TY - JOUR
TI - Arithmetic properties of Picard–Fuchs equations and holonomic recurrences
AU - Li, Zane Kun
AU - Walker, Alexander W.
T2 - Journal of Number Theory
AB - The coefficient series of the holomorphic Picard–Fuchs differential equation associated with the periods of elliptic curves often have surprising number-theoretic properties. These have been widely studied in the case of the torsion-free, genus zero congruence subgroups of index 6 and 12 (e.g. the Beauville families). Here, we consider arithmetic properties of the Picard–Fuchs solutions associated to general elliptic families, with a particular focus on the index 24 congruence subgroups. We prove that elliptic families with rational parameters admit linear reparametrizations such that their associated Picard–Fuchs solutions lie in Z〚t〛. A sufficient condition is given such that the same holds for holomorphic solutions at infinity. An Atkin–Swinnerton-Dyer congruence is proven for the coefficient series attached to Γ1(7). We conclude with a consideration of asymptotics, wherein it is proved that many coefficient series satisfy asymptotic expressions of the form un∼ℓλn/n. Certain arithmetic results extend to the study of general holonomic recurrences.
DA - 2013/8//
PY - 2013/8//
DO - 10.1016/j.jnt.2013.02.001
VL - 133
IS - 8
SP - 2770-2793
J2 - Journal of Number Theory
LA - en
OP -
SN - 0022-314X
UR - http://dx.doi.org/10.1016/j.jnt.2013.02.001
DB - Crossref
ER -
TY - JOUR
TI - Arithmetic Properties of Picard-Fuchs Equations and Holonomic Recurrences
DA - 2013/3/31/
PY - 2013/3/31/
ER -
TY - JOUR
TI - Quadratic Twists of Elliptic Curves with 3-Selmer Rank 1
AB - A weaker form of a 1979 conjecture of Goldfeld states that for every elliptic curve E/ℚ, a positive proportion of its quadratic twists E (d) have rank 1. Using tools from Galois cohomology, we give criteria on E and d which force a positive proportion of the quadratic twists of E to have 3-Selmer rank 1 and global root number -1. We then give four nonisomorphic infinite families of elliptic curves E m,n which satisfy these criteria. Conditional on the rank part of the Birch and Swinnerton-Dyer conjecture, this verifies the aforementioned conjecture for infinitely many elliptic curves. Our elliptic curves are easy to give explicitly and we state precisely which quadratic twists d to use. Furthermore, our methods have the potential of being generalized to elliptic curves over other number fields.
DA - 2013/11/21/
PY - 2013/11/21/
DO - 10.1142/s1793042114500213
ER -
TY - JOUR
TI - A regime-switching Heston model for VIX and S&P 500 implied volatilities
AU - Papanicolaou, Andrew
AU - Sircar, Ronnie
T2 - Quantitative Finance
AB - Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular, there is growing interest in options on the VIX volatility index. A number of recent empirical studies have examine whether there is significantly greater risk premium in VIX option prices compared with S&P 500 option prices. We address this issue by proposing and analysing a stochastic volatility model with regime switching. The basic Heston model cannot capture VIX-implied volatilities, as has been documented. We show that the incorporation of sharp regime shifts can bridge this shortcoming. We take advantage of asymptotic and Fourier methods to make the extension tractable, and we present a fit to data, both in times of crisis and relative calm, which shows the effectiveness of the regime switching.
DA - 2013/7/24/
PY - 2013/7/24/
DO - 10.1080/14697688.2013.814923
VL - 14
IS - 10
SP - 1811-1827
J2 - Quantitative Finance
LA - en
OP -
SN - 1469-7688 1469-7696
UR - http://dx.doi.org/10.1080/14697688.2013.814923
DB - Crossref
KW - Applied mathematical finance
KW - Calibration of stochastic volatility
KW - VIX options
KW - Model calibration
ER -
TY - JOUR
TI - Dimension Reduction in Discrete Time Portfolio Optimization with Partial Information
AU - Papanicolaou, Andrew
T2 - SIAM Journal on Financial Mathematics
AB - This paper considers the problem of portfolio optimization in a market with partial information and discretely observed price processes. Partial information refers to the setting where assets have unobserved factors in the rate of return and the level of volatility. Standard filtering techniques are used to compute the posterior distribution of the hidden variables, but there is difficulty in finding the optimal portfolio because the dynamic programming problem is non-Markovian. However, fast time scale asymptotics can be exploited to obtain an approximate dynamic program (ADP) that is Markovian and is therefore much easier to compute. Of consideration is a model where the latent variables (also referred to as hidden states) have fast mean reversion to an invariant distribution that is parameterized by a Markov chain $\theta_t$, where $\theta_t$ represents the regime-state of the market and reverts to its own invariant distribution over a much longer time scale. Data and numerical examples are also presented, and there appears to be evidence that unobserved drift results in an information premium.
DA - 2013/1//
PY - 2013/1//
DO - 10.1137/120897596
VL - 4
IS - 1
SP - 916-960
UR - http://dx.doi.org/10.1137/120897596
KW - filtering
KW - fast mean reversion
KW - partial information
KW - portfolio optimization
KW - approximate dynamic programming
KW - dimension reduction
ER -
TY - CHAP
TI - Factorization of multivariate polynomials
AU - Kaltofen, Erich
AU - Lecerf, Grégoire
T2 - Handbook of Finite Fields
A2 - Mullen, Gary L.
A2 - Panario, Daniel
PY - 2013///
SP - 382–392
PB - CRC Press, Taylor & Francis Group
ER -
TY - CHAP
TI - An(1)-Geometric Crystal Corresponding to Dynkin Index i=2 and Its Ultra-Discretization
AU - Misra, Kailash C.
AU - Nakashima, Toshiki
T2 - Symmetries, Integrable Systems and Representations
A2 - Iohara, K.
A2 - Morier-Genoud, S.
A2 - Remy, B.
T3 - Springer Proceedings in Mathematics & Statistics
AB - Let \(\mathfrak{g}\) be an affine Lie algebra with index set I={0,1,2,…,n} and \(\mathfrak{g}^{L}\) be its Langlands dual. It is conjectured in Kashiwara et al. (Trans. Am. Math. Soc. 360(7):3645–3686, 2008) that for each i∈I∖{0} the affine Lie algebra \(\mathfrak{g}\) has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of certain coherent family of perfect crystals for \(\mathfrak{g}^{L}\). We prove this conjecture for i=2 and \(\mathfrak{g} = A_{n}^{(1)}\).
PY - 2013///
DO - 10.1007/978-1-4471-4863-0_12
SP - 297-318
PB - Springer
SN - 9781447148623 9781447148630
SV - 40
UR - http://dx.doi.org/10.1007/978-1-4471-4863-0_12
ER -
TY - JOUR
TI - REDUCED RELATIVE TUTTE, KAUFFMAN BRACKET AND JONES POLYNOMIALS OF VIRTUAL LINK FAMILIES
AU - KAUFFMAN, LOUIS H.
AU - JABLAN, SLAVIK
AU - RADOVIĆ, LJILJANA
AU - SAZDANOVIĆ, RADMILA
T2 - Journal of Knot Theory and Its Ramifications
AB - This paper contains general formulae for the reduced relative Tutte, Kauffman bracket and Jones polynomials of families of virtual knots and links given in Conway notation and discussion of a counterexample to the Z-move conjecture of Fenn, Kauffman and Manturov.
DA - 2013/4//
PY - 2013/4//
DO - 10.1142/s0218216513400038
VL - 22
IS - 04
SP - 1340003
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84877608644&partnerID=MN8TOARS
KW - Conway notation
KW - virtual knot
KW - Tutte polynomial
KW - Bollobas-Riordan polynomial
KW - relative Tutte polynomial
KW - reduced relative Tutte polynomial
KW - Jones polynomial
KW - Kauffman bracket polynomial
KW - link family
ER -
TY - JOUR
TI - Simplicial Models and Topological Inference in Biological Systems
AU - Nanda, Vidit
AU - Sazdanović, Radmila
T2 - Discrete and Topological Models in Molecular Biology
AB - This article is a user’s guide to algebraic topological methods for data analysis with a particular focus on applications to datasets arising in experimental biology. We begin with the combinatorics and geometry of simplicial complexes and outline the standard techniques for imposing filtered simplicial structures on a general class of datasets. From these structures, one computes topological statistics of the original data via the algebraic theory of (persistent) homology. These statistics are shown to be computable and robust measures of the shape underlying a dataset. Finally, we showcase some appealing instances of topology-driven inference in biological settings, from the detection of a new type of breast cancer to the analysis of various neural structures.
DA - 2013/10/10/
PY - 2013/10/10/
DO - 10.1007/978-3-642-40193-0_6
SP - 109-141
ER -
TY - JOUR
TI - A Comparison of Feature Selection and Classification Algorithms in Identifying Baseball Pitches
AU - Tran, H.
AU - Attarian, A.
AU - Danis, G.
AU - Gronsbell, J.
AU - Iervolino, G.
T2 - International MultiConference of Engineers and Computer Scientists : IMECS 2013 : 13-15 March, 2013, the Royal Garden Hotel, Kowloon, Hong Kong
DA - 2013///
PY - 2013///
SP - 263–268
ER -
TY - JOUR
TI - The Secant-Newton Map is Optimal Among Contracting Quadratic Maps
for Square Root Computation
AU - Erascu, Madalina
AU - Hong, Hoon
T2 - Reliab. Comput.
DA - 2013///
PY - 2013///
VL - 18
SP - 73-81
UR - http://interval.louisiana.edu/reliable-computing-journal/volume-18/reliable-computing-18-pp-073-081.pdf
ER -
TY - JOUR
TI - Reducing Pairing Inversion to Exponentiation Inversion using Non-degenerate
Auxiliary Pairing
AU - Chang, Seunghwan
AU - Hong, Hoon
AU - Lee, Eunjeong
AU - Lee, Hyang-Sook
T2 - IACR Cryptol. ePrint Arch.
DA - 2013///
PY - 2013///
VL - 2013
SP - 313
UR - http://eprint.iacr.org/2013/313
ER -
TY - CONF
TI - Pairing Inversion via Non-degenerate Auxiliary Pairings
AU - Chang, Seunghwan
AU - Hong, Hoon
AU - Lee, Eunjeong
AU - Lee, Hyang-Sook
A2 - Cao, Zhenfu
A2 - Zhang, Fangguo
C2 - 2013///
C3 - Pairing-Based Cryptography - Pairing 2013 - 6th International Conference,
Beijing, China, November 22-24, 2013, Revised Selected Papers
DA - 2013///
DO - 10.1007/978-3-319-04873-4\_5
VL - 8365
SP - 77-96
PB - Springer
UR - https://doi.org/10.1007/978-3-319-04873-4\_5
ER -
TY - CONF
TI - Simulation and Optimization of Systems with Delays
AU - Betts, J.T.
AU - Campbell, S.L.
AU - Thompson, K.
C2 - 2013///
C3 - Proceedings of the 2013 Spring Simulation Multiconference Poster Session
DA - 2013///
SP - 1084–1085
PB - Society for Computer Simulation International
ER -
TY - JOUR
TI - Strong shape derivative for the wave equation with Neumann boundary condition
T2 - D. Homberg and F. Troltzsch (Eds.): CSMO 2011, IFIP AICT 391, International Federation for Information Processing
DA - 2013///
PY - 2013///
ER -
TY - JOUR
TI - Determinantal representations of hyperbolic plane curves: An elementary approach
AU - Plaumann, Daniel
AU - Vinzant, Cynthia
T2 - Journal of Symbolic Computation
AB - If a real symmetric matrix of linear forms is positive definite at some point, then its determinant is a hyperbolic hypersurface. In 2007, Helton and Vinnikov proved a converse in three variables, namely that every hyperbolic plane curve has a definite real symmetric determinantal representation. The goal of this paper is to give a more concrete proof of a slightly weaker statement. Here we show that every hyperbolic plane curve has a definite determinantal representation with Hermitian matrices. We do this by relating the definiteness of a matrix to the real topology of its minors and extending a construction of Dixon from 1902. Like Helton and Vinnikov's theorem, this implies that every hyperbolic region in the plane is defined by a linear matrix inequality.
DA - 2013/10//
PY - 2013/10//
DO - 10.1016/J.JSC.2013.05.004
VL - 57
SP - 48-60
J2 - Journal of Symbolic Computation
LA - en
OP -
SN - 0747-7171
UR - http://dx.doi.org/10.1016/J.JSC.2013.05.004
DB - Crossref
KW - Hyperbolic polynomials
KW - Determinantal representations
KW - Interlacing
KW - Hermitian matrices of linear forms
ER -
TY - JOUR
TI - The entropic discriminant
AU - Sanyal, Raman
AU - Sturmfels, Bernd
AU - Vinzant, Cynthia
T2 - Advances in Mathematics
AB - The entropic discriminant is a non-negative polynomial associated to a matrix. It arises in contexts ranging from statistics and linear programming to singularity theory and algebraic geometry. It describes the complex branch locus of the polar map of a real hyperplane arrangement, and it vanishes when the equations defining the analytic center of a linear program have a complex double root. We study the geometry of the entropic discriminant, and we express its degree in terms of the characteristic polynomial of the underlying matroid. Singularities of reciprocal linear spaces play a key role. In the corank-one case, the entropic discriminant admits a sum of squares representation derived from the discriminant of a characteristic polynomial of a symmetric matrix.
DA - 2013/9//
PY - 2013/9//
DO - 10.1016/J.AIM.2013.05.019
VL - 244
SP - 678-707
J2 - Advances in Mathematics
LA - en
OP -
SN - 0001-8708
UR - http://dx.doi.org/10.1016/J.AIM.2013.05.019
DB - Crossref
KW - Matroid
KW - Discriminant
KW - Hyperplane arrangement
KW - Ramification locus
KW - Fully real system
ER -
TY - JOUR
TI - Experimental design for vector output systems
AU - Banks, H.T.
AU - Rehm, K.L.
T2 - Inverse Problems in Science and Engineering
AB - We formulate an optimal design problem for the selection of best states to observe and optimal sampling times for parameter estimation or inverse problems involving complex nonlinear dynamical systems. An iterative algorithm for implementation of the resulting methodology is proposed. Its use and efficacy is illustrated on two applied problems of practical interest: (i) dynamic models of HIV progression and (ii) modeling of the Calvin cycle in plant metabolism and growth.
DA - 2013/5/17/
PY - 2013/5/17/
DO - 10.1080/17415977.2013.797973
VL - 22
IS - 4
SP - 557-590
J2 - Inverse Problems in Science and Engineering
LA - en
OP -
SN - 1741-5977 1741-5985
UR - http://dx.doi.org/10.1080/17415977.2013.797973
DB - Crossref
KW - optimal design
KW - inverse problems
KW - optimal selection of observables and sampling times
KW - HIV models
KW - plant metabolism and growth
ER -
TY - JOUR
TI - A graph-based approach to find teleconnections in climate data
AU - Kawale, Jaya
AU - Liess, Stefan
AU - Kumar, Arjun
AU - Steinbach, Michael
AU - Snyder, Peter
AU - Kumar, Vipin
AU - Ganguly, Auroop R.
AU - Samatova, Nagiza F.
AU - Semazzi, Fredrick
T2 - Statistical Analysis and Data Mining
AB - Pressure dipoles are important long distance climate phenomena (teleconnection) characterized by pressure anomalies of the opposite polarity appearing at two different locations at the same time. Such dipoles have been proven important for understanding and explaining the variability in climate in many regions of the world, e.g. the El Niño Southern Oscillation (ENSO) climate phenomenon, which is described by opposite pressure anomalies between the west and east Pacific and is known to be responsible for precipitation and temperature anomalies worldwide. This paper presents a graph-based approach called shared reciprocal nearest neighbor approach that considers only reciprocal positive and negative edges in the shared nearest neighbor graph to find the dipoles. One crucial aspect of our approach to the analysis of such networks is a careful treatment of negative correlations, whose proper consideration is critical for finding the dipoles. Further, our work shows the importance of modeling the time-dependent patterns of the dipoles in a changing climate in order to better capture the impact of important climate phenomena on the globe. To show the utility of finding dipoles using our approach, we show that the data driven dynamic climate indices generated from our algorithm generally perform better than static indices formed from the fixed locations used by climate scientists in terms of capturing impact on global temperature and precipitation. Our approach can generate a single snapshot picture of all the dipole interconnections on the globe in a given dataset and thus makes it possible to study the changes in dipole interactions and movements. As teleconnections are crucial in the understanding of the global climate system, there is a pressing need to better understand the behavior and interactions of these atmospheric processes as well as to capture them precisely. Our systematic graph-based approach to find the teleconnections in climate data is an attempt in that direction. © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 6: 158–179, 2013
DA - 2013/4/17/
PY - 2013/4/17/
DO - 10.1002/SAM.11181
VL - 6
IS - 3
SP - 158-179
J2 - Statistical Analy Data Mining
LA - en
OP -
SN - 1932-1864
UR - http://dx.doi.org/10.1002/SAM.11181
DB - Crossref
KW - graph algorithm
KW - teleconnections
KW - dipole discovery
ER -
TY - CONF
TI - A joint robust estimation and random matrix framework with application to array processing
AU - Couillet, Romain
AU - Pascal, Frederic
AU - Silverstein, Jack W.
T2 - ICASSP 2013 - 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
AB - An original interface between robust estimation theory and random matrix theory for the estimation of population covariance matrices is proposed. Consider a random vector x = A _{N} y ∈ C ^{N} with y ∈ C ^{M} made of M ≥ N independent entries, E[y] = 0, and E[yy*] = I _{N} . It is shown that a class of robust estimators Ĉ _{N} of C _{N} = A _{N} A* _{N} , obtained from n independent copies of x, is (N, n)-consistent with the traditional sample covariance matrix r̂ _{N} in the sense that ∥Ĉ _{N} - αr̂ _{N} ∥ → 0 in spectral norm for some α > 0, almost surely, as N, n → ∞ with N/n and M/N bounded. This result, in general not valid in the fixed N regime, is used to propose improved subspace estimation techniques, among which an enhanced direction-of-arrival estimator called robust G-MUSIC.
C2 - 2013/5//
C3 - 2013 IEEE International Conference on Acoustics, Speech and Signal Processing
DA - 2013/5//
DO - 10.1109/icassp.2013.6638930
PB - IEEE
SN - 9781479903566
UR - http://dx.doi.org/10.1109/icassp.2013.6638930
DB - Crossref
ER -
TY - JOUR
TI - Singular gradient flow of the distance function and homotopy equivalence
AU - Albano, P.
AU - Cannarsa, P.
AU - Nguyen, K.T.
AU - Sinestrari, C.
T2 - Mathematische Annalen
AB - Let $$M$$ be a Riemannian manifold and let $$\varOmega $$ be a bounded open subset of $$M$$ . It is well known that significant information about the geometry of $$\varOmega $$ is encoded into the properties of the distance, $$d_{\partial \varOmega }$$ , from the boundary of $$\varOmega $$ . Here, we show that the generalized gradient flow associated with the distance preserves singularities, that is, if $$x_0$$ is a singular point of $$d_{\partial \varOmega }$$ then the generalized characteristic starting at $$x_0$$ stays singular for all times. As an application, we deduce that the singular set of $$d_{\partial \varOmega }$$ has the same homotopy type as $$\varOmega $$ .
DA - 2013///
PY - 2013///
DO - 10.1007/s00208-012-0835-8
VL - 356
IS - 1
SP - 23-43
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84875709062&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Developing predictive approaches to characterize adaptive responses of the reproductive endocrine axis to aromatase inhibition: II. Computational modeling
AU - Breen, Miyuki
AU - Villeneuve, Daniel L
AU - Ankley, Gerald T
AU - Bencic, David C
AU - Breen, Michael S
AU - Watanabe, Karen H
AU - Lloyd, Alun L
AU - Conolly, Rory B
T2 - toxicological sciences
DA - 2013///
PY - 2013///
VL - 133
IS - 2
SP - 234-247
ER -
TY - JOUR
TI - Developmental timing of mutations revealed by whole-genome sequencing of twins with acute lymphoblastic leukemia
AU - Ma, Y.
AU - Dobbins, S. E.
AU - Sherborne, A. L.
AU - Chubb, D.
AU - Galbiati, M.
AU - Cazzaniga, G.
AU - Micalizzi, C.
AU - Tearle, R.
AU - Lloyd, A. L.
AU - Hain, R.
AU - Greaves, M.
AU - Houlston, R. S.
T2 - Proceedings of the National Academy of Sciences
AB - Acute lymphoblastic leukemia (ALL) is the major pediatric cancer. At diagnosis, the developmental timing of mutations contributing critically to clonal diversification and selection can be buried in the leukemia's covert natural history. Concordance of ALL in monozygotic, monochorionic twins is a consequence of intraplacental spread of an initiated preleukemic clone. Studying monozygotic twins with ALL provides a unique means of uncovering the timeline of mutations contributing to clonal evolution, pre- and postnatally. We sequenced the whole genomes of leukemic cells from two twin pairs with ALL to comprehensively characterize acquired somatic mutations in ALL, elucidating the developmental timing of all genetic lesions. Shared, prenatal, coding-region single-nucleotide variants were limited to the putative initiating lesions. All other nonsynonymous single-nucleotide variants were distinct between tumors and, therefore, secondary and postnatal. These changes occurred in a background of noncoding mutational changes that were almost entirely discordant in twin pairs and likely passenger mutations acquired during leukemic cell proliferation.
DA - 2013/4/8/
PY - 2013/4/8/
DO - 10.1073/PNAS.1221099110
VL - 110
IS - 18
SP - 7429-7433
J2 - Proceedings of the National Academy of Sciences
LA - en
OP -
SN - 0027-8424 1091-6490
UR - http://dx.doi.org/10.1073/PNAS.1221099110
DB - Crossref
KW - fusion gene
KW - copy number variants
ER -
TY - CHAP
TI - Improving Angular Speed Uniformity by C 1 Piecewise Reparameterization
AU - Yang, Jing
AU - Wang, Dongming
AU - Hong, Hoon
T2 - Automated Deduction in Geometry
AB - We show how to compute a C 1 piecewise-rational reparameterization that closely approximates to the arc-angle parameterization of any plane curve by C 1 piecewise Mobius transformation. By making use of the information provided by the first derivative of the angular speed function, the unit interval is partitioned such that the obtained reparameterization has high uniformity and continuous angular speed. An iteration process is used to refine the interval partition. Experimental results are presented to show the performance of the proposed method and the geometric behavior of the computed reparameterizations.
PY - 2013///
DO - 10.1007/978-3-642-40672-0_3
SP - 33-47
OP -
PB - Springer Berlin Heidelberg
SN - 9783642406713 9783642406720
UR - http://dx.doi.org/10.1007/978-3-642-40672-0_3
DB - Crossref
ER -
TY - JOUR
TI - Acoustic localisation of coronary artery stenosis: Wave propagation in soft tissue mimicking gels
AU - Greenwald, S.E.
AU - Banks, H.T.
AU - Birch, M.J.
AU - Brewin, M.P.
AU - Hu, S.
AU - Kenz, Z.R.
AU - Kruse, C.
AU - Mehta, D.
AU - Reeves, J.
AU - Shaw, S.
AU - Whiteman, J.R.
T2 - Artery Research
AB - WAVE PROPAGATION IN SOFT TISSUE MIMICKING GEL H. Thomas Banks, Malcolm J. Birch, Mark P. Brewin, Steve E. Greenwald, Shuhua Hu, Zack R. Kenz, Carola Kruse, Dwij Mehta, Simon Shaw, John R. Whiteman Blizard Institute, Barts and The London School of Medicine and Dentistry, Queen Mary, University of London, UK; Clinical Physics, Barts Health NHS Trust, London, UK; Institute of Computational Mathematics, Brunel University, UK; Department of Mathematics, North Carolina State University, Raleigh NC, USA
DA - 2013/9//
PY - 2013/9//
DO - 10.1016/J.ARTRES.2013.10.081
VL - 7
IS - 3-4
SP - 124
J2 - Artery Research
LA - en
OP -
SN - 1872-9312
UR - http://dx.doi.org/10.1016/J.ARTRES.2013.10.081
DB - Crossref
ER -
TY - JOUR
TI - Towards computational diagnosis of coronary artery disease
AU - Shaw, S.
AU - Whiteman, J.R.
AU - Greenwald, S.E.
AU - Kruse, C.
AU - Banks, H.T.
AU - Birch, M.J.
AU - Kenz, Z.R.
AU - Reeves, J.
AU - Hu, S.
AU - Brewin, M.P.
T2 - Artery Research
DA - 2013/9//
PY - 2013/9//
DO - 10.1016/J.ARTRES.2013.10.079
VL - 7
IS - 3-4
SP - 123-124
J2 - Artery Research
LA - en
OP -
SN - 1872-9312
UR - http://dx.doi.org/10.1016/J.ARTRES.2013.10.079
DB - Crossref
ER -
TY - JOUR
TI - Experimental design for distributed parameter vector systems
AU - Banks, H.T.
AU - Rehm, K.L.
T2 - Applied Mathematics Letters
AB - We formulate an optimal design problem for the selection of best states to observe and optimal sampling times and locations for parameter estimation or inverse problems involving complex nonlinear nonlinear partial differential systems. An iterative algorithm for implementation of the resulting methodology is proposed.
DA - 2013/1//
PY - 2013/1//
DO - 10.1016/j.aml.2012.08.003
VL - 26
IS - 1
SP - 10-14
J2 - Applied Mathematics Letters
LA - en
OP -
SN - 0893-9659
UR - http://dx.doi.org/10.1016/j.aml.2012.08.003
DB - Crossref
KW - Optimal design
KW - Inverse problems
KW - Optimal selection of observables
KW - Sampling points
ER -
TY - CONF
TI - Cardiovascular Dynamics during Head-up Tilt assessed Via a Pulsatile and Non-pulsatile Model
AU - Tran, H.
AU - Williams, N.
AU - Olufsen, M.S.
T2 - Special Session on Modelling and Simulation in Biology and Medicine
C2 - 2013///
C3 - Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications
DA - 2013///
DO - 10.5220/0004624006730680
VL - 1
SP - 673–680
PB - SciTePress - Science and and Technology Publications
SN - 9789898565693
UR - http://dx.doi.org/10.5220/0004624006730680
ER -
TY - JOUR
TI - PEDESTRIAN FLOW MODELS WITH SLOWDOWN INTERACTIONS
AU - Chertock, Alina
AU - Kurganov, Alexander
AU - Polizzi, Anthony
AU - Timofeyev, Ilya
T2 - Mathematical Models and Methods in Applied Sciences
AB - In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for pedestrians moving in two opposite directions. Coarse-grained mesoscopic and macroscopic analogs are derived leading to the coupled system of PDEs for the density of the pedestrian traffic. The obtained first-order system of conservation laws is only conditionally hyperbolic. We also derive higher-order nonlinear diffusive corrections resulting in a parabolic macroscopic PDE model. Numerical experiments comparing and contrasting the behavior of the microscopic stochastic model and the resulting coarse-grained PDEs for various parameter settings and initial conditions are performed. These numerical experiments demonstrate that the nonlinear diffusion is essential for reproducing the behavior of the stochastic system in the nonhyperbolic regime.
DA - 2013/12/12/
PY - 2013/12/12/
DO - 10.1142/s0218202513400083
VL - 24
IS - 02
SP - 249-275
J2 - Math. Models Methods Appl. Sci.
LA - en
OP -
SN - 0218-2025 1793-6314
UR - http://dx.doi.org/10.1142/s0218202513400083
DB - Crossref
KW - Pedestrian traffic flow
KW - stochastic cellular automata model
KW - mesoscopic and macroscopic models
KW - exclusion process
KW - nonlinear diffusion
ER -
TY - CONF
TI - High Order Numerical Simulation of the Transmission and Scattering of Waves Using the Method of Difference Potentials
AU - Britt, S.
AU - Medvinsky, M.
AU - Tsynkov, S.
AU - Turkel, E.
C2 - 2013/5/27/
C3 - Proceedings of the International Conference "Difference Schemes and Applications" in honor of the 90-th Birthday of Prof. V. S. Ryaben'kii
DA - 2013/5/27/
SP - 33-34
PB - Keldysh Institute of Applied Mathematics
ER -
TY - JOUR
TI - Providing easy access to radio networks
DA - 2013/6/19/
PY - 2013/6/19/
UR - http://appft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&co1=AND&d=PG01&s1=%22Providing+easy+access+radio+networks%22.TTL.&OS=TTL/%22Providing+easy+access+to+radio+networks%22&RS=TTL/%22Providing+easy+access+to+radio+networks%22
ER -
TY - THES
TI - High order numerical simulation of waves using regular grids and non-conforming interfaces
DA - 2013/10/6/
PY - 2013/10/6/
UR - http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA617619
ER -
TY - JOUR
TI - Detecting invariant manifolds, attractors, and generalized KAM tori in aperiodically forced mechanical systems
AU - Hadjighasem, A.
AU - Farazmand, M.
AU - Haller, G.
T2 - Nonlinear Dynamics
AB - We show how the recently developed theory of geodesic transport barriers for fluid flows can be used to uncover key invariant manifolds in externally forced, one-degree-of-freedom mechanical systems. Specifically, invariant sets in such systems turn out to be shadowed by least-stretching geodesics of the Cauchy–Green strain tensor computed from the flow map of the forced mechanical system. This approach enables the finite-time visualization of generalized stable and unstable manifolds, attractors and generalized KAM curves under arbitrary forcing, when Poincaré maps are not available. We illustrate these results by detailed visualizations of the key finite-time invariant sets of conservatively and dissipatively forced Duffing oscillators.
DA - 2013///
PY - 2013///
DO - 10.1007/s11071-013-0823-x
VL - 73
IS - 1-2
SP - 689-704
KW - Stability of mechanical systems
KW - Non-autonomous dynamical systems
KW - Invariant manifolds
KW - Coherent structures
ER -
TY - JOUR
TI - Attracting and repelling Lagrangian coherent structures from a single computation
AU - Farazmand, M.
AU - Haller, G.
T2 - Chaos
AB - Hyperbolic Lagrangian Coherent Structures (LCSs) are locally most repelling or most attracting material surfaces in a finite-time dynamical system. To identify both types of hyperbolic LCSs at the same time instance, the standard practice has been to compute repelling LCSs from future data and attracting LCSs from past data. This approach tacitly assumes that coherent structures in the flow are fundamentally recurrent, and hence gives inconsistent results for temporally aperiodic systems. Here we resolve this inconsistency by showing how both repelling and attracting LCSs are computable at the same time instance from a single forward or a single backward run. These LCSs are obtained as surfaces normal to the weakest and strongest eigenvectors of the Cauchy-Green strain tensor.
DA - 2013///
PY - 2013///
DO - 10.1063/1.4800210
VL - 15
SP - 023101
ER -
TY - CONF
TI - Efficient Solutions to the NDA-NCA Low-Order Eigenvalue Problem
AU - Willert, J.
AU - Kelley, C.T.
C2 - 2013///
C3 - Proceedings of International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering
DA - 2013///
SP - 2725–2735
ER -
TY - CONF
TI - An Efficient Parallel Solution to the Wigner-Poisson Equations
AU - Costolanski, A.S.
AU - Kelley, C.T.
AU - Howell, G.W.
AU - Salinger, A.G.
A2 - Liu, F.
C2 - 2013/4//
C3 - High Performance Computing Symposium (HPC 2013), Simulation Series Vol. 45, Society for Modeling & Simulation International
DA - 2013/4//
VL - 45
SP - 773–780
PB - Curran Associates Inc.
ER -
TY - CHAP
TI - High Order Numerical Simulation of the Transmission and
Scattering of Waves Using the Method of Difference Potentials
AU - Britt, S.
AU - Medvinsky, M.
AU - Turkel, E.
AU - Tsynkov, S.
T2 - Proceedings of the International Conference Difference Schemes and Applications
in honor of the 90-th Birthday of Prof. V. S. Ryaben'kii, Moscow, Russia, May 27--31, 2013
PY - 2013///
SP - 33-34
UR - https://stsynkov.math.ncsu.edu/publications/Tsynkov_abstract_for_Ryabenkii-90.pdf
ER -
TY - CONF
TI - Mechanism of Drug Action on Alzheimer's Disease Protein
AU - Briggs, E.
AU - Hodak, M
AU - Rose, F
AU - Lu, W
AU - Kelley, C.T.
AU - Bernholc, J
C2 - 2013///
C3 - Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
CY - Denver CO
DA - 2013///
PB - IEEE Computer Society Press
ER -
TY - JOUR
TI - Hybrid Deterministic/Monte Carlo Neutronics
AU - Willert, Jeff
AU - Kelley, C T
AU - Knoll, D A
AU - Park, H K
T2 - SIAM J. Sci. Comp.
AB - In this paper we describe a hybrid deterministic/Monte Carlo algorithm for neutron transport simulation. The algorithm is based on nonlinear accelerators for source iteration, using Monte Carlo methods for the purely absorbing high-order problem and a Jacobian-free Newton--Krylov iteration for the low-order problem. We couple the Monte Carlo solution with the low-order problem using filtering to smooth the flux and current from the Monte Carlo solver and an analytic Jacobian-vector product to avoid numerical differentiation of the Monte Carlo results. We use a continuous energy deposition tally for the Monte Carlo simulation. We conclude the paper with numerical results which illustrate the effectiveness of the new algorithm.
DA - 2013///
PY - 2013///
DO - http://dx.doi.org/10.1137/120880021
VL - 35
IS - 5
SP - S62-S83
ER -
TY - JOUR
TI - Explicit Pseudo-Transient Continuation
AU - Kelley, C T
AU - Liao, Li-Zhi
T2 - Pacific J. Opt.
DA - 2013///
PY - 2013///
VL - 9
IS - 1
SP - 77-91
ER -
TY - JOUR
TI - A mathematical model of RNA3 recruitment in the replication cycle of Brome Mosaic Virus
AU - Huffman, T.
AU - Link, K.
AU - Nardini, J.
AU - Poag, L.
AU - Flores, K.
AU - Banks, H.T.
AU - Blasco, B.
AU - Jungfleisch, J.
AU - Diez, J.
T2 - International Journal of Pure and Applied Mathematics
DA - 2013/12/12/
PY - 2013/12/12/
DO - 10.12732/ijpam.v89i2.9
VL - 89
IS - 2
SP - 251-274
SN - 1311-8080 1314-3395
UR - http://dx.doi.org/10.12732/ijpam.v89i2.9
ER -
TY - JOUR
TI - Nonconvexity of the set of hypergraph degree sequences
AU - Liu, Ricky Ini
T2 - Electronic Journal of Combinatorics
DA - 2013/1//
PY - 2013/1//
VL - 20
IS - 1
ER -
TY - CONF
TI - Two Fluid Flow in Porous Media
AU - Shearer, Michael
C2 - 2013///
C3 - Proceedings of HYP2012
DA - 2013///
VL - 8
SP - 212–232
PB - American Institute of Mathematical Sciences
ER -
TY - JOUR
TI - Estimating arrival rate of nonhomogeneous Poisson processes with semidefinite programming
AU - Alizadeh, Farid
AU - Papp, David
T2 - Annals of Operations Research
DA - 2013/1/8/
PY - 2013/1/8/
DO - 10.1007/s10479-011-1020-2
VL - 208
IS - 1
SP - 291-308
J2 - Ann Oper Res
LA - en
OP -
SN - 0254-5330 1572-9338
UR - http://dx.doi.org/10.1007/s10479-011-1020-2
DB - Crossref
ER -
TY - JOUR
TI - Variable metric quasi-Fejér monotonicity
AU - Combettes, Patrick L.
AU - Vũ, Bằng C.
T2 - Nonlinear Analysis: Theory, Methods & Applications
AB - The notion of quasi-Fejér monotonicity has proven to be an efficient tool to simplify and unify the convergence analysis of various algorithms arising in applied nonlinear analysis. In this paper, we extend this notion in the context of variable metric algorithms, whereby the underlying norm is allowed to vary at each iteration. Applications to convex optimization and inverse problems are demonstrated.
DA - 2013/2//
PY - 2013/2//
DO - 10.1016/j.na.2012.09.008
VL - 78
SP - 17-31
J2 - Nonlinear Analysis: Theory, Methods & Applications
LA - en
OP -
SN - 0362-546X
UR - http://dx.doi.org/10.1016/j.na.2012.09.008
DB - Crossref
KW - Convex feasibility problem
KW - Convex optimization
KW - Hilbert space
KW - Inverse problems
KW - Proximal Landweber method
KW - Proximal point algorithm
KW - Quasi-Fejer sequence
KW - Variable metric
ER -
TY - JOUR
TI - Moreau’s decomposition in Banach spaces
AU - Combettes, Patrick L.
AU - Reyes, Noli N.
T2 - Mathematical Programming
AB - Moreau’s decomposition is a powerful nonlinear hilbertian analysis tool that has been used in various areas of optimization and applied mathematics. In this paper, it is extended to reflexive Banach spaces and in the context of generalized proximity measures. This extension unifies and significantly improves upon existing results.
DA - 2013/3/22/
PY - 2013/3/22/
DO - 10.1007/s10107-013-0663-y
VL - 139
IS - 1-2
SP - 103-114
J2 - Math. Program.
LA - en
OP -
SN - 0025-5610 1436-4646
UR - http://dx.doi.org/10.1007/s10107-013-0663-y
DB - Crossref
KW - Banach space
KW - Bregman distance
KW - Convex optimization
KW - Infimal convolution
KW - Legendre function
KW - Moreau's decomposition
KW - Proximity operator
ER -
TY - JOUR
TI - Systems of Structured Monotone Inclusions: Duality, Algorithms, and Applications
AU - Combettes, Patrick L.
T2 - SIAM Journal on Optimization
AB - A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed. Each inclusion in the primal system features compositions with linear operators, parallel sums, and Lipschitzian operators. All the operators involved in this structured model are used separately in the proposed algorithm, most steps of which can be executed in parallel. This provides a flexible solution method applicable to a variety of problems beyond the reach of the state-of-the-art. Several applications are discussed to illustrate this point.
DA - 2013/1//
PY - 2013/1//
DO - 10.1137/130904160
VL - 23
IS - 4
SP - 2420-2447
J2 - SIAM J. Optim.
LA - en
OP -
SN - 1052-6234 1095-7189
UR - http://dx.doi.org/10.1137/130904160
DB - Crossref
KW - convex minimization
KW - coupled system
KW - infimal convolution
KW - monotone inclusion
KW - monotone operator
KW - operator splitting
KW - parallel algorithm
KW - structured minimization problem
ER -
TY - CHAP
TI - Monotone Operator Methods for Nash Equilibria in Non-potential Games
AU - Briceño-Arias, Luis M.
AU - Combettes, Patrick L.
T2 - Computational and Analytical Mathematics
AB - We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications to generalized Nash equilibria, zero-sum games, and cyclic proximation problems are demonstrated.
PY - 2013///
DO - 10.1007/978-1-4614-7621-4_9
SP - 143-159
OP -
PB - Springer New York
SN - 9781461476207 9781461476214
UR - http://dx.doi.org/10.1007/978-1-4614-7621-4_9
DB - Crossref
KW - Monotone operator
KW - Nash equilibrium
KW - Potential game
KW - Proximal algorithm
KW - Splitting method
KW - Zero-sum game
ER -
TY - CONF
TI - Sparse multivariate function recovery from values with noise and outlier errors
AU - Kaltofen, Erich L.
AU - Yang, Zhengfeng
T2 - the 38th international symposium
AB - Error-correcting decoding is generalized to multivariate sparse rational function recovery from evaluations that can be numerically inaccurate and where several evaluations can have severe errors (outliers). The generalization of the Berlekamp-Welch decoder to exact Cauchy interpolation of univariate rational functions from values with faults is by Kaltofen and Pernet in 2012. We give a different univariate solution based on structured linear algebra that yields a stable decoder with floating point arithmetic. Our multivariate polynomial and rational function interpolation algorithm combines Zippel's symbolic sparse polynomial interpolation technique [Ph.D. Thesis MIT 1979] with the numeric algorithm by Kaltofen, Yang, and Zhi [Proc. SNC 2007], and removes outliers (cleans up data) through techniques from error correcting codes. Our multivariate algorithm can build a sparse model from a number of evaluations that is linear in the sparsity of the model.
C2 - 2013///
C3 - Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation - ISSAC '13
DA - 2013///
DO - 10.1145/2465506.2465524
PB - ACM Press
SN - 9781450320597
UR - http://dx.doi.org/10.1145/2465506.2465524
DB - Crossref
ER -
TY - CONF
TI - Direct Transcription Solution of Optimal Control Problems with Differential Algebraic Equations with Delays
AU - Betts, John T.
AU - Campbell, Stephen L.
AU - Thompson, Karmethia C.
T2 - Power and Energy
AB - Many physical systems are naturally modeled as differential algebraic equations or DAEs. Many physical systems also possess delays either in the dynamics or in the application of the control. Direct transcription is a popular approach in industry for numerically solving nondelayed optimal control problems because of its ability to handle problems with constraints. This paper reports on progress in developing an industrial strength direct transcription optimal control software package that can solve many problems with delays and DAE models. In particular, we focus in this paper on how the use of the DAE formalism allows for the consideration of a much greater variety of delays.
C2 - 2013///
C3 - Power and Energy / 807: Intelligent Systems and Control / 808: Technology for Education and Learning
DA - 2013///
DO - 10.2316/p.2013.807-003
PB - ACTAPRESS
SN - 9780889869615
UR - http://dx.doi.org/10.2316/p.2013.807-003
DB - Crossref
ER -
TY - CHAP
TI - Strong Shape Derivative for the Wave Equation with Neumann Boundary Condition
AU - Zolésio, Jean-Paul
AU - Bociu, Lorena
T2 - IFIP Advances in Information and Communication Technology
AB - The paper provides shape derivative analysis for the wave equation with mixed boundary conditions on a moving domain Ω s in the case of non smooth neumann boundary datum. The key ideas in the paper are (i) bypassing the classical sensitivity analysis of the state by using parameter differentiability of a functional expressed in the form of Min-Max of a convex-concave Lagrangian with saddle point, and (ii) using a new regularity result on the solution of the wave problem (where the Dirichlet condition on the fixed part of the boundary is essential) to analyze the strong derivative.
PY - 2013///
DO - 10.1007/978-3-642-36062-6_45
SP - 445-460
OP -
PB - Springer Berlin Heidelberg
SN - 9783642360619 9783642360626
UR - http://dx.doi.org/10.1007/978-3-642-36062-6_45
DB - Crossref
ER -
TY - JOUR
TI - Sensitivity analysis for a free boundary fluid-elasticity interaction
AU - Bociu, Lorena
AU - Zolésio, Jean-Paul
T2 - Evolution Equations and Control Theory
AB - In this paper a total linearization is derived for the free boundary nonlinear elasticity - incompressible fluid interaction. The equations and the free boundary are linearized together and the new linearization turns out to be different from the usualcoupling of classical linear models. New extra terms are present on the common interface, some of them involving the boundary curvatures. These terms play an important rolein the final linearized system and can not be neglected.
DA - 2013/1//
PY - 2013/1//
DO - 10.3934/eect.2013.2.55
VL - 2
IS - 1
SP - 55-79
J2 - EECT
LA - en
OP -
SN - 2163-2480
UR - http://dx.doi.org/10.3934/eect.2013.2.55
DB - Crossref
KW - Free boundary
KW - nonlinear elasticity
KW - Navier-Stokes
KW - linearization
KW - coupled system
KW - shape derivative
ER -
TY - JOUR
TI - Direct leaf trajectory optimization for volumetric modulated arc therapy planning with sliding window delivery
AU - Papp, Dávid
AU - Unkelbach, Jan
T2 - Medical Physics
AB - Purpose: The authors propose a novel optimization model for volumetric modulated arc therapy (VMAT) planning that directly optimizes deliverable leaf trajectories in the treatment plan optimization problem, and eliminates the need for a separate arc-sequencing step. Methods: In this model, a 360° arc is divided into a given number of arc segments in which the leaves move unidirectionally. This facilitates an algorithm that determines the optimal piecewise linear leaf trajectories for each arc segment, which are deliverable in a given treatment time. Multileaf collimator constraints, including maximum leaf speed and interdigitation, are accounted for explicitly. The algorithm is customized to allow for VMAT delivery using constant gantry speed and dose rate, however, the algorithm generalizes to variable gantry speed if beneficial. Results: The authors demonstrate the method for three different tumor sites: a head-and-neck case, a prostate case, and a paraspinal case. The authors first obtain a reference plan for intensity modulated radiotherapy (IMRT) using fluence map optimization and 20 intensity-modulated fields in equally spaced beam directions, which is beyond the standard of care. Modeling the typical clinical setup for the treatment sites considered, IMRT plans using seven or nine beams are also computed. Subsequently, VMAT plans are optimized by dividing the 360° arc into 20 corresponding arc segments. Assuming typical machine parameters (a dose rate of 600 MU/min, and a maximum leaf speed of 3 cm/s), it is demonstrated that the optimized VMAT plans with 2–3 min delivery time are of noticeably better quality than the 7–9 beam IMRT plans. The VMAT plan quality approaches the quality of the 20-beam IMRT benchmark plan for delivery times between 3 and 4 min. Conclusions: The results indicate that high quality treatments can be delivered in a single arc with 20 arc segments if sufficient time is allowed for modulation in each segment.
DA - 2013/12/4/
PY - 2013/12/4/
DO - 10.1118/1.4835435
VL - 41
IS - 1
SP - 011701
J2 - Med. Phys.
LA - en
OP -
SN - 0094-2405
UR - http://dx.doi.org/10.1118/1.4835435
DB - Crossref
KW - arc therapy
KW - optimization
KW - sliding window
KW - VMAT
ER -
TY - JOUR
TI - Semidefinite Characterization of Sum-of-Squares Cones in Algebras
AU - Papp, Dávid
AU - Alizadeh, Farid
T2 - SIAM Journal on Optimization
AB - We extend Nesterov's semidefinite programming characterization of squared functional systems, and Faybusovich's abstraction to bilinear symmetric maps, to cones of sum-of-squares elements in general abstract algebras. Using algebraic techniques such as isomorphism, linear isomorphism, tensor products, sums, and direct sums, we show that many concrete cones are in fact sum-of-squares cones with respect to some algebra and thus are representable by the cone of positive semidefinite matrices. We also consider nonnegativity with respect to a proper cone $\mathcal{K}$ and show that in some cases cones of $\mathcal{K}$-nonnegative functions are either sum of squares or at least semidefinite representable. For example, we show that some well-known Chebyshev systems, when extended to Euclidean Jordan algebras, induce cones that are semidefinite representable. Finally we will discuss some concrete examples and applications, including minimum ellipsoid enclosing given space curves, minimization of eigenvalues of polynomial matrix pencils, approximation of functions by shape-constrained functions, and approximation of combinatorial optimization problems by polynomial programming.
DA - 2013/1//
PY - 2013/1//
DO - 10.1137/110843265
VL - 23
IS - 3
SP - 1398-1423
J2 - SIAM J. Optim.
LA - en
OP -
SN - 1052-6234 1095-7189
UR - http://dx.doi.org/10.1137/110843265
DB - Crossref
KW - sum of squares
KW - semidefinite programming
KW - semidefinite representability
KW - nonnegative polynomials
KW - sum-of-squares functional systems
ER -
TY - JOUR
TI - Generating Moment Matching Scenarios Using Optimization Techniques
AU - Mehrotra, Sanjay
AU - Papp, Dávid
T2 - SIAM Journal on Optimization
AB - An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the distribution can be defined over an arbitrary set. This allows for a reduction in the number of scenarios and allows the scenarios to be better tailored to the problem at hand. The method is based on a semi-infinite linear programming formulation of the problem that is shown to be solvable with polynomial iteration complexity. A practical column generation method is implemented. The column generation subproblems are polynomial optimization problems; however, they need not be solved to optimality. It is found that the columns in the column generation approach can be efficiently generated by random sampling. The number of scenarios generated matches a lower bound of Tchakaloff's. The rate of convergence of the approximation error is established for continuous integrands, and an improved bound is given for smooth integrands. Extensive numerical experiments are presented in which variants of the proposed method are compared to Monte Carlo and quasi-Monte Carlo methods on both numerical integration problems and stochastic optimization problems. The benefits of being able to match any prescribed set of moments, rather than all moments up to a certain order, is also demonstrated using optimization problems with 100-dimensional random vectors. Empirical results show that the proposed approach outperforms Monte Carlo and quasi-Monte Carlo based approaches on the tested problems.
DA - 2013/1//
PY - 2013/1//
DO - 10.1137/110858082
VL - 23
IS - 2
SP - 963-999
J2 - SIAM J. Optim.
LA - en
OP -
SN - 1052-6234 1095-7189
UR - http://dx.doi.org/10.1137/110858082
DB - Crossref
KW - scenario generation
KW - moment matching
KW - cubature
KW - column generation
KW - convex programming
KW - statistical bounds
KW - semi-infinite programming
ER -
TY - JOUR
TI - Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K
AU - Bakalov, Bojko
AU - D’Andrea, Alessandro
AU - Kac, Victor G.
T2 - Advances in Mathematics
AB - One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra. A Lie pseudoalgebra is a generalization of the notion of a Lie conformal algebra for which C[∂] is replaced by the universal enveloping algebra H of a finite-dimensional Lie algebra. The finite (i.e., finitely generated over H) simple Lie pseudoalgebras were classified in our previous work (Bakalov et al., 2001) [2]. The present paper is the second in our series on representation theory of simple Lie pseudoalgebras. In the first paper we showed that any finite irreducible module over a simple Lie pseudoalgebra of type W or S is either an irreducible tensor module or the kernel of the differential in a member of the pseudo de Rham complex. In the present paper we establish a similar result for Lie pseudoalgebras of type K, with the pseudo de Rham complex replaced by a certain reduction called the contact pseudo de Rham complex. This reduction in the context of contact geometry was discovered by Rumin.
DA - 2013/1//
PY - 2013/1//
DO - 10.1016/j.aim.2012.09.012
VL - 232
IS - 1
SP - 188-237
J2 - Advances in Mathematics
LA - en
OP -
SN - 0001-8708
UR - http://dx.doi.org/10.1016/j.aim.2012.09.012
DB - Crossref
KW - Lie pseudoalgebra
KW - Lie-Cartan algebra of vector fields
KW - Hopf algebra
KW - Rumin complex
ER -
TY - JOUR
TI - The Role of Methylation of DNA in Environmental Adaptation
AU - Flores, K. B.
AU - Wolschin, F.
AU - Amdam, G. V.
T2 - Integrative and Comparative Biology
AB - Methylation of DNA is an epigenetic mechanism that influences patterns of gene expression. DNA methylation marks contribute to adaptive phenotypic variation but are erased during development. The role of DNA methylation in adaptive evolution is therefore unclear. We propose that environmentally-induced DNA methylation causes phenotypic heterogeneity that provides a substrate for selection via forces that act on the epigenetic machinery. For example, selection can alter environmentally-induced methylation of DNA by acting on the molecular mechanisms used for the genomic targeting of DNA methylation. Another possibility is that specific methylation marks that are environmentally-induced, yet non-heritable, could influence preferential survival and lead to consistent methylation of the same genomic regions over time. As methylation of DNA is known to increase the likelihood of cytosine-to-thymine transitions, non-heritable adaptive methylation marks can drive an increased likelihood of mutations targeted to regions that are consistently marked across several generations. Some of these mutations could capture, genetically, the phenotypic advantage of the epigenetic mark. Thereby, selectively favored transitory alterations in the genome invoked by DNA methylation could ultimately become selectable genetic variation through mutation. We provide evidence for these concepts using examples from different taxa, but focus on experimental data on large-scale DNA sequencing that expose between-group genetic variation after bidirectional selection on honeybees, Apis mellifera.
DA - 2013/4/25/
PY - 2013/4/25/
DO - 10.1093/icb/ict019
VL - 53
IS - 2
SP - 359-372
J2 - Integrative and Comparative Biology
LA - en
OP -
SN - 1540-7063 1557-7023
UR - http://dx.doi.org/10.1093/icb/ict019
DB - Crossref
ER -
TY - JOUR
TI - Bayesian Inference of Drag Parameters Using AXBT Data from Typhoon Fanapi
AU - Sraj, Ihab
AU - Iskandarani, Mohamed
AU - Srinivasan, Ashwanth
AU - Thacker, W. Carlisle
AU - Winokur, Justin
AU - Alexanderian, Alen
AU - Lee, Chia-Ying
AU - Chen, Shuyi S.
AU - Knio, Omar M.
T2 - Monthly Weather Review
AB - Abstract The authors introduce a three-parameter characterization of the wind speed dependence of the drag coefficient and apply a Bayesian formalism to infer values for these parameters from airborne expendable bathythermograph (AXBT) temperature data obtained during Typhoon Fanapi. One parameter is a multiplicative factor that amplifies or attenuates the drag coefficient for all wind speeds, the second is the maximum wind speed at which drag coefficient saturation occurs, and the third is the drag coefficient's rate of change with increasing wind speed after saturation. Bayesian inference provides optimal estimates of the parameters as well as a non-Gaussian probability distribution characterizing the uncertainty of these estimates. The efficiency of this approach stems from the use of adaptive polynomial expansions to build an inexpensive surrogate for the high-resolution numerical model that couples simulated winds to the oceanic temperature data, dramatically reducing the computational burden of the Markov chain Monte Carlo sampling. These results indicate that the most likely values for the drag coefficient saturation and the corresponding wind speed are about 2.3 × 10−3 and 34 m s−1, respectively; the data were not informative regarding the drag coefficient behavior at higher wind speeds.
DA - 2013/7//
PY - 2013/7//
DO - 10.1175/mwr-d-12-00228.1
VL - 141
IS - 7
SP - 2347-2367
J2 - Mon. Wea. Rev.
LA - en
OP -
SN - 0027-0644 1520-0493
UR - http://dx.doi.org/10.1175/mwr-d-12-00228.1
DB - Crossref
ER -
TY - JOUR
TI - On spectral methods for variance based sensitivity analysis
AU - Alexanderian, Alen
T2 - Probability Surveys
AB - Consider a mathematical model with a finite number of random parameters. Variance based sensitivity analysis provides a framework to characterize the contribution of the individual parameters to the total variance of the model response. We consider the spectral methods for variance based sensitivity analysis which utilize representations of square integrable random variables in a generalized polynomial chaos basis. Taking a measure theoretic point of view, we provide a rigorous and at the same time intuitive perspective on the spectral methods for variance based sensitivity analysis. Moreover, we discuss approximation errors incurred by fixing inessential random parameters, when approximating functions with generalized polynomial chaos expansions.
DA - 2013///
PY - 2013///
DO - 10.1214/13-ps219
VL - 10
IS - 0
SP - 51-68
J2 - Probab. Surveys
LA - en
OP -
SN - 1549-5787
UR - http://dx.doi.org/10.1214/13-ps219
DB - Crossref
KW - Variance based sensitivity analysis
KW - analysis of variance
KW - spectral methods
KW - generalized polynomial chaos
KW - orthogonal polynomials
KW - conditional expectation
ER -
TY - JOUR
TI - Preconditioned Bayesian Regression for Stochastic Chemical Kinetics
AU - Alexanderian, Alen
AU - Rizzi, Francesco
AU - Rathinam, Muruhan
AU - Le Maître, Olivier P.
AU - Knio, Omar M.
T2 - Journal of Scientific Computing
DA - 2013/7/4/
PY - 2013/7/4/
DO - 10.1007/s10915-013-9745-5
VL - 58
IS - 3
SP - 592-626
J2 - J Sci Comput
LA - en
OP -
SN - 0885-7474 1573-7691
UR - http://dx.doi.org/10.1007/s10915-013-9745-5
DB - Crossref
KW - Polynomial chaos
KW - Bayesian regression
KW - Preconditioner
KW - Stochastic simulation algorithm
KW - Chemical kinetics
ER -
TY - THES
TI - High order numerical simulation of waves using regular grids and non-conforming interfaces
AU - Medvinsky, M.
DA - 2013///
PY - 2013///
M3 - Ph.D Dissertation
PB - Tel Aviv University
ER -
TY - JOUR
TI - Wave equations with nonlinear sources and damping: weak vs. regular solutions
AU - Bociu, Lorena
AU - Toundykov, D.
T2 - Palestine Journal of Mathematics
DA - 2013///
PY - 2013///
VL - 2
IS - 2
SP - 175–186
ER -
TY - CONF
TI - A Hybrid Approach to the Neutron Transport k-Eigenvalue Problem using NDA-based Algorithms
AU - Willert, J.
AU - Kelley, C.T.
AU - Knoll, D.A.
AU - Park, H.K.
C2 - 2013///
C3 - Proceedings of International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering
DA - 2013///
SP - 1934–1941
ER -
TY - JOUR
TI - Non-Lipschitz points and the SBV regularity of the minimum time function
AU - Colombo, Giovanni
AU - Nguyen, Khai T.
AU - Nguyen, Luong V.
T2 - Calculus of Variations and Partial Differential Equations
DA - 2013/11/12/
PY - 2013/11/12/
DO - 10.1007/s00526-013-0682-9
VL - 51
IS - 1-2
SP - 439-463
SN - 0944-2669 1432-0835
UR - http://dx.doi.org/10.1007/s00526-013-0682-9
ER -
TY - JOUR
TI - Toric cubes
AU - Engström, Alexander
AU - Hersh, Patricia
AU - Sturmfels, Bernd
T2 - Rendiconti del Circolo Matematico di Palermo
DA - 2013/2/12/
PY - 2013/2/12/
DO - 10.1007/s12215-013-0115-9
VL - 62
IS - 1
SP - 67-78
J2 - Rend. Circ. Mat. Palermo
LA - en
OP -
SN - 0009-725X 1973-4409
UR - http://dx.doi.org/10.1007/s12215-013-0115-9
DB - Crossref
KW - Cube
KW - CW complex
KW - Monomial map
KW - Toric variety
KW - Somialgebraic set
ER -
TY - JOUR
TI - Comparison of Frequentist and Bayesian Confidence Analysis Methods on a Viscoelastic Stenosis Model
AU - Kenz, Zackary R.
AU - Banks, H. T.
AU - Smith, Ralph C.
T2 - SIAM/ASA Journal on Uncertainty Quantification
AB - We compare the performance of three methods for quantifying uncertainty in model parameters: asymptotic theory, bootstrapping, and Bayesian estimation. We study these methods on an existing model for one-dimensional wave propagation in a viscoelastic medium, as well as corresponding data from lab experiments using a homogeneous, tissue-mimicking gel phantom. In addition to parameter estimation, we use the results from the three algorithms to quantify complex correlations between our model parameters, which are best seen using the more computationally expensive bootstrapping or Bayesian methods. We also hold constant the parameter causing the most complex correlation, obtaining results from all three methods which are more consistent than those obtained when estimating all parameters. Concerns regarding computational time and algorithm complexity are incorporated into a discussion on differences between the frequentist and Bayesian perspectives.
DA - 2013/1//
PY - 2013/1//
DO - 10.1137/130917867
VL - 1
IS - 1
SP - 348-369
J2 - SIAM/ASA J. Uncertainty Quantification
LA - en
OP -
SN - 2166-2525
UR - http://dx.doi.org/10.1137/130917867
DB - Crossref
KW - viscoelastic model
KW - asymptotic theory
KW - bootstrapping
KW - Bayesian
KW - MCMC
KW - DRAM
ER -
TY - JOUR
TI - CONFIDENCE INTERVAL ESTIMATION FOR AN EMPIRICAL MODEL QUANTIFYING THE EFFECT OF SOIL MOISTURE AND PLANT DEVELOPMENT ON SOYBEAN (GLYCINE MAX (L.) MERR.) LEAF CONDUCTANCE
AU - Matthews, J.L.
AU - Smith, R.C.
AU - Fiscus, E.L.
T2 - International Journal of Pure and Apllied Mathematics
AB - In this work, we address uncertainty analysis for a model, pre- sented in a separate paper, quantifying the effect of soil moisture and plant age on soybean (Glycine max (L.) Merr.) leaf conductance. To achieve this we present several methods for confidence interval estimation. Estimation of confidence intervals for model parameters and predictions is investigated using asymptotic theory, Monte Carlo methods, and bootstrap methods. A compu- tationally feasible solution for estimating confidence intervals for model param- eters via asymptotic theory is unattainable. Confidence intervals for model
DA - 2013/3/12/
PY - 2013/3/12/
DO - 10.12732/ijpam.v83i3.6
VL - 83
IS - 3
J2 - Int. J. of Pure and Appl. Math.
LA - en
OP -
SN - 1311-8080 1314-3395
UR - http://dx.doi.org/10.12732/ijpam.v83i3.6
DB - Crossref
ER -
TY - JOUR
TI - Smooth Periodic Solutions of a 2x2 System of Nonlinear Hyperbolic Conservation Laws
AU - Shearer, M.
T2 - Applied Mathematics Research eXpress
AB - The Keyfitz–Kranzer system of two conservation laws has the property that it can be written as a triangular system of equations that can be solved successively. In this paper, we show that the system reduces to a linearly degenerate system if the tension T is given by Hooke’s law. This linearly degenerate system has a formula for time-periodic smooth solutions that are easily generated numerically.
DA - 2013/7/12/
PY - 2013/7/12/
DO - 10.1093/amrx/abt006
VL - 7
J2 - Applied Mathematics Research eXpress
LA - en
OP -
SN - 1687-1200 1687-1197
UR - http://dx.doi.org/10.1093/amrx/abt006
DB - Crossref
ER -
TY - JOUR
TI - Graphical models
AU - García-Puente, Luis
AU - Petrović, Sonja
AU - Sullivant, Seth
T2 - Journal of Software for Algebra and Geometry
DA - 2013///
PY - 2013///
DO - 10.2140/jsag.2013.5.1
VL - 5
IS - 1
SP - 1-7
J2 - JSAG
LA - en
OP -
SN - 1948-7916 1948-7916
UR - http://dx.doi.org/10.2140/jsag.2013.5.1
DB - Crossref
ER -
TY - JOUR
TI - Graph manifolds, left-orderability and amalgamation
AU - Clay, Adam
AU - Lidman, Tye
AU - Watson, Liam
T2 - Algebraic & Geometric Topology
AB - We show that every irreducible toroidal integer homology sphere graph manifold has a left-orderable fundamental group. This is established by way of a specialization of a result due to Bludov and Glass for the almagamated products that arise, and in this setting work of Boyer, Rolfsen and Wiest may be applied. Our result then depends on input from 3-manifold topology and Heegaard Floer homology.
DA - 2013/7/2/
PY - 2013/7/2/
DO - 10.2140/agt.2013.13.2347
VL - 13
IS - 4
SP - 2347-2368
J2 - Algebr. Geom. Topol.
LA - en
OP -
SN - 1472-2739 1472-2747
UR - http://dx.doi.org/10.2140/agt.2013.13.2347
DB - Crossref
ER -
TY - JOUR
TI - Discrete Calderon’s projections on parallelepipeds and their application to computing exterior magnetic fields for FRC plasmas
AU - Kansa, E.
AU - Shumlak, U.
AU - Tsynkov, S.
T2 - Journal of Computational Physics
AB - Confining dense plasma in a field reversed configuration (FRC) is considered a promising approach to fusion. Numerical simulation of this process requires setting artificial boundary conditions (ABCs) for the magnetic field because whereas the plasma itself occupies a bounded region (within the FRC coils), the field extends from this region all the way to infinity. If the plasma is modeled using single fluid magnetohydrodynamics (MHD), then the exterior magnetic field can be considered quasi-static. This field has a scalar potential governed by the Laplace equation. The quasi-static ABC for the magnetic field is obtained using the method of difference potentials, in the form of a discrete Calderon boundary equation with projection on the artificial boundary shaped as a parallelepiped. The Calderon projection itself is computed by convolution with the discrete fundamental solution on the three-dimensional Cartesian grid.
DA - 2013/2//
PY - 2013/2//
DO - 10.1016/j.jcp.2012.09.033
VL - 234
IS -
SP - 172-198
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2012.09.033
DB - Crossref
KW - Field reversed configuration (FRC)
KW - Single fluid magnetohydrodynamics (MHD)
KW - Quasi-static magnetic field
KW - Artificial boundary condition (ABC)
KW - The method of difference potentials
KW - Calderon's potentials and projections
KW - Boundary equations with projections
ER -
TY - JOUR
TI - On the infinity flavor of Heegaard Floer homology and the integral cohomology ring
AU - Lidman, Tye
T2 - Commentarii Mathematici Helvetici
AB - For a three-manifold $Y$ and torsion $\mathrm{Spin}^c$ structure $\mathfrak{s}$, Ozsváth and Szabóconstruct a spectral sequence with $E^2$ term an exterior algebra over $H^1(Y;\mathbb{Z})$ converging to $H F^\infty(Y,\mathfrak{s})$. They conjecture that the differentials are completely determined by the integral triple cup product form. In this paper, we prove that $H\hskip-2pt F^\infty(Y,\mathfrak{s})$ is in fact determined by the cohomology ring when $\mathfrak{s}$ is torsion. Furthermore, we give a complete calculation of such $HF^\infty(Y,\mathfrak{s})$, with mod 2 coefficients, in the case where $b\_1(Y)$ is 3 or 4.
DA - 2013///
PY - 2013///
DO - 10.4171/cmh/306
VL - 88
IS - 4
SP - 875-898
J2 - Comment. Math. Helv.
LA - en
OP -
SN - 0010-2571
UR - http://dx.doi.org/10.4171/cmh/306
DB - Crossref
KW - Heegaard Floer homology
KW - Dehn surgery
KW - knot theory
ER -
TY - JOUR
TI - Some regularity results for a class of upper semicontinuous functions
AU - Marigonda, Antonio
AU - Nguyen, Khai Tien
AU - Vittone, Davide
T2 - Indiana University Mathematics Journal
AB - We study regularity properties enjoyed by a class of real-valued upper semicontinuous functions f : R d ! R whose hypograph satis es a geometric property implying, for each point P on the boundary of hypo f, the existence of a sort of (uniform) subquadratic tangent hypersurface whose intersection with hypo f in a neighbourhood of P reduces to P. This geometric property generalizes both the concepts of semiconcave functions and functions whose hypograph has positive reach in the sense of Federer; the associated class of functions arises in the study of regularity properties for the minimum time function of certain classes of nonlinear control systems and di erential inclusions. We will prove that these functions share several regularity properties with semiconcave functions. In particular, they are locally BV and di erentiable a.e. Our approach consists in providing upper bounds for the dimension of the set of nondi erentiability points. Moreover, a ner classi cation of the singularities can be performed according to the dimension of the normal cone to the hypograph, thus generalizing a similar result proved by Federer for sets with positive reach. Techniques of nonsmooth analysis and geometric measure theory are used.
DA - 2013///
PY - 2013///
DO - 10.1512/iumj.2013.62.4896
VL - 62
IS - 1
SP - 45-89
J2 - Indiana Univ. Math. J.
LA - en
OP -
SN - 0022-2518
UR - http://dx.doi.org/10.1512/iumj.2013.62.4896
DB - Crossref
KW - exterior sphere condition
KW - sets with positive reach
KW - reduced boundary
ER -
TY - JOUR
TI - On the minimum time function around the origin
AU - Colombo, Giovanni
AU - Nguyen, Khai T.
T2 - Mathematical Control and Related Fields
AB - We deal with finite dimensional linear and nonlinear control systems. If the system is linear and autonomous and satisfies theclassical normality assumption, we improve the well known result on the strict convexity of the reachable set from the origin by giving apolynomial estimate. The result is based on a careful analysis of the switching function.We extend this result to nonautonomous linear systems, provided the time dependent system is not too far fromthe autonomous system obtained by taking the time to be $0$ in the dynamics. Using a linearization approach, we prove a bang-bang principle, valid in dimensions $2$ and $3$ for a class of nonlinear systems, affine and symmetricwith respect to the control. Moreover we show that, for two dimensional systems, the reachable set from the originsatisfies the same polynomial strict convexity property as for the linearized dynamics, provided the nonlinearity is small enough.Finally, under the same assumptions we show that the epigraph of the minimumtime function has positive reach, hence proving the first result of this type in a nonlinear setting.In all the above results, we require that the linearization at the origin be normal.We provide examples showing the sharpness of our assumptions.
DA - 2013/2//
PY - 2013/2//
DO - 10.3934/mcrf.2013.3.51
VL - 3
IS - 1
SP - 51-82
J2 - MCRF
LA - en
OP -
SN - 2156-8472
UR - http://dx.doi.org/10.3934/mcrf.2013.3.51
DB - Crossref
KW - Reachable sets
KW - exterior sphere condition
KW - maximum principle
ER -
TY - JOUR
TI - Fast Algorithms for Bayesian Inversion
AU - Ambikasaran, Sivaram
AU - Saibaba, Arvind K.
AU - Darve, Eric F.
AU - Kitanidis, Peter K.
T2 - Computational Challenges in the Geosciences
AB - In this article, we review a few fast algorithms for solving large-scale stochastic inverse problems using Bayesian methods. After a brief introduction to the Bayesian stochastic inverse methodology, we review the following computational techniques, to solve large scale problems: the fast Fourier transform, the fast multipole method (classical and a black-box version), and finallym the hierarchical matrix approach. We emphasize that this is mainly a survey paper presenting a few fast algorithms applicable to large-scale Bayesian inversion techniques, applicable to applications arising from geostatistics. The article is presented at a level accessible to graduate students and computational engineers. Hence, we mainly present the algorithmic ideas and theoretical results.
DA - 2013///
PY - 2013///
DO - 10.1007/978-1-4614-7434-0_5
SP - 101-142
KW - Bayesian stochastic inverse modeling
KW - Large-scale problems
KW - Geostatistical estimation
KW - Numerical linear algebra
KW - Fast Fourier transform
KW - Ast multipole method
KW - Hierarchical matrices
ER -
TY - JOUR
TI - A flexible krylov solver for shifted systemswith application to oscillatory hydraulic tomography
AU - Saibaba, A.K.
AU - Bakhos, T.
AU - Kitanidis, P.K.
T2 - SIAM Journal on Scientific Computing
AB - We discuss efficient solutions to systems of shifted linear systems arising in computations for oscillatory hydraulic tomography. The reconstruction of hydrogeological parameters such as hydraulic conductivity and specific storage using limited discrete measurements of pressure (head) obtained from sequential oscillatory pumping tests, leads to a nonlinear inverse problem. We tackle this using the quasi-linear geostatistical approach [Kitanidis, Water Resources Res., 31 (1995), pp. 2411--2419]. This method requires repeated solution of the forward (and adjoint) problem for multiple frequencies, for which we use flexible preconditioned Krylov subspace solvers specifically designed for shifted systems based on ideas in [Gu, Zhou, and Lin, J. Comput. Math., 25 (2007), pp. 522--530]. The solvers allow the preconditioner to change at each iteration. We analyze the convergence of the solver and perform an error analysis when an iterative solver is used for inverting the preconditioner matrices. Finally, we apply our algorithm to a challenging application taken from oscillatory hydraulic tomography to demonstrate the computational gains by using the resulting method.
DA - 2013///
PY - 2013///
DO - 10.1137/120902690
VL - 35
IS - 6
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84892607644&partnerID=MN8TOARS
KW - Krylov solvers
KW - shifted systems
KW - hydraulic tomography
KW - inverse problems
ER -
TY - BOOK
TI - Nonlinear optimal control theory
AU - Berkovitz, L. D.
AU - Medhin, N. G.
AB - Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniqu
DA - 2013///
PY - 2013///
DO - 10.1201/b12739
PB - Boca Raton: CRC Press
ER -
TY - JOUR
TI - Traveling wave solutions in coupled Chua's circuits, part I: Periodic solutions
AU - Chow, S. N.
AU - Jiang, M.
AU - Lin, X. B.
T2 - Journal of Applied Analysis and Computation
DA - 2013///
PY - 2013///
VL - 3
IS - 3
SP - 213-237
ER -
TY - JOUR
TI - Parameter selection methods in inverse problem formulation
AU - Banks, H. T.
AU - Cintron-Arias, A.
AU - Kappel, F.
T2 - Mathematical modeling and validation in physiology: applications to the cardiovascular and respiratory systems
DA - 2013///
PY - 2013///
VL - 2064
SP - 43-73
ER -
TY - JOUR
TI - Development of Patient Specific Cardiovascular Models Predicting Dynamics in Response to Orthostatic Stress Challenges
AU - Ottesen, Johnny T.
AU - Novak, Vera
AU - Olufsen, Mette S.
T2 - MATHEMATICAL MODELING AND VALIDATION IN PHYSIOLOGY: APPLICATIONS TO THE CARDIOVASCULAR AND RESPIRATORY SYSTEMS
AB - Physiological realistic models of the controlled cardiovascular system are constructed and validated against clinical data. Special attention is paid to the control of blood pressure, cerebral blood flow velocity, and heart rate during postural challenges, including sit-to-stand and head-up tilt. This study describes development of patient specific models, and how sensitivity analysis and nonlinear optimization methods can be used to predict patient specific characteristics when analyzed using experimental data. Finally, we discuss how a given model can be used to understand physiological changes between groups of individuals and how to use modeling to identify biomarkers.
DA - 2013///
PY - 2013///
DO - 10.1007/978-3-642-32882-4_10
VL - 2064
SP - 177-213
SN - 1617-9692
ER -
TY - JOUR
TI - Application of the Unscented Kalman Filtering to Parameter Estimation
AU - Attarian, Adam
AU - Batzel, Jerry J.
AU - Matzuka, Brett
AU - Tran, Hien
T2 - MATHEMATICAL MODELING AND VALIDATION IN PHYSIOLOGY: APPLICATIONS TO THE CARDIOVASCULAR AND RESPIRATORY SYSTEMS
AB - Filtering is a methodology used to combine a set of observations with a model to obtain the optimal state. This technique can be extended to estimate the state of the system as well as the unknown model parameters. Estimating the model parameters given a set of data is often referred to as the inverse problem. Filtering provides many benefits to the inverse problem by providing estimates in real time and allowing model errors to be taken into account. Assuming a linear model and Gaussian noises, the optimal filter is the Kalman filter. However, these assumptions rarely hold for many problems of interest, so a number of extensions have been proposed in the literature to deal with nonlinear dynamics. In this chapter, we illustrate the application of one approach to deal with nonlinear model dynamics, the so-called unscented Kalman filter. In addition, we will also show how some of the tools for model validation discussed in other chapters of this volume can be used to improve the estimation process.
DA - 2013///
PY - 2013///
DO - 10.1007/978-3-642-32882-4_4
VL - 2064
SP - 75-88
SN - 0075-8434
ER -
TY - CHAP
TI - Observer based fault detection in differential algebraic equations
AU - Scott, Jason R.
AU - Campbell, Stephen L.
T2 - 2013 Proceedings of the Conference on Control and its Applications
AB - Previous chapter Next chapter Full AccessProceedings 2013 Proceedings of the Conference on Control and its Applications (CT)Observer based fault detection in differential algebraic equationsJason R. Scott and Stephen L. CampbellJason R. Scott and Stephen L. Campbellpp.176 - 183Chapter DOI:https://doi.org/10.1137/1.9781611973273.24PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Fault detection is an important part of most modern industrial systems and processes. One approach to fault detection is based on the use of observers. Many physical processes are most naturally modeled by differential algebraic equations. Recently there has been significant progress in the design of observers for complex differential algebraic equations. This paper examines the use of observers for fault detection in systems modeled by differential algebraic equations. Previous chapter Next chapter RelatedDetails Published:2013eISBN:978-1-61197-327-3 https://doi.org/10.1137/1.9781611973273Book Series Name:ProceedingsBook Code:PRCT13Book Pages:1-229
PY - 2013/7/8/
DO - 10.1137/1.9781611973273.24
SP - 176-183
OP -
PB - Society for Industrial and Applied Mathematics
SN - 9781611973273
UR - http://dx.doi.org/10.1137/1.9781611973273.24
DB - Crossref
ER -
TY - JOUR
TI - Coupled Heterogeneous Association Rule Mining (CHARM): Application toward Inference of Modulatory Climate Relationships
AU - Gonzalez, Doel L., II
AU - Pendse, Saurabh V.
AU - Padmanabhan, Kanchana
AU - Angus, Michael P.
AU - Tetteh, Isaac K.
AU - Srinivas, Shashank
AU - Villanes, Andrea
AU - Semazzi, Fredrick
AU - Kumar, Vipin
AU - Samatova, Nagiza F.
T2 - 2013 IEEE 13TH INTERNATIONAL CONFERENCE ON DATA MINING (ICDM)
AB - The complex dynamic climate system often exhibits hierarchical modularity of its organization and function. Scientists have spent decades trying to discover and understand the driving mechanisms behind western African Sahel summer rainfall variability, mostly via hypothesis-driven and/or first-principles based research. Their work has furthered theory regarding the connections between various climate patterns, but the key relationships are still not fully understood. We present Coupled Heterogeneous Association Rule Mining (CHARM), a computationally efficient methodology that mines higher-order relationships between these subsystems' anomalous temporal phases with respect to their effect on the system's response. We apply this to climate science data, aiming to infer putative pathways/cascades of modulating events and the modulating signs that collectively define the network of pathways for the rainfall anomaly in the Sahel. Experimental results are consistent with fundamental theories of phenomena in climate science, especially physical processes that best describe sub-regional climate.
DA - 2013///
PY - 2013///
DO - 10.1109/icdm.2013.142
SP - 1055-1060
SN - 1550-4786
KW - association rules
KW - climate
KW - data coupling
KW - discovery
ER -
TY - JOUR
TI - Exploring accurate Poisson-Boltzmann methods for biomolecular simulations
AU - Wang, Changhao
AU - Wang, Jun
AU - Cai, Qin
AU - Li, Zhilin
AU - Zhao, Hong-Kai
AU - Luo, Ray
T2 - COMPUTATIONAL AND THEORETICAL CHEMISTRY
AB - Accurate and efficient treatment of electrostatics is a crucial step in computational analyses of biomolecular structures and dynamics. In this study, we have explored a second-order finite-difference numerical method to solve the widely used Poisson–Boltzmann equation for electrostatic analyses of realistic biomolecules. The so-called immersed interface method was first validated and found to be consistent with the classical weighted harmonic averaging method for a diversified set of test biomolecules. The numerical accuracy and convergence behaviors of the new method were next analyzed in its computation of numerical reaction field grid potentials, energies, and atomic solvation forces. Overall similar convergence behaviors were observed as those by the classical method. Interestingly, the new method was found to deliver more accurate and better-converged grid potentials than the classical method on or nearby the molecular surface, though the numerical advantage of the new method is reduced when grid potentials are extrapolated to the molecular surface. Our exploratory study indicates the need for further improving interpolation/extrapolation schemes in addition to the developments of higher-order numerical methods that have attracted most attention in the field.
DA - 2013/11/15/
PY - 2013/11/15/
DO - 10.1016/j.comptc.2013.09.021
VL - 1024
SP - 34-44
SN - 1872-7999
KW - Poisson-Boltzmann equation
KW - Finite difference method
KW - Immersed interface method
KW - Continuum solvent models
ER -
TY - JOUR
TI - A FRATTINI THEORY FOR LEIBNIZ ALGEBRAS
AU - Batten, Chelsie
AU - Bosko-Dunbar, Lindsey
AU - Hedges, Allison
AU - Hird, J. T.
AU - Stagg, Kristen
AU - Stitzinger, Ernest
T2 - COMMUNICATIONS IN ALGEBRA
AB - A Frattini theory for non-associative algebras was developed in [13 Towers , D. ( 1973 ). A Frattini theory for algebras . Proc. London Math. Soc. 27 : 440 – 462 .[Crossref], [Web of Science ®] , [Google Scholar]] and results for particular classes of algebras have appeared in various articles. Especially plentiful are results on Lie algebras. It is the purpose of this paper to extend some of the Lie algebra results to Leibniz algebras.
DA - 2013/4/22/
PY - 2013/4/22/
DO - 10.1080/00927872.2011.643844
VL - 41
IS - 4
SP - 1547-1557
SN - 1532-4125
KW - Elementary
KW - Frattini
KW - Leibniz
KW - Lie
ER -
TY - JOUR
TI - 'Mountain Vineyard' hybrid grape tomato and its parents: NC 4 Grape and NC 5 Grape tomato breeding lines
AU - Panthee, D. R.
AU - Gardner, R. G.
T2 - HortScience
DA - 2013///
PY - 2013///
VL - 48
IS - 9
SP - 1189-1191
ER -
TY - JOUR
TI - 'Mountain Honey' hybrid grape tomato and its parent NC 6 Grape breeding line
AU - Panthee, D. R.
AU - Gardner, R. G.
T2 - HortScience
DA - 2013///
PY - 2013///
VL - 48
IS - 9
SP - 1192-1194
ER -
TY - JOUR
TI - Scalable Hybrid Deterministic/Monte Carlo Neutronics Simulations in Two Space Dimensions
AU - Willert, Jeffrey
AU - Kelley, C. T.
AU - Knoll, D. A.
AU - Park, H.
T2 - 2013 12TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING AND APPLICATIONS TO BUSINESS, ENGINEERING & SCIENCE (DCABES)
AB - In this paper we discuss a parallel hybrid deterministic/Monte Carlo (MC) method for the solution of the neutron transport equation in two space dimensions. The algorithm uses an NDA formulation of the transport equation, with a MC solver for the high-order equation. The scalability arises from the concentration of work in the MC phase of the algorithm, while the overall run-time is a consequence of the deterministic phase.
DA - 2013///
PY - 2013///
DO - 10.1109/dcabes.2013.8
SP - 7-10
KW - Neutron Transport
KW - Jacobian-Free Newton-Krylov
KW - NDA
KW - Monte Carlo
ER -
TY - JOUR
TI - Modeling the Dynamics of a Non-Limited and a Self-Limited Gene Drive System in Structured Aedes aegypti Populations
AU - Legros, Mathieu
AU - Xu, Chonggang
AU - Morrison, Amy
AU - Scott, Thomas W.
AU - Lloyd, Alun L.
AU - Gould, Fred
T2 - PLoS ONE
AB - Recently there have been significant advances in research on genetic strategies to control populations of disease-vectoring insects. Some of these strategies use the gene drive properties of selfish genetic elements to spread physically linked anti-pathogen genes into local vector populations. Because of the potential of these selfish elements to spread through populations, control approaches based on these strategies must be carefully evaluated to ensure a balance between the desirable spread of the refractoriness-conferring genetic cargo and the avoidance of potentially unwanted outcomes such as spread to non-target populations. There is also a need to develop better estimates of the economics of such releases. We present here an evaluation of two such strategies using a biologically realistic mathematical model that simulates the resident Aedes aegypti mosquito population of Iquitos, Peru. One strategy uses the selfish element Medea, a non-limited element that could permanently spread over a large geographic area; the other strategy relies on Killer-Rescue genetic constructs, and has been predicted to have limited spatial and temporal spread. We simulate various operational approaches for deploying these genetic strategies, and quantify the optimal number of released transgenic mosquitoes needed to achieve definitive spread of Medea-linked genes and/or high frequencies of Killer-Rescue-associated elements. We show that for both strategies the most efficient approach for achieving spread of anti-pathogen genes within three years is generally to release adults of both sexes in multiple releases over time. Even though females in these releases should not transmit disease, there could be public concern over such releases, making the less efficient male-only release more practical. This study provides guidelines for operational approaches to population replacement genetic strategies, as well as illustrates the use of detailed spatial models to assist in safe and efficient implementation of such novel genetic strategies.
DA - 2013/12/10/
PY - 2013/12/10/
DO - 10.1371/journal.pone.0083354
VL - 8
IS - 12
SP - e83354
J2 - PLoS ONE
LA - en
OP -
SN - 1932-6203
UR - http://dx.doi.org/10.1371/journal.pone.0083354
DB - Crossref
ER -
TY - JOUR
TI - Eigenvalue placement in completions of DAES
AU - Campbell, Stephen L.
AU - Holte, Lise E.
T2 - Electronic Journal of Linear Algebra
AB - Differential algebraic equations (DAEs) are used to describe many physical processes. A completion of a DAE is an ordinary differential equation whose solutions include those of the DAE. Algorithms exists for designing stabilized completions of differential algebraic equations. Recent work on observers for DAEs has shown the need for more information on, and control of the placement of, the additional eigenvalues of the completion. This paper investigates this eigenvalue placement problem. Results are given relating the additional eigenvalues of the completion and the choice of stabilization matrix for certain important classes of linear DAEs.
DA - 2013/1/1/
PY - 2013/1/1/
DO - 10.13001/1081-3810.1667
VL - 26
IS - 1
SP - 520–534
ER -
TY - JOUR
TI - ENUMERATING QUASIPLATONIC CYCLIC GROUP ACTIONS
AU - Benim, Robert
AU - Wootton, Aaron
T2 - ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
AB - It is an open problem to determine the number of topologically distinct ways that a finite group can act upon a compact oriented surface X of genus g(X) 2 2. We provide an explicit answer to this problem for special classes of cyclic groups and illustrate our results with detailed examples.
DA - 2013///
PY - 2013///
DO - 10.1216/rmj-2013-43-5-1459
VL - 43
IS - 5
SP - 1459-1480
SN - 1945-3795
ER -
TY - JOUR
TI - Capillary fracture of soft gels
AU - Bostwick, Joshua B.
AU - Daniels, Karen E.
T2 - PHYSICAL REVIEW E
AB - A liquid droplet resting on a soft gel substrate can deform that substrate to the point of material failure, whereby fractures develop on the gel surface that propagate outwards from the contact line in a starburst pattern. In this paper, we characterize (i) the initiation process, in which the number of arms in the starburst is controlled by the ratio of the surface tension contrast to the gel's elastic modulus, and (ii) the propagation dynamics showing that once fractures are initiated they propagate with a universal power law $L\ensuremath{\propto}{t}^{3/4}$. We develop a model for crack initiation by treating the gel as a linear elastic solid and computing the deformations within the substrate from the liquid-solid wetting forces. The elastic solution shows that both the location and the magnitude of the wetting forces are critical in providing a quantitative prediction for the number of fractures and, hence, an interpretation of the initiation of capillary fractures. This solution also reveals that the depth of the gel is an important factor in the fracture process, as it can help mitigate large surface tractions; this finding is confirmed with experiments. We then develop a model for crack propagation by considering the transport of an inviscid fluid into the fracture tip of an incompressible material and find that a simple energy-conservation argument can explain the observed material-independent power law. We compare predictions for both linear elastic and neo-Hookean solids, finding that the latter better explains the observed exponent.
DA - 2013/10/28/
PY - 2013/10/28/
DO - 10.1103/physreve.88.042410
VL - 88
IS - 4
SP -
SN - 1550-2376
ER -
TY - JOUR
TI - A novel statistical analysis and interpretation of flow cytometry data
AU - Banks, H. T.
AU - Kapraun, D. F.
AU - Thompson, W. Clayton
AU - Peligero, Cristina
AU - Argilaguet, Jordi
AU - Meyerhans, Andreas
T2 - JOURNAL OF BIOLOGICAL DYNAMICS
AB - A recently developed class of models incorporating the cyton model of population generation structure into a conservation-based model of intracellular label dynamics is reviewed. Statistical aspects of the data collection process are quantified and incorporated into a parameter estimation scheme. This scheme is then applied to experimental data for PHA-stimulated CD4+T and CD8+T cells collected from two healthy donors. This novel mathematical and statistical framework is shown to form the basis for accurate, meaningful analysis of cellular behaviour for a population of cells labelled with the dye carboxyfluorescein succinimidyl ester and stimulated to divide.
DA - 2013/12/1/
PY - 2013/12/1/
DO - 10.1080/17513758.2013.812753
VL - 7
IS - 1
SP - 96-132
SN - 1751-3766
KW - immunology
KW - flow cytometry
KW - cyton models
KW - mathematical and statistical models
KW - label dynamics
KW - parameter estimation
KW - cellular models
ER -
TY - JOUR
TI - A note on state decomposition independent local invariants
AU - Zhang, Ting-Gui
AU - Jing, Naihuan
AU - Li-Jost, Xianqing
AU - Zhao, Ming-Jing
AU - Fei, Shao-Ming
T2 - EUROPEAN PHYSICAL JOURNAL D
AB - We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum state. They also give rise to necessary conditions for the equivalence of quantum states under local unitary transformations.
DA - 2013/8/6/
PY - 2013/8/6/
DO - 10.1140/epjd/e2013-40068-7
VL - 67
IS - 8
SP -
SN - 1434-6079
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84887595495&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Viral Substitution Rate Variation Can Arise from the Interplay between Within-Host and Epidemiological Dynamics
AU - Scholle, Stacy O.
AU - Ypma, Rolf J. F.
AU - Lloyd, Alun L.
AU - Koelle, Katia
T2 - AMERICAN NATURALIST
AB - The evolutionary rates of RNA viruses can differ from one another by several orders of magnitude. Much of this variation has been explained by differences in viral mutation rates and selective environments. However, substitution rates also vary considerably across viral populations belonging to the same species. In particular, viral lineages from epidemic regions tend to have higher substitution rates than those from endemic regions, and lineages from populations with higher contact rates tend to have higher substitution rates than those from populations with lower contact rates. We address the mechanism behind these patterns by using a nested modeling approach, whereby we integrate within-host viral replication dynamics with a population-level epidemiological model. Through numerical simulations and analytical approximations, we show that variation in viral substitution rates over the course of an infection, coupled with differences in age of infection of transmitting hosts under different epidemiological scenarios, can explain these evolutionary patterns. We further derive analytical estimates of expected substitution rate differences under epidemic versus endemic epidemiological conditions. By comparing these estimates to empirical data for four viral species, we show that these factors are sufficient to explain observed variation in substitution rates in three of four cases. This work shows that even in neutrally evolving viral populations, epidemiological dynamics can alter substitution rates via the interplay between within-host replication dynamics and population-level disease dynamics.
DA - 2013/10/1/
PY - 2013/10/1/
DO - 10.1086/672000
VL - 182
IS - 4
SP - 494-513
SN - 1537-5323
KW - substitution rate variation
KW - RNA virus evolution
KW - within-host dynamics
KW - epidemiological model
KW - disease dynamics
ER -
TY - JOUR
TI - Potential energy landscapes for the 2D XY model: Minima, transition states, and pathways
AU - Mehta, Dhagash
AU - Hughes, Ciaran
AU - Schroeck, Mario
AU - Wales, David J.
T2 - JOURNAL OF CHEMICAL PHYSICS
AB - We describe a numerical study of the potential energy landscape for the two-dimensional XY model (with no disorder), considering up to 100 spins and central processing unit and graphics processing unit implementations of local optimization, focusing on minima and saddles of index one (transition states). We examine both periodic and anti-periodic boundary conditions, and show that the number of stationary points located increases exponentially with increasing lattice size. The corresponding disconnectivity graphs exhibit funneled landscapes; the global minima are readily located because they exhibit relatively large basins of attraction compared to the higher energy minima as the lattice size increases.
DA - 2013/11/21/
PY - 2013/11/21/
DO - 10.1063/1.4830400
VL - 139
IS - 19
SP -
SN - 1089-7690
ER -
TY - JOUR
TI - On the Matrix Berlekamp-Massey Algorithm
AU - Kaltofen, Erich
AU - Yuhasz, George
T2 - ACM TRANSACTIONS ON ALGORITHMS
AB - We analyze the Matrix Berlekamp/Massey algorithm, which generalizes the Berlekamp/Massey algorithm [Massey 1969] for computing linear generators of scalar sequences. The Matrix Berlekamp/Massey algorithm computes a minimal matrix generator of a linearly generated matrix sequence and has been first introduced by Rissanen [1972a], Dickinson et al. [1974], and Coppersmith [1994]. Our version of the algorithm makes no restrictions on the rank and dimensions of the matrix sequence. We also give new proofs of correctness and complexity for the algorithm, which is based on self-contained loop invariants and includes an explicit termination criterion for a given determinantal degree bound of the minimal matrix generator.
DA - 2013/9//
PY - 2013/9//
DO - 10.1145/2500122
VL - 9
IS - 4
SP -
SN - 1549-6333
KW - Linear generated sequences
KW - matrix polynomials
KW - minimal generators
KW - vector Berlekamp/Massey algorithm
KW - multivariable linear control
ER -
TY - JOUR
TI - Modeling the Afferent Dynamics of the Baroreflex Control System
AU - Mahdi, Adam
AU - Sturdy, Jacob
AU - Ottesen, Johnny T.
AU - Olufsen, Mette S.
T2 - PLoS Computational Biology
AB - In this study we develop a modeling framework for predicting baroreceptor firing rate as a function of blood pressure. We test models within this framework both quantitatively and qualitatively using data from rats. The models describe three components: arterial wall deformation, stimulation of mechanoreceptors located in the BR nerve-endings, and modulation of the action potential frequency. The three sub-systems are modeled individually following well-established biological principles. The first submodel, predicting arterial wall deformation, uses blood pressure as an input and outputs circumferential strain. The mechanoreceptor stimulation model, uses circumferential strain as an input, predicting receptor deformation as an output. Finally, the neural model takes receptor deformation as an input predicting the BR firing rate as an output. Our results show that nonlinear dependence of firing rate on pressure can be accounted for by taking into account the nonlinear elastic properties of the artery wall. This was observed when testing the models using multiple experiments with a single set of parameters. We find that to model the response to a square pressure stimulus, giving rise to post-excitatory depression, it is necessary to include an integrate-and-fire model, which allows the firing rate to cease when the stimulus falls below a given threshold. We show that our modeling framework in combination with sensitivity analysis and parameter estimation can be used to test and compare models. Finally, we demonstrate that our preferred model can exhibit all known dynamics and that it is advantageous to combine qualitative and quantitative analysis methods.
DA - 2013/12/12/
PY - 2013/12/12/
DO - 10.1371/journal.pcbi.1003384
VL - 9
IS - 12
SP - e1003384
J2 - PLoS Comput Biol
LA - en
OP -
SN - 1553-7358
UR - http://dx.doi.org/10.1371/journal.pcbi.1003384
DB - Crossref
ER -
TY - JOUR
TI - A framework for improving uniformity of parameterizations of curves
AU - Hong, Hoon
AU - DongMing, Wang
AU - Jing, Yang
T2 - SCIENCE CHINA-INFORMATION SCIENCES
DA - 2013/10//
PY - 2013/10//
DO - 10.1007/s11432-013-4924-4
VL - 56
IS - 10
SP -
SN - 1869-1919
UR - http://dx.doi.org/10.1007/s11432-013-4924-4
KW - parametric curve
KW - framework
KW - quasi-speed
KW - uniform parameterization
KW - uniformity-improved reparameterization
KW - optimal Mobius transformation
ER -
TY - JOUR
TI - Three-Layer Approximation of Two-Layer Shallow Water Equations
AU - Chertock, Alina
AU - Kurganov, Alexander
AU - Qu, Zhuolin
AU - Wu, Tong
T2 - MATHEMATICAL MODELLING AND ANALYSIS
AB - Two-layer shallow water equations describe flows that consist of two layers of inviscid fluid of different (constant) densities flowing over bottom topography. Unlike the single-layer shallow water system, the two-layer one is only conditionally hyperbolic: the system loses its hyperbolicity because of the momentum exchange terms between the layers and as a result its solutions may develop instabilities. We study a three-layer approximation of the two-layer shallow water equations by introducing an intermediate layer of a small depth. We examine the hyperbolicity range of the three-layer model and demonstrate that while it still may lose hyperbolicity, the three-layer approximation may improve stability properties of the two-layer shallow water system.
DA - 2013///
PY - 2013///
DO - 10.3846/13926292.2013.869269
VL - 18
IS - 5
SP - 675-693
SN - 1648-3510
UR - https://doi-org.prox.lib.ncsu.edu/10.3846/13926292.2013.869269
KW - two-layer shallow water equations
KW - central-upwind scheme
KW - well-balanced scheme
KW - conditional hyperbolicity
ER -
TY - JOUR
TI - Stability of Traveling Waves in Partly Parabolic Systems
AU - Ghazaryan, A.
AU - Latushkin, Y.
AU - Schecter, S.
T2 - MATHEMATICAL MODELLING OF NATURAL PHENOMENA
AB - We review recent results on stability of traveling waves in partly parabolic reaction-diffusion systems with stable or marginally stable equilibria. We explain how attention to what are apparently mathematical technicalities has led to theorems that allow one to convert spectral calculations, which are used in the sciences and engineering to study stability of a wave, into detailed, theoretically-based information about the behavior of perturbations of the wave.
DA - 2013///
PY - 2013///
DO - 10.1051/mmnp/20138503
VL - 8
IS - 5
SP - 31-47
SN - 1760-6101
KW - traveling wave
KW - spectral stability
KW - linear stability
KW - nonlinear stability
KW - exponential weights
ER -
TY - JOUR
TI - PROJECTIVE ISOMONODROMY AND GALOIS GROUPS
AU - Mitschi, Claude
AU - Singer, Michael F.
T2 - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
AB - In this article we introduce the notion of projective isomonodromy, which is a special type of monodromy-evolving deformation of linear differential equations, based on the example of the Darboux-Halphen equation. We give an algebraic condition for a parameterized linear differential equation to be projectively isomonodromic, in terms of the derived group of its parameterized Picard-Vessiot group.
DA - 2013/2//
PY - 2013/2//
DO - 10.1090/s0002-9939-2012-11499-6
VL - 141
IS - 2
SP - 605-617
SN - 1088-6826
ER -
TY - JOUR
TI - Markov processes with redistribution
AU - Grigorescu, I.
AU - Kang, M.
T2 - Markov Processes and Related Fields
DA - 2013///
PY - 2013///
VL - 19
IS - 3
SP - 497-520
ER -
TY - JOUR
TI - Equations for Lower Bounds on Border Rank
AU - Hauenstein, Jonathan D.
AU - Ikenmeyer, Christian
AU - Landsberg, J. M.
T2 - EXPERIMENTAL MATHEMATICS
AB - We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r=6 in the space of bilinear maps . This space of bilinear maps includes the matrix multiplication operator M 2 for 2×2 matrices. We show that these newly obtained polynomials do not vanish on the matrix multiplication operator M 2, which gives a new proof that the border rank of the multiplication of 2×2 matrices is seven. Other examples are considered along with an explanation of how to implement the methods.
DA - 2013/10/2/
PY - 2013/10/2/
DO - 10.1080/10586458.2013.825892
VL - 22
IS - 4
SP - 372-383
SN - 1944-950X
KW - border rank
KW - matrix multiplication
ER -
TY - JOUR
TI - Comparison of an l(1)-regression-based and a RANSAC-based Planar Segmentation Procedure for Urban Terrain Data with Many Outliers
AU - Luo, Jian
AU - Deng, Zhibin
AU - Bulatov, Dimitri
AU - Lavery, John E.
AU - Fang, Shu-Cherng
T2 - IMAGE AND SIGNAL PROCESSING FOR REMOTE SENSING XIX
AB - For urban terrain data with many outliers, we compare an l 1- regression-based and a RANSAC-based planar
segmentation procedure. The procedure consists of 1) calculating the normal at each of the points using l 1
regression or RANSAC, 2) clustering the normals thus generated using DBSCAN or fuzzy c-means, 3) within
each cluster, identifying segments (roofs, walls, ground) by DBSCAN-based-subclustering of the 3D points that
correspond to each cluster of normals and 4) fitting the subclusters by the same method as that used in Step 1
(l 1 regression or RANSAC). Domain decomposition is used to handle data sets that are too large for processing
as a whole. Computational results for a point cloud of a building complex in Bonnland, Germany obtained
from a depth map of seven UAV-images are presented. The l 1- regression-based procedure is slightly over 25%
faster than the RANSAC-based procedure and produces better dominant roof segments. However, the roof
polygonalizations and cutlines based on these dominant segments are roughly equal in accuracy for the two
procedures. For a set of artificial data, l 1 regression is much more accurate and much faster than RANSAC. We
outline the complete building reconstruction procedure into which the l 1 -regression-based and RANSAC-based
segmentation procedures will be integrated in the future.
DA - 2013///
PY - 2013///
DO - 10.1117/12.2028627
VL - 8892
SP -
SN - 1996-756X
KW - DBSCAN
KW - fuzzy c-means
KW - l(1) regression
KW - outlier-rich
KW - planar
KW - RANSAC
KW - segmentation
KW - urban terrain
ER -
TY - JOUR
TI - A Reduce and Replace Strategy for Suppressing Vector-Borne Diseases: Insights from a Stochastic, Spatial Model
AU - Okamoto, Kenichi W.
AU - Robert, Michael A.
AU - Lloyd, Alun L.
AU - Gould, Fred
T2 - PLOS ONE
AB - Two basic strategies have been proposed for using transgenic Aedes aegypti mosquitoes to decrease dengue virus transmission: population reduction and population replacement. Here we model releases of a strain of Ae. aegypti carrying both a gene causing conditional adult female mortality and a gene blocking virus transmission into a wild population to assess whether such releases could reduce the number of competent vectors. We find this "reduce and replace" strategy can decrease the frequency of competent vectors below 50% two years after releases end. Therefore, this combined approach appears preferable to releasing a strain carrying only a female-killing gene, which is likely to merely result in temporary population suppression. However, the fixation of anti-pathogen genes in the population is unlikely. Genetic drift at small population sizes and the spatially heterogeneous nature of the population recovery after releases end prevent complete replacement of the competent vector population. Furthermore, releasing more individuals can be counter-productive in the face of immigration by wild-type mosquitoes, as greater population reduction amplifies the impact wild-type migrants have on the long-term frequency of the anti-pathogen gene. We expect the results presented here to give pause to expectations for driving an anti-pathogen construct to fixation by relying on releasing individuals carrying this two-gene construct. Nevertheless, in some dengue-endemic environments, a spatially heterogeneous decrease in competent vectors may still facilitate decreasing disease incidence.
DA - 2013/12/20/
PY - 2013/12/20/
DO - 10.1371/journal.pone.0081860
VL - 8
IS - 12
SP -
SN - 1932-6203
ER -
TY - JOUR
TI - W-constraints for the total descendant potential of a simple singularity
AU - Bakalov, Bojko
AU - Milanov, Todor
T2 - COMPOSITIO MATHEMATICA
AB - Abstract Simple, or Kleinian, singularities are classified by Dynkin diagrams of type $ADE$ . Let $\mathfrak {g}$ be the corresponding finite-dimensional Lie algebra, and $W$ its Weyl group. The set of $\mathfrak {g}$ -invariants in the basic representation of the affine Kac–Moody algebra $\hat {\mathfrak {g}}$ is known as a $\mathcal {W}$ -algebra and is a subalgebra of the Heisenberg vertex algebra $\mathcal {F}$ . Using period integrals, we construct an analytic continuation of the twisted representation of $\mathcal {F}$ . Our construction yields a global object, which may be called a $W$ -twisted representation of $\mathcal {F}$ . Our main result is that the total descendant potential of the singularity, introduced by Givental, is a highest-weight vector for the $\mathcal {W}$ -algebra.
DA - 2013/5//
PY - 2013/5//
DO - 10.1112/s0010437x12000668
VL - 149
IS - 5
SP - 840-888
SN - 1570-5846
KW - Frobenius manifold
KW - simple singularity
KW - total descendant potential
KW - vertex algebra
KW - W-algebra
ER -
TY - JOUR
TI - Separable State Decompositions for a Class of Mixed States
AU - Zhang, Ting-Gui
AU - Huang, Xiaofen
AU - Li-Jost, Xianqing
AU - Jing, Naihuan
AU - Fei, Shao-Ming
T2 - INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
AB - We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of n×n bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable pure state decompositions of these states are explicitly constructed when they are PPT.
DA - 2013/11//
PY - 2013/11//
DO - 10.1007/s10773-013-1727-8
VL - 52
IS - 11
SP - 4148-4154
SN - 1572-9575
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84884908137&partnerID=MN8TOARS
KW - Quantum state
KW - PPT
KW - Separability
ER -
TY - JOUR
TI - Quantification of parameter uncertainty for robust control of shape memory alloy bending actuators
AU - Crews, John H.
AU - McMahan, Jerry A.
AU - Smith, Ralph C.
AU - Hannen, Jennifer C.
T2 - SMART MATERIALS AND STRUCTURES
AB - In this paper, we employ Bayesian parameter estimation techniques to derive gains for robust control of smart materials. Specifically, we demonstrate the feasibility of utilizing parameter uncertainty estimation provided by Markov chain Monte Carlo (MCMC) methods to determine controller gains for a shape memory alloy bending actuator. We treat the parameters in the equations governing the actuator's temperature dynamics as uncertain and use the MCMC method to construct the probability densities for these parameters. The densities are then used to derive parameter bounds for robust control algorithms. For illustrative purposes, we construct a sliding mode controller based on the homogenized energy model and experimentally compare its performance to a proportional-integral controller. While sliding mode control is used here, the techniques described in this paper provide a useful starting point for many robust control algorithms.
DA - 2013/11//
PY - 2013/11//
DO - 10.1088/0964-1726/22/11/115021
VL - 22
IS - 11
SP -
SN - 1361-665X
ER -
TY - JOUR
TI - On a coupled system of reaction-diffusion-transport equations arising from catalytic converter
AU - Pao, C. V.
AU - Chang, Yu-Hsien
AU - Jau, Guo-Chin
T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
AB - Abstract This paper is concerned with two mathematical models which describe the transient behavior of a catalytic converter in automobile engineering. The first model consists of a coupled system of a heat-conduction equation and two integral equations while the second model involves only one integral equation. It is shown that for any nonnegative initial and boundary functions the three-equation model has a unique bounded global solution while the solution of the two-equation model blows up in finite time. The proof for the global existence and finite-time blow-up property of the solution is by the method of upper and lower solutions and its associated monotone iteration. This method can be used to develop computational algorithms for numerical solutions of the coupled systems.
DA - 2013/12//
PY - 2013/12//
DO - 10.1016/j.nonrwa.2013.04.004
VL - 14
IS - 6
SP - 2152-2165
SN - 1468-1218
ER -
TY - JOUR
TI - Numerical elimination and moduli space of vacua
AU - Hauenstein, Jonathan
AU - He, Yang-Hui
AU - Mehta, Dhagash
T2 - JOURNAL OF HIGH ENERGY PHYSICS
AB - We propose a new computational method to understand the vacuum moduli space of (supersymmetric) field theories. By combining numerical algebraic geometry (NAG) and elimination theory, we develop a powerful, efficient, and parallelizable algorithm to extract important information such as the dimension, branch structure, Hilbert series and subsequent operator counting, as well as variation according to coupling constants and mass parameters. We illustrate this method on a host of examples from gauge theory, string theory, and algebraic geometry.
DA - 2013/9/16/
PY - 2013/9/16/
DO - 10.1007/jhep09(2013)083
IS - 9
SP -
SN - 1029-8479
KW - Supersymmetric gauge theory
KW - Differential and Algebraic Geometry
KW - Super-string Vacua
KW - Solitons Monopoles and Instantons
ER -
TY - JOUR
TI - HYBRID DETERMINISTIC/MONTE CARLO NEUTRONICS
AU - Willert, Jeffrey
AU - Kelley, C. T.
AU - Knoll, D. A.
AU - Park, H.
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - In this paper we describe a hybrid deterministic/Monte Carlo algorithm for neutron transport simulation. The algorithm is based on nonlinear accelerators for source iteration, using Monte Carlo methods for the purely absorbing high-order problem and a Jacobian-free Newton--Krylov iteration for the low-order problem. We couple the Monte Carlo solution with the low-order problem using filtering to smooth the flux and current from the Monte Carlo solver and an analytic Jacobian-vector product to avoid numerical differentiation of the Monte Carlo results. We use a continuous energy deposition tally for the Monte Carlo simulation. We conclude the paper with numerical results which illustrate the effectiveness of the new algorithm.
DA - 2013///
PY - 2013///
DO - 10.1137/120880021
VL - 35
IS - 5
SP - S62-S83
SN - 1095-7197
KW - JFNK methods
KW - neutron transport
KW - Monte Carlo simulation
KW - hybrid methods
ER -
TY - JOUR
TI - Generalized McKay quivers of rank three
AU - Hu, Xiao Li
AU - Jing, Naihuan
AU - Cai, Wu Xing
T2 - ACTA MATHEMATICA SINICA-ENGLISH SERIES
AB - For each finite subgroup G of SL(n, C), we introduce the generalized Cartan matrix C_{G} in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semi-definiteness as in the classical case of affine Cartan matrices (the case of SL(2,C)). The complete McKay quivers for SL(3,C) are explicitly described and classified based on representation theory.
DA - 2013/7//
PY - 2013/7//
DO - 10.1007/s10114-013-1005-y
VL - 29
IS - 7
SP - 1351-1368
SN - 1439-7617
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84879197022&partnerID=MN8TOARS
KW - McKay correspondence
KW - McKay quivers
KW - generalized Dynkin diagrams
ER -
TY - JOUR
TI - GASLESS COMBUSTION FRONTS WITH HEAT LOSS
AU - Ghazaryan, Anna
AU - Schecter, Stephen
AU - Simon, Peter L.
T2 - SIAM JOURNAL ON APPLIED MATHEMATICS
AB - For a model of gasless combustion with heat loss, we use geometric singular perturbation theory to show existence of traveling combustion fronts. We show that the fronts are nonlinearly stable in an appropriate sense if an Evans function criterion, which can be verified numerically, is satisfied. For a solid reactant and exothermicity parameter that is not too large, we verify numerically that the criterion is satisfied.
DA - 2013///
PY - 2013///
DO - 10.1137/110854540
VL - 73
IS - 3
SP - 1303-1326
SN - 0036-1399
KW - geometric singular perturbation theory
KW - traveling wave
KW - Evans function
KW - stability
ER -
TY - JOUR
TI - Fermionic shock waves: Distinguishing dissipative versus dispersive regularizations
AU - Lowman, N. K.
AU - Hoefer, M. A.
T2 - PHYSICAL REVIEW A
AB - The collision of two clouds of Fermi gas at unitarity (UFG) has been recently observed to lead to shock waves whose regularization mechanism, dissipative or dispersive, is being debated. While classical, dissipative shocks, as in gas dynamics, develop a steep, localized shock front that translates at a well-defined speed, dispersively regularized shocks are distinguished by an expanding region of short wavelength oscillations with two speeds, those of the leading and trailing edges. For typical UFG experimental conditions, the theoretical oscillation length scale is smaller than the resolution of present imaging systems so it is unclear how to determine the shock type from its structure alone. Two experimental methods to determine the appropriate regularization mechanism are proposed: measurement of the shock speed and observation of a one-dimensional collision experiment with sufficiently tight radial confinement.
DA - 2013/7/3/
PY - 2013/7/3/
DO - 10.1103/physreva.88.013605
VL - 88
IS - 1
SP -
SN - 1094-1622
ER -
TY - JOUR
TI - Effects of Dietary Chromium Methionine on Growth Performance, Carcass Composition, Meat Colour and Expression of the Colour-related Gene Myoglobin of Growing-finishing Pigs
AU - Li, Y. S.
AU - Zhu, N. H.
AU - Niu, P. P.
AU - Shi, F. X.
AU - Hughes, C. L.
AU - Tian, G. X.
AU - Huang, R. H.
T2 - ASIAN-AUSTRALASIAN JOURNAL OF ANIMAL SCIENCES
AB - To investigate the effect of dietary chromium (Cr) as Cr methionine (CrMet) on growth performance, carcass traits, pork quality, meat colour and expression of meat colour-related genes in growing-finishing pigs, 189 crossbred Duroc×(Landrace×Yorkshire) growing-finishing pigs (male, castrated, average initial BW 74.58±1.52 kg) were selected and randomly allocated into four groups. Dietary treatments per kg of feed were as follows: 0 (CT), 0.3 mg/kg (T1), 0.6 mg/kg (T2) and 0.9 mg/kg (T3) Cr (in the form of CrMet; as-fed basis), and each treatment was replicated five times with 8 to 10 pigs per replicate pen. During the 28 d of the experiment, both the ADG and the ADFI increased linearly (p<0.05) as the level of dietary Cr increased. The F/G ratio decreased linearly (p<0.05). As dietary Cr increased, loin muscle areas (linear, p = 0.013) and average backfat thickness (linear, p = 0.072) decreased. Shear force (linear, p = 0.070) and Commission Internationale de I'Éclairage (CIE) redness (quadratic, p = 0.028) were increased. In addition, CIE Lightness (quadratic, p = 0.053) were decreased as dietary Cr increased. As dietary Cr increased, total myglobin (Mb) content (quadratic, p = 0.015) and the mb mRNA levels (quadratic, p = 0.046) in longissimus muscles of pigs were up-regulated. In conclusion, supplementation of dietary Cr improved growth and meat colour, but increased shear force and decreased IMF reduced palatability of longissimus muscles. Moreover, the increasing total Mb content and mb mRNA levels indicated that CrMet dietary supplementation may improve meat colour via up-regulating expression of the mb gene.
DA - 2013/7//
PY - 2013/7//
DO - 10.5713/ajas.2013.13012
VL - 26
IS - 7
SP - 1021-1029
SN - 1976-5517
KW - Growing-finishing Pigs
KW - Chromium Methionine
KW - Meat Colour
KW - Myoglobin
ER -
TY - JOUR
TI - Discovery of extreme events-related communities in contrasting groups of physical system networks
AU - Chen, Zhengzhang
AU - Hendrix, William
AU - Guan, Hang
AU - Tetteh, Isaac K.
AU - Choudhary, Alok
AU - Semazzi, Fredrick
AU - Samatova, Nagiza F.
T2 - DATA MINING AND KNOWLEDGE DISCOVERY
AB - The latent behavior of a physical system that can exhibit extreme events such as hurricanes or rainfalls, is complex. Recently, a very promising means for studying complex systems has emerged through the concept of complex networks. Networks representing relationships between individual objects usually exhibit community dynamics. Conventional community detection methods mainly focus on either mining frequent subgraphs in a network or detecting stable communities in time-varying networks. In this paper, we formulate a novel problem—detection of predictive and phase-biased communities in contrasting groups of networks, and propose an efficient and effective machine learning solution for finding such anomalous communities. We build different groups of networks corresponding to different system’s phases, such as higher or low hurricane activity, discover phase-related system components as seeds to help bound the search space of community generation in each network, and use the proposed contrast-based technique to identify the changing communities across different groups. The detected anomalous communities are hypothesized (1) to play an important role in defining the target system’s state(s) and (2) to improve the predictive skill of the system’s states when used collectively in the ensemble of predictive models. When tested on the two important extreme event problems—identification of tropical cyclone-related and of African Sahel rainfall-related climate indices—our algorithm demonstrated the superior performance in terms of various skill and robustness metrics, including 8–16 % accuracy increase, as well as physical interpretability of detected communities. The experimental results also show the efficiency of our algorithm on synthetic datasets.
DA - 2013/9//
PY - 2013/9//
DO - 10.1007/s10618-012-0289-3
VL - 27
IS - 2
SP - 225-258
SN - 1573-756X
KW - Spatio-temporal data mining
KW - Complex network analysis
KW - Community detection
KW - Comparative analysis
KW - Networkmotif detection
KW - Extreme event prediction
ER -
TY - JOUR
TI - Analytical theory of modulated magnetic solitons
AU - Bookman, L. D.
AU - Hoefer, M. A.
T2 - PHYSICAL REVIEW B
AB - Droplet solitons are coherently precessing solitary waves that have been recently realized in thin ferromagnets with perpendicular anisotropy.In the strongly nonlinear regime, droplets can be well approximated by a slowly precessing, circular domain wall with a hyperbolic tangent form. Utilizing this representation, this work develops a general droplet modulation theory and applies it to study the long range effects of the magnetostatic field and a nanocontact spin torque oscillator (NC-STO) where spin polarized currents act as a gain source to counteract magnetic damping. An analysis of the dynamical equations for the droplet's center, frequency and phase demonstrates a negative processional frequency shift due to long range dipolar interactions, dependent on film thickness. Further analysis also demonstrates the onset of a saddle-node bifurcation at the minimum sustaining current for the NC-STO. The basin of attraction associated with the stable node demonstrates that spin torque enacts a restoring force to excursions of the droplet from the nanocontact center, observed previously in numerical simulations. Large excursions lead to the droplet's eventual decay into spin waves.
DA - 2013/11/4/
PY - 2013/11/4/
DO - 10.1103/physrevb.88.184401
VL - 88
IS - 18
SP -
SN - 1550-235X
ER -
TY - JOUR
TI - Adaptive mesh refinement techniques for the immersed interface method applied to flow problems
AU - Li, Zhilin
AU - Song, Peng
T2 - COMPUTERS & STRUCTURES
AB - In this paper, we develop an adaptive mesh refinement strategy of the Immersed Interface Method for flow problems with a moving interface. The work is built on the AMR method developed for two-dimensional elliptic interface problems in the paper [12] (CiCP, 12(2012), 515–527). The interface is captured by the zero level set of a Lipschitz continuous function φ(x, y, t). Our adaptive mesh refinement is built within a small band of ∣φ(x, y, t)∣ ⩽ δ with finer Cartesian meshes. The AMR-IIM is validated for Stokes and Navier–Stokes equations with exact solutions, moving interfaces driven by the surface tension, and classical bubble deformation problems. A new simple area preserving strategy is also proposed in this paper for the level set method.
DA - 2013/6//
PY - 2013/6//
DO - 10.1016/j.compstruc.2013.03.013
VL - 122
SP - 249-258
SN - 0045-7949
KW - Adaptive mesh refinement method
KW - Immersed interface method
KW - Stokes and Navier-Stokes equations
KW - Surface tension
KW - Bubble deformation
KW - Level set method
ER -
TY - JOUR
TI - A NEW PHYSIOLOGICAL BOUNDARY CONDITION FOR HEMODYNAMICS
AU - Cousins, Will
AU - Gremaud, Pierre A.
AU - Tartakovsky, Daniel M.
T2 - SIAM JOURNAL ON APPLIED MATHEMATICS
AB - We propose a new physiologically-based outflow boundary condition for hemodynamics under general transient regimes. This is in contrast to previous studies that impose restrictions of temporal periodicity. The new condition is analyzed and its numerical implementation is discussed in detail. We show that existing impedance boundary conditions can be viewed as numerical approximations of the new condition. Our study provides a partial justification for using some of these existing conditions beyond the periodic problems for which they were designed. Moreover, the new condition has better stability properties. The theoretical results are illustrated by numerical experiments pertaining to cerebral blood flow.
DA - 2013///
PY - 2013///
DO - 10.1137/120895470
VL - 73
IS - 3
SP - 1203-1223
SN - 1095-712X
KW - hemodynamics
KW - network
KW - transport
KW - modeling
KW - boundary conditions
KW - numerics
ER -
TY - JOUR
TI - A High-Order Numerical Method for the Helmholtz Equation with Nonstandard Boundary Conditions
AU - Britt, D. S.
AU - Tsynkov, S. V.
AU - Turkel, E.
T2 - SIAM Journal on Scientific Computing
AB - We describe a high-order accurate methodology for the numerical simulation of time-harmonic waves governed by the Helmholtz equation. Our approach combines compact finite difference schemes that provide an inexpensive venue toward high-order accuracy with the method of difference potentials developed by Ryaben'kii. The latter can be interpreted as a generalized discrete version of the method of Calderon's operators in the theory of partial differential equations. The method of difference potentials can accommodate nonconforming boundaries on regular structured grids with no loss of accuracy due to staircasing. It introduces a universal framework for treating boundary conditions of any type. A significant advantage of this method is that changing the boundary condition within a fairly broad variety does not require any major changes to the algorithm and is computationally inexpensive. In this paper, we address various types of boundary conditions using the method of difference potentials. We demonstrate the resulting numerical capabilities by solving a range of nonstandard boundary value problems for the Helmholtz equation. These include problems with variable coefficient Robin boundary conditions (including discontinuous coefficients) and problems with mixed (Dirichlet/Neumann) boundary conditions. In all our simulations, we use a Cartesian grid and a circular boundary curve. For those test cases where the overall solution was smooth, our methodology has consistently demonstrated the design fourth-order rate of grid convergence, whereas when the regularity of the solution was not sufficient, the convergence slowed down, as expected. We also show that every additional boundary condition requires only an incremental additional expense.
DA - 2013/1//
PY - 2013/1//
DO - 10.1137/120902689
VL - 35
IS - 5
SP - A2255-A2292
J2 - SIAM J. Sci. Comput.
LA - en
OP -
SN - 1064-8275 1095-7197
UR - http://dx.doi.org/10.1137/120902689
DB - Crossref
KW - difference potentials
KW - boundary projections
KW - Calderon's operators
KW - regular grids
KW - curvilinear boundaries
KW - boundary value problems
KW - variable coefficients
KW - Robin boundary conditions
KW - mixed/piecewise boundary conditions
KW - compact differencing
KW - high-order accuracy
ER -
TY - JOUR
TI - A Bounded and Discretized Nelder-Mead Algorithm Suitable for RFIC Calibration
AU - Wyers, Eric J.
AU - Steer, Michael B.
AU - Kelley, C. T.
AU - Franzon, Paul D.
T2 - IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
AB - This paper describes a calibration technique for noisy and nonconvex circuit responses based on the Nelder-Mead direct search algorithm. As Nelder-Mead is intended for unconstrained optimization problems, we present an implementation of the algorithm which is suitable for bounded and discretized RFIC calibration problems. We apply the proposed algorithm to the problem of spurious tone reduction via VCO control line ripple minimization for a PLL operating at a frequency of 12 GHz. For this nonconvex calibration test case, we show that a gradient descent-based algorithm has difficulty in reducing the VCO control line ripple, while the proposed algorithm reduces the relative power of the first harmonic reference spurs by at least 10 dBc and effectively enables design complexity reduction in the supporting analog calibration circuitry.
DA - 2013/7//
PY - 2013/7//
DO - 10.1109/tcsi.2012.2230496
VL - 60
IS - 7
SP - 1787-1799
SN - 1558-0806
KW - Calibration
KW - derivative-free optimization
KW - Nelder-Mead direct search algorithm
KW - PLL spurious tone reduction
KW - radio frequency integrated circuit calibration
ER -
TY - CONF
TI - The homogenized energy model for characterizing magnetization and strains in ferromagnetic materials
AU - Blaircum, L. Van
AU - Smith, Ralph
AB - Ferromagnetic materials exhibit rate-dependent hysteresis, creep and constitutive nonlinearities due to their inherent domain structure. For model-based control applications, these non-linear attributes must be incorporated in a models in a manner that facilitates model calibration and real-time control implementation. In this paper, we present a homogenized energy model for these materials. This is a multiscale framework that quantifies energy at the domain level and then employs stochastic homogenization techniques to provide macroscopic models that are highly efficient to implement. The accuracy of models will be validated using a variety of experimental data.
C2 - 2013///
C3 - Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol 1
DA - 2013///
DO - 10.1115/smasis2012-8137
SP - 489–496
ER -
TY - JOUR
TI - Steady states for chemical process plants: A legacy code, time-stepping approach
AU - Kavouras, Andreas
AU - Georgakis, Christos
AU - Kelley, C. T.
AU - Siettos, Constantinos
AU - Kevrekidis, Ioannis G.
T2 - AICHE JOURNAL
AB - Given a legacy dynamic simulator of a chemical process plant, we construct a computational procedure that can be “wrapped around” the simulator to compute its steady states (both stable and unstable) and their dependence on input parameters. We apply this approach to the Tennessee Eastman (TE) challenge problem presented by Downs and Vogel, who also provided a FORTRAN process model. Using the FORTRAN simulator as a black-box input-output map, we enable it to systematically converge to isolated solutions and study their stability and parametric dependence within the equation-free framework. The presence of neutrally stable modes in TE problem (due to so-called inventories), their interplay with the problem formulation and the convergence of the solution procedure is explored and rationalized. Interestingly, our time-stepper formulation can automatically take advantage of separation of time scales, when present, to enhance computational convergence. The approach enables legacy dynamic simulators to calculate several dynamic problem characteristics useful for controller design and/or process optimization. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3308–3321, 2013
DA - 2013/9//
PY - 2013/9//
DO - 10.1002/aic.14199
VL - 59
IS - 9
SP - 3308-3321
SN - 0001-1541
KW - equation-free computations
KW - legacy dynamic simulator
KW - unstable processes
KW - inventories
KW - time-steppers
ER -
TY - CONF
TI - Sliding mode control for inverse compensated hysteretic smart systems
AU - McMahan, J. A.
AU - Smith, R. C.
C2 - 2013///
C3 - Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol 1
DA - 2013///
SP - 335–344
ER -
TY - JOUR
TI - Recovery of inclusions in 2D and 3D domains for Poisson's equation
AU - Ito, Kazufumi
AU - Liu, Ji-Chuan
T2 - INVERSE PROBLEMS
AB - In this paper, we consider the recovery problem of inclusions in three-dimensional and three-dimensional domains for Poisson's equation from noisy observation data. We propose effective reconstruction algorithms to recover hidden inclusions within a body when one can only make measurements of voltage and current on the external boundary. Our motivation is to detect the number, the location, the size and the shape of inclusions. This problem is nonlinear and severely ill posed, thus we should apply regularization techniques in our approaches in order to improve the corresponding approximation. We give several examples to show the viability of our proposed methods.
DA - 2013/7//
PY - 2013/7//
DO - 10.1088/0266-5611/29/7/075005
VL - 29
IS - 7
SP -
SN - 1361-6420
ER -
TY - JOUR
TI - Improving angular speed uniformity by reparameterization
AU - Yang, Jing
AU - Wang, Dongming
AU - Hong, Hoon
T2 - Computer Aided Geometric Design
AB - We introduce the notion of angular speed uniformity as a quality measure for parameter-izations of plane curves and propose an algorithm to compute uniform reparameterizations for quadratic and cubic curves. We prove that only straight lines have uniform rational parameterizations. For any plane curve other than lines, we show how to find a rational reparameterization that has the maximum uniformity among all the rational parameterizations of the same degree. We also establish specific results for quadratic and certain cubic Bézier curves.
DA - 2013/10//
PY - 2013/10//
DO - 10.1016/j.cagd.2013.04.001
VL - 30
IS - 7
SP - 636-652
UR - http://dx.doi.org/10.1016/j.cagd.2013.04.001
ER -
TY - CONF
TI - Homogenized energy model and markov chain Monte Carlo simulations for macro fiber composites operating in broadband regimes
AU - Hu, Z. Z.
AU - Smith, R. C.
AU - Burch, N.
AU - Hays, M.
AU - Oates, W. S.
C2 - 2013///
C3 - Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol 1
DA - 2013///
SP - 321–327
ER -
TY - JOUR
TI - Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation
AU - Baskaran, Arvind
AU - Hu, Zhengzheng
AU - Lowengrub, John S.
AU - Wang, Cheng
AU - Wise, Steven M.
AU - Zhou, Peng
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - In this paper we present two unconditionally energy stable finite difference schemes for the Modified Phase Field Crystal (MPFC) equation, a sixth-order nonlinear damped wave equation, of which the purely parabolic Phase Field Crystal (PFC) model can be viewed as a special case. The first is a convex splitting scheme based on an appropriate decomposition of the discrete energy and is first order accurate in time and second order accurate in space. The second is a new, fully second-order scheme that also respects the convex splitting of the energy. Both schemes are nonlinear but may be formulated from the gradients of strictly convex, coercive functionals. Thus, both are uniquely solvable regardless of the time and space step sizes. The schemes are solved by efficient nonlinear multigrid methods. Numerical results are presented demonstrating the accuracy, energy stability, efficiency, and practical utility of the schemes. In particular, we show that our multigrid solvers enjoy optimal, or nearly optimal complexity in the solution of the nonlinear schemes.
DA - 2013/10/1/
PY - 2013/10/1/
DO - 10.1016/j.jcp.2013.04.024
VL - 250
SP - 270-292
SN - 1090-2716
KW - Phase field crystal
KW - Modified phase field crystal
KW - Finite difference
KW - Nonlinear multigrid
ER -
TY - CONF
TI - Development of robust control algorithms for shape memory alloy bending actuators
AU - Crews, J. H.
AU - Smith, Ralph
AU - Hannen, J. C.
AB - In this paper, we present a systematic approach to developing robust control algorithms for a single-tendon shape memory alloy (SMA) bending actuator. Parameter estimation and uncertainty quantification are accomplished using Bayesian techniques. Specifically, we utilize Markov Chain Monte Carlo (MCMC) methods to estimate parameter uncertainty. The Bayesian parameter estimation results are used to construct a sliding mode control (SMC) algorithm where the bounds on uncertainty are used to guarantee controller robustness. The sliding mode controller utilizes the homogenized energy model (HEM) for SMA. The inverse HEM compensates for hysteresis and converts a reference bending angle to a reference temperature. Temperature in the SMA actuator is estimated using an observer, and the sliding mode controller ensures that the observer temperature tracks the reference temperature. The SMC is augmented with proportional-integral (PI) control on the bending angle error.
C2 - 2013///
C3 - Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol 1
DA - 2013///
DO - 10.1115/smasis2012-7989
SP - 391–400
ER -
TY - JOUR
TI - A practical approach to parameter estimation applied to model predicting heart rate regulation
AU - Olufsen, Mette S.
AU - Ottesen, Johnny T.
T2 - JOURNAL OF MATHEMATICAL BIOLOGY
AB - Mathematical models have long been used for prediction of dynamics in biological systems. Recently, several efforts have been made to render these models patient specific. One way to do so is to employ techniques to estimate parameters that enable model based prediction of observed quantities. Knowledge of variation in parameters within and between groups of subjects have potential to provide insight into biological function. Often it is not possible to estimate all parameters in a given model, in particular if the model is complex and the data is sparse. However, it may be possible to estimate a subset of model parameters reducing the complexity of the problem. In this study, we compare three methods that allow identification of parameter subsets that can be estimated given a model and a set of data. These methods will be used to estimate patient specific parameters in a model predicting baroreceptor feedback regulation of heart rate during head-up tilt. The three methods include: structured analysis of the correlation matrix, analysis via singular value decomposition followed by QR factorization, and identification of the subspace closest to the one spanned by eigenvectors of the model Hessian. Results showed that all three methods facilitate identification of a parameter subset. The “best” subset was obtained using the structured correlation method, though this method was also the most computationally intensive. Subsets obtained using the other two methods were easier to compute, but analysis revealed that the final subsets contained correlated parameters. In conclusion, to avoid lengthy computations, these three methods may be combined for efficient identification of parameter subsets.
DA - 2013/7//
PY - 2013/7//
DO - 10.1007/s00285-012-0535-8
VL - 67
IS - 1
SP - 39-68
SN - 1432-1416
KW - Parameter estimation
KW - Inverse problems
KW - Subset selection
KW - Simulation and modeling
KW - Nonlinear heart rate model
KW - Medical applications
KW - Patient specific modeling
ER -
TY - JOUR
TI - A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws
AU - Hao, W. R.
AU - Hauenstein, J. D.
AU - Shu, C. W.
AU - Sommese, A. J.
AU - Xu, Z. L.
AU - Zhang, Y. T.
T2 - Journal of Computational Physics
DA - 2013///
PY - 2013///
DO - 10.21236/ada568170
VL - 250
SP - 332-346
ER -
TY - JOUR
TI - A fraction free Matrix Berlekamp/Massey algorithm
AU - Kaltofen, Erich
AU - Yuhasz, George
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - We describe a fraction free version of the Matrix Berlekamp/Massey algorithm. The algorithm computes a minimal matrix generator of linearly generated square matrix sequences in an integral domain. The algorithm performs all operations in the integral domain, so all divisions performed are exact. For scalar sequences, the matrix algorithm specializes to a different algorithm than the algorithm currently in the literature. This new scalar algorithm has smaller intermediate values than the known fraction free Berlekamp/Massey algorithm.
DA - 2013/11/1/
PY - 2013/11/1/
DO - 10.1016/j.laa.2013.06.016
VL - 439
IS - 9
SP - 2515-2526
SN - 1873-1856
KW - Exact division
KW - Linear recurrences
KW - Matrix recurrences
KW - Block Hankel systems
KW - Block Toeplitz systems
KW - Integer sequences
ER -
TY - JOUR
TI - A Reduce and Replace Strategy for Suppressing Vector-Borne Diseases: Insights from a Deterministic Model
AU - Robert, Michael A.
AU - Okamoto, Kenichi
AU - Lloyd, Alun L.
AU - Gould, Fred
T2 - PLOS ONE
AB - Genetic approaches for controlling disease vectors have aimed either to reduce wild-type populations or to replace wild-type populations with insects that cannot transmit pathogens. Here, we propose a Reduce and Replace (R&R) strategy in which released insects have both female-killing and anti-pathogen genes. We develop a mathematical model to numerically explore release strategies involving an R&R strain of the dengue vector Aedes aegypti. We show that repeated R&R releases may lead to a temporary decrease in mosquito population density and, in the absence of fitness costs associated with the anti-pathogen gene, a long-term decrease in competent vector population density. We find that R&R releases more rapidly reduce the transient and long-term competent vector densities than female-killing releases alone. We show that releases including R&R females lead to greater reduction in competent vector density than male-only releases. The magnitude of reduction in total and competent vectors depends upon the release ratio, release duration, and whether females are included in releases. Even when the anti-pathogen allele has a fitness cost, R&R releases lead to greater reduction in competent vectors than female-killing releases during the release period; however, continued releases are needed to maintain low density of competent vectors long-term. We discuss the results of the model as motivation for more detailed studies of R&R strategies.
DA - 2013/9/4/
PY - 2013/9/4/
DO - 10.1371/journal.pone.0073233
VL - 8
IS - 9
SP -
SN - 1932-6203
ER -
TY - JOUR
TI - A Novel Candidate Vaccine for Cytauxzoonosis Inferred from Comparative Apicomplexan Genomics
AU - Tarigo, Jaime L.
AU - Scholl, Elizabeth H.
AU - Bird, David McK
AU - Brown, Corrie C.
AU - Cohn, Leah A.
AU - Dean, Gregg A.
AU - Levy, Michael G.
AU - Doolan, Denise L.
AU - Trieu, Angela
AU - Nordone, Shila K.
AU - Felgner, Philip L.
AU - Vigil, Adam
AU - Birkenheuer, Adam J.
T2 - PLOS ONE
AB - Cytauxzoonosis is an emerging infectious disease of domestic cats (Felis catus) caused by the apicomplexan protozoan parasite Cytauxzoon felis. The growing epidemic, with its high morbidity and mortality points to the need for a protective vaccine against cytauxzoonosis. Unfortunately, the causative agent has yet to be cultured continuously in vitro, rendering traditional vaccine development approaches beyond reach. Here we report the use of comparative genomics to computationally and experimentally interpret the C. felis genome to identify a novel candidate vaccine antigen for cytauxzoonosis. As a starting point we sequenced, assembled, and annotated the C. felis genome and the proteins it encodes. Whole genome alignment revealed considerable conserved synteny with other apicomplexans. In particular, alignments with the bovine parasite Theileria parva revealed that a C. felis gene, cf76, is syntenic to p67 (the leading vaccine candidate for bovine theileriosis), despite a lack of significant sequence similarity. Recombinant subdomains of cf76 were challenged with survivor-cat antiserum and found to be highly seroreactive. Comparison of eleven geographically diverse samples from the south-central and southeastern USA demonstrated 91-100% amino acid sequence identity across cf76, including a high level of conservation in an immunogenic 226 amino acid (24 kDa) carboxyl terminal domain. Using in situ hybridization, transcription of cf76 was documented in the schizogenous stage of parasite replication, the life stage that is believed to be the most important for development of a protective immune response. Collectively, these data point to identification of the first potential vaccine candidate antigen for cytauxzoonosis. Further, our bioinformatic approach emphasizes the use of comparative genomics as an accelerated path to developing vaccines against experimentally intractable pathogens.
DA - 2013/8/20/
PY - 2013/8/20/
DO - 10.1371/journal.pone.0071233
VL - 8
IS - 8
SP -
SN - 1932-6203
ER -
TY - JOUR
TI - A Fourier finite volume element method for solving two-dimensional quasi-geostrophic equations on a sphere
AU - Wang, Quanxiang
AU - Zhang, Zhiyue
AU - Li, Zhilin
T2 - APPLIED NUMERICAL MATHEMATICS
AB - Abstract A new Fourier finite volume element method for solving quasi-geostrophic (QG) equations on a sphere has been developed in this paper. Using the spherical coordinates, a Fourier discretization is used in the longitudinal direction while a finite volume element approximation is used in the latitudinal direction. In our proposed numerical method, the trial and test function spaces are carefully chosen to get accurate approximations. The pole singularity associated with the spherical coordinates is eliminated by changing the resolution near the pole. Some numerical experiments are presented to illustrate accuracy and efficiency of our method and some geostrophic implications of the QG model.
DA - 2013/9//
PY - 2013/9//
DO - 10.1016/j.apnum.2013.03.007
VL - 71
SP - 1-13
SN - 0168-9274
KW - Fourier finite volume element method
KW - Quasi-geostrophic equations on a sphere
KW - Trial and test function spaces
KW - Pole singularity
ER -
TY - JOUR
TI - Separation of the largest eigenvalues in eigenanalysis of genotype data from discrete subpopulations
AU - Bryc, Katarzyna
AU - Bryc, Wlodek
AU - Silverstein, Jack W.
T2 - THEORETICAL POPULATION BIOLOGY
AB - We present a mathematical model, and the corresponding mathematical analysis, that justifies and quantifies the use of principal component analysis of biallelic genetic marker data for a set of individuals to detect the number of subpopulations represented in the data. We indicate that the power of the technique relies more on the number of individuals genotyped than on the number of markers.
DA - 2013/11//
PY - 2013/11//
DO - 10.1016/j.tpb.2013.08.004
VL - 89
SP - 34-43
SN - 1096-0325
KW - Principal components analysis
KW - Eigenanalysis
KW - Population structure
KW - Eigenvalues
KW - Number of subpopulations
ER -
TY - JOUR
TI - Regulation of Aedes aegypti Population Dynamics in Field Systems: Quantifying Direct and Delayed Density Dependence
AU - Walsh, Rachael K.
AU - Gould, Fred
AU - Lloyd, Alun L.
AU - Scott, Thomas W.
AU - Ramsey, Janine M.
AU - Valerio, Laura
AU - Facchinelli, Luca
AU - Aguilar, Cristobal L.
T2 - The American Journal of Tropical Medicine and Hygiene
AB - Transgenic strains of Aedes aegypti have been engineered to help control transmission of dengue virus. Although resources have been invested in developing the strains, we lack data on the ecology of mosquitoes that could impact the success of this approach. Although studies of intra-specific competition have been conducted using Ae. aegypti larvae, none of these studies examine mixed age cohorts at densities that occur in the field, with natural nutrient levels. Experiments were conducted in Mexico to determine the impact of direct and delayed density dependence on Ae. aegypti populations. Natural water, food, and larval densities were used to estimate the impacts of density dependence on larval survival, development, and adult body size. Direct and delayed density-dependent factors had a significant impact on larval survival, larval development, and adult body size. These results indicate that control methods attempting to reduce mosquito populations may be counteracted by density-dependent population regulation.
DA - 2013/7/10/
PY - 2013/7/10/
DO - 10.4269/ajtmh.12-0378
VL - 89
IS - 1
SP - 68-77
LA - en
OP -
SN - 0002-9637 1476-1645
UR - http://dx.doi.org/10.4269/ajtmh.12-0378
DB - Crossref
ER -
TY - JOUR
TI - Quasilinear parabolic and elliptic systems with mixed quasimonotone functions
AU - Pao, C. V.
AU - Ruan, W. H.
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - This paper deals with a class of quasilinear parabolic and elliptic systems with mixed quasimonotone reaction functions. The boundary condition in the system may be Dirichlet, nonlinear, or a combination of these two types. The elliptic operators in the system are allowed to be degenerate. The aim is to show the existence and uniqueness of a classical solution to the parabolic system, the existence of maximal and minimal solutions or quasisolutions of the elliptic system, and the asymptotic behavior of the solution of the parabolic system. This consideration leads to a global attractor of the parabolic system as well as an one-sided stability of the maximal and minimal solutions. Applications of these results are given to three models arising from biology and ecology where diffusion coefficients are density-dependent and are degenerate. These applications exhibit quite distinct dynamical behavior of the population species between degenerate density-dependent diffusion and constant diffusion.
DA - 2013/10/1/
PY - 2013/10/1/
DO - 10.1016/j.jde.2013.05.015
VL - 255
IS - 7
SP - 1515-1553
SN - 1090-2732
KW - Degenerate parabolic and elliptic system
KW - Global existence
KW - Maximal-minimal solutions
KW - Global attractor
KW - Predator-prey problems
ER -
TY - JOUR
TI - Inversion algorithms for the homogenized energy model for hysteresis in ferroelectric and shape memory alloy compounds
AU - McMahan, J. A.
AU - Crews, J. H.
AU - Smith, Ralph
T2 - Journal of Intelligent Material Systems and Structures
AB - Ferroelectric and ferromagnetic materials have the advantage of broadband and dual actuator and sensor capabilities. Ferroelastic compounds such as shape memory alloys have large energy densities and are biocompatible. However, to take full advantage of these properties, it is necessary to employ models and control designs that account for the rate-dependent hysteresis, creep, and constitutive nonlinearities inherent to the materials. Inverse compensation is one technique that achieves this purpose. We present an inversion algorithm based on a binary search of a discretized input grid and apply this to the homogenized energy model for modeling hysteresis. The inversion algorithm is shown to provide a reasonable balance between accuracy and computational speed. Numerical examples are presented for three specific cases of the homogenized energy model.
DA - 2013///
PY - 2013///
DO - 10.1177/1045389x12471868
VL - 24
IS - 15
SP - 1796–1821
ER -
TY - JOUR
TI - Fixation Time for an Evolutionary Model
AU - Grigorescu, Ilie
AU - Kang, Min
T2 - STOCHASTIC MODELS
AB - We study the asymptotic value as L → ∞ of the time for evolution τ, understood as the first time to reach a preferred word of length L using an alphabet with N letters. The word is updated at unit time intervals randomly, but configurations with letters matching with the preferred word are sticky, i.e., the probability to leave the configuration equals 0 ≤ γ ≤1, where γ may depend on the configuration. The model is introduced in Ref.[ 5 Wilf , H.S. ; Ewens , W.J. There's plenty of time for evolution . PNAS 2010 , 107 : 22454 – 22456 . www. pnas.org/cgi/doi/10.1073/pnas.1016207107 [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] ] in the case γ = 0, where it was shown that E[τ] ∼ Nln (L). We first give an alternative proof of the logarithmic scale, by evaluating the mode of τ. We then answer positively a question posed by H. Wilf on whether τ is exponential when γ ≠ 0. The natural scaling γ =O(L −1) gives rise to several finite order limits, including the interacting model when γ depends linearly on the number of matches with the preferred word. The scaling limit of the number of non-matching letters follows a Galton-Watson process with immigration. In a related model, the empirical measure converges to the solution of a discrete logistic equation with possible nonzero steady state. In conclusion, the length of τ is a question of scaling.
DA - 2013/7/3/
PY - 2013/7/3/
DO - 10.1080/15326349.2013.808908
VL - 29
IS - 3
SP - 328-340
SN - 1532-6349
KW - Discrete logistic equation
KW - Evolution
KW - Fixation time
KW - Galton-Watson scaling limit
ER -
TY - JOUR
TI - DATA AND IMPLICATION BASED COMPARISON OF TWO CHRONIC MYELOID LEUKEMIA MODELS
AU - Everett, R. A.
AU - Zhao, Y.
AU - Flores, K. B.
AU - Kuang, Y.
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - Chronic myeloid leukemia, a disorder of hematopoietic stem cells, is currently treated using targeted molecular therapy with imatinib. We compare two models that describe the treatment of CML, a multi-scale model (Model 1) and a simple cell competition model (Model 2).Both models describe the competition of leukemic and normal cells, however Model 1 also describes the dynamics of BCR-ABL, the oncogene targeted by imatinib, at the sub-cellular level. Using clinical data, we analyze the differences in estimated parameters between the models and the capacity for each model to predict drug resistance. We found that while both models fit the data well, Model 1 is more biologically relevant. The estimated parameter ranges for Model 2 are unrealistic, whereas the parameter ranges for Model 1 are close to values found in literature. We also found that Model 1 predicts long-term drug resistance from patient data, which is exhibited by both an increase in the proportion of leukemic cells as well as an increase in BCR-ABL/ABL%. Model 2, however, is not able to predict resistance and accurately model the clinical data. These results suggest that including sub-cellular mechanisms in a mathematical model of CML can increase the accuracy of parameter estimation and may help to predict long-term drug resistance.
DA - 2013///
PY - 2013///
DO - 10.3934/mbe.2013.10.1501
VL - 10
IS - 5-6
SP - 1501-1518
SN - 1551-0018
KW - Chronic myeloid leukemia
KW - clinical data
KW - drug resistance
KW - cancer modeling
ER -
TY - JOUR
TI - A Comparison of Stochastic Systems with Different Types of Delays
AU - Banks, H. T.
AU - Catenacci, Jared
AU - Hu, Shuhua
T2 - STOCHASTIC ANALYSIS AND APPLICATIONS
AB - In this article, we investigate the effects of different types of delays, a fixed delay and a random delay, on the dynamics of stochastic systems as well as their relationship with each other in the context of a just-in-time network model. The specific example on which we focus is a pork production network model. We numerically explore the corresponding deterministic approximations for the stochastic systems with these two different types of delays. Numerical results reveal that the agreement of stochastic systems with fixed and random delays depend on the population size and the variance of the random delay, even when the mean value of the random delay is chosen the same as the value of the fixed delay. When the variance of the random delay is sufficiently small, the histograms of state solutions to the stochastic system with a random delay are similar to those of the stochastic model with a fixed delay regardless of the population size. We also compared the stochastic system with a Gamma distributed random delay to the stochastic system constructed based on the Kurtz's limit theorem from a system of deterministic delay differential equations with a Gamma distributed delay. We found that with the same population size the histogram plots for the solution to the second system appear more dispersed than the corresponding ones obtained for the first case. In addition, we found that there is more agreement between the histograms of these two stochastic systems as the variance of the Gamma distributed random delay decreases.
DA - 2013/11/2/
PY - 2013/11/2/
DO - 10.1080/07362994.2013.806217
VL - 31
IS - 6
SP - 913-955
SN - 1532-9356
KW - Fixed vs
KW - random delays
KW - Gamma distribution and the linear chain trick
KW - Kurtz limit theorem
KW - Markov Chain stochastic vs
KW - deterministic approximations
KW - Systems with delays
ER -
TY - JOUR
TI - Tensor Spline Approximation in Economic Dynamics with Uncertainties
AU - Chu, Moody T.
AU - Kuo, Chun-Hung
AU - Lin, Matthew M.
T2 - COMPUTATIONAL ECONOMICS
DA - 2013/8//
PY - 2013/8//
DO - 10.1007/s10614-012-9331-1
VL - 42
IS - 2
SP - 175-198
SN - 1572-9974
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84879954290&partnerID=MN8TOARS
KW - Economic dynamics
KW - Dynamic programming
KW - Stochastic uncertainties
KW - Bellman equation
KW - Euler equation
KW - Policy function
KW - Cubic spline
KW - Tensor operation
ER -
TY - JOUR
TI - Substrate constraint modifies the Rayleigh spectrum of vibrating sessile drops
AU - Chang, Chun-Ti
AU - Bostwick, Joshua B.
AU - Steen, Paul H.
AU - Daniel, Susan
T2 - PHYSICAL REVIEW E
AB - In this work, we study the resonance behavior of mechanically oscillated, sessile water drops. By mechanically oscillating sessile drops vertically and within prescribed ranges of frequencies and amplitudes, a rich collection of resonance modes are observed and their dynamics subsequently investigated. We first present our method of identifying each mode uniquely, through association with spherical harmonics and according to their geometric patterns. Next, we compare our measured resonance frequencies of drops to theoretical predictions using both the classical theory of Lord Rayleigh and Lamb for free, oscillating drops, and a prediction by Bostwick and Steen that explicitly considers the effect of the solid substrate on drop dynamics. Finally, we report observations and analysis of drop mode mixing, or the simultaneous coexistence of multiple mode shapes within the resonating sessile drop driven by one sinusoidal signal of a single frequency. The dynamic response of a deformable liquid drop constrained by the substrate it is in contact with is of interest in a number of applications, such as drop atomization and ink jet printing, switchable electronically controlled capillary adhesion, optical microlens devices, as well as digital microfluidic applications where control of droplet motion is induced by means of a harmonically driven substrate.
DA - 2013/8/14/
PY - 2013/8/14/
DO - 10.1103/physreve.88.023015
VL - 88
IS - 2
SP -
SN - 1550-2376
ER -
TY - JOUR
TI - Quantifying Plant Age and Available Water Effects on Soybean Leaf Conductance
AU - Matthews, Jessica L.
AU - Fiscus, Edwin L.
AU - Smith, Ralph C.
AU - Heitman, Joshua L.
T2 - AGRONOMY JOURNAL
AB - Given the ever‐present threat of drought and the knowledge that water availability is the strongest limiting factor in vegetation growth, it is important to characterize the effect of water limitations on agricultural production. In this study, a small field plot technique for controlling soil moisture content suitable for physiological research in moist, humid areas was tested. We characterized the effect of water stress on total leaf conductance ( g l ) for two distinct determinate soybean [ Glycine max (L.) Merr.] genotypes. Based on these findings, a model of g l as a function of plant age and soil moisture content was formulated and validated. The dependency of g l on plant age was well represented by a parabolic function that increased throughout the vegetative period, peaked around anthesis, and decreased throughout the reproductive period and senescence. A sigmoidal function explained the relation of g l to plant‐available soil water content. This new empirical model effectively quantifies the response of g l to plant‐available soil water and plant age with a functional form similar to the abscisic acid related Tardieu–Davies model.
DA - 2013///
PY - 2013///
DO - 10.2134/agronj2012.0263
VL - 105
IS - 1
SP - 28-36
SN - 1435-0645
ER -
TY - JOUR
TI - Optimal filtering of complex turbulent systems with memory depth through consistency constraints
AU - Bakunova, Eugenia S.
AU - Harlim, John
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - In this article, we develop a linear theory for optimal filtering of complex turbulent signals with model errors through linear autoregressive models. We will show that when the autoregressive model parameters are chosen such that they satisfy absolute stability and consistency conditions of at least order-2 of the classical multistep method for solving initial value problems, the filtered solutions with autoregressive models of order p⩾2 are optimal in the sense that they are comparable to the estimates obtained from the true filter with perfect model. This result is reminiscent of the Lax-equivalence fundamental theorem in the analysis of finite difference discretization scheme for the numerical solutions of partial differential equations. We will apply this linear theory to filter two nonlinear problems, the slowest mode of the truncated Burgers–Hopf and the Lorenz-96 model. On these nonlinear problems, we will show that whenever these linear conditions are satisfied, the filtered solutions accuracy is significantly improved. Finally, we will also apply the recently developed offline test criteria to understand the robustness of the multistep filter on various turbulent nature, including the stochastically forced linear advection–diffusion equation and a toy model for barotropic turbulent Rossby waves.
DA - 2013/3/15/
PY - 2013/3/15/
DO - 10.1016/j.jcp.2012.11.028
VL - 237
SP - 320-343
SN - 1090-2716
KW - AR(p)-filter
KW - Optimal multistep filter
KW - Data assimilation
KW - Model error
ER -
TY - JOUR
TI - ON TENSOR PRODUCT DECOMPOSITION OF (sl)over-cap(n) MODULES
AU - Misra, Kailash C.
AU - Wilson, Evan A.
T2 - JOURNAL OF ALGEBRA AND ITS APPLICATIONS
AB - We decompose the [Formula: see text]-module V(Λ 0 ) ⊗ V(Λ 0 ) and give generating function identities for the outer multiplicities. In the process we discover an infinite family of partition identities, which are seemingly new even in the n = 3 case.
DA - 2013/12//
PY - 2013/12//
DO - 10.1142/s0219498813500540
VL - 12
IS - 8
SP -
SN - 1793-6829
KW - Affine Lie algebra
KW - integrable module
KW - crystal base
KW - tensor product
ER -
TY - JOUR
TI - Dispersive hydrodynamics in viscous fluid conduits
AU - Lowman, N. K.
AU - Hoefer, M. A.
T2 - PHYSICAL REVIEW E
AB - The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous authors have proposed an approximate model equation based on physical arguments, but a precise theoretical treatment for this two fluid system with a free boundary is lacking. Here, a derivation of the interfacial equation via a multiple scales, perturbation technique is presented. Perturbations about a state of vertically uniform, laminar conduit flow are considered in the context of the Navier-Stokes equations with appropriate boundary conditions. The ratio of interior to exterior viscosities is the small parameter used in the asymptotic analysis, which leads systematically to a maximal balance between buoyancy driven, nonlinear self-steepening and viscous, interfacial stress induced, nonlinear dispersion. This results in a scalar, nonlinear partial differential equation describing large amplitude dynamics of the cross-sectional area of the intrusive fluid conduit, in agreement with previous derivations. The leading order behavior of the two fluid system is completely characterized in terms of the interfacial dynamics. The regime of model validity is characterized and shown to agree with previous experimental studies. Viscous fluid conduits provide a robust setting for the study of nonlinear, dispersive wave phenomena.
DA - 2013/8/19/
PY - 2013/8/19/
DO - 10.1103/physreve.88.023016
VL - 88
IS - 2
SP -
SN - 1550-2376
ER -
TY - JOUR
TI - Cell decomposition of almost smooth real algebraic surfaces
AU - Besana, Gian Mario
AU - Di Rocco, Sandra
AU - Hauenstein, Jonathan D.
AU - Sommese, Andrew J.
AU - Wampler, Charles W.
T2 - NUMERICAL ALGORITHMS
DA - 2013/8//
PY - 2013/8//
DO - 10.1007/s11075-012-9646-y
VL - 63
IS - 4
SP - 645-678
SN - 1572-9265
KW - Algebraic surface
KW - Algebraic curve
KW - Cell decomposition
KW - Numerical algebraic geometry
KW - Homotopy
KW - Polynomial system
ER -
TY - JOUR
TI - CENTER PROBLEM FOR THIRD-ORDER ODES
AU - Mahdi, Adam
T2 - INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
AB - We obtain necessary and sufficient conditions for the existence of a center on a local center manifold for three 4-parameter families of quadratic systems on ℝ 3 . We also give a positive answer to an open question posed in [Dias & Mello, 2010] related to similar systems.
DA - 2013/5//
PY - 2013/5//
DO - 10.1142/s0218127413500788
VL - 23
IS - 5
SP -
SN - 1793-6551
KW - Center-focus problem
KW - center manifold
KW - first integral
ER -
TY - JOUR
TI - A two-stage method for inverse medium scattering
AU - Ito, Kazufumi
AU - Jin, Bangti
AU - Zou, Jun
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with mixed regularization. The first step is strictly direct and of sampling type, and faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer sizes as well as intensities. The model is efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the approach is accurate, computationally efficient, and robust with respect to data noise.
DA - 2013/3/15/
PY - 2013/3/15/
DO - 10.1016/j.jcp.2012.12.004
VL - 237
SP - 211-223
SN - 0021-9991
KW - Inverse medium scattering problem
KW - Reconstruction algorithm
KW - Direct sampling method
KW - Mixed regularization
KW - Semi-smooth Newton method
ER -
TY - JOUR
TI - A twisted quantum toroidal algebra
AU - Jing, Naihuan
AU - Liu, Rongjia
T2 - FRONTIERS OF MATHEMATICS IN CHINA
AB - As an analog of the quantum TKK algebra, a twisted quantum toroidal algebra of type A 1 is introduced. Explicit realization of the new quantum TKK algebra is constructed with the help of twisted quantum vertex operators over a Fock space.
DA - 2013/10//
PY - 2013/10//
DO - 10.1007/s11464-013-0316-8
VL - 8
IS - 5
SP - 1117-1128
SN - 1673-3576
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84882836530&partnerID=MN8TOARS
KW - Vertex operator
KW - toroidal algebra
KW - quantum algebra
ER -
TY - JOUR
TI - A direct sampling method for inverse electromagnetic medium scattering
AU - Ito, Kazufumi
AU - Jin, Bangti
AU - Zou, Jun
T2 - INVERSE PROBLEMS
AB - In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric or magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. The method is applicable even with one incident field and needs only to compute inner products of the measured scattered field with the fundamental solutions located at sampling points. Hence it is strictly direct, computationally very efficient, and highly tolerant to the presence of noise in the data. Two- and three-dimensional numerical experiments indicate that it can provide reliable support estimates of one single and multiple scatterers in case of both exact and highly noisy data.
DA - 2013/9//
PY - 2013/9//
DO - 10.1088/0266-5611/29/9/095018
VL - 29
IS - 9
SP -
SN - 1361-6420
ER -
TY - JOUR
TI - Test models for filtering and prediction of moisture-coupled tropical waves
AU - Harlim, John
AU - Majda, Andrew J.
T2 - QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY
AB - The filtering/data assimilation and prediction of moisture-coupled tropical waves is a contemporary topic with significant implications for extended-range forecasting. The development of efficient algorithms to capture such waves is limited by the unstable multiscale features of tropical convection which can organize large-scale circulations and the sparse observations of the moisture-coupled wave in both the horizontal and vertical. The approach proposed here is to address these difficult issues of data assimilation and prediction through a suite of analogue models which, despite their simplicity, capture key features of the observational record and physical processes in moisture-coupled tropical waves. The analogue models emphasized here involve the multicloud convective parametrization based on three cloud types (congestus, deep, and stratiform) above the boundary layer. Two test examples involving an MJO-like turbulent travelling wave and the initiation of a convectively coupled wave train are introduced to illustrate the approach. A suite of reduced filters with judicious model errors for data assimilation of sparse observations of tropical waves, based on linear stochastic models in a moisture-coupled eigenmode basis is developed here and applied to the two test problems. Both the reduced filter and 3D-Var with a full moist background covariance matrix can recover the unobserved troposphere humidity and precipitation rate; on the other hand, 3D-Var with a dry background covariance matrix fails to recover these unobserved variables. The skill of the reduced filtering methods in recovering the unobserved precipitation, congestus, and stratiform heating rates as well as the front-to-rear tilt of the convectively coupled waves exhibits a subtle dependence on the sparse observation network and the observation time. Copyright © 2012 Royal Meteorological Society
DA - 2013/1//
PY - 2013/1//
DO - 10.1002/qj.1956
VL - 139
IS - 670
SP - 119-136
SN - 1477-870X
KW - tropical data assimilation
KW - reduced stochastic filters
KW - multicloud models
KW - Madden-Julian Oscillation
ER -
TY - JOUR
TI - Stability of standing waves for monostable reaction-convection equations in a large bounded domain with boundary conditions
AU - Lin, Xiao-Biao
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - It is well known that the standing wave u 0 for the KPP type convection–diffusion equation is stable if the perturbations of the initial data are in the weighted function spaces proposed by Sattinger. We study boundary conditions so that in a large finite domain, there is a stable standing wave u ˜ near u 0 . The standing wave u ˜ may not be monotone, and the stability is proved by pseudo exponential dichotomies that are weighted both in the spatial variable ξ and in the dual variable s to the time t .
DA - 2013/7/1/
PY - 2013/7/1/
DO - 10.1016/j.jde.2013.03.010
VL - 255
IS - 1
SP - 58-84
SN - 1090-2732
KW - Traveling waves
KW - KPP/Fisher equations
KW - Stability on large intervals
KW - Weighted norms
KW - Exponential dichotomies
KW - Lambda Lemma
ER -
TY - JOUR
TI - Spin Torque-Generated Magnetic Droplet Solitons
AU - Mohseni, S. M.
AU - Sani, S. R.
AU - Persson, J.
AU - Nguyen, T. N. Anh
AU - Chung, S.
AU - Pogoryelov, Ye.
AU - Muduli, P. K.
AU - Iacocca, E.
AU - Eklund, A.
AU - Dumas, R. K.
AU - Bonetti, S.
AU - Deac, A.
AU - Hoefer, M. A.
AU - Akerman, J.
T2 - SCIENCE
AB - Magnetic Droplet When a solitary wave travels atop the surface of a fluid, its shape generally changes with time, with some of its components traveling at velocities slightly different than others. In nonlinear media, this spreading effect may be countered by a slimming effect stemming from the non-linearity, which generates an object with perfectly preserved shape, called a soliton. Solitons have been observed in fluids, granular media, and other systems. Mohseni et al. (p. 1295 ) detected a dissipative soliton (one that also balances gain and dissipation) in a magnetic system, in the form of a magnetic droplet consisting of a core of spins pointing opposite to the external magnetic field. The droplet exhibited peculiar dynamics and could be controlled by electric current.
DA - 2013/3/15/
PY - 2013/3/15/
DO - 10.1126/science.1230155
VL - 339
IS - 6125
SP - 1295-1298
SN - 0036-8075
ER -
TY - JOUR
TI - Membership tests for images of algebraic sets by linear projections
AU - Hauenstein, Jonathan D.
AU - Sommese, Andrew J.
T2 - APPLIED MATHEMATICS AND COMPUTATION
AB - Given a witness set for an irreducible variety V and a linear map π, we describe membership tests for both the constructible algebraic set π(V) and the algebraic set π(V)¯. We also provide applications and examples of these new tests including computing the codimension one components of π(V)¯⧹π(V)¯. Additionally, we also describe computing the geometric genus of a curve section of an irreducible component of the solution set of a polynomial system and a test for deciding whether a plane quartic curve is a Lüroth quartic.
DA - 2013/2/15/
PY - 2013/2/15/
DO - 10.1016/j.amc.2012.12.060
VL - 219
IS - 12
SP - 6809-6818
SN - 1873-5649
KW - Numerical algebraic geometry
KW - Polynomial system
KW - Witness sets
KW - Projections
KW - Membership test
KW - Numerical irreducible decomposition
KW - Geometric genus
KW - Luroth quartics
ER -
TY - JOUR
TI - Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology
AU - Banks, H. T.
AU - Hu, S. H.
AU - Kenz, Z. R.
AU - Kruse, C.
AU - Shaw, S.
AU - Whiteman, J. R.
AU - Brewin, M. P.
AU - Greenwald, S. E.
AU - Birch, M. J.
T2 - Journal of Inverse and Ill-Posed Problems
DA - 2013///
PY - 2013///
VL - 21
IS - 1
SP - 25-57
ER -
TY - JOUR
TI - LAND SURFACE ALBEDO FROM GEOSTATIONARY SATELLITES: A Multiagency Collaboration within SCOPE-CM
AU - Lattanzio, Alessio
AU - Schulz, Joerg
AU - Matthews, Jessica
AU - Okuyama, Arata
AU - Theodore, Bertrand
AU - Bates, John J.
AU - Knapp, Kenneth R.
AU - Kosaka, Yuki
AU - Schueller, Lothar
T2 - BULLETIN OF THE AMERICAN METEOROLOGICAL SOCIETY
AB - Climate has been recognized to have direct and indirect impact on society and economy, both in the long term and daily life. The challenge of understanding the climate system, with its variability and changes, is enormous and requires a joint long-term international commitment from research and governmental institutions. An important international body to coordinate worldwide climate monitoring efforts is the World Meteorological Organization (WMO). The Global Climate Observing System (GCOS) has the mission to provide coordination and the requirements for global observations and essential climate variables (ECVs) to monitor climate changes. The WMO-led activity on Sustained, Coordinated Processing of Environmental Satellite Data for Climate Monitoring (SCOPE-CM) is responding to these requirements by ensuring a continuous and sustained generation of climate data records (CDRs) from satellite data in compliance with the principles and guidelines of GCOS. SCOPE-CM represents a new partnership between operational space agencies to coordinate the generation of CDRs. To this end, pilot projects for different ECVs, such as surface albedo, cloud properties, water vapor, atmospheric motion winds, and upper-tropospheric humidity, have been initiated. The coordinated activity on land surface albedo involves the operational meteorological satellite agencies in Europe [European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT)], in Japan [the Japan Meteorological Agency (JMA)], and in the United States [National Oceanic and Atmospheric Administration (NOAA)]. This paper presents the first results toward the generation of a unique land surface albedo CDR, involving five different geostationary satellite positions and approximately three decades of data starting in the 1980s, and combining close to 30 different satellite instruments.
DA - 2013/2//
PY - 2013/2//
DO - 10.1175/bams-d-11-00230.1
VL - 94
IS - 2
SP - 205-214
SN - 1520-0477
ER -
TY - JOUR
TI - Isomorphism between two realizations of the Yangian Y(so(3))
AU - Jing, Naihuan
AU - Liu, Ming
T2 - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
AB - The isomorphism between Drinfeld's new realization and the FRT realization is proved for the Yangian algebra Y(so_3) by using Gauss decomposition.
DA - 2013/2/22/
PY - 2013/2/22/
DO - 10.1088/1751-8113/46/7/075201
VL - 46
IS - 7
SP -
SN - 1751-8121
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84873890099&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective
AU - Helminck, G. F.
AU - Helminck, A. G.
AU - Panasenko, E. A.
T2 - THEORETICAL AND MATHEMATICAL PHYSICS
DA - 2013/1//
PY - 2013/1//
DO - 10.1007/s11232-013-0011-7
VL - 174
IS - 1
SP - 134-153
SN - 0040-5779
KW - integrable deformation
KW - pseudodifferential operator
KW - Lax equation
KW - Kadomtsev-Petviashvili hierarchy
KW - zero-curvature relation
KW - linearization
ER -
TY - JOUR
TI - Explicit pseudo-transient continuation
AU - Kelley, C. T.
AU - Liao, L. Z.
T2 - Pacific Journal of Optimization
DA - 2013///
PY - 2013///
VL - 9
IS - 1
SP - 77-91
ER -
TY - JOUR
TI - Dispersive shock waves in viscously deformable media
AU - Lowman, Nicholas K.
AU - Hoefer, M. A.
T2 - JOURNAL OF FLUID MECHANICS
AB - The viscously dominated, low Reynolds' number dynamics of multi-phase, compacting media can lead to nonlinear, dissipationless/dispersive behavior when viewed appropriately. In these systems, nonlinear self-steepening competes with wave dispersion, giving rise to dispersive shock waves (DSWs). Example systems considered here include magma migration through the mantle as well as the buoyant ascent of a low density fluid through a viscously deformable conduit. These flows are modeled by a third-order, degenerate, dispersive, nonlinear wave equation for the porosity (magma volume fraction) or cross-sectional area, respectively. Whitham averaging theory for step initial conditions is used to compute analytical, closed form predictions for the DSW speeds and the leading edge amplitude in terms of the constitutive parameters and initial jump height. Novel physical behaviors are identified including backflow and DSW implosion for initial jumps sufficient to cause gradient catastrophe in the Whitham modulation equations. Theoretical predictions are shown to be in excellent agreement with long-time numerical simulations for the case of small to moderate amplitude DSWs. Verifiable criteria identifying the breakdown of this modulation theory in the large jump regime, applicable to a wide class of DSW problems, are presented.
DA - 2013/3//
PY - 2013/3//
DO - 10.1017/jfm.2012.628
VL - 718
SP - 524-557
SN - 1469-7645
KW - magma and lava flow
KW - shock waves
KW - solitary waves
ER -
TY - JOUR
TI - A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010
AU - Reiner, Robert C., Jr.
AU - Perkins, T. Alex
AU - Barker, Christopher M.
AU - Niu, Tianchan
AU - Fernando Chaves, Luis
AU - Ellis, Alicia M.
AU - George, Dylan B.
AU - Le Menach, Arnaud
AU - Pulliam, Juliet R. C.
AU - Bisanzio, Donal
AU - Buckee, Caroline
AU - Chiyaka, Christinah
AU - Cummings, Derek A. T.
AU - Garcia, Andres J.
AU - Gatton, Michelle L.
AU - Gething, Peter W.
AU - Hartley, David M.
AU - Johnston, Geoffrey
AU - Klein, Eili Y.
AU - Michael, Edwin
AU - Lindsay, Steven W.
AU - Lloyd, Alun L.
AU - Pigott, David M.
AU - Reisen, William K.
AU - Ruktanonchai, Nick
AU - Singh, Brajendra K.
AU - Tatem, Andrew J.
AU - Kitron, Uriel
AU - Hay, Simon I.
AU - Scott, Thomas W.
AU - Smith, David L.
T2 - JOURNAL OF THE ROYAL SOCIETY INTERFACE
AB - Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.
DA - 2013/4/6/
PY - 2013/4/6/
DO - 10.1098/rsif.2012.0921
VL - 10
IS - 81
SP -
SN - 1742-5662
UR - https://publons.com/wos-op/publon/671080/
KW - infectious disease dynamics
KW - vector-borne disease
KW - epidemiology
KW - dengue
KW - West Nile
KW - filariasis
ER -
TY - JOUR
TI - TEST MODELS FOR FILTERING WITH SUPERPARAMETERIZATION
AU - Harlim, John
AU - Majda, Andrew J.
T2 - MULTISCALE MODELING & SIMULATION
AB - Superparameterization is a fast numerical algorithm to mitigate implicit scale separation of dynamical systems with large-scale, slowly varying “mean” and smaller-scale, rapidly fluctuating “eddy” term. The main idea of superparameterization is to embed parallel highly resolved simulations of small-scale eddies on each grid cell of coarsely resolved large-scale dynamics. In this paper, we study the effect of model errors in using superparameterization for filtering multiscale turbulent dynamical systems. In particular, we use a simple test model, designed to mimic typical multiscale turbulent dynamics with small-scale intermittencies without local statistical equilibriation conditional to the large-scale mean dynamics, and simultaneously force the large-scale dynamics through eddy flux terms. In this paper, we consider the Fourier domain Kalman filter for filtering regularly spaced sparse observations of the large-scale mean variables. We find high filtering and statistical prediction skill with superparameterization (identical to the skill with perfect model), beyond conventional approaches such as the “bare truncation model” that ignores completely the eddy fluxes and the “equilibrium closure” model that crudely approximates the eddy fluxes with classical averaging theory. We show that this high filtering skill is robust even for very sparse observation networks and turbulent signals with a very steep, $-6$, spectrum. This is a counterexample to naive thinking that the small-scale processes are not so important in multiscale turbulent dynamics with steep energy spectrum. We find that the high filtering skill with superparameterization is robust for small enough scale gap, provided that the filter prior model satisfies the classical linear controllability condition. We will demonstrate a spectacular failure of filtering deterministically forced true signals with the exactly perfect model that does not satisfy controllability condition and a dramatic improvement when the controllability condition is restored with additional stochastic forcings. This result reconfirms and justifies the counterintuitive viewpoint that judicious model errors (or noises) can help filtering turbulent signals.
DA - 2013///
PY - 2013///
DO - 10.1137/120890594
VL - 11
IS - 1
SP - 282-308
SN - 1540-3467
KW - superparameterization
KW - Kalman filter
KW - no scale separation
KW - data assimilation
ER -
TY - JOUR
TI - Symmetric Chain Decomposition for Cyclic Quotients of Boolean Algebras and Relation to Cyclic Crystals
AU - Hersh, Patricia
AU - Schilling, Anne
T2 - INTERNATIONAL MATHEMATICS RESEARCH NOTICES
AB - The quotient of a Boolean algebra by a cyclic group is proven to have a symmetric chain decomposition. This generalizes earlier work of Griggs, Killian and Savage on the case of prime order, giving an explicit construction for any order, prime or composite. The combinatorial map specifying how to proceed downward in a symmetric chain is shown to be a natural cyclic analogue of the $\mathfrak{sl}_2$ lowering operator in the theory of crystal bases.
DA - 2013///
PY - 2013///
DO - 10.1093/imrn/rnr254
VL - 2013
IS - 2
SP - 463-473
SN - 1687-0247
ER -
TY - JOUR
TI - Simulation of Longitudinal Exposure Data with Variance-Covariance Structures Based on Mixed Models
AU - Song, Peng
AU - Xue, Jianping
AU - Li, Zhilin
T2 - RISK ANALYSIS
AB - Longitudinal data are important in exposure and risk assessments, especially for pollutants with long half-lives in the human body and where chronic exposures to current levels in the environment raise concerns for human health effects. It is usually difficult and expensive to obtain large longitudinal data sets for human exposure studies. This article reports a new simulation method to generate longitudinal data with flexible numbers of subjects and days. Mixed models are used to describe the variance-covariance structures of input longitudinal data. Based on estimated model parameters, simulation data are generated with similar statistical characteristics compared to the input data. Three criteria are used to determine similarity: the overall mean and standard deviation, the variance components percentages, and the average autocorrelation coefficients. Upon the discussion of mixed models, a simulation procedure is produced and numerical results are shown through one human exposure study. Simulations of three sets of exposure data successfully meet above criteria. In particular, simulations can always retain correct weights of inter- and intrasubject variances as in the input data. Autocorrelations are also well followed. Compared with other simulation algorithms, this new method stores more information about the input overall distribution so as to satisfy the above multiple criteria for statistical targets. In addition, it generates values from numerous data sources and simulates continuous observed variables better than current data methods. This new method also provides flexible options in both modeling and simulation procedures according to various user requirements.
DA - 2013/3//
PY - 2013/3//
DO - 10.1111/j.1539-6924.2012.01869.x
VL - 33
IS - 3
SP - 469-479
SN - 0272-4332
KW - Autocorrelation
KW - longitudinal data
KW - mixed models
KW - simulation
KW - variance-covariance structure
ER -
TY - JOUR
TI - Regression models with memory for the linear response of turbulent dynamical systems
AU - Kang, E. L.
AU - Harlim, J.
AU - Majda, A. J.
T2 - Communications in Mathematical Sciences
AB - Calculating the statistical linear response of turbulent dynamical systems to the change in external forcing is a problem of wide contemporary interest. Here the authors apply linear regression models with memory, AR(p) models, to approximate this statistical linear response by directly fitting the autocorrelations of the underlying turbulent dynamical system without further computational experiments. For highly nontrivial energy conserving turbulent dynamical systems like the Kruskal-Zabusky (KZ) or Truncated Burgers-Hopf (TBH) models, these AR(p) models exactly recover the mean linear statistical response to the change in external forcing at all response times with negligible errors. For a forced turbulent dynamical system like the Lorenz-96 (L-96) model, these approximations have improved skill comparable to the mean response with the quasi-Gaussian approximation for weakly chaotic turbulent dynamical systems. These AR(p) models also give new insight into the memory depth of the mean linear response operator for turbulent dynamical systems.
DA - 2013///
PY - 2013///
DO - 10.4310/cms.2013.v11.n2.a8
VL - 11
IS - 2
SP - 481-498
ER -
TY - JOUR
TI - Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry
AU - Bates, Daniel J.
AU - Hauenstein, Jonathan D.
AU - McCoy, Timothy M.
AU - Peterson, Chris
AU - Sommese, Andrew J.
T2 - EXPERIMENTAL MATHEMATICS
AB - Let be a set of homogeneous polynomials. Let Z denote the complex projective algebraic set determined by the zero locus of . Numerical-continuation-based methods can be used to produce arbitrary-precision numerical approximations of generic points on each irreducible component of Z. Consider the ideal and the prime decomposition over . This article illustrates how lattice-reduction algorithms may take as input numerically approximated generic points on Z and effectively extract exact elements for each Pi . A collection of examples serves to illustrate the approach and indicate some of the application areas for which this technique is valuable.
DA - 2013/1/1/
PY - 2013/1/1/
DO - 10.1080/10586458.2013.737640
VL - 22
IS - 1
SP - 38-50
SN - 1944-950X
KW - 65H10
KW - 68W30
KW - 14Q99
KW - witness set
KW - generic point
KW - homotopy continuation
KW - numerical algebraic geometry
KW - numerical irreducible decomposition
KW - primary decomposition
KW - algebraic set
KW - algebraic variety
KW - LLL
ER -
TY - JOUR
TI - Physics constrained nonlinear regression models for time series
AU - Majda, Andrew J.
AU - Harlim, John
T2 - NONLINEARITY
AB - A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data.
DA - 2013/1//
PY - 2013/1//
DO - 10.1088/0951-7715/26/1/201
VL - 26
IS - 1
SP - 201-217
SN - 1361-6544
ER -
TY - JOUR
TI - Field Cage Studies and Progressive Evaluation of Genetically-Engineered Mosquitoes
AU - Facchinelli, Luca
AU - Valerio, Laura
AU - Ramsey, Janine M.
AU - Gould, Fred
AU - Walsh, Rachael K.
AU - Bond, Guillermo
AU - Robert, Michael A.
AU - Lloyd, Alun L.
AU - James, Anthony A.
AU - Alphey, Luke
AU - Scott, Thomas W.
T2 - PLOS NEGLECTED TROPICAL DISEASES
AB - Background A genetically-engineered strain of the dengue mosquito vector Aedes aegypti, designated OX3604C, was evaluated in large outdoor cage trials for its potential to improve dengue prevention efforts by inducing population suppression. OX3604C is engineered with a repressible genetic construct that causes a female-specific flightless phenotype. Wild-type females that mate with homozygous OX3604C males will not produce reproductive female offspring. Weekly introductions of OX3604C males eliminated all three targeted Ae. aegypti populations after 10–20 weeks in a previous laboratory cage experiment. As part of the phased, progressive evaluation of this technology, we carried out an assessment in large outdoor field enclosures in dengue endemic southern Mexico. Methodology/Principal Findings OX3604C males were introduced weekly into field cages containing stable target populations, initially at 10∶1 ratios. Statistically significant target population decreases were detected in 4 of 5 treatment cages after 17 weeks, but none of the treatment populations were eliminated. Mating competitiveness experiments, carried out to explore the discrepancy between lab and field cage results revealed a maximum mating disadvantage of up 59.1% for OX3604C males, which accounted for a significant part of the 97% fitness cost predicted by a mathematical model to be necessary to produce the field cage results. Conclusions/Significance Our results indicate that OX3604C may not be effective in large-scale releases. A strain with the same transgene that is not encumbered by a large mating disadvantage, however, could have improved prospects for dengue prevention. Insights from large outdoor cage experiments may provide an important part of the progressive, stepwise evaluation of genetically-engineered mosquitoes.
DA - 2013/1//
PY - 2013/1//
DO - 10.1371/journal.pntd.0002001
VL - 7
IS - 1
SP -
SN - 1935-2735
ER -
TY - JOUR
TI - Coupled oscillations of deformable spherical-cap droplets. Part 2. Viscous motions
AU - Bostwick, J. B.
AU - Steen, P. H.
T2 - JOURNAL OF FLUID MECHANICS
AB - Abstract A spherical drop is constrained by a solid support arranged as a latitudinal belt. The spherical belt splits the drop into two deformable spherical caps. The edges of the belt support are given by lower and upper latitudes, yielding a support of prescribed extent and position: a two-parameter family of geometrical constraints. In this paper we study the linear oscillations of the two coupled surfaces in the viscous case, the inviscid case having been dealt with in Part 1 (Bostwick & Steen, J. Fluid Mech. , vol. 714, 2013, pp. 312–335), restricting to axisymmetric disturbances. For the viscous case, limiting geometries are the spherical-bowl constraint of Strani & Sabetta ( J. Fluid Mech. , vol. 189, 1988, pp. 397–421) and free viscous drop of Prosperetti ( J. Méc. , vol. 19, 1980 b , pp. 149–182). In this paper, a boundary-integral approach leads to an integro-differential boundary-value problem governing the interface disturbances, where the constraint is incorporated into the function space. Viscous effects arise due to relative internal motions and to the no-slip boundary condition on the support surface. No-slip is incorporated using a modified set of shear boundary conditions. The eigenvalue problem is then reduced to a truncated set of algebraic equations using a spectral method in the standard way. Limiting cases recover literature results to validate the proposed modification. Complex frequencies, as they depend upon the viscosity parameter and the support geometry, are reported for both the drop and bubble cases. Finally, for the drop, an approximate boundary between over- and under-damped motions is mapped over the constraint parameter plane.
DA - 2013/1/10/
PY - 2013/1/10/
DO - 10.1017/jfm.2012.480
VL - 714
SP - 336-360
SN - 1469-7645
KW - bubble dynamics
KW - capillary flows
KW - drops
ER -
TY - JOUR
TI - Coupled oscillations of deformable spherical-cap droplets. Part 1. Inviscid motions
AU - Bostwick, J. B.
AU - Steen, P. H.
T2 - JOURNAL OF FLUID MECHANICS
AB - Abstract A spherical drop is constrained by a solid support arranged as a latitudinal belt. This belt support splits the drop into two deformable spherical caps. The edges of the support are given by lower and upper latitudes yielding a ‘spherical belt’ of prescribed extent and position: a two-parameter family of constraints. This is a belt-constrained Rayleigh drop. In this paper we study the linear oscillations of the two coupled spherical-cap surfaces in the inviscid case, and the viscous case is studied in Part 2 (Bostwick & Steen, J. Fluid Mech. , vol. 714, 2013, pp. 336–360), restricting to deformations symmetric about the axis of constraint symmetry. The integro-differential boundary-value problem governing the interface deformation is formulated as a functional eigenvalue problem on linear operators and reduced to a truncated set of algebraic equations using a Rayleigh–Ritz procedure on a constrained function space. This formalism allows mode shapes with different contact angles at the edges of the solid support, as observed in experiment, and readily generalizes to accommodate viscous motions (Part 2). Eigenvalues are mapped in the plane of constraints to reveal where near-multiplicities occur. The full problem is then approximated as two coupled harmonic oscillators by introducing a volume-exchange constraint. The approximation yields eigenvalue crossings and allows post-identification of mass and spring constants for the oscillators.
DA - 2013/1/10/
PY - 2013/1/10/
DO - 10.1017/jfm.2012.483
VL - 714
SP - 312-335
SN - 0022-1120
KW - bubble dynamics
KW - capillary flows
KW - drops
ER -
TY - JOUR
TI - Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters
AU - Brown, Kristen A.
AU - Harlim, John
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - In this paper, we consider a practical filtering approach for assimilating irregularly spaced, sparsely observed turbulent signals through a hierarchical Bayesian reduced stochastic filtering framework. The proposed hierarchical Bayesian approach consists of two steps, blending a data-driven interpolation scheme and the Mean Stochastic Model (MSM) filter. We examine the potential of using the deterministic piecewise linear interpolation scheme and the ordinary kriging scheme in interpolating irregularly spaced raw data to regularly spaced processed data and the importance of dynamical constraint (through MSM) in filtering the processed data on a numerically stiff state estimation problem. In particular, we test this approach on a two-layer quasi-geostrophic model in a two-dimensional domain with a small radius of deformation to mimic ocean turbulence. Our numerical results suggest that the dynamical constraint becomes important when the observation noise variance is large. Second, we find that the filtered estimates with ordinary kriging are superior to those with linear interpolation when observation networks are not too sparse; such robust results are found from numerical simulations with many randomly simulated irregularly spaced observation networks, various observation time intervals, and observation error variances. Third, when the observation network is very sparse, we find that both the kriging and linear interpolations are comparable.
DA - 2013/2/15/
PY - 2013/2/15/
DO - 10.1016/j.jcp.2012.11.006
VL - 235
SP - 143-160
SN - 1090-2716
KW - Hierarchical Bayesian reduced stochastic filter
KW - Mean Stochastic Model
KW - Data assimilation
KW - Filtering interpolated data
ER -
TY - JOUR
TI - The role of additive and multiplicative noise in filtering complex dynamical systems
AU - Gottwald, Georg A.
AU - Harlim, John
T2 - PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
AB - Covariance inflation is an ad hoc treatment that is widely used in practical real-time data assimilation algorithms to mitigate covariance underestimation owing to model errors, nonlinearity, or/and, in the context of ensemble filters, insufficient ensemble size. In this paper, we systematically derive an effective ‘statistical’ inflation for filtering multi-scale dynamical systems with moderate scale gap, , to the case of no scale gap with , in the presence of model errors through reduced dynamics from rigorous stochastic subgrid-scale parametrizations. We will demonstrate that for linear problems, an effective covariance inflation is achieved by a systematically derived additive noise in the forecast model, producing superior filtering skill. For nonlinear problems, we will study an analytically solvable stochastic test model, mimicking turbulent signals in regimes ranging from a turbulent energy transfer range to a dissipative range to a laminar regime. In this context, we will show that multiplicative noise naturally arises in addition to additive noise in a reduced stochastic forecast model. Subsequently, we will show that a ‘statistical’ inflation factor that involves mean correction in addition to covariance inflation is necessary to achieve accurate filtering in the presence of intermittent instability in both the turbulent energy transfer range and the dissipative range.
DA - 2013/7/8/
PY - 2013/7/8/
DO - 10.1098/rspa.2013.0096
VL - 469
IS - 2155
SP -
SN - 1471-2946
KW - data assimilation
KW - covariance inflation
KW - stochastic parametrization
KW - additive noise
KW - multiplicative noise
KW - model error
ER -
TY - JOUR
TI - Stimulus features, resetting curves, and the dependence on adaptation
AU - Arthur, Joseph G.
AU - Burton, Shawn D.
AU - Ermentrout, G. Bard
T2 - JOURNAL OF COMPUTATIONAL NEUROSCIENCE
AB - We derive a formula that relates the spike-triggered covariance (STC) to the phase resetting curve (PRC) of a neural oscillator. We use this to show how changes in the shape of the PRC alter the sensitivity of the neuron to different stimulus features, which are the eigenvectors of the STC. We compute the PRC and STC for some biophysical models. We compare the STCs and their spectral properties for a two-parameter family of PRCs. Surprisingly, the skew of the PRC has a larger effect on the spectrum and shape of the STC than does the bimodality of the PRC (which plays a large role in synchronization properties). Finally, we relate the STC directly to the spike-triggered average and apply this theory to an olfactory bulb mitral cell recording.
DA - 2013/6//
PY - 2013/6//
DO - 10.1007/s10827-012-0433-5
VL - 34
IS - 3
SP - 505-520
SN - 0929-5313
KW - Spike-triggered covariance
KW - Neural oscillator
KW - Phase resetting curve
KW - Perturbation
KW - Adaptation
ER -
TY - JOUR
TI - Spreading and bistability of droplets on differentially heated substrates
AU - Bostwick, J. B.
T2 - JOURNAL OF FLUID MECHANICS
AB - Abstract An axisymmetric drop spreads on a radially heated, partially wetting solid substrate in a rotating geometry. The lubrication approximation is applied to the field equations for this thin viscous drop to yield an evolution equation that captures the dependence of viscosity, surface tension, gravity, centrifugal forces and thermocapillarity. We study the quasi-static spreading regime, whereby droplet motion is controlled by a constitutive law that relates the contact angle to the contact-line speed. Non-uniform heating of the substrate can generate both vertical and radial temperature gradients along the drop interface, which produce distinct thermocapillary forces and equivalently flows that affect the spreading process. For the non-rotating system, competition between surface chemistry (wetting) and thermocapillary flows induced by the thermal gradients gives rise to bistability in certain regions of parameter space in which the droplets converge to an equilibrium shape. The centrifugal forces that develop in a rotating geometry enlarge the bistability regions. Parameter regimes in which the droplet spreads indefinitely are identified and spreading laws are computed to compare with experimental results from the literature.
DA - 2013/6//
PY - 2013/6//
DO - 10.1017/jfm.2013.196
VL - 725
SP - 566-587
SN - 0022-1120
KW - drops and bubbles
KW - interfacial flows (free surface)
KW - thermocapillarity
ER -
TY - JOUR
TI - Soliton cellular automaton associated with D-n((1))-crystal B-2,B-s
AU - Misra, Kailash C.
AU - Wilson, Evan A.
T2 - JOURNAL OF MATHEMATICAL PHYSICS
AB - A solvable vertex model in ferromagnetic regime gives rise to a soliton cellular automaton which is a discrete dynamical system in which site variables take on values in a finite set. We study the scattering of a class of soliton cellular automata associated with the $U_q(D_n^{(1)})$-perfect crystal $B^{2,s}$. We calculate the combinatorial $R$ matrix for all elements of $B^{2,s} \otimes B^{2,1}$. In particular, we show that the scattering rule for our soliton cellular automaton can be identified with the combinatorial $R$ matrix for $U_q(A_1^{(1)}) \oplus U_q(D_{n-2}^{(1)})$-crystals.
DA - 2013/4//
PY - 2013/4//
DO - 10.1063/1.4801448
VL - 54
IS - 4
SP -
SN - 1089-7658
ER -
TY - JOUR
TI - Simple and exact formula for minimum loop length in Ate (i) pairing based on Brezing-Weng curves
AU - Hong, Hoon
AU - Lee, Eunjeong
AU - Lee, Hyang-Sook
AU - Park, Cheol-Min
T2 - DESIGNS CODES AND CRYPTOGRAPHY
AB - We provide a simple and exact formula for the minimum Miller loop length in Ate i pairing based on Brezing–Weng curves, in terms of the involved parameters, under a mild condition on the parameters. It will also be shown that almost all cryptographically useful/meaningful parameters satisfy the mild condition. Hence the simple and exact formula is valid for them. It will also turn out that the formula depends only on essentially two parameters, providing freedom to choose the other parameters to address the design issues other than minimizing the loop length.
DA - 2013/5//
PY - 2013/5//
DO - 10.1007/s10623-011-9605-y
VL - 67
IS - 2
SP - 271-292
SN - 0925-1022
UR - http://dx.doi.org/10.1007/s10623-011-9605-y
KW - Pairing-based cryptosystem
KW - Elliptic curves
KW - Miller algorithm
ER -
TY - JOUR
TI - Quantifying CFSE label decay in flow cytometry data
AU - Banks, H. T.
AU - Choi, A.
AU - Huffman, T.
AU - Nardini, J.
AU - Poag, L.
AU - Thompson, W. C.
T2 - APPLIED MATHEMATICS LETTERS
AB - We developed a series of models for the label decay in cell proliferation assays when the intracellular dye carboxyfluorescein succinimidyl ester (CFSE) is used as a staining agent. Data collected from two healthy patients were used to validate the models and to compare the models with the Akiake Information Criteria. The distinguishing features of multiple decay rates in the data are readily characterized and explained via time dependent decay models such as the logistic and Gompertz models.
DA - 2013/5//
PY - 2013/5//
DO - 10.1016/j.aml.2012.12.010
VL - 26
IS - 5
SP - 571-577
SN - 0893-9659
KW - Carboxyfluorescein succinimidyl ester (CFSE)
KW - Ordinary differential equation models
KW - Inverse problems
KW - Exponential decay
KW - Gompertz growth
KW - Akiake Information
ER -
TY - JOUR
TI - Patient-specific modeling of cardiovascular and respiratory dynamics during hypercapnia
AU - Ellwein, L.M.
AU - Pope, S.R.
AU - Xie, A.
AU - Batzel, J.J.
AU - Kelley, C.T.
AU - Olufsen, M.S.
T2 - Mathematical Biosciences
AB - This study develops a lumped cardiovascular–respiratory system-level model that incorporates patient-specific data to predict cardiorespiratory response to hypercapnia (increased CO2 partial pressure) for a patient with congestive heart failure (CHF). In particular, the study focuses on predicting cerebral CO2 reactivity, which can be defined as the ability of vessels in the cerebral vasculature to expand or contract in response CO2 induced challenges. It is difficult to characterize cerebral CO2 reactivity directly from measurements, since no methods exist to dynamically measure vasomotion of vessels in the cerebral vasculature. In this study we show how mathematical modeling can be combined with available data to predict cerebral CO2 reactivity via dynamic predictions of cerebral vascular resistance, which can be directly related to vasomotion of vessels in the cerebral vasculature. To this end we have developed a coupled cardiovascular and respiratory model that predicts blood pressure, flow, and concentration of gasses (CO2 and O2) in the systemic, cerebral, and pulmonary arteries and veins. Cerebral vascular resistance is incorporated via a model parameter separating cerebral arteries and veins. The model was adapted to a specific patient using parameter estimation combined with sensitivity analysis and subset selection. These techniques allowed estimation of cerebral vascular resistance along with other cardiovascular and respiratory parameters. Parameter estimation was carried out during eucapnia (breathing room air), first for the cardiovascular model and then for the respiratory model. Then, hypercapnia was introduced by increasing inspired CO2 partial pressure. During eucapnia, seven cardiovascular parameters and four respiratory parameters was be identified and estimated, including cerebral and systemic resistance. During the transition from eucapnia to hypercapnia, the model predicted a drop in cerebral vascular resistance consistent with cerebral vasodilation.
DA - 2013/1//
PY - 2013/1//
DO - 10.1016/j.mbs.2012.09.003
VL - 241
IS - 1
SP - 56-74
J2 - Mathematical Biosciences
LA - en
OP -
SN - 0025-5564
UR - http://dx.doi.org/10.1016/j.mbs.2012.09.003
DB - Crossref
KW - Sensitivity analysis
KW - Parameter estimation
KW - Physiological models
KW - Cerebral blood flow
KW - Complex models
ER -
TY - JOUR
TI - Optimal control laws for traffic flow
AU - Aihara, K.
AU - Ito, K.
AU - Nakagawa, J.
AU - Takeuchi, T.
T2 - APPLIED MATHEMATICS LETTERS
AB - Optimal “on–off” laws for the traffic signals are developed based on the bilinear control problem with the binary constraints. A Lyapunov function based feedback law for regulating traffic congestions is developed. Also, a real-time optimal signal law is developed using a novel binary optimization method. Both methods are tested and compared, and our tests demonstrate that the both methods provide very effective and efficient traffic control laws.
DA - 2013/6//
PY - 2013/6//
DO - 10.1016/j.aml.2012.12.021
VL - 26
IS - 6
SP - 617-623
SN - 0893-9659
KW - Traffic signal control
KW - Binary optimization
KW - Lyapunov method
KW - Real time optimal control
ER -
TY - JOUR
TI - On the numerical treatment of linear-quadratic optimal control problems for general linear time-varying differential-algebraic equations
AU - Campbell, Stephen L.
AU - Kunkel, Peter
T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
AB - The development of numerical methods for finding optimal solutions of control problems modeled by differential-algebraic equations (DAEs) is an important task. Usually restrictions are placed on the DAE such as being semi-explicit. Here the numerical solution of optimal control problems with linear time-varying DAEs as the process and quadratic cost functionals is considered. The leading coefficient is allowed to be time-varying and the DAE may be of higher index. Both a direct transcription approach and the solution of the necessary conditions are examined for two important discretizations.
DA - 2013/4//
PY - 2013/4//
DO - 10.1016/j.cam.2012.10.011
VL - 242
SP - 213-231
SN - 1879-1778
KW - Differential-algebraic equation
KW - Optimal control
KW - Radau
KW - Gauss-Lobatto
KW - Direct transcription
KW - Numerical methods
ER -
TY - JOUR
TI - Numerical simulation of water resources problems: Models, methods, and trends
AU - Miller, Cass T.
AU - Dawson, Clint N.
AU - Farthing, Matthew W.
AU - Hou, Thomas Y.
AU - Huang, Jingfang
AU - Kees, Christopher E.
AU - Kelley, C. T.
AU - Langtangen, Hans Petter
T2 - ADVANCES IN WATER RESOURCES
AB - Mechanistic modeling of water resources systems is a broad field with abundant challenges. We consider classes of model formulations that are considered routine, the focus of current work, and the foundation of foreseeable work over the coming decade. These model formulations are used to assess the current and evolving state of solution algorithms, discretization methods, nonlinear and linear algebraic solution methods, computational environments, and hardware trends and implications. The goal of this work is to provide guidance to enable modelers of water resources systems to make sensible choices when developing solution methods based upon the current state of knowledge and to focus future collaborative work among water resources scientists, applied mathematicians, and computational scientists on productive areas.
DA - 2013/1//
PY - 2013/1//
DO - 10.1016/j.advwatres.2012.05.008
VL - 51
SP - 405-437
SN - 1872-9657
KW - Adaptive methods
KW - Problem solving environments
KW - Multiscale methods
KW - Integral methods
KW - GPUs
KW - Error estimation and control
ER -
TY - JOUR
TI - Isosingular Sets and Deflation
AU - Hauenstein, Jonathan D.
AU - Wampler, Charles W.
T2 - FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
AB - This article introduces the concept of isosingular sets, which are irreducible algebraic subsets of the set of solutions to a system of polynomial equations constructed by taking the closure of points with a common singularity structure. The definition of these sets depends on deflation, a procedure that uses differentiation to regularize solutions. A weak form of deflation has proven useful in regularizing algebraic sets, making them amenable to treatment by the algorithms of numerical algebraic geometry. We introduce a strong form of deflation and define deflation sequences, which, in a different context, are the sequences arising in Thom–Boardman singularity theory. We then define isosingular sets in terms of deflation sequences. We also define the isosingular local dimension and examine the properties of isosingular sets. While isosingular sets are of theoretical interest as constructs for describing singularity structures of algebraic sets, they also expand the kinds of algebraic set that can be investigated with methods from numerical algebraic geometry.
DA - 2013/6//
PY - 2013/6//
DO - 10.1007/s10208-013-9147-y
VL - 13
IS - 3
SP - 371-403
SN - 1615-3383
KW - Irreducible algebraic set
KW - Deflation
KW - Deflation sequence
KW - Multiplicity
KW - Isosingular set
KW - Isosingular point
KW - Isosingular local dimension
KW - Numerical algebraic geometry
KW - Polynomial system
KW - Witness point
KW - Witness set
KW - Local dimension
ER -
TY - JOUR
TI - Generalized Bell states and principal realization of the Yangian Y(sl(N))
AU - Liu, Ming
AU - Bai, Chengming
AU - Ge, Mo-Lin
AU - Jing, Naihuan
T2 - JOURNAL OF MATHEMATICAL PHYSICS
AB - We prove that the action of the Yangian algebra $Y(\mathfrak {sl}_N)$Y(slN) is better described by the principal generators on the tensor product of the fundamental representation and its dual. The generalized Bell states or maximally entangled states are permuted by the principal generators in a dramatically simple manner on the tensor product. Under the Yangian symmetry the new quantum number $\bf J^2$J2 is also explicitly computed, which gives an explanation for these maximally entangled states.
DA - 2013/2//
PY - 2013/2//
DO - 10.1063/1.4789317
VL - 54
IS - 2
SP -
SN - 1089-7658
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84874725231&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Developing Predictive Approaches to Characterize Adaptive Responses of the Reproductive Endocrine Axis to Aromatase Inhibition: II. Computational Modeling
AU - Breen, Miyuki
AU - Villeneuve, Daniel L.
AU - Ankley, Gerald T.
AU - Bencic, David C.
AU - Breen, Michael S.
AU - Watanabe, Karen H.
AU - Lloyd, Alun L.
AU - Conolly, Rory B.
T2 - TOXICOLOGICAL SCIENCES
AB - Endocrine-disrupting chemicals can affect reproduction and development in humans and wildlife. We developed a computational model of the hypothalamic-pituitary-gonadal (HPG) axis in female fathead minnows to predict dose-response and time-course (DRTC) behaviors for endocrine effects of the aromatase inhibitor, fadrozole (FAD). The model describes adaptive responses to endocrine stress involving regulated secretion of a generic gonadotropin (LH/FSH) from the hypothalamic-pituitary complex. For model development, we used plasma 17β-estradiol (E2) concentrations and ovarian cytochrome P450 (CYP) 19A aromatase mRNA data from two time-course experiments, each of which included both an exposure and a depuration phase, and plasma E2 data from a third 4-day study. Model parameters were estimated using E2 concentrations for 0, 0.5, and 3 µg/l FAD exposure concentrations, and good fits to these data were obtained. The model accurately predicted CYP19A mRNA fold changes for controls and three FAD doses (0, 0.5, and 3 µg/l) and plasma E2 dose response from the 4-day study. Comparing the model-predicted DRTC with experimental data provided insight into how the feedback control mechanisms in the HPG axis mediate these changes: specifically, adaptive changes in plasma E2 levels occurring during exposure and "overshoot" occurring postexposure. This study demonstrates the value of mechanistic modeling to examine and predict dynamic behaviors in perturbed systems. As this work progresses, we will obtain a refined understanding of how adaptive responses within the vertebrate HPG axis affect DRTC behaviors for aromatase inhibitors and other types of endocrine-active chemicals and apply that knowledge in support of risk assessments.
DA - 2013/6//
PY - 2013/6//
DO - 10.1093/toxsci/kft067
VL - 133
IS - 2
SP - 234-247
SN - 1096-0929
KW - endocrine disruptors
KW - biological modeling
KW - non-mammalian species
KW - dose response
KW - biomarkers
ER -
TY - JOUR
TI - Communication: Certifying the potential energy landscape
AU - Mehta, Dhagash
AU - Hauenstein, Jonathan D.
AU - Wales, David J.
T2 - JOURNAL OF CHEMICAL PHYSICS
AB - It is highly desirable for numerical approximations to stationary points for a potential energy landscape to lie in the corresponding quadratic convergence basin. However, it is possible that an approximation may lie only in the linear convergence basin, or even in a chaotic region, and hence not converge to the actual stationary point when further optimization is attempted. Proving that a numerical approximation will quadratically converge to the associated stationary point is termed certification. Here, we apply Smale's α-theory to stationary points, providing a certification serving as a mathematical proof that the numerical approximation does indeed correspond to an actual stationary point, independent of the precision employed. As a practical example, employing recently developed certification algorithms, we show how the α-theory can be used to certify all the known minima and transition states of Lennard-Jones LJN atomic clusters for N = 7, …, 14.
DA - 2013/5/7/
PY - 2013/5/7/
DO - 10.1063/1.4803162
VL - 138
IS - 17
SP -
SN - 0021-9606
ER -
TY - JOUR
TI - Center conditions and cyclicity for a family of cubic systems: Computer algebra approach
AU - Fercec, Brigita
AU - Mahdi, Adam
T2 - MATHEMATICS AND COMPUTERS IN SIMULATION
AB - Using methods of computational algebra we obtain an upper bound for the cyclicity of a family of cubic systems. We overcame the problem of nonradicality of the associated Bautin ideal by moving from the ring of polynomials to a coordinate ring. Finally, we determine the number of limit cycles bifurcating from each component of the center variety.
DA - 2013/1//
PY - 2013/1//
DO - 10.1016/j.matcom.2013.02.003
VL - 87
SP - 55-67
SN - 0378-4754
KW - Cyclicity
KW - Limit cycles
KW - Center-focus problem
ER -
TY - JOUR
TI - A lifelong model for the female reproductive cycle with an antimullerian hormone treatment to delay menopause
AU - Margolskee, Alison
AU - Selgrade, James F.
T2 - JOURNAL OF THEORETICAL BIOLOGY
AB - A system of 16 non-linear, delay differential equations with 66 parameters is developed to model hormonal regulation of the menstrual cycle of a woman from age 20 to 51. This mechanistic model predicts changes in follicle numbers and reproductive hormones that naturally occur over that time span. In particular, the model illustrates the decline in the pool of primordial follicles from age 20 to menopause as reported in the biological literature. Also, model simulations exhibit a decrease in antimüllerian hormone (AMH) and inhibin B and an increase in FSH with age corresponding to the experimental data. Model simulations using the administration of exogenous AMH show that the transfer of non-growing primordial follicles to the active state can be slowed enough to provide more follicles for development later in life and to cause a delay in the onset of menopause as measured by the number of primordial follicles remaining in the ovaries. Other effects of AMH agonists and antagonists are investigated in the setting of this model.
DA - 2013/6/7/
PY - 2013/6/7/
DO - 10.1016/j.jtbi.2013.02.007
VL - 326
SP - 21-35
SN - 1095-8541
KW - Menstrual cycle
KW - Primordial follicle
KW - Parameter identification
ER -
TY - JOUR
TI - Subresultants in multiple roots
AU - Bostan, A.
AU - D'Andrea, C.
AU - Krick, T.
AU - Szanto, Agnes
AU - Valdettaro, M.
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - We extend our previous work on Poisson-like formulas for subresultants in roots to the case of polynomials with multiple roots in both the univariate and multivariate case, and also explore some closed formulas in roots for univariate polynomials in this multiple roots setting.
DA - 2013/3/1/
PY - 2013/3/1/
DO - 10.1016/j.laa.2012.11.004
VL - 438
IS - 5
SP - 1969-1989
SN - 1873-1856
KW - subresultants
KW - Sylvester sums
KW - root multiplicity
KW - Hermite interpolation
ER -
TY - JOUR
TI - Reduction of ionospheric distortions for spaceborne synthetic aperture radar with the help of image registration
AU - Gilman, Mikhail
AU - Smith, Erick
AU - Tsynkov, Semyon
T2 - Inverse Problems
AB - We propose a robust technique for reducing the ionospheric distortions in spaceborne synthetic aperture radar (SAR) images. It is based on probing the terrain on two distinct carrier frequencies. Compared to our previous work on the subject (Smith and Tsynkov 2011 SIAM J. Imaging Sciences 4 501–42), the increase in robustness is achieved by applying an area-based image registration algorithm to the two images obtained on two frequencies. This enables an accurate evaluation of the shift between the two images, which, in turn, translates into an accurate estimate of the total electron content and its along-track gradient in the ionosphere. These estimates allow one to correct the matched filter and thus improve the quality of the image. Moreover, for the analysis of SAR resolution in the current paper we take into account the Ohm conductivity in the ionosphere (in addition to its temporal dispersion), and also consider the true Kolmogorov spectrum of the ionospheric turbulence, as opposed to its approximate representation that we have used previously.
DA - 2013/4/18/
PY - 2013/4/18/
DO - 10.1088/0266-5611/29/5/054005
VL - 29
IS - 5
SP - 054005
J2 - Inverse Problems
OP -
SN - 0266-5611 1361-6420
UR - http://dx.doi.org/10.1088/0266-5611/29/5/054005
DB - Crossref
ER -
TY - JOUR
TI - Positivity for Gaussian graphical models
AU - Draisma, Jan
AU - Sullivant, Seth
AU - Talaska, Kelli
T2 - ADVANCES IN APPLIED MATHEMATICS
AB - Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient condition in terms of the graph for when a subdeterminant is zero for all covariance matrices that belong to the Gaussian graphical model. Here we extend this result to give explicit cancellation-free formulas for the expansions of non-zero subdeterminants.
DA - 2013/5//
PY - 2013/5//
DO - 10.1016/j.aam.2013.03.001
VL - 50
IS - 5
SP - 661-674
SN - 0196-8858
KW - Gaussian graphical model
KW - Conditional independence
KW - Determinant
KW - Lindstrom-Gessel-Viennot Lemma
ER -
TY - JOUR
TI - Polyhedral combinatorics of UPGMA cones
AU - Davidson, Ruth
AU - Sullivant, Seth
T2 - ADVANCES IN APPLIED MATHEMATICS
AB - Distance-based methods such as UPGMA (Unweighted Pair Group Method with Arithmetic Mean) continue to play a significant role in phylogenetic research. We use polyhedral combinatorics to analyze the natural subdivision of the positive orthant induced by classifying the input vectors according to tree topologies returned by the algorithm. The partition lattice informs the study of UPGMA trees. We give a closed form for the extreme rays of UPGMA cones on n taxa, and compute the spherical volumes of the UPGMA cones for small n .
DA - 2013/2//
PY - 2013/2//
DO - 10.1016/j.aam.2012.10.002
VL - 50
IS - 2
SP - 327-338
SN - 1090-2074
KW - Phylogenetic trees
KW - Polyhedral combinatorics
KW - Partition lattice
ER -
TY - JOUR
TI - Object-Image Correspondence for Algebraic Curves under Projections
AU - Burdis, Joseph M.
AU - Kogan, Irina A.
AU - Hong, Hoon
T2 - SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
AB - We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. The motivation comes from the problem of establishing a correspondence between an object and an image, taken by a camera with unknown position and parameters. A straightforward approach to this problem consists of setting up a system of conditions on the projection parameters and then checking whether or not this system has a solution. The computational advantage of the algorithm presented here, in comparison to algorithms based on the straightforward approach, lies in a significant reduction of a number of real parameters that need to be eliminated in order to establish existence or non-existence of a projection that maps a given spatial curve to a given planar curve. Our algorithm is based on projection criteria that reduce the projection problem to a certain modification of the equivalence problem of planar curves under affine and projective transformations. To solve the latter problem we make an algebraic adaptation of signature construction that has been used to solve the equivalence problems for smooth curves. We introduce a notion of a classifying set of rational differential invariants and produce explicit formulas for such invariants for the actions of the projective and the affine groups on the plane.
DA - 2013///
PY - 2013///
DO - 10.3842/sigma.2013.023
VL - 9
SP -
SN - 1815-0659
UR - http://dx.doi.org/10.3842/sigma.2013.023
KW - central and parallel projections
KW - finite and affine cameras
KW - camera decomposition
KW - curves
KW - classifying differential invariants
KW - projective and affine transformations
KW - signatures
KW - machine vision
ER -
TY - JOUR
TI - Numerically Computing Real Points on Algebraic Sets
AU - Hauenstein, Jonathan D.
T2 - ACTA APPLICANDAE MATHEMATICAE
AB - Given a polynomial system f, a fundamental question is to determine if f has real roots. Many algorithms involving the use of infinitesimal deformations have been proposed to answer this question. In this article, we transform an approach of Rouillier, Roy, and Safey El Din, which is based on a classical optimization approach of Seidenberg, to develop a homotopy based approach for computing at least one point on each connected component of a real algebraic set. Examples are presented demonstrating the effectiveness of this parallelizable homotopy based approach.
DA - 2013/6//
PY - 2013/6//
DO - 10.1007/s10440-012-9782-3
VL - 125
IS - 1
SP - 105-119
SN - 1572-9036
KW - Real algebraic geometry
KW - Infinitesimal deformation
KW - Homotopy
KW - Numerical algebraic geometry
KW - Polynomial system
ER -
TY - JOUR
TI - High order numerical simulation of the transmission and scattering of waves using the method of difference potentials
AU - Medvinsky, M.
AU - Tsynkov, S.
AU - Turkel, E.
T2 - Journal of Computational Physics
AB - The method of difference potentials generalizes the method of Calderon’s operators from PDEs to arbitrary difference equations and systems. It offers several key advantages, such as the capability of handling boundaries/interfaces that are not aligned with the discretization grid, variable coefficients, and nonstandard boundary conditions. In doing so, the complexity of the algorithm remains comparable to that of an ordinary finite difference scheme on a regular structured grid. Previously, we have applied the method of difference potentials to solving several variable coefficient interior Helmholtz problems with fourth and sixth order accuracy. We have employed compact finite difference schemes as a core discretization methodology. Those schemes enable high order accuracy on narrow stencils and hence require only as many boundary conditions as needed for the underlying differential equation itself. Numerical experiments corroborate the high order accuracy of our method for variable coefficients, regular grids, and non-conforming boundaries. In the current paper, we extend the previously developed methodology to exterior problems. We present a complete theoretical analysis of the algorithm, as well as the results of a series of numerical simulations. Specifically, we study the scattering of time-harmonic waves about smooth shapes, subject to various boundary conditions. We also solve the transmission/scattering problems, in which not only do the waves scatter off a given shape but also propagate through the interface and travel across the heterogeneous medium inside. In all the cases, our methodology guarantees high order accuracy for regular grids and non-conforming boundaries and interfaces.
DA - 2013/6//
PY - 2013/6//
DO - 10.1016/j.jcp.2013.03.014
VL - 243
SP - 305-322
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2013.03.014
DB - Crossref
KW - Difference potentials
KW - Boundary projections
KW - Calderon's operators
KW - Regular grids
KW - Curvilinear boundaries
KW - Non-conforming boundaries/interfaces
KW - Variable coefficients
KW - Compact differencing
KW - High order accuracy
KW - Exterior problems
KW - Artificial boundary conditions
ER -
TY - JOUR
TI - Granular Free Surfaces
AU - Gordon-Wright, Rachael
AU - Gremaud, Pierre A.
T2 - SIAM REVIEW
AB - We explore the notion of angle of repose for granular materials. As an illustration, we solve free surface problems for centrifuged granular piles. These have recently been considered as an affordable and simple way to experiment with powders and dust in reduced gravity environments such as on the Moon or on Mars.
DA - 2013///
PY - 2013///
DO - 10.1137/090747944
VL - 55
IS - 1
SP - 168-184
SN - 1095-7200
KW - free surfaces
KW - friction
KW - mechanics
KW - granular material
KW - differential inclusions
KW - partial differential equations
ER -
TY - JOUR
TI - A structured population modeling framework for quantifying and predicting gene expression noise in flow cytometry data
AU - Flores, Kevin B.
T2 - APPLIED MATHEMATICS LETTERS
AB - We formulated a structured population model with distributed parameters to identify mechanisms that contribute to gene expression noise in time-dependent flow cytometry data. The model was validated using cell population-level gene expression data from two experiments with synthetically engineered eukaryotic cells. Our model captures the qualitative noise features of both experiments and accurately fit the data from the first experiment. Our results suggest that cellular switching between high and low expression states and transcriptional re-initiation are important factors needed to accurately describe gene expression noise with a structured population model.
DA - 2013/7//
PY - 2013/7//
DO - 10.1016/j.aml.2013.03.003
VL - 26
IS - 7
SP - 794-798
SN - 0893-9659
KW - Structured population models
KW - Distributed parameters
KW - Gene regulatory networks
KW - Gene expression noise
KW - Synthetic biology
ER -
TY - JOUR
TI - Numerical Poisson-Boltzmann model for continuum membrane systems
AU - Botello-Smith, Wesley M.
AU - Liu, Xingping
AU - Cai, Qin
AU - Li, Zhilin
AU - Zhao, Hongkai
AU - Luo, Ray
T2 - CHEMICAL PHYSICS LETTERS
AB - Membrane protein systems are important computational research topics due to their roles in rational drug design. In this study, we developed a continuum membrane model utilizing a level set formulation under the numerical Poisson-Boltzmann framework within the AMBER molecular mechanics suite for applications such as protein-ligand binding affinity and docking pose predictions. Two numerical solvers were adapted for periodic systems to alleviate possible edge effects. Validation on systems ranging from organic molecules to membrane proteins up to 200 residues, demonstrated good numerical properties. This lays foundations for sophisticated models with variable dielectric treatments and second-order accurate modeling of solvation interactions.
DA - 2013/1/3/
PY - 2013/1/3/
DO - 10.1016/j.cplett.2012.10.081
VL - 555
SP - 274-281
SN - 1873-4448
ER -
TY - JOUR
TI - Numerical methods for a coupled system of differential equations arising from a thermal ignition problem
AU - Pao, C. V.
AU - Chang, Yu-Hsien
AU - Jau, Guo-Chin
T2 - NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
AB - Abstract This article is concerned with monotone iterative methods for numerical solutions of a coupled system of a first‐order partial differential equation and an ordinary differential equation which arises from fast‐igniting catalytic converters in automobile engineering. The monotone iterative scheme yields a straightforward marching process for the corresponding discrete system by the finite‐difference method, and it gives not only a computational algorithm for numerical solutions of the problem but also the existence and uniqueness of a finite‐difference solution. Particular attention is given to the “finite‐time” blow‐up property of the solution. In terms of minimal sequence of the monotone iterations, some necessary and sufficient conditions for the blow‐up solution are obtained. Also given is the convergence of the finite‐difference solution to the continuous solution as the mesh size tends to zero. Numerical results of the problem, including a case where the continuous solution is explicitly known, are presented and are compared with the known solution. Special attention is devoted to the computation of the blow‐up time and the critical value of a physical parameter which determines the global existence and the blow‐up property of the solution. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013
DA - 2013/1//
PY - 2013/1//
DO - 10.1002/num.21708
VL - 29
IS - 1
SP - 251-279
SN - 0749-159X
KW - blow-up solution
KW - catalytic converter
KW - finite difference solution
KW - monotone iteration
KW - system of first-order equations
ER -
TY - JOUR
TI - Linear algebraic groups as parameterized Picard-Vessiot Galois groups
AU - Singer, Michael F.
T2 - JOURNAL OF ALGEBRA
AB - We show that a linear algebraic group is the Galois group of a parameterized Picard–Vessiot extension of k(x), x′=1, for certain differential fields k, if and only if its identity component has no one-dimensional quotient as a linear algebraic group.
DA - 2013/1/1/
PY - 2013/1/1/
DO - 10.1016/j.jalgebra.2012.09.037
VL - 373
SP - 153-161
SN - 1090-266X
KW - Parameterized Picard-Vessiot theory
KW - Linear algebraic groups
KW - Inverse problem
ER -
TY - JOUR
TI - First Report of Potato spindle tuber viroid Naturally Infecting Greenhouse Tomatoes in North Carolina
AU - Ling, K. -S.
AU - Li, R.
AU - Panthee, D. R.
AU - Gardner, R. G.
T2 - PLANT DISEASE
AB - In spring 2012, a severe disease was observed on a limited number of tomato plants (Solanum lycopersicum L.) in a research greenhouse facility in western North Carolina. The first symptoms noted were downward curling of the terminal leaves accompanied by a rough puckered darker green texture. This was followed in time by greater distortion of the leaves with pale green on leaf margins. Older leaves with symptoms developed necrosis, with necrotic spots and streaks appearing on a few fruits. On some of these affected fruits, stems, peduncles, pedicels, and sepals also showed symptoms. Infected plants were badly stunted, and fruits in the upper parts of plants displaying severe symptoms remained very small. In just a few months, the disease spread to other tomato plants inside the greenhouse. A survey in May 2012 showed a disease incidence of 18% (156 symptomatic plants out of a total of 864) in this greenhouse. Initial screenings for possible viruses using ELISA (Agdia, Elkhart, IN), as well as a reverse transcription (RT)-PCR panel of 15 common tomato viruses in our laboratory were negative. Because of the symptoms and negative results for viruses, a viroid infection was suspected. Total plant RNA was prepared using TRIzol reagent (Invitrogen, Carlsbad, CA) from leaf tissues of eight diseased plants and one seed sample. Using real-time RT-PCR developed against Potato spindle tuber viroid (PSTVd) and some related pospiviroids (1), positive signals were observed with a mean Ct = 13.24 for leaf tissues and Ct = 19.91 for the seed sample. To obtain a full viroid genome, RT-PCR using two different sets of primers, one specific for PSTVd (PSTVd-F and PSTVd-R) (2), and a universal primer set for pospiviroids (MTTVd-F and MTTVd-R) (3) was performed. RT-PCR generated amplicons with expected size of ~360 bp from all eight leaf and one seed samples, but not from a healthy control. PCR products were cloned using the TOPO TA cloning kit (Invitrogen, Carlsbad, CA). A total of 22 full genomic sequences were obtained. A multi-sequence alignment generated a consensus sequence of 360 nt, designated as NC12-01 (GenBank Accession No. JX280944). BLASTn search in the NCBI database revealed the highest sequence identity of 96.9% to Australian (AY962324) and UK (AJ583449) isolates of PSTVd and 95.9% identity to the tomato isolate of PSTVd-CA1 (HM753555). Similar disease symptoms were observed on two ‘Rutgers’ tomato plants 2 weeks post mechanical inoculation and the presence of PSTVd was confirmed by real-time RT-PCR (1). A mock-inoculated plant did not show any symptoms. In the U.S., natural infection of PSTVd on tomato was first identified in California in 2010 (3). To our knowledge, this is the first report of a natural occurrence of PSTVd on tomato in the eastern U.S. The diseased plants were contained, properly disposed of, and eradicated in this location. The broader geographic distribution of PSTVd on tomato in the U.S., and the potential latent infection in potato and a number of ornamentals (4), emphasizes the need for better plant and seed health tests for viroids on these plants. References: (1) N. Boonham et al. J. Virol. Methods 116:139, 2004. (2) H. Bostan et al. J. Virol. Methods 116:189, 2004. (3) K.-S. Ling and D. Sfetcu. Plant Dis. 94:1376, 2010. (4) R. A. Owens and J. Th. J. Verhoeven. The Plant Health Instructor. DOI: 10.1094/PHI-I-2009-0804-01, 2009.
DA - 2013/1//
PY - 2013/1//
DO - 10.1094/pdis-07-12-0679-pdn
VL - 97
IS - 1
SP - 148-149
SN - 0191-2917
ER -
TY - JOUR
TI - Exploring a charge-central strategy in the solution of Poisson's equation for biomolecular applications
AU - Liu, Xingping
AU - Wang, Changhao
AU - Wang, Jun
AU - Li, Zhilin
AU - Zhao, Hongkai
AU - Luo, Ray
T2 - PHYSICAL CHEMISTRY CHEMICAL PHYSICS
AB - Continuum solvent treatments based on the Poisson–Boltzmann equation have been widely accepted for energetic analysis of biomolecular systems. In these approaches, the molecular solute is treated as a low dielectric region and the solvent is treated as a high dielectric continuum. The existence of a sharp dielectric jump at the solute–solvent interface poses a challenge to model the solvation energetics accurately with such a simple mathematical model. In this study, we explored and evaluated a strategy based on the “induced surface charge” to eliminate the dielectric jump within the finite-difference discretization scheme. In addition to the use of the induced surface charges in solving the equation, the second-order accurate immersed interface method is also incorporated to discretize the equation. The resultant linear system is solved with the GMRES algorithm to explicitly impose the flux conservation condition across the solvent–solute interface. The new strategy was evaluated on both analytical and realistic biomolecular systems. The numerical tests demonstrate the feasibility of utilizing induced surface charge in the finite-difference solution of the Poisson–Boltzmann equation. The analysis data further show that the strategy is consistent with theory and the classical finite-difference method on the tested systems. Limitations of the current implementations and further improvements are also analyzed and discussed to fully bring out its potential of achieving higher numerical accuracy.
DA - 2013///
PY - 2013///
DO - 10.1039/c2cp41894k
VL - 15
IS - 1
SP - 129-141
SN - 1463-9084
ER -
TY - JOUR
TI - Darboux integrability of the Lu system
AU - Llibre, Jaume
AU - Mahdi, Adam
AU - Valls, Claudia
T2 - JOURNAL OF GEOMETRY AND PHYSICS
AB - We characterize all the values of the parameters of the Lü system, for which it admits a Darboux first integral.
DA - 2013/1//
PY - 2013/1//
DO - 10.1016/j.geomphys.2012.10.003
VL - 63
SP - 118-128
SN - 1879-1662
KW - Darboux integrability
KW - Exponential factor
KW - Darboux polynomials
KW - Lu systems
ER -
TY - JOUR
TI - Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number
AU - Turkel, Eli
AU - Gordon, Dan
AU - Gordon, Rachel
AU - Tsynkov, Semyon
T2 - Journal of Computational Physics
AB - Several studies have presented compact fourth order accurate finite difference approximation for the Helmholtz equation in two or three dimensions. Several of these formulae allow for the wave number k to be variable. Other papers have extended this further to include variable coefficients within the Laplacian which models non-homogeneous materials in electromagnetism. Later papers considered more accurate compact sixth order methods but these were restricted to constant k. In this paper we extend these compact sixth order schemes to variable k in both two and three dimensions. Results on 2D and 3D problems with known analytic solutions verify the sixth order accuracy. We demonstrate that for large wave numbers, the second order scheme cannot produce comparable results with reasonable grid sizes.
DA - 2013/1//
PY - 2013/1//
DO - 10.1016/j.jcp.2012.08.016
VL - 232
IS - 1
SP - 272-287
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2012.08.016
DB - Crossref
KW - Helmholtz equation
KW - Compact high order schemes
KW - Variable wave number
KW - High frequency
KW - Large wave number
KW - Parallel computing
KW - CARP-CG
ER -