of the precipitation over LVB. Intensification/weakening of precipitation over the lake occur with increasing/decreasing LST for both uniform and asymmetrical LST distribution. However, the relationship between rainfall anomalies and LST variations is nonlinear. Replacing the LST directly derived from global weather forecast models by the mean area-averaged LST of Lake Victoria (approximately 24°C) leads to improved rainfall simulation. However, LST with realistic cross-basin gradient is necessary to obtain a rainfall pattern consistent with the observations. The fact that rainfall and wind patterns over the lake are sensitive to LST distribution suggests the need to monitor the mesoscale LST pattern for accurate weather and climate prediction over LVB. It is also found that although the LST distribution exerts significant impact on the observed rainfall pattern, the area and location of the rainband are quite persistent under different LST forcing. This suggests that although the details of the rainfall pattern over LVB are strongly influenced by LST, the broad rainfall pattern is likely controlled by the atmospheric circulation and orography in the region.
DA - 2015/4//
PY - 2015/4//
DO - 10.1175/mwr-d-14-00049.1
VL - 143
IS - 4
SP - 1179-1192
SN - 1520-0493
ER -
TY - JOUR
TI - An immersed finite volume element method for 2D PDEs with discontinuous coefficients and non-homogeneous jump conditions
AU - Zhu, Ling
AU - Zhang, Zhiyue
AU - Li, Zhilin
T2 - COMPUTERS & MATHEMATICS WITH APPLICATIONS
AB - An immersed finite volume element method is developed to solve 2D elliptic interface problems with a variable coefficient that has a finite jump across an interface. The solution and the flux may also have a finite jump across the interface. Using the source removal technique, an equivalent elliptic interface problem with homogeneous jump conditions is obtained. The nodal basis functions are constructed to satisfy the homogeneous jump conditions near the interface and the usual finite element nodal basis functions are applied away from the interface. The resulting linear problem is simple and easy to solve. A proof of the error estimate in the energy norm is given. Numerical experiments demonstrate the convergence rates of the proposed method with the usual O(h2) in the L2, the L∞ norms, and O(h) in the H1 norm.
DA - 2015/7//
PY - 2015/7//
DO - 10.1016/j.camwa.2015.04.012
VL - 70
IS - 2
SP - 89-103
SN - 1873-7668
KW - Finite volume element method
KW - Source removal technique
KW - Interface problem
KW - Jump conditions
ER -
TY - JOUR
TI - A Mathematical Model for SAR Imaging beyond the First Born Approximation
AU - Gilman, Mikhail
AU - Tsynkov, Semyon
T2 - SIAM Journal on Imaging Sciences
AB - The assumption of weak scattering is standard for the mathematical analysis of synthetic aperture radar (SAR), as it helps linearize the inverse problem via the first Born approximation and thus makes it amenable to solution. Yet it is not consistent with another common assumption, that the interrogating waves do not penetrate into the target material and get scattered off its surface only, which essentially means that the scattering is strong. In the paper, we revisit the foundations of the SAR ambiguity theory in order to address this and other existing inconsistencies, such as the absence of the Bragg scale in scattering. We introduce a new model for radar targets that allows us to compute the scattered field from first principles. This renders the assumption of weak scattering unnecessary yet keeps the overall inverse scattering problem linear. Finally, we show how one can incorporate the Leontovich boundary condition into SAR ambiguity theory.
DA - 2015/1//
PY - 2015/1//
DO - 10.1137/140973025
VL - 8
IS - 1
SP - 186-225
J2 - SIAM J. Imaging Sci.
LA - en
OP -
SN - 1936-4954
UR - http://dx.doi.org/10.1137/140973025
DB - Crossref
KW - synthetic aperture imaging
KW - SAR ambiguity theory
KW - linearized scattering
KW - linearized inverse problem
KW - backscattering
KW - Bragg resonance
KW - weak scattering
KW - strong scattering
ER -
TY - JOUR
TI - Using Kalman Filtering to Predict Time-Varying Parameters in a Model Predicting Baroreflex Regulation During Head-Up Tilt
AU - Matzuka, Brett
AU - Mehlsen, Jesper
AU - Tran, Hien
AU - Olufsen, Mette Sofie
T2 - IEEE Transactions on Biomedical Engineering
AB - The cardiovascular control system is continuously engaged to maintain homeostasis, but it is known to fail in a large cohort of patients suffering from orthostatic intolerance. Numerous clinical studies have been put forward to understand how the system fails, yet noninvasive clinical data are sparse, typical studies only include measurements of heart rate and blood pressure, as a result it is difficult to determine what mechanisms that are impaired. It is known, that blood pressure regulation is mediated by changes in heart rate, vascular resistance, cardiac contractility, and a number of other factors. Given that numerous factors contribute to changing these quantities, it is difficult to devise a physiological model describing how they change in time. One way is to build a model that allows these controlled quantities to change and to compare dynamics between subject groups. To do so, it requires more knowledge of how these quantities change for healthy subjects. This study compares two methods predicting time-varying changes in cardiac contractility and vascular resistance during head-up tilt. Similar to the study by Williams et al.[51], the first method uses piecewise linear splines, while the second uses the ensemble transform Kalman filter (ETKF) [1] , [11], [12], [33]. In addition, we show that the delayed rejection adaptive Metropolis (DRAM) algorithm can be used for predicting parameter uncertainties within the spline methodology, which is compared with the variability obtained with the ETKF. While the spline method is easier to set up, this study shows that the ETKF has a significantly shorter computational time. Moreover, while uncertainty of predictions can be augmented to spline predictions using DRAM, these are readily available with the ETKF.
DA - 2015/8//
PY - 2015/8//
DO - 10.1109/tbme.2015.2409211
VL - 62
IS - 8
SP - 1992-2000
J2 - IEEE Trans. Biomed. Eng.
OP -
SN - 0018-9294 1558-2531
UR - http://dx.doi.org/10.1109/TBME.2015.2409211
DB - Crossref
KW - Baroreflex regulation
KW - cardiovascular
KW - DRAM
KW - ensemble transform Kalman filter
KW - head-up tilt
KW - Kalman filtering
KW - parameter estimation
ER -
TY - JOUR
TI - Twisted Vertex Operators and Unitary Lie Algebras
AU - Chen, Fulin
AU - Gao, Yun
AU - Jing, Naihuan
AU - Tan, Shaobin
T2 - CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
AB - A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by-product, some fundamental representations of affine Kac-Moody Lie algebra of type $A_n^{(2)}$ are recovered by the new method.
DA - 2015/6//
PY - 2015/6//
DO - 10.4153/cjm-2014-010-1
VL - 67
IS - 3
SP - 573-596
SN - 1496-4279
KW - Lie algebra
KW - vertex operator
KW - representation theory
ER -
TY - JOUR
TI - The genomes of two key bumblebee species with primitive eusocial organization
AU - Sadd, B. M.
AU - Barribeau, S. M.
AU - Bloch, G.
AU - Graaf, D. C.
AU - Dearden, P.
AU - Elsik, C. G.
AU - Gadau, J.
AU - Grimmelikhuijzen, C. J. P.
AU - Hasselmann, M.
AU - Lozier, J. D.
AU - Robertson, H. M.
AU - Smagghe, G.
AU - Stolle, E.
AU - Van Vaerenbergh, M.
AU - Waterhouse, R. M.
T2 - Genome Biology
DA - 2015///
PY - 2015///
VL - 16
ER -
TY - JOUR
TI - Statistical validation of structured population models for Daphnia magna
AU - Adoteye, Kaska
AU - Banks, H. T.
AU - Cross, Karissa
AU - Eytcheson, Stephanie
AU - Flores, Kevin B.
AU - LeBlanc, Gerald A.
AU - Nguyen, Timothy
AU - Ross, Chelsea
AU - Smith, Emmaline
AU - Stemkovski, Michael
AU - Stokely, Sarah
T2 - MATHEMATICAL BIOSCIENCES
AB - In this study we use statistical validation techniques to verify density-dependent mechanisms hypothesized for populations of Daphnia magna. We develop structured population models that exemplify specific mechanisms and use multi-scale experimental data in order to test their importance. We show that fecundity and survival rates are affected by both time-varying density-independent factors, such as age, and density-dependent factors, such as competition. We perform uncertainty analysis and show that our parameters are estimated with a high degree of confidence. Furthermore, we perform a sensitivity analysis to understand how changes in fecundity and survival rates affect population size and age-structure.
DA - 2015/8//
PY - 2015/8//
DO - 10.1016/j.mbs.2015.06.003
VL - 266
SP - 73-84
SN - 1879-3134
KW - Sensitivity analysis
KW - Structured population model
KW - Uncertainty quantification
KW - Density-dependence
KW - Multi-scale data
KW - Daphnia magna
ER -
TY - JOUR
TI - One-way deficit of two-qubit X states
AU - Wang, Yao-Kun
AU - Jing, Naihuan
AU - Fei, Shao-Ming
AU - Wang, Zhi-Xi
AU - Cao, Jun-Peng
AU - Fan, Heng
T2 - QUANTUM INFORMATION PROCESSING
AB - Quantum deficit originates in questions regarding work extraction from quantum systems coupled to a heat bath (Oppenheim et al. in Phys Rev Lett 89:180402, 2002). It links quantum correlations with quantum thermodynamics and provides a new standpoint for understanding quantum non-locality. In this paper, we propose a new method to evaluate the one-way deficit for a class of two-qubit states. The dynamic behavior of the one-way deficit under decoherence channel is investigated, and it is shown that the one-way deficit of the $$X$$ states with five parameters is more robust against decoherence than entanglement.
DA - 2015/7//
PY - 2015/7//
DO - 10.1007/s11128-015-1005-1
VL - 14
IS - 7
SP - 2487-2497
SN - 1573-1332
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84930758767&partnerID=MN8TOARS
KW - One-way deficit
KW - Concurrence
KW - Phase flip channel
ER -
TY - JOUR
TI - Multiple transverse homoclinic solutions near a degenerate homoclinic orbit
AU - Lin, Xiao-Biao
AU - Long, Bin
AU - Zhu, Changrong
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - Consider an autonomous ordinary differential equation in Rn that has a homoclinic solution asymptotic to a hyperbolic equilibrium. The homoclinic solution is degenerate in the sense that the linear variational equation has 2 bounded, linearly independent solutions. We study bifurcation of the homoclinic solution under periodic perturbations. Using exponential dichotomies and Lyapunov–Schmidt reduction, we obtain general conditions under which the perturbed system can have transverse homoclinic solutions and nearby periodic or chaotic solutions.
DA - 2015/7/5/
PY - 2015/7/5/
DO - 10.1016/j.jde.2015.01.046
VL - 259
IS - 1
SP - 1-24
SN - 1090-2732
KW - Degenerate homoclinic bifurcation
KW - Lyapunov-Schmidt reduction
KW - Exponential dichotomies
KW - Chaotic motions
KW - Codiagonalization of quadratic forms
ER -
TY - JOUR
TI - Local unitary invariants of generic multiqubit states
AU - Jing, Naihuan
AU - Fei, Shao-Ming
AU - Li, Ming
AU - Li-Jost, Xianqing
AU - Zhang, Tinggui
T2 - PHYSICAL REVIEW A
AB - We present a complete set of local unitary invariants for generic multi-qubit systems which gives necessary and sufficient conditions for two states being local unitary equivalent. These invariants are canonical polynomial functions in terms of the generalized Bloch representation of the quantum states. In particular, we prove that there are at most 12 polynomial local unitary invariants for two-qubit states and at most 90 polynomials for three-qubit states. Comparison with Makhlin's 18 local unitary invariants is given for two-quibit systems.
DA - 2015/8/4/
PY - 2015/8/4/
DO - 10.1103/physreva.92.022306
VL - 92
IS - 2
SP -
SN - 1094-1622
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84939450244&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Information content in data sets for a nucleated-polymerization model
AU - Banks, H. T.
AU - Doumic, Marie
AU - Kruse, Carola
AU - Prigent, Stephanie
AU - Rezaei, Human
T2 - JOURNAL OF BIOLOGICAL DYNAMICS
AB - We illustrate the use of statistical tools (asymptotic theories of standard error quantification using appropriate statistical models, bootstrapping, and model comparison techniques) in addition to sensitivity analysis that may be employed to determine the information content in data sets. We do this in the context of recent models [S. Prigent, A. Ballesta, F. Charles, N. Lenuzza, P. Gabriel, L.M. Tine, H. Rezaei, and M. Doumic, An efficient kinetic model for assemblies of amyloid fibrils and its application to polyglutamine aggregation, PLoS ONE 7 (2012), e43273. doi:10.1371/journal.pone.0043273.] for nucleated polymerization in proteins, about which very little is known regarding the underlying mechanisms; thus, the methodology we develop here may be of great help to experimentalists. We conclude that the investigated data sets will support with reasonable levels of uncertainty only the estimation of the parameters related to the early steps of the aggregation process.
DA - 2015/1/1/
PY - 2015/1/1/
DO - 10.1080/17513758.2015.1050465
VL - 9
IS - 1
SP - 172-197
SN - 1751-3766
KW - inverse problems
KW - polyglutamine and aggregation modelling
KW - information content
KW - sensitivity
KW - uncertainty quantification
KW - 65M32
KW - 62P10
KW - 64B10
KW - 49Q12
ER -
TY - JOUR
TI - Immersed finite elements for optimal control problems of elliptic PDEs with interfaces
AU - Zhang, Qian
AU - Ito, Kazufumi
AU - Li, Zhilin
AU - Zhang, Zhiyue
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - This paper presents a numerical method and analysis, based on the variational discretization concept, for optimal control problems governed by elliptic PDEs with interfaces. The method uses a simple uniform mesh which is independent of the interface. Due to the jump of the coefficient across the interface, the standard linear finite element method cannot achieve optimal convergence when the uniform mesh is used. Therefore the immersed finite element method (IFEM) developed in Li et al. [20] is used to discretize the state equation required in the variational discretization approach. Optimal error estimates for the control, state and adjoint state are derived. Numerical examples are provided to confirm the theoretical results.
DA - 2015/10/1/
PY - 2015/10/1/
DO - 10.1016/j.jcp.2015.05.050
VL - 298
SP - 305-319
SN - 1090-2716
KW - PDE-constrained optimization
KW - Variational discretization
KW - Immersed finite element
KW - Elliptic interface problem
ER -
TY - JOUR
TI - Explicit formula for optimal ate pairing over cyclotomic family of elliptic curves
AU - Hong, Hoon
AU - Lee, Eunjeong
AU - Lee, Hyang-Sook
T2 - FINITE FIELDS AND THEIR APPLICATIONS
AB - Pairings on elliptic curves play an important role in cryptography. We provide an explicit formula for vectors of polynomials describing optimal ate pairings over cyclotomic family of elliptic curves. The explicit formula is simple in that it only involves partitioning a certain cyclotomic polynomial. The simplicity of the formula allows us to analyze the sparsity of the vector.
DA - 2015/7//
PY - 2015/7//
DO - 10.1016/j.ffa.2014.12.007
VL - 34
SP - 45-74
SN - 1090-2465
UR - http://dx.doi.org/10.1016/j.ffa.2014.12.007
KW - Pairing-based cryptosystem
KW - Elliptic curve
KW - Cyclotomic polynomial
ER -
TY - JOUR
TI - Convergence Analysis for Anderson Acceleration
AU - Toth, Alex
AU - Kelley, C. T.
T2 - SIAM Journal on Numerical Analysis
AB - Anderson($m$) is a method for acceleration of fixed point iteration which stores m+1 prior evaluations of the fixed point map and computes the new iteration as a linear combination of those evaluations. Anderson(0) is fixed point iteration. In this paper we show that Anderson($m$) is locally r-linearly convergent if the fixed point map is a contraction and the coefficients in the linear combination remain bounded. Without assumptions on the coefficients, we prove q-linear convergence of Anderson(1) and, in the case of linear problems, Anderson($m$). We observe that the optimization problem for the coefficients can be formulated and solved in nonstandard ways and report on numerical experiments which illustrate the ideas.
DA - 2015/1//
PY - 2015/1//
DO - 10.1137/130919398
VL - 53
IS - 2
SP - 805-819
J2 - SIAM J. Numer. Anal.
LA - en
OP -
SN - 0036-1429 1095-7170
UR - http://dx.doi.org/10.1137/130919398
DB - Crossref
KW - nonlinear equations
KW - Anderson acceleration
KW - local convergence
ER -
TY - JOUR
TI - Categorifications of the polynomial ring
AU - Khovanov, Mikhail
AU - Sazdanovic, Radmila
T2 - FUNDAMENTA MATHEMATICAE
AB - We develop a diagrammatic categorification of the polynomial ring ${\mathbb {Z}}[x]$. Our categorification satisfies a version of Bernstein–Gelfand–Gelfand reciprocity property with the indecomposable projective modules corresponding to $x^n$
DA - 2015///
PY - 2015///
DO - 10.4064/fm230-3-3
VL - 230
IS - 3
SP - 251-280
SN - 1730-6329
KW - categorification
KW - Bernstein-Gelfand-Gelfand reciprocity
KW - polynomial ring
ER -
TY - JOUR
TI - CLASSIFYING EXTENSIONS OF THE FIELD OF FORMAL LAURENT SERIES OVER F-p
AU - Brown, Jim
AU - Hasmani, Alfeen
AU - Hiltner, Lindsey
AU - Kraft, Angela
AU - Scofield, Daniel
AU - Wash, Kirsti
T2 - ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
AB - In previous works, Jones and Roberts and Pauli and Roblot have studied finite extensions of the $p$-adic numbers $\mathbb{Q}_p$. This paper focuses on results for local fields of characteristic~$p$. In particular, we are able to produce analogous results to Jones and Roberts in the case that the characteristic does not divide the degree of the field extension. Also, in this case, following from the work of Pauli and Roblot, we prove that the defining polynomials of these extensions can be written in a simple form amenable to computation. Finally, if $p$ is the degree of the extension, we show there are infinitely many extensions of this degree and thus these cannot be classified in the same manner.
DA - 2015///
PY - 2015///
DO - 10.1216/rmj-2015-45-1-115
VL - 45
IS - 1
SP - 115-130
SN - 1945-3795
ER -
TY - JOUR
TI - A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions
AU - Li, Zhilin
AU - Xiao, Li
AU - Cai, Qin
AU - Zhao, Hongkai
AU - Luo, Ray
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - In this paper, a new Navier–Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier–Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.
DA - 2015/9/15/
PY - 2015/9/15/
DO - 10.1016/j.jcp.2015.05.003
VL - 297
SP - 182-193
SN - 1090-2716
KW - Navier-Stokes Navier-Stokes equations
KW - Finite difference approximation
KW - Irregular domain
KW - Open and traction boundary conditions
KW - Local pressure boundary condition
KW - Augmented immersed interface method (IIM)
ER -
TY - JOUR
TI - A lift of Schur's Q-functions to the peak algebra
AU - Jing, Naihuan
AU - Li, Yunnan
T2 - JOURNAL OF COMBINATORIAL THEORY SERIES A
AB - We construct a lift of Schur's Q-functions to the peak algebra of the symmetric group, called the noncommutative Schur Q-functions, and extract from them a new natural basis with several nice properties such as the positive right-Pieri rule, combinatorial expansion, etc. Dually, we get a basis of the Stembridge algebra of peak functions refining Schur's P-functions in a simple way.
DA - 2015/10//
PY - 2015/10//
DO - 10.1016/j.jcta.2015.05.006
VL - 135
SP - 268-290
SN - 1096-0899
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84930946254&partnerID=MN8TOARS
KW - Peak algebra
KW - Noncommutative Schur Q-functions
KW - Quasisymmetric Schur P-functions
ER -
TY - JOUR
TI - A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
AU - Carrillo, Jose A.
AU - Chertock, Alina
AU - Huang, Yanghong
T2 - COMMUNICATIONS IN COMPUTATIONAL PHYSICS
AB - Abstract We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate computations of stationary states and long-time asymptotics demonstrated by suitably chosen test cases in which these features of the scheme are essential. The proposed scheme is able to cope with non-smooth stationary states, different time scales including metastability, as well as concentrations and self-similar behavior induced by singular nonlocal kernels. We use the scheme to explore properties of these equations beyond their present theoretical knowledge.
DA - 2015/1//
PY - 2015/1//
DO - 10.4208/cicp.160214.010814a
VL - 17
IS - 1
SP - 233-258
SN - 1991-7120
UR - https://doi-org.prox.lib.ncsu.edu/10.4208/cicp.160214.010814a
KW - Finite-volume method
KW - gradient flow
KW - nonlinear nonlocal equations
ER -
TY - JOUR
TI - 2-recognizeable classes of Leibniz algebras
AU - Burch, Tiffany
AU - Harris, Meredith
AU - McAlister, Allison
AU - Rogers, Elyse
AU - Stitzinger, Ernie
AU - Sullivan, S. McKay
T2 - JOURNAL OF ALGEBRA
AB - We show that for fields that are of characteristic 0 or algebraically closed of characteristic greater than 5, that certain classes of Leibniz algebras are 2-recognizeable. These classes are solvable, strongly solvable and supersolvable. These same results hold in Lie algebras and in general for groups.
DA - 2015/2/1/
PY - 2015/2/1/
DO - 10.1016/j.jalgebra.2014.10.039
VL - 423
SP - 506-513
SN - 1090-266X
KW - 2-recognizeable
KW - Strongly solvable
KW - Supersolvable
KW - Leibniz algebras
ER -
TY - JOUR
TI - WELL-POSEDNESS ANALYSIS FOR A LINEARIZATION OF A FLUID-ELASTICITY INTERACTION
AU - Bociu, Lorena
AU - Toundykov, Daniel
AU - Zolesio, Jean-Paul
T2 - SIAM JOURNAL ON MATHEMATICAL ANALYSIS
AB - We study the well-posedness of a total linearization, with respect to a perturbation of the external forcing, of a free-boundary nonlinear elasticity--incompressible fluid interaction. The total linearization for the coupling modeled by the Navier--Stokes equations and the nonlinear equations of elastodynamics was obtained recently in [L. Bociu and J.-P. Zolésio, Evol. Equ. Control Theory, 2 (2013), pp. 55--79]. The equations and the free boundary were linearized together, and the result turned out to be quite different from the usual coupling of classical linear models. New additional terms are present on the common interface, some of them involving boundary curvatures and boundary acceleration. These terms play an important role in the final linearized system and cannot be neglected; their presence also introduces new challenges in the well-posedness analysis, which proceeds to establish that the evolution operator associated to the linearized system can be represented as a bounded perturbation of a maximal dissipative semigroup generator.
DA - 2015///
PY - 2015///
DO - 10.1137/140970689
VL - 47
IS - 3
SP - 1958-2000
SN - 1095-7154
KW - fluid-structure
KW - free boundary
KW - moving boundary
KW - linearization
KW - well-posedness
KW - semigroup
ER -
TY - JOUR
TI - Travelling waves in the Holling-Tanner model with weak diffusion
AU - Ghazaryan, Anna
AU - Manukian, Vahagn
AU - Schecter, Stephen
T2 - PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
AB - For a wide range of parameters, we study travelling waves in a diffusive version of the Holling–Tanner predator–prey model from population dynamics. Fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields. We focus on the appearance of the fronts in various singular limits. In addition, periodic travelling waves of relaxation oscillation type are constructed using a recent generalization of the entry–exit function.
DA - 2015/5/8/
PY - 2015/5/8/
DO - 10.1098/rspa.2015.0045
VL - 471
IS - 2177
SP -
SN - 1471-2946
KW - geometric singular perturbation theory
KW - travelling front
KW - periodic wave train
KW - predator-prey model
KW - diffusive Holling-Tanner model
KW - entry-exit function
ER -
TY - JOUR
TI - The random matrix regime of Maronna's M-estimator with elliptically distributed samples
AU - Couillet, Romain
AU - Pascal, Frederic
AU - Silverstein, Jack W.
T2 - JOURNAL OF MULTIVARIATE ANALYSIS
AB - This article demonstrates that the robust scatter matrix estimator CˆN∈CN×N of a multivariate elliptical population x1,…,xn∈CN originally proposed by Maronna in 1976, and defined as the solution (when existent) of an implicit equation, behaves similar to a well-known random matrix model in the limiting regime where the population N and sample n sizes grow at the same speed. We show precisely that CˆN∈CN×N is defined for all n large with probability one and that, under some light hypotheses, ‖CˆN−SˆN‖→0 almost surely in spectral norm, where SˆN follows a classical random matrix model. As a corollary, the limiting eigenvalue distribution of CˆN is derived. This analysis finds applications in the fields of statistical inference and signal processing.
DA - 2015/7//
PY - 2015/7//
DO - 10.1016/j.jmva.2015.02.020
VL - 139
SP - 56-78
SN - 0047-259X
KW - Random matrix theory
KW - Robust estimation
KW - Elliptical distribution
ER -
TY - JOUR
TI - Optimal sampling frequency and timing of threatened tropical bird populations: A modeling approach
AU - Banks, J. E.
AU - Banks, H. T.
AU - Rinnovatore, K.
AU - Jackson, C. M.
T2 - ECOLOGICAL MODELLING
AB - Abstract Conservation of threatened or endangered species relies critically on accurate population counts over time. In practice, many population censuses are conducted by non-governmental organizations or volunteer citizen scientists who are constrained by fiscal and temporal resources. Less than optimal sampling regimens (characterized by infrequent and/or irregular schedules) for conducting population censuses can result in woefully misleading population estimates – and thus have dire consequences for management and conservation. We illustrate this using an East African case study in which 14 years of bird data was collected in the Arabuko-Sokoke Forest in coastal Kenya. We first estimate life history parameters in a discrete matrix model. Desiring a data collection protocol which would lessen observation error and lend to a deeper understanding of population projections and dynamics of a threatened species, we carry out mathematical and statistical modeling efforts with an adaptation of a Leslie model for simulated population estimates stemming from different population sampling schemes. We illustrate how resource managers might take a strategic approach, using simple quantitative models, to develop an optimal sampling scheme that considers important species traits, such as breeding season, and balances the tradeoff between resources and accuracy.
DA - 2015/5/10/
PY - 2015/5/10/
DO - 10.1016/j.ecolmodel.2015.02.005
VL - 303
SP - 70-77
SN - 1872-7026
KW - Arabuko-Sokoke Forest
KW - Inverse problem
KW - Kenya
KW - Least squares optimization
KW - Leslie matrix
KW - Sheppardia gunningi
ER -
TY - JOUR
TI - Immuno-modulatory strategies for reduction of HIV reservoir cells
AU - Banks, H. T.
AU - Flores, Kevin B.
AU - Hu, Shuhua
AU - Rosenberg, Eric
AU - Buzon, Maria
AU - Yu, Xu
AU - Lichterfeld, Matthias
T2 - JOURNAL OF THEORETICAL BIOLOGY
AB - Antiretroviral therapy is able to suppress the viral load to below the detection limit, but it is not able to eradicate HIV reservoirs. Thus, there is a critical need for a novel treatment to eradicate (or reduce) the reservoir in order to eliminate the need for a lifelong adherence to antiretroviral therapy, which is expensive and potentially toxic. In this paper, we investigate the possible pharmacological strategies or combinations of strategies that may be beneficial to reduce or possibly eradicate the latent reservoir. We do this via studies with a validated mathematical model, where the parameter values are obtained with newly acquired clinical data for HIV patients. Our findings indicate that the strategy of reactivating the reservoir combined with enhancement of the killing rate of HIV-specific CD8+ T cells is able to eradicate the reservoir. In addition, our analysis shows that a targeted suppression of the immune system is also a possible strategy to eradicate the reservoir.
DA - 2015/5/7/
PY - 2015/5/7/
DO - 10.1016/j.jtbi.2015.02.006
VL - 372
SP - 146-158
SN - 1095-8541
KW - Immune response
KW - Mathematical model
KW - Inverse problem
KW - Stability analysis
ER -
TY - JOUR
TI - Algebraic geometrization of the Kuramoto model: Equilibria and stability analysis
AU - Mehta, Dhagash
AU - Daleo, Noah S.
AU - Doerfler, Florian
AU - Hauenstein, Jonathan D.
T2 - CHAOS
AB - Finding equilibria of the finite size Kuramoto model amounts to solving a nonlinear system of equations, which is an important yet challenging problem. We translate this into an algebraic geometry problem and use numerical methods to find all of the equilibria for various choices of coupling constants K, natural frequencies, and on different graphs. We note that for even modest sizes (N ~ 10-20), the number of equilibria is already more than 100 000. We analyze the stability of each computed equilibrium as well as the configuration of angles. Our exploration of the equilibrium landscape leads to unexpected and possibly surprising results including non-monotonicity in the number of equilibria, a predictable pattern in the indices of equilibria, counter-examples to conjectures, multi-stable equilibrium landscapes, scenarios with only unstable equilibria, and multiple distinct extrema in the stable equilibrium distribution as a function of the number of cycles in the graph.
DA - 2015/5//
PY - 2015/5//
DO - 10.1063/1.4919696
VL - 25
IS - 5
SP -
SN - 1089-7682
ER -
TY - JOUR
TI - A modular approach to intensity-modulated arc therapy optimization with noncoplanar trajectories
AU - Papp, David
AU - Bortfeld, Thomas
AU - Unkelbach, Jan
T2 - PHYSICS IN MEDICINE AND BIOLOGY
AB - Utilizing noncoplanar beam angles in volumetric modulated arc therapy (VMAT) has the potential to combine the benefits of arc therapy, such as short treatment times, with the benefits of noncoplanar intensity modulated radiotherapy (IMRT) plans, such as improved organ sparing. Recently, vendors introduced treatment machines that allow for simultaneous couch and gantry motion during beam delivery to make noncoplanar VMAT treatments possible. Our aim is to provide a reliable optimization method for noncoplanar isocentric arc therapy plan optimization. The proposed solution is modular in the sense that it can incorporate different existing beam angle selection and coplanar arc therapy optimization methods. Treatment planning is performed in three steps. First, a number of promising noncoplanar beam directions are selected using an iterative beam selection heuristic; these beams serve as anchor points of the arc therapy trajectory. In the second step, continuous gantry/couch angle trajectories are optimized using a simple combinatorial optimization model to define a beam trajectory that efficiently visits each of the anchor points. Treatment time is controlled by limiting the time the beam needs to trace the prescribed trajectory. In the third and final step, an optimal arc therapy plan is found along the prescribed beam trajectory. In principle any existing arc therapy optimization method could be incorporated into this step; for this work we use a sliding window VMAT algorithm. The approach is demonstrated using two particularly challenging cases. The first one is a lung SBRT patient whose planning goals could not be satisfied with fewer than nine noncoplanar IMRT fields when the patient was treated in the clinic. The second one is a brain tumor patient, where the target volume overlaps with the optic nerves and the chiasm and it is directly adjacent to the brainstem. Both cases illustrate that the large number of angles utilized by isocentric noncoplanar VMAT plans can help improve dose conformity, homogeneity, and organ sparing simultaneously using the same beam trajectory length and delivery time as a coplanar VMAT plan.
DA - 2015/7/7/
PY - 2015/7/7/
DO - 10.1088/0031-9155/60/13/5179
VL - 60
IS - 13
SP - 5179-5198
SN - 1361-6560
UR - http://dx.doi.org/10.1088/0031-9155/60/13/5179
KW - arc therapy (VMAT)
KW - optimization
KW - noncoplanar radiotherapy
KW - 4pi
KW - treatment planning
ER -
TY - JOUR
TI - Irreducible projective characters of wreath products
AU - Hu, X.
AU - Jing, N.
T2 - Proceedings of the American Mathematical Society
AB - The irreducible character values of the spin wreath products of the symmetric group and an arbitrary finite group are completely determined.
DA - 2015///
PY - 2015///
DO - 10.1090/s0002-9939-2014-12343-4
VL - 143
IS - 3
SP - 1015-1026
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84919999433&partnerID=MN8TOARS
ER -
TY - JOUR
TI - FINITE DIFFERENCE APPROXIMATIONS FOR MEASURE-VALUED SOLUTIONS OF A HIERARCHICALLY SIZE-STRUCTURED POPULATION MODEL
AU - Ackleh, Azmy S.
AU - Chellamuthu, Vinodh K.
AU - Ito, Kazufumi
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - We study a quasilinear hierarchically size-structured population modelpresented in [4]. In this model the growth, mortality andreproduction rates are assumed to depend on a function of thepopulation density. In [4] we showed that solutions to thismodel can become singular (measure-valued) in finite time even ifall the individual parameters are smooth. Therefore, in this paperwe develop a first order finite difference scheme to compute thesemeasure-valued solutions. Convergence analysis for this method isprovided. We also develop a high resolution second order scheme tocompute the measure-valued solution of the model and perform a comparative study between thetwo schemes.
DA - 2015/4//
PY - 2015/4//
DO - 10.3934/mbe.2015.12.233
VL - 12
IS - 2
SP - 233-258
SN - 1551-0018
KW - Hierarchically size-structured population model
KW - measure-valued solutions
KW - finite-difference approximations
KW - convergence analysis
ER -
TY - JOUR
TI - Existence and dynamics of quasilinear parabolic systems with time delays
AU - Pao, C. V.
AU - Ruan, W. H.
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - This paper is concerned with a coupled system of quasilinear parabolic equations where the effect of time delays is taken into consideration in the reaction functions of the system. The partial differential operators in the system may be degenerate and the reaction functions possess some mixed quasimonotone property, including quasimonotone nondecreasing functions. The aim of the paper is to show the existence and uniqueness of a global solution to the parabolic system, the existence of positive quasisolutions or maximal–minimal solutions of the corresponding elliptic system, and the asymptotic behavior of the solution of the parabolic system in relation to the quasisolutions or maximal–minimal solutions of the elliptic system. Applications are given to three reaction–diffusion models arising from mathematical biology and ecology where the diffusion coefficients are density dependent and are degenerate. This degenerate density-dependent diffusion leads to some interesting distinct asymptotic behavior of the time-dependent solution when compared with density-independent diffusion.
DA - 2015/3/5/
PY - 2015/3/5/
DO - 10.1016/j.jde.2015.01.010
VL - 258
IS - 9
SP - 3248-3285
SN - 1090-2732
KW - Parabolic system with time delays
KW - Degenerate reaction-diffusion equations
KW - Global existence and positive quasisolutions
KW - Asymptotic behavior and attractors
KW - Predator-prey models
ER -
TY - JOUR
TI - A computational framework of gradient flows for general linear matrix equations
AU - Wang, Liqi
AU - Chu, Moody T.
AU - Bo, Yu
T2 - NUMERICAL ALGORITHMS
DA - 2015/1//
PY - 2015/1//
DO - 10.1007/s11075-014-9885-1
VL - 68
IS - 1
SP - 121-141
SN - 1572-9265
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85027952357&partnerID=MN8TOARS
KW - Linear matrix equation
KW - Adjoint operator
KW - Least squares
KW - Generalized normal equation
KW - Gradient flow
KW - Low-precision ODE integrator
ER -
TY - JOUR
TI - Optimization approaches to volumetric modulated arc therapy planning
AU - Unkelbach, Jan
AU - Bortfeld, Thomas
AU - Craft, David
AU - Alber, Markus
AU - Bangert, Mark
AU - Bokrantz, Rasmus
AU - Chen, Danny
AU - Li, Ruijiang
AU - Xing, Lei
AU - Men, Chunhua
AU - Nill, Simeon
AU - Papp, David
AU - Romeijn, Edwin
AU - Salari, Ehsan
T2 - MEDICAL PHYSICS
AB - Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years. A large number of treatment planning studies have evaluated the potential for VMAT for different disease sites based on the currently available commercial implementations of VMAT planning. In contrast, literature on the underlying mathematical optimization methods used in treatment planning is scarce. VMAT planning represents a challenging large scale optimization problem. In contrast to fluence map optimization in intensity‐modulated radiotherapy planning for static beams, VMAT planning represents a nonconvex optimization problem. In this paper, the authors review the state‐of‐the‐art in VMAT planning from an algorithmic perspective. Different approaches to VMAT optimization, including arc sequencing methods, extensions of direct aperture optimization, and direct optimization of leaf trajectories are reviewed. Their advantages and limitations are outlined and recommendations for improvements are discussed.
DA - 2015/3//
PY - 2015/3//
DO - 10.1118/1.4908224
VL - 42
IS - 3
SP - 1367-1377
SN - 2473-4209
UR - http://dx.doi.org/10.1118/1.4908224
KW - radiotherapy
KW - treatment plan optimization
KW - VMAT
ER -
TY - JOUR
TI - On the data-driven inference of modulatory networks in climate science: an application to West African rainfall
AU - Gonzalez, D. L., II
AU - Angus, M. P.
AU - Tetteh, I. K.
AU - Bello, G. A.
AU - Padmanabhan, K.
AU - Pendse, S. V.
AU - Srinivas, S.
AU - Yu, J.
AU - Semazzi, F.
AU - Kumar, V.
AU - Samatova, N. F.
T2 - NONLINEAR PROCESSES IN GEOPHYSICS
AB - Abstract. Decades of hypothesis-driven and/or first-principles research have been applied towards the discovery and explanation of the mechanisms that drive climate phenomena, such as western African Sahel summer rainfall~variability. Although connections between various climate factors have been theorized, not all of the key relationships are fully understood. We propose a data-driven approach to identify candidate players in this climate system, which can help explain underlying mechanisms and/or even suggest new relationships, to facilitate building a more comprehensive and predictive model of the modulatory relationships influencing a climate phenomenon of interest. We applied coupled heterogeneous association rule mining (CHARM), Lasso multivariate regression, and dynamic Bayesian networks to find relationships within a complex system, and explored means with which to obtain a consensus result from the application of such varied methodologies. Using this fusion of approaches, we identified relationships among climate factors that modulate Sahel rainfall. These relationships fall into two categories: well-known associations from prior climate knowledge, such as the relationship with the El Niño–Southern Oscillation (ENSO) and putative links, such as North Atlantic Oscillation, that invite further research.
DA - 2015///
PY - 2015///
DO - 10.5194/npg-22-33-2015
VL - 22
IS - 1
SP - 33-46
SN - 1607-7946
ER -
TY - JOUR
TI - Model comparison tests to determine data information content
AU - Banks, H. T.
AU - Banks, J. E.
AU - Link, Kathryn
AU - Rosenheim, J. A.
AU - Ross, Chelsea
AU - Tillman, K. A.
T2 - APPLIED MATHEMATICS LETTERS
AB - In the context of inverse or parameter estimation problems we demonstrate the use of statistically based model comparison tests in several examples of practical interest. In these examples we are interested in questions related to information content of a particular given data set and whether the data will support a more complicated model to describe it. In the first example we compare fits for several different models to describe simple decay in a size histogram for aggregates in amyloid fibril formation. In a second example we investigate whether the information content in data sets for the pest Lygus hesperus in cotton fields as it is currently collected is sufficient to support a model in which one distinguishes between nymphs and adults. Finally in a third example with data for patients having undergone an organ transplant, we question whether the data content is sufficient to estimate more than 5 of the fundamental parameters in a particular dynamic model.
DA - 2015/5//
PY - 2015/5//
DO - 10.1016/j.aml.2014.11.002
VL - 43
SP - 10-18
SN - 0893-9659
KW - Ordinary least squares
KW - Model comparison in inverse problems
KW - Information content
ER -
TY - JOUR
TI - Continuity of the Perron root
AU - Meyer, Carl D.
T2 - LINEAR & MULTILINEAR ALGEBRA
AB - AbstractThat the Perron root of a square nonnegative matrix varies continuously with the entries in is a corollary of theorems regarding continuity of eigenvalues or roots of polynomial equations, the proofs of which necessarily involve complex numbers. But since continuity of the Perron root is a question that is entirely in the field of real numbers, it seems reasonable that there should exist a development involving only real analysis. This article presents a simple and completely self-contained development that depends only on real numbers and first principles.Keywords: Perron rootPerron–Frobenius theorynonnegative matricesAMS Subject Classifications: 150215A1815B48 AcknowledgementsThe author wishes to thank the referee for providing suggestions and corrections that enhanced the exposition. The referee is also responsible for example (Equation66 ), and for pointing out the work in [Citation4]. In addition, thanks are extended to Stephen Campbell for suggesting the simple explanation of why the convergence of (Equation55 ) is not uniform.
DA - 2015/7/3/
PY - 2015/7/3/
DO - 10.1080/03081087.2014.934233
VL - 63
IS - 7
SP - 1332-1336
SN - 1563-5139
KW - nonnegative matrices
KW - Perron-Frobenius theory
KW - Perron root
KW - 1502
KW - 15B48
KW - 15A18
ER -
TY - JOUR
TI - Bosonizations of (sl)over-cap(2) and Integrable Hierarchies
AU - Bakalov, Bojko
AU - Fleisher, Daniel
T2 - SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
AB - We construct embeddings of $\widehat{\mathfrak{sl}}_2$ in lattice vertex algebras by composing the Wakimoto realization with the Friedan-Martinec-Shenker bosonization. The Kac-Wakimoto hierarchy then gives rise to two new hierarchies of integrable, non-autonomous, non-linear partial differential equations. A new feature of our construction is that it works for any value of the central element of $\widehat{\mathfrak{sl}}_2$; that is, the level becomes a parameter in the equations.
DA - 2015///
PY - 2015///
DO - 10.3842/sigma.2015.005
VL - 11
SP -
SN - 1815-0659
KW - affine Kac-Moody algebra
KW - Casimir element
KW - Friedan-Martinec-Shenker bosonization
KW - lattice vertex algebra
KW - Virasoro algebra
KW - Wakimoto realization
ER -
TY - JOUR
TI - An algebraic method for constructing stable and consistent autoregressive filters
AU - Harlim, John
AU - Hong, Hoon
AU - Robbins, Jacob L.
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - In this paper, we introduce an algebraic method to construct stable and consistent univariate autoregressive (AR) models of low order for filtering and predicting nonlinear turbulent signals with memory depth. By stable, we refer to the classical stability condition for the AR model. By consistent, we refer to the classical consistency constraints of Adams–Bashforth methods of order-two. One attractive feature of this algebraic method is that the model parameters can be obtained without directly knowing any training data set as opposed to many standard, regression-based parameterization methods. It takes only long-time average statistics as inputs. The proposed method provides a discretization time step interval which guarantees the existence of stable and consistent AR model and simultaneously produces the parameters for the AR models. In our numerical examples with two chaotic time series with different characteristics of decaying time scales, we find that the proposed AR models produce significantly more accurate short-term predictive skill and comparable filtering skill relative to the linear regression-based AR models. These encouraging results are robust across wide ranges of discretization times, observation times, and observation noise variances. Finally, we also find that the proposed model produces an improved short-time prediction relative to the linear regression-based AR-models in forecasting a data set that characterizes the variability of the Madden–Julian Oscillation, a dominant tropical atmospheric wave pattern.
DA - 2015/2/15/
PY - 2015/2/15/
DO - 10.1016/j.jcp.2014.12.004
VL - 283
SP - 241-257
SN - 1090-2716
UR - http://dx.doi.org/10.1016/j.jcp.2014.12.004
KW - Autoregressive filter
KW - Kalman filter
KW - Parameter estimation
KW - Model error
ER -
TY - JOUR
TI - USING WEATHER FORECASTS TO HELP MANAGE MENINGITIS IN THE WEST AFRICAN SAHEL
AU - Pandya, Rajul
AU - Hodgson, Abraham
AU - Hayden, Mary H.
AU - Akweongo, Patricia
AU - Hopson, Thomas
AU - Forgor, Abudulai Adams
AU - Yoksas, Tom
AU - Dalaba, Maxwell Ayindenaba
AU - Dukic, Vanja
AU - Mera, Roberto
AU - Dumont, Arnaud
AU - McCormack, Kristen
AU - Anaseba, Dominic
AU - Awine, Timothy
AU - Boehnert, Jennifer
AU - Nyaaba, Gertrude
AU - Laing, Arlene
AU - Semazzi, Fredrick
T2 - BULLETIN OF THE AMERICAN METEOROLOGICAL SOCIETY
AB - Abstract Understanding and acting on the link between weather and meningitis in the Sahel could help improve vaccine distribution and save lives. People living there know that meningitis epidemics occur in the dry season and end after the start of the rainy season. Integrating and analyzing newly available epidemiological and meteorological data quantified this relationship, showing that that the risk of meningitis epidemics climbed from a background level of 2% to a maximum risk of 25% during the dry season. These data also suggested that, of all meteorological variables, relative humidity has the strongest correlation to cases of meningitis. Weather acts alongside a complex set of environmental, social, and economic drivers, and a complementary investigation of local and regional knowledge, attitudes, and practices suggested several additional interventions to manage meningitis. These include improved awareness of early meningitis symptoms and vaccinations for farmworkers who migrate seasonally. An economic survey showed that the cost of a single case of meningitis is 3 times the average annual household income, underscoring the need for improved vaccination strategy. Using these insights, meteorologists and public health workers developed a tool to guide vaccination decisions. Iterative development allowed a multinational team of public health officials to use the tool while guiding its refinement and directed research toward maximum practical use. That meant focusing on predicting areas where high humidity would naturally end epidemics so vaccines could be moved elsewhere. Using this tool and this approach could have prevented an estimated 24,000 cases of meningitis over a 3-yr period.
DA - 2015/1//
PY - 2015/1//
DO - 10.1175/bams-d-13-00121.1
VL - 96
IS - 1
SP - 103-115
SN - 1520-0477
ER -
TY - JOUR
TI - Subresultants, Sylvester sums and the rational interpolation problem
AU - D'Andrea, Carlos
AU - Krick, Teresa
AU - Szanto, Agnes
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without multiplicities), we give explicit formulas for the solution in terms of symmetric functions of the input data, generalizing the well-known formulas for Lagrange interpolation. In the case of the osculatory rational interpolation (interpolation with multiplicities), we give determinantal expressions in terms of the input data, making explicit some matrix formulations that can independently be derived from previous results by Beckermann and Labahn.
DA - 2015///
PY - 2015///
DO - 10.1016/j.jsc.2014.08.008
VL - 68
SP - 72-83
SN - 0747-7171
KW - Rational interpolation
KW - Cauchy interpolation
KW - Osculatory interpolation
KW - Rational Hermite interpolation
KW - Subresultants
KW - Sylvester sums
ER -
TY - JOUR
TI - Overdetermined Weierstrass iteration and the nearest consistent system
AU - Ruatta, Olivier
AU - Sciabica, Mark
AU - Szanto, Agnes
T2 - THEORETICAL COMPUTER SCIENCE
AB - We propose a generalization of the Weierstrass iteration for overdetermined systems of equations and we prove that the proposed method is the Gauss–Newton iteration to find the nearest system which has at least k common roots and which is obtained via a perturbation of prescribed structure. In the univariate case we show the connection of our method to the optimization problem formulated by Karmarkar and Lakshman for the nearest GCD. In the multivariate case we generalize the expressions of Karmarkar and Lakshman, and give explicitly several iteration functions to compute the optimum. The arithmetic complexity of the iterations is detailed.
DA - 2015/1/11/
PY - 2015/1/11/
DO - 10.1016/j.tcs.2014.10.008
VL - 562
SP - 346-364
SN - 1879-2294
UR - http://dx.doi.org/10.1016/j.tcs.2014.10.008
KW - Approximate GCD
KW - Overdetermined systems
KW - Nearest consistent system
KW - Weierstrass-Durand-Kerner method
ER -
TY - JOUR
TI - Optimization of Klystron Designs Using Deterministic Sampling Methods
AU - Tran, Hien
AU - Lankford, George
AU - Read, Michael E.
AU - Ives, R. Lawrence
AU - Reppert, Kelsey
AU - Cline, Kayla
AU - Guzman, Juan
T2 - IEEE Transactions on Electron Devices
AB - A method is presented for optimizing the design of klystron circuits. This automates the selection of cavity positions, resonant frequencies, quality factors, R/Q and other circuit parameters to maximize the efficiency with required gain. The method is based on deterministic sampling methods. In this paper, we describe the procedure and give several examples for both narrow-band and wideband klystrons, using the klystron codes AJDISK and TESLA.
DA - 2015/3//
PY - 2015/3//
DO - 10.1109/ted.2015.2394479
VL - 62
IS - 3
SP - 1032-1036
J2 - IEEE Trans. Electron Devices
OP -
SN - 0018-9383 1557-9646
UR - http://dx.doi.org/10.1109/ted.2015.2394479
DB - Crossref
KW - Design optimization
KW - klystrons
KW - numerical simulation
KW - sampling methods
ER -
TY - JOUR
TI - Imaginary Verma modules and Kashiwara algebras for U-q((g)over-cap)
AU - Cox, B.
AU - Futorny, V.
AU - Misra, K. C.
T2 - Journal of Algebra
DA - 2015///
PY - 2015///
VL - 424
SP - 390-415
ER -
TY - JOUR
TI - Identifiability of 3-class Jukes-Cantor mixtures
AU - Long, Colby
AU - Sullivant, Seth
T2 - ADVANCES IN APPLIED MATHEMATICS
AB - We prove identifiability of the tree parameters of the 3-class Jukes–Cantor mixture model. The proof uses ideas from algebraic statistics, in particular: finding phylogenetic invariants that separate the varieties associated to different triples of trees; computing dimensions of the resulting phylogenetic varieties; and using the disentangling number to reduce to trees with a small number of leaves. Symbolic computation also plays a key role in handling the many different cases and finding relevant phylogenetic invariants.
DA - 2015/3//
PY - 2015/3//
DO - 10.1016/j.aam.2014.12.003
VL - 64
SP - 89-110
SN - 1090-2074
KW - Phylogenetic mixture models
KW - Identifiability
KW - Tropical geometry
KW - Disentangling number
ER -
TY - JOUR
TI - Estimation of time-varying mortality rates using continuous models for Daphnia magna
AU - Adoteye, Kaska
AU - Banks, H. T.
AU - Flores, Kevin B.
AU - LeBlanc, Gerald A.
T2 - APPLIED MATHEMATICS LETTERS
AB - Structured population models that make the assumption of constant demographic rates do not accurately describe the complex life histories seen in many species. We investigated the accuracy of using constant versus time-varying mortality rates within discrete and continuously structured models for Daphnia magna. We tested the accuracy of the models we considered using density-independent survival data for 90 daphnids. We found that a continuous differential equation model with a time-varying mortality rate was the most accurate model for describing our experimental D. magna survival data. Our results suggest that differential equation models with variable parameters are an accurate tool for estimating mortality rates in biological scenarios in which mortality might vary significantly with age.
DA - 2015/6//
PY - 2015/6//
DO - 10.1016/j.aml.2014.12.014
VL - 44
SP - 12-16
SN - 1873-5452
KW - Structured population model
KW - Leslie matrix model
KW - Sinko-Streifer model
KW - Daphnia magna
KW - Time-dependent mortality rate
ER -
TY - JOUR
TI - Dynamics of Lotka-Volterra cooperation systems governed by degenerate quasilinear reaction-diffusion equations
AU - Pao, C. V.
T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
AB - This paper deals with a class of Lotka–Volterra cooperation system where the densities of the cooperating species are governed by a finite number of degenerate reaction–diffusion equations. Three basic types of Dirichlet, Neumann, and Robin boundary conditions and two types of reaction functions, with and without saturation, are considered. The aim of the paper is to show the existence of positive minimal and maximal steady-state solutions, including the uniqueness of the positive solution, the existence and uniqueness of a global time-dependent solution, and the asymptotic behavior of the time-dependent solution in relation to the steady-state solutions. Some very simple conditions on the physical parameters for the above objectives are obtained. Also discussed is the finite-time blow up property of the time-dependent solution and the non-existence of positive steady-state solution for the system with Neumann boundary condition.
DA - 2015/6//
PY - 2015/6//
DO - 10.1016/j.nonrwa.2014.11.002
VL - 23
SP - 47-60
SN - 1468-1218
KW - Lotka-Volterra cooperation system
KW - Degenerate quasilinear equations
KW - Positive minimal and maximal solutions
KW - Asymptotic behavior and stability
KW - Upper and lower solutions
ER -
TY - JOUR
TI - A parallel Robin-Robin domain decomposition method for H(div)-elliptic problems
AU - Zeng, Yuping
AU - Chen, Jinru
AU - Li, Zhilin
T2 - INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
AB - In this paper, a parallel Robin–Robin domain decomposition method for H(div)-elliptic problems is proposed. The convergence of the method is proved for both the continuous problem and the finite element approximation. Some numerical testes are also presented to demonstrate the effectiveness of the method.
DA - 2015/2/1/
PY - 2015/2/1/
DO - 10.1080/00207160.2014.892587
VL - 92
IS - 2
SP - 394-410
SN - 1029-0265
KW - 65F10
KW - 65N55
KW - 65N30
KW - Robin-Robin domain decomposition method
KW - H(div)-elliptic problems
KW - Raviart-Thomas finite element
KW - convergence analysis
KW - non-overlapping domain decomposition
ER -
TY - JOUR
TI - Optimal design of non-equilibrium experiments for genetic network interrogation
AU - Adoteye, Kaska
AU - Banks, H. T.
AU - Flores, Kevin B.
T2 - APPLIED MATHEMATICS LETTERS
AB - Many experimental systems in biology, especially synthetic gene networks, are amenable to perturbations that are controlled by the experimenter. We developed an optimal design algorithm that calculates optimal observation times in conjunction with optimal experimental perturbations in order to maximize the amount of information gained from longitudinal data derived from such experiments. We applied the algorithm to a validated model of a synthetic Brome Mosaic Virus (BMV) gene network and found that optimizing experimental perturbations may substantially decrease uncertainty in estimating BMV model parameters.
DA - 2015/2//
PY - 2015/2//
DO - 10.1016/j.aml.2014.09.013
VL - 40
SP - 84-89
SN - 0893-9659
KW - Optimal experimental design
KW - Inverse problem
KW - Uncertainty analysis
KW - Brome mosaic virus
KW - Synthetic biology
KW - Genetic networks
ER -
TY - JOUR
TI - Dynamics of Lotka-Volterra competition reaction-diffusion systems with degenerate diffusion
AU - Pao, C. V.
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - This paper is dealt with a class of Lotka–Volterra competition reaction–diffusion system and a competitor–competitor–mutualist system with density-dependent diffusion in a bounded domain under the three basic types of Dirichlet, Neumann and Robin boundary conditions. The governing equations for the competition system consist of an arbitrary number of degenerate quasilinear parabolic equations while the competitor–competitor–mutualist system involves three degenerate equations. The goal of the paper is to show: the existence of positive steady-state solutions or quasi-solutions, the existence and uniqueness of a classical global time-dependent solution, and the asymptotic behavior of the time-dependent solution in relation to the steady-state solutions or quasi-solutions. The above goals are achieved under a very simple condition on the reaction rates of the reaction functions and these results yield a global attractor and the coexistence of the competing species. In the case of Neumann boundary condition the system has a unique constant positive steady-state solution which is a global attractor of all the competing species. The above conclusions lead to some interesting distinct dynamic behavior between degenerate quasilinear reaction–diffusion systems and the corresponding semilinear reaction–diffusion systems in which some or all of the competing species may be in extinction.
DA - 2015/1/15/
PY - 2015/1/15/
DO - 10.1016/j.jmaa.2014.07.070
VL - 421
IS - 2
SP - 1721-1742
SN - 1096-0813
KW - Degenerate reaction-diffusion equation
KW - Lotka-Volterra competition system
KW - Positive steady-state solution
KW - Global attractor
KW - Coexistence
KW - Asymptotic behavior
ER -
TY - JOUR
TI - Some regular sums
AU - Patricio, P.
AU - Hartwig, R. E.
T2 - LINEAR & MULTILINEAR ALGEBRA
AB - In this paper, we examine the question of regularity of sums of special elements that appear in the study of orthogonality and invertibility.
DA - 2015/1/2/
PY - 2015/1/2/
DO - 10.1080/03081087.2013.860592
VL - 63
IS - 1
SP - 185-200
SN - 1563-5139
KW - 16E50
KW - 15A09
KW - Pierce decomposition
KW - group inverse
KW - reflexive inverses
KW - outer inverses
KW - block matrices
KW - inverse
ER -
TY - JOUR
TI - An imaginary PBW basis for quantum affine algebras of type 1
AU - Cox, Ben
AU - Futorny, Vyacheslav
AU - Misra, Kailash C.
T2 - JOURNAL OF PURE AND APPLIED ALGEBRA
AB - Let $\hat{\mathfrak g}$ be an affine Lie algebra of type 1. We give a PBW basis for the quantum affine algebra $U_q(\hat{\mathfrak g})$ with respect to the triangular decomposition of $\hat{\mathfrak g}$ associated with the imaginary positive root system.
DA - 2015/1//
PY - 2015/1//
DO - 10.1016/j.jpaa.2014.04.011
VL - 219
IS - 1
SP - 83-100
SN - 1873-1376
ER -