TY - JOUR
TI - An $l^2$ decoupling interpretation of efficient congruencing: the parabola
DA - 2018/5/26/
PY - 2018/5/26/
ER -
TY - CONF
TI - Video: Dynamics of thin films down vertical fibers
AU - Sadeghpour, Abolfazl
AU - Zeng, Zezhi
AU - Ji, Hangjie
AU - Falcon, Claudia
AU - Ju, Y. Sungtaek
AU - Bertozzi, Andrea
C2 - 2018/11//
C3 - 71th Annual Meeting of the APS Division of Fluid Dynamics - Gallery of Fluid Motion
DA - 2018/11//
DO - 10.1103/aps.dfd.2018.gfm.v0005
PB - American Physical Society
ER -
TY - JOUR
TI - Numerical methods for thermally stressed shallow shell equations
AU - Ji, H.
AU - Li, L.
T2 - Journal of Computational and Applied Mathematics
AB - We develop efficient and accurate numerical methods to solve a class of shallow shell problems of the von Karman type. The governing equations form a fourth-order coupled system of nonlinear biharnomic equations for the transverse deflection and Airy's stress function. A second-order finite difference discretization with three iterative methods (Picard, Newton and Trust-Region Dogleg) are proposed for the numerical solution of the nonlinear PDE system. Three simple boundary conditions and two application-motivated mixed boundary conditions are considered. Along with the nonlinearity of the system, boundary singularities that appear when mixed boundary conditions are specified are the main numerical challenges. Two approaches that use either a transition function or local corrections are developed to deal with these boundary singularities. All the proposed numerical methods are validated using carefully designed numerical tests, where expected orders of accuracy and rates of convergence are observed. A rough run-time performance comparison is also conducted to illustrate the efficiency of our methods. As an application of the methods, a snap-through thermal buckling problem is considered. The critical thermal loads of shell buckling with various boundary conditions are numerically calculated, and snap-through bifurcation curves are also obtained using our numerical methods together with a pseudo-arclength continuation method. Our results are consistent with previous studies.
DA - 2018///
PY - 2018///
DO - 10.1016/j.cam.2018.10.005
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85056263014&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Instability and dynamics of volatile thin films
AU - Ji, Hangjie
AU - Witelski, Thomas P.
T2 - Physical Review Fluids
AB - Volatile viscous fluids on partially-wetting solid substrates can exhibit interesting interfacial instabilities and pattern formation. We study the dynamics of vapor condensation and fluid evaporation governed by a one-sided model in a low Reynolds number lubrication approximation incorporating surface tension, intermolecular effects and evaporative fluxes. Parameter ranges for evaporation- dominated and condensation-dominated regimes and a critical case are identified. Interfacial instabilities driven by the competition between the disjoining pressure and evaporative effects are studied via linear stability analysis. Transient pattern formation in nearly-flat evolving films in the critical case is investigated. In the weak evaporation limit unstable modes of finite amplitude non-uniform steady states lead to rich droplet dynamics, including flattening, symmetry breaking, and droplet merging. Numerical simulations show long time behaviors leading to evaporation or condensation are sensitive to transitions between film-wise and drop-wise dynamics.
DA - 2018///
PY - 2018///
DO - 10.1103/PhysRevFluids.3.024001
VL - 3
IS - 2
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85043242689&partnerID=MN8TOARS
ER -
TY - JOUR
TI - A vicinal surface model for epitaxial growth with logarithmic free energy
AU - Gao, Y.
AU - Ji, H.
AU - Liu, J.-G.
AU - Witelski, T.P.
T2 - Discrete and Continuous Dynamical Systems - Series B
AB - We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, $u_t = -u^2(u^3+α u)_{hhhh}$, gives the evolution for the surface slope $u$ as a function of the local height $h$ in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of $u$ converging to a constant that only depends on the initial data is also investigated both analytically and numerically.
DA - 2018///
PY - 2018///
DO - 10.3934/dcdsb.2018170
VL - 23
IS - 10
SP - 4433-4453
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85054181122&partnerID=MN8TOARS
ER -
TY - JOUR
TI - A nodal finite element approximation of a phase field model for shape and topology optimization
AU - Hu, Xianliang
AU - Li, Yixin
AU - Ji, Hangjie
T2 - Applied Mathematics and Computation
AB - We propose a nodal finite element method to the problem of finding optimal structural shapes based on a phase field model motivated by the work of Takezawa et al. (2010). Compared to finite differences used in the original study, the proposed method better characterizes optimal configurations and is not sensitive to initial guesses or element shapes. Using nodal finite elements as a basis, we also investigate the application of two semi-implicit time-stepping schemes, the first-order and second-order semi-implicit backward Euler time-stepping schemes (1-SBEM and 2-SBDF), to the optimization problem. We then discuss the stability of these schemes and a classic finite-difference based upwind scheme using benchmark problems of compliance minimization with volume constraints. Numerical evidences show that the nodal FEM approach alleviates the initial dependency problem of structural optimization, and the 1-SBEM scheme is more stable than the other two schemes in tracking the moving boundary.
DA - 2018/12//
PY - 2018/12//
DO - 10.1016/j.amc.2018.07.049
VL - 339
SP - 675-684
UR - https://doi.org/10.1016/j.amc.2018.07.049
ER -
TY - JOUR
TI - VIRTUALIZATION MAP FOR THE LITTELMANN PATH MODEL
AU - PAN, JIANPING
AU - SCRIMSHAW, TRAVIS
T2 - Transformation Groups
AB - We show the natural embedding of weight lattices from a diagram folding is a virtualization map for the Littelmann path model, which recovers a result of Kashiwara. As an application, we give a type independent proof that certain Kirillov--Reshetikhin crystals respect diagram foldings, which is a known result on a special case of a conjecture given by Okado, Schilling, and Shimozono.
DA - 2018/12//
PY - 2018/12//
DO - 10.1007/s00031-017-9456-3
VL - 23
IS - 4
SP - 1045-1061
UR - http://dx.doi.org/10.1007/s00031-017-9456-3
ER -
TY - JOUR
TI - Backward SDEs for control with partial information
AU - Papanicolaou, Andrew
T2 - Mathematical Finance
AB - This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one of its state variables. This is of significant difficulty because the filtering distribution is a stochastic probability measure of infinite dimension, and therefore the dynamic program has a state that cannot be differentiated in the traditional sense. This lack of differentiability means that the problem cannot be solved using a Hamilton-Jacobi-Bellman (HJB) equation. This paper will show how the problem can be analyzed and solved using backward stochastic differential equations (BSDEs), with a key tool being the problem's dual formulation.
DA - 2018/2/18/
PY - 2018/2/18/
DO - 10.1111/mafi.12174
VL - 29
IS - 1
SP - 208-248
J2 - Mathematical Finance
LA - en
OP -
SN - 0960-1627 1467-9965
UR - http://dx.doi.org/10.1111/mafi.12174
DB - Crossref
KW - backward stochastic differential equations
KW - non-Markov control
KW - partial information
KW - portfolio optimization
ER -
TY - JOUR
TI - Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options
AU - Papanicolaou, A.
T2 - SIAM Journal on Financial Mathematics
AB - This article explores the relationship between the SPX and VIX options markets. High-strike VIX call options are used to hedge tail risk in the SPX, which means that SPX options are a reflection of the extreme-strike asymptotics of VIX options, and vice versa. This relationship can be quantified using moment formulas in a model-free way. Comparisons are made between VIX and SPX implied volatilities along with various examples of stochastic volatility models.
DA - 2018/1//
PY - 2018/1//
DO - 10.1137/141001615
VL - 9
IS - 2
SP - 401-434
J2 - SIAM J. Finan. Math.
LA - en
OP -
SN - 1945-497X
UR - http://dx.doi.org/10.1137/141001615
DB - Crossref
KW - VIX options
KW - moment formulas
KW - extreme strikes
KW - model free
ER -
TY - JOUR
TI - Protein pocket detection via convex hull surface evolution and associated Reeb graph
AU - Zhao, Rundong
AU - Cang, Zixuan
AU - Tong, Yiying
AU - Wei, Guo-Wei
T2 - Bioinformatics
AB - Abstract Motivation Protein pocket information is invaluable for drug target identification, agonist design, virtual screening and receptor-ligand binding analysis. A recent study indicates that about half holoproteins can simultaneously bind multiple interacting ligands in a large pocket containing structured sub-pockets. Although this hierarchical pocket and sub-pocket structure has a significant impact to multi-ligand synergistic interactions in the protein binding site, there is no method available for this analysis. This work introduces a computational tool based on differential geometry, algebraic topology and physics-based simulation to address this pressing issue. Results We propose to detect protein pockets by evolving the convex hull surface inwards until it touches the protein surface everywhere. The governing partial differential equations (PDEs) include the mean curvature flow combined with the eikonal equation commonly used in the fast marching algorithm in the Eulerian representation. The surface evolution induced Morse function and Reeb graph are utilized to characterize the hierarchical pocket and sub-pocket structure in controllable detail. The proposed method is validated on PDBbind refined sets of 4414 protein-ligand complexes. Extensive numerical tests indicate that the proposed method not only provides a unique description of pocket-sub-pocket relations, but also offers efficient estimations of pocket surface area, pocket volume and pocket depth. Availability and implementation Source code available at https://github.com/rdzhao/ProteinPocketDetection. Webserver available at http://weilab.math.msu.edu/PPD/.
DA - 2018/9/1/
PY - 2018/9/1/
DO - 10.1093/bioinformatics/bty598
VL - 34
IS - 17
SP - i830-i837
UR - http://dx.doi.org/10.1093/bioinformatics/bty598
ER -
TY - JOUR
TI - Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening
AU - Cang, Zixuan
AU - Mu, Lin
AU - Wei, Guo-Wei
T2 - PLOS Computational Biology
AB - This work introduces a number of algebraic topology approaches, including multi-component persistent homology, multi-level persistent homology, and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. In contrast to the conventional persistent homology, multi-component persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for protein-ligand binding analysis and virtual screening of small molecules. Extensive numerical experiments involving 4,414 protein-ligand complexes from the PDBBind database and 128,374 ligand-target and decoy-target pairs in the DUD database are performed to test respectively the scoring power and the discriminatory power of the proposed topological learning strategies. It is demonstrated that the present topological learning outperforms other existing methods in protein-ligand binding affinity prediction and ligand-decoy discrimination.
DA - 2018/1/8/
PY - 2018/1/8/
DO - 10.1371/journal.pcbi.1005929
VL - 14
IS - 1
SP - e1005929
UR - https://doi.org/10.1371/journal.pcbi.1005929
ER -
TY - JOUR
TI - Integration of element specific persistent homology and machine learning for protein‐ligand binding affinity prediction
AU - Cang, Zixuan
AU - Wei, Guo‐Wei
T2 - International Journal for Numerical Methods in Biomedical Engineering
AB - Protein-ligand binding is a fundamental biological process that is paramount to many other biological processes, such as signal transduction, metabolic pathways, enzyme construction, cell secretion, and gene expression. Accurate prediction of protein-ligand binding affinities is vital to rational drug design and the understanding of protein-ligand binding and binding induced function. Existing binding affinity prediction methods are inundated with geometric detail and involve excessively high dimensions, which undermines their predictive power for massive binding data. Topology provides the ultimate level of abstraction and thus incurs too much reduction in geometric information. Persistent homology embeds geometric information into topological invariants and bridges the gap between complex geometry and abstract topology. However, it oversimplifies biological information. This work introduces element specific persistent homology (ESPH) or multicomponent persistent homology to retain crucial biological information during topological simplification. The combination of ESPH and machine learning gives rise to a powerful paradigm for macromolecular analysis. Tests on 2 large data sets indicate that the proposed topology-based machine-learning paradigm outperforms other existing methods in protein-ligand binding affinity predictions. ESPH reveals protein-ligand binding mechanism that can not be attained from other conventional techniques. The present approach reveals that protein-ligand hydrophobic interactions are extended to 40Å away from the binding site, which has a significant ramification to drug and protein design.
DA - 2018/2/16/
PY - 2018/2/16/
DO - 10.1002/cnm.2914
VL - 34
IS - 2
UR - https://doi.org/10.1002/cnm.2914
KW - protein-ligand binding affinity
KW - machine learning
KW - topology
ER -
TY - CONF
TI - Vietoris–Rips and Cech Complexes of Metric Gluings
AU - Adamaszek, M.
AU - Adams, H.
AU - Gasparovic, E.
AU - Gommel, M.
AU - Purvine, E.
AU - Sazdanovic, R.
AU - Wang, B.
AU - Wang, Y.
AU - Ziegelmeier, L.
T2 - 34th International Symposium on Computational Geometry
A2 - Speckmann, Bettina
A2 - Toth, Csaba D.
T3 - LIPIcs - Leibniz International Proceedings in Informatics
C2 - 2018///
C3 - 34th International Symposium on Computational Geometry (SoCG 2018)
DA - 2018///
PY - 2018///
VL - 3
SP - 218–246
M1 - 1-3
PB - Wadern Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH
ER -
TY - CONF
TI - Vietoris-rips and čech complexes of metric gluings
AU - Adamaszek, M.
AU - Adams, H.
AU - Gasparovic, E.
AU - Gommel, M.
AU - Purvine, E.
AU - Sazdanovic, R.
AU - Wang, B.
AU - Wang, Y.
AU - Ziegelmeier, L.
AB - We study Vietoris-Rips and Cech complexes of metric wedge sums and metric gluings. We show that the Vietoris-Rips (resp. Cech) complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips (resp. Cech) complexes. We also provide generalizations for certain metric gluings, i.e. when two metric spaces are glued together along a common isometric subset. As our main example, we deduce the homotopy type of the Vietoris-Rips complex of two metric graphs glued together along a sufficiently short path. As a result, we can describe the persistent homology, in all homological dimensions, of the Vietoris-Rips complexes of a wide class of metric graphs.
C2 - 2018///
C3 - Leibniz International Proceedings in Informatics, LIPIcs
DA - 2018///
DO - 10.4230/LIPIcs.SoCG.2018.3
VL - 99
SP - 32-315
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85048959293&partnerID=MN8TOARS
ER -
TY - JOUR
TI - A Complete Characterization of the One-Dimensional Intrinsic Čech Persistence Diagrams for Metric Graphs
AU - Gasparovic, Ellen
AU - Gommel, Maria
AU - Purvine, Emilie
AU - Sazdanovic, Radmila
AU - Wang, Bei
AU - Wang, Yusu
AU - Ziegelmeier, Lori
T2 - Research in Computational Topology
AB - Metric graphs are special types of metric spaces used to model and represent simple, ubiquitous, geometric relations in data such as biological networks, social networks, and road networks. We are interested in giving a qualitative description of metric graphs using topological summaries. In particular, we provide a complete characterization of the one-dimensional intrinsic Čech persistence diagrams for finite metric graphs using persistent homology. Together with complementary results by Adamaszek et al., which imply the results on intrinsic Čech persistence diagrams in all dimensions for a single cycle, our results constitute the important steps toward characterizing intrinsic Čech persistence diagrams for arbitrary finite metric graphs across all dimensions.
DA - 2018///
PY - 2018///
DO - 10.1007/978-3-319-89593-2_3
SP - 33-56
ER -
TY - JOUR
TI - Affine geometric crystal of An(1) and limit of Kirillov–Reshetikhin perfect crystals
AU - Misra, Kailash C.
AU - Nakashima, Toshiki
T2 - Journal of Algebra
AB - Let g be an affine Lie algebra with index set I={0,1,2,⋯,n} and gL be its Langlands dual. It is conjectured in [16] that for each k∈I∖{0} the affine Lie algebra g has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of certain coherent family of perfect crystals for gL. Motivated by this conjecture we construct a positive geometric crystal for the affine Lie algebra g=An(1) for each Dynkin index k∈I∖{0} and show that its ultra-discretization is isomorphic to the limit of a coherent family of perfect crystals for An(1) given in [24]. In the process we develop and use some lattice-path combinatorics.
DA - 2018/8/1/
PY - 2018/8/1/
DO - 10.1016/J.JALGEBRA.2018.03.041
VL - 507
SP - 249-291
SN - 0021-8693
UR - http://dx.doi.org/10.1016/J.JALGEBRA.2018.03.041
KW - Geometric crystal
KW - Crystal base
KW - Perfect crystal
KW - Kirillov-Reshetikhin crystal
KW - Ultra-discretization
KW - Tropicalization
KW - Affine Weyl group
ER -
TY - JOUR
TI - Physics-based probing and prediction of extreme events
AU - Farazmand, M.
AU - Sapsis, T
T2 - SIAM News
DA - 2018/1//
PY - 2018/1//
VL - 51
IS - 1
SP - 1, 3
UR - https://www.researchgate.net/profile/Mohammad_Farazmand/publication/323245041_Physics-based_probing_and_prediction_of_extreme_events/links/5a887e4daca272017e5f5bef/Physics-based-probing-and-prediction-of-extreme-events.pdf
ER -
TY - CONF
TI - Positive Solutions of Systems of Signed Parametric Polynomial Inequalities
AU - Hong, Hoon
AU - Sturm, Thomas
A2 - Gerdt, Vladimir P.
A2 - Koepf, Wolfram
A2 - Seiler, Werner M.
A2 - Vorozhtsov, Evgenii V.
C2 - 2018///
C3 - Computer Algebra in Scientific Computing - 20th International Workshop,
CASC 2018, Lille, France, September 17-21, 2018, Proceedings
DA - 2018///
DO - 10.1007/978-3-319-99639-4\_17
VL - 11077
SP - 238-253
PB - Springer
UR - https://doi.org/10.1007/978-3-319-99639-4\_17
ER -
TY - CONF
TI - Ensemble Kalman Filtering for Inverse Optimal Control
AU - Tran, H.
AU - Arnold, A.
T2 - International MultiConference of Engineers and Computer Scientists : IMECS 2018
A2 - Ao, Sio-long
A2 - Castillo, Oscar
A2 - Douglas, Craig
A2 - Feng, David Dagan
A2 - Korunsky, Alexander
T3 - Lecture notes in engineering and computer science
C2 - 2018///
C3 - International MultiConference of Engineers and Computer Scientists : IMECS 2018: 14-16 March, 2018, the Royal Garden Hotel, Kowloon, Hong Kong
CY - Royal Garden Hotel, Kowloon, Hong Kong
DA - 2018///
PY - 2018/3/14/
VL - II
SP - 526–530
PB - Newswood Limited, International Association of Engineers
SN - 9789881404886
ER -
TY - JOUR
TI - Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure
AU - Congy, T.
AU - El, G.A.
AU - Hoefer, M.A.
AU - Shearer, M.
T2 - Studies in Applied Mathematics
AB - The nonlinear Schrödinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains, albeit in differing amplitude-frequency domains. In this paper, we take advantage of the overlapping asymptotic regime that applies to both the NLS and Whitham modulation descriptions in order to develop a universal analytical description of dispersive shock waves (DSWs) generated in Riemann problems for a broad class of integrable and nonintegrable nonlinear dispersive equations. The proposed method extends DSW fitting theory that prescribes the motion of a DSW's edges into the DSW's interior, that is, this work reveals the DSW structure. Our approach also provides a natural framework in which to analyze DSW stability. We consider several representative, physically relevant examples that illustrate the efficacy of the developed general theory. Comparisons with direct numerical simulations show that inclusion of higher order terms in the NLS equation enables a remarkably accurate description of the DSW structure in a broad region that extends from the harmonic, small amplitude edge.
DA - 2018/11/29/
PY - 2018/11/29/
DO - 10.1111/sapm.12247
VL - 142
IS - 3
SP - 241-268
J2 - Studies in Applied Mathematics
LA - en
OP -
SN - 0022-2526
UR - http://dx.doi.org/10.1111/sapm.12247
DB - Crossref
KW - asymptotic analysis
KW - nonlinear waves
KW - partial differential equations
ER -
TY - BOOK
TI - Representations of Lie algebras, quantum groups and related topics
DA - 2018///
PY - 2018///
ER -
TY - JOUR
TI - From Frobenius character formula to vertex operators
AU - Naihuan, Jing
T2 - SCIENTIA SINICA Mathematica
AB - In this paper, simplified derivation of Frobenius character formula for thesymmetric group and Spechts character formula for the wreath products is given. It is shown that vertex operatorshad their presence in Frobenius formula via the multiplication of the Grothendieck ring. The same method is applied tothe Grothendieck ring of the wreath products of symmetric groups and any finite group to givea simplified proof of the Specht formula.
DA - 2018/10//
PY - 2018/10//
DO - 10.1360/n012018-00110
VL - 48
IS - 11
SP - 1717
ER -
TY - JOUR
TI - A Debt Management Problem with Currency Devaluation
DA - 2018/5/14/
PY - 2018/5/14/
ER -
TY - JOUR
TI - Generalized Control Systems in the Space of Probability Measures
AU - Cavagnari, G.
AU - Marigonda, A.
AU - Nguyen, K.T.
AU - Priuli, F.S.
T2 - Set-Valued and Variational Analysis
DA - 2018///
PY - 2018///
DO - 10.1007/s11228-017-0414-y
VL - 26
IS - 3
SP - 663-691
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85051296819&partnerID=MN8TOARS
KW - Optimal transport
KW - Differential inclusions
KW - Time-optimal control
KW - Set-valued analysis
ER -
TY - JOUR
TI - Contributions from the silent majority dominate dengue virus transmission
AU - Bosch, Quirine A
AU - Clapham, Hannah E
AU - Lambrechts, Louis
AU - Duong, Veasna
AU - Buchy, Philippe
AU - Althouse, Benjamin M
AU - Lloyd, Alun L
AU - Waller, Lance A
AU - Morrison, Amy C
AU - Kitron, Uriel
AU - others
T2 - PLOS Pathogens
DA - 2018///
PY - 2018///
VL - 14
IS - 5
SP - e1006965
ER -
TY - JOUR
TI - Efficacy of Aedes aegypti control by indoor Ultra Low Volume (ULV) insecticide spraying in Iquitos, Peru
AU - Gunning, Christian E
AU - Okamoto, Kenichi
AU - Astete, Helvio
AU - Vasquez, Gissella M
AU - Erhardt, Erik
AU - Del Aguila, Clara
AU - Pinedo, Raul
AU - Cardenas, Roldan
AU - Pacheco, Carlos
AU - Chalco, Enrique
AU - others
T2 - PLoS neglected tropical diseases
DA - 2018///
PY - 2018///
VL - 12
IS - 4
SP - e0006378
ER -
TY - JOUR
TI - Lattice Paths, Young Tableaux, and Weight Multiplicities
AU - Jayne, Rebecca L.
AU - Misra, Kailash C.
T2 - Annals of Combinatorics
AB - For $${\ell \geq 1}$$
and $${k \geq 2}$$
, we consider certain admissible sequences of k−1 lattice paths in a colored $${\ell \times \ell}$$
square. We show that the number of such admissible sequences of lattice paths is given by the sum of squares of the number of standard Young tableaux of shape $${\lambda \vdash \ell}$$
with $${l(\lambda) \leq k}$$
, which is also the number of (k + 1)k··· 21-avoiding permutations in $${S_\ell}$$
. Finally, we apply this result to the representation theory of the affine Lie algebra $${\widehat{sl}(n)}$$
and show that this gives the multiplicity of certain maximal dominant weights in the irreducible highest weight $${\widehat{sl}(n)}$$
-module $${V(k \Lambda_0)}$$
.
DA - 2018/2/2/
PY - 2018/2/2/
DO - 10.1007/S00026-018-0374-4
VL - 22
IS - 1
SP - 147-156
J2 - Ann. Comb.
LA - en
OP -
SN - 0218-0006 0219-3094
UR - http://dx.doi.org/10.1007/S00026-018-0374-4
DB - Crossref
KW - lattice path
KW - Young tableau
KW - avoiding permutation
KW - affine Lie algebra
KW - weight multiplicity
ER -
TY - JOUR
TI - Twisted quantum affinizations and their vertex representations
AU - Chen, Fulin
AU - Jing, Naihuan
AU - Kong, Fei
AU - Tan, Shaobin
T2 - Journal of Mathematical Physics
AB - In this paper, we generalize Drinfeld’s twisted quantum affine algebras to construct twisted quantum algebras for all simply laced generalized Cartan matrices and present their vertex representation realizations.
DA - 2018/8//
PY - 2018/8//
DO - 10.1063/1.5023790
VL - 59
IS - 8
SP - 081701
J2 - Journal of Mathematical Physics
LA - en
OP -
SN - 0022-2488 1089-7658
UR - http://dx.doi.org/10.1063/1.5023790
DB - Crossref
ER -
TY - JOUR
TI - Isomorphism Between the R-Matrix and Drinfeld Presentations of Yangian in Types B, C and D
AU - Jing, Naihuan
AU - Liu, Ming
AU - Molev, Alexander
T2 - Communications in Mathematical Physics
AB - It is well-known that the Gauss decomposition of the generator matrix in the R-matrix presentation of the Yangian in type A yields generators of its Drinfeld presentation. Defining relations between these generators are known in an explicit form, thus providing an isomorphism between the presentations. It has been an open problem since the pioneering work of Drinfeld to extend this result to the remaining types. We give a solution for the classical types B, C and D by constructing an explicit isomorphism between the R-matrix and Drinfeld presentations of the Yangian. It is based on an embedding theorem which allows us to consider the Yangian of rank $${n-1}$$ as a subalgebra of the Yangian of rank n of the same type.
DA - 2018/6/26/
PY - 2018/6/26/
DO - 10.1007/S00220-018-3185-X
VL - 361
IS - 3
SP - 827-872
J2 - Commun. Math. Phys.
LA - en
OP -
SN - 0010-3616 1432-0916
UR - http://dx.doi.org/10.1007/S00220-018-3185-X
DB - Crossref
ER -
TY - JOUR
TI - PO-0900: Spatiotemporal fractionation schemes for liver stereotactic body radiotherapy
AU - Unkelbach, J.
AU - Papp, D.
AU - Gaddy, M.
AU - Andratschke, N.
AU - Hong, T.
AU - Guckenberger, M.
T2 - Radiotherapy and Oncology
DA - 2018/4//
PY - 2018/4//
DO - 10.1016/S0167-8140(18)31210-6
VL - 127
SP - S479-S480
J2 - Radiotherapy and Oncology
LA - en
OP -
SN - 0167-8140
UR - http://dx.doi.org/10.1016/S0167-8140(18)31210-6
DB - Crossref
ER -
TY - JOUR
TI - On Best-Response Dynamics in Potential Games
AU - Swenson, Brian
AU - Murray, Ryan
AU - Kar, Soummya
T2 - SIAM Journal on Control and Optimization
AB - The paper studies the convergence properties of (continuous-time) best-response dynamics from game theory. Despite their fundamental role in game theory, best-response dynamics are poorly understoo...
DA - 2018/1//
PY - 2018/1//
DO - 10.1137/17m1139461
VL - 56
IS - 4
SP - 2734-2767
KW - game theory
KW - learning
KW - best-response dynamics
KW - fictitious play
KW - potential games
KW - convergence rate
ER -
TY - JOUR
TI - Best-Response Dynamics in Continuous Potential Games: Non-Convergence to Saddle Points
AU - Swenson, Brian
AU - Murray, Ryan
AU - Kar, Soummya
AU - Poor, H. Vincent
T2 - 2018 52nd Asilomar Conference on Signals, Systems, and Computers
AB - The paper studies properties of best-response (BR) dynamics in potential games with continuous action sets. It is known that BR dynamics converge to the set of Nash equilibria (NE) in potential games. The set of NE in potential games is composed of local maximizers and saddle points of the potential function. The paper studies non-convergence of BR dynamics to saddle points of the potential function. Under relatively mild assumptions it is shown that BR dynamics may only converge to an interior saddle-point from a measure-zero set of initial conditions. This provides a weak stable manifold theorem in this context.
DA - 2018/10//
PY - 2018/10//
DO - 10.1109/acssc.2018.8645541
ER -
TY - JOUR
TI - A model for system uncertainty in reinforcement learning
AU - Murray, Ryan
AU - Palladino, Michele
T2 - Systems & Control Letters
AB - Abstract This work provides a rigorous framework for studying continuous-time control problems in uncertain environments. The framework models uncertainty in state dynamics as a probability measure on the space of functions. Such a probability measure is permitted to change over time as agents learn about their environment. This model can be seen as a variant of either Bayesian reinforcement learning (RL) or adaptive optimal control. We study conditions for locally optimal trajectories within this model, in particular deriving an appropriate dynamic programming principle and Hamilton–Jacobi equations. Some discussion of variants of the model are also provided, including one potential framework for studying the tradeoff between exploration and exploitation in RL.
DA - 2018/12//
PY - 2018/12//
DO - 10.1016/j.sysconle.2018.09.011
VL - 122
SP - 24-31
UR - https://doi.org/10.1016/j.sysconle.2018.09.011
KW - Dynamic programming
KW - Learning systems
KW - Machine learning
KW - Adaptive control
ER -
TY - JOUR
TI - Cambrian frameworks for cluster algebras of affine type
AU - Reading, Nathan
AU - Speyer, David E.
T2 - Trans. Amer. Math. Soc.
AB - We give a combinatorial model for the exchange graph and g-vector fan associated to any acyclic exchange matrix B of affine type. More specifically, we construct a reflection framework for B in the sense of [N. Reading and D. E. Speyer, Combinatorial frameworks for cluster algebras] and establish good properties of this framework. The framework (and in particular the g-vector fan) is constructed by combining a copy of the Cambrian fan for B with an antipodal copy of the Cambrian fan for -B.
DA - 2018///
PY - 2018///
DO - 10.1090/tran/7193
VL - 370
IS - 2
SP - 1429-1468
UR - https://doi.org/10.1090/tran/7193
ER -
TY - CHAP
TI - Hepatitis C Viral Dynamics Using a Combination Therapy of Interferon, Ribavirin, and Telaprevir: Mathematical Modeling and Model Validation
AU - Aston, Philip
AU - Cranfield, Katie
AU - O’Farrell, Haley
AU - Cassenote, Alex
AU - Mendes-Correa, Cassia J.
AU - Segurado, Aluisio
AU - Hoang, Phuong
AU - Lankford, George
AU - Tran, Hien
T2 - Hepatitis C - From Infection to Cure
AB - Groundbreaking new drugs called direct acting antivirals have been introduced recently for the treatment of chronic Hepatitis C virus infection. We introduce a mathematical model for Hepatitis C dynamics treated with the direct acting antiviral drug, telaprevir, alongside traditional interferon and ribavirin treatments to understand how this combination therapy affects the viral load of patients exhibiting different types of response. We use sensitivity and identifiability techniques to determine which model parameters can be best estimated from viral load data. Parameter estimation with these best estimable parameters is then performed to give patient-specific fits of the model to partial virologic response, sustained virologic response and breakthrough patients.
PY - 2018/10/10/
DO - 10.5772/intechopen.75761
OP -
PB - InTech
SN - 9781789842074 9781789842081
UR - http://dx.doi.org/10.5772/intechopen.75761
DB - Crossref
ER -
TY - CHAP
TI - War-Gaming Applications for Achieving Optimum Acquisition of Future Space Systems
AU - Nguyen, Tien M.
AU - Guillen, Andy T.
AU - Matsunaga, Sumner S.
AU - Tran, Hien T.
AU - Bui, Tung X.
T2 - Simulation and Gaming
PY - 2018/2/14/
DO - 10.5772/intechopen.71044
OP -
PB - InTech
SN - 9789535138037 9789535138006
UR - http://dx.doi.org/10.5772/intechopen.71044
DB - Crossref
ER -
TY - JOUR
TI - Optimal control of immunosuppressants in renal transplant recipients susceptible to BKV infection
AU - Murad, Neha
AU - Tran, H.T.
AU - Banks, H.T.
T2 - Optimal Control Applications and Methods
AB - Kidney transplant recipients are put on a lifelong regime of immunosuppressants to prevent the body from rejecting the allograft. Suppressing the immune system renders the body susceptible to infections. The key to a successful transplant is to ensure the immune system is sufficiently suppressed to prevent organ rejection but adequately strong to fight infections. Finding the optimal balance between over and undersuppression of the immune response is crucial in preventing allograft failure. In this paper, we design a feedback control formulation to predict the optimal amount of immunosuppression required by renal transplant recipients in the context of infections caused by BK virus. We use a receding horizon control methodology to construct the feedback control. Data, as they are currently collected, provide information for only some model states, so we use nonlinear Kalman filtering to estimate the remaining model states for feedback control. We conclude that, using the presented methodology, an individualized adaptive treatment schedule can be built for renal transplant recipients.
DA - 2018/11/22/
PY - 2018/11/22/
DO - 10.1002/oca.2478
VL - 40
IS - 2
SP - 292-309
J2 - Optim Control Appl Meth
LA - en
OP -
SN - 0143-2087
UR - http://dx.doi.org/10.1002/oca.2478
DB - Crossref
KW - BK virus
KW - immunosuppression
KW - Kalman filtering
KW - optimal feedback control
KW - receding horizon control
KW - renal transplant
ER -
TY - CONF
TI - Linear convergence of stochastic block-coordinate fixed point algorithms
AU - Combettes, P.L.
AU - Pesquet, J.-C.
T2 - European Signal Processing Conference
AB - Recent random block-coordinate fixed point algorithms are particularly well suited to large-scale optimization in signal and image processing. These algorithms feature random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and they allow for stochastic errors in the evaluation of the operators. The present paper provides new linear convergence results. These convergence rates are compared to those of standard deterministic algorithms both theoretically and experimentally in an image recovery problem.
C2 - 2018///
C3 - Proceedings of the European Signal Processing Conference
CY - Rome, Italy
DA - 2018///
PY - 2018/9/3/
DO - 10.23919/EUSIPCO.2018.8552941
SP - 747–751
ER -
TY - CONF
TI - Cross-Channel Contamination of PolSAR Images due to Frequency Dependence of Faraday Rotation Angle
AU - Gilman, Mikhail
AU - Tsynkov, Semyon
T2 - 2018 IEEE Conference on Antenna Measurements & Applications (CAMA)
AB - Compensation of the Faraday rotation (FR) effect in polarimetric synthetic aperture radar (PolSAR) involves a rotation matrix, with the FR angle determined by the magnetic field, total electron content, signal frequency, and propagation direction. We analyze the conditions where the signal frequency and/or propagation direction cannot be considered constants. In other words, the rotation matrix based on the main look direction and central radar frequency may have a significant mismatch with the received signal in fast or slow time. We derive estimates for the resulting polarimetric distortions and their effect on applications such as instrument calibration in space and measurement of the aboveground biomass.
C2 - 2018/9//
C3 - 2018 IEEE Conference on Antenna Measurements & Applications (CAMA)
DA - 2018/9//
DO - 10.1109/CAMA.2018.8530603
VL -
SP - 1-4
M1 -
PB - IEEE
SN - 9781538657959
UR - http://dx.doi.org/10.1109/CAMA.2018.8530603
DB - Crossref
ER -
TY - CHAP
TI - Well-Balanced Central-Upwind Schemes for 2x2 Systems of Balance Laws
AU - Chertock, Alina
AU - Herty, Michael
AU - Özcan, Şeyma Nur
T2 - Theory, Numerics and Applications of Hyperbolic Problems I
AB - In this study, we have developed a well-balanced second-order central-upwind scheme for $$2\times 2$$ systems of balance laws, in particular, the models of isothermal gas dynamics with source and traffic flow with relaxation to equilibrium velocities. The new scheme is based on modifications in the reconstruction and evolution steps of a Godunov-type central-upwind method. The first step of this modification is to introduce an equilibrium variable obtained from incorporating the source term into the flux. By reconstructing equilibrium variables and using them in the well-balanced evolution process, we have illustrated that the proposed scheme being well balanced, namely, it preserves steady states of the system.
PY - 2018///
DO - 10.1007/978-3-319-91545-6_28
VL - 236
SP - 345-361
PB - Springer International Publishing
SN - 9783319915449 9783319915456
UR - http://dx.doi.org/10.1007/978-3-319-91545-6_28
ER -
TY - JOUR
TI - A Smoothing Direct Search Method for Monte Carlo-Based Bound Constrained Composite Nonsmooth Optimization
AU - Chen, Xiaojun
AU - Kelley, C. T.
AU - Xu, Fengmin
AU - Zhang, Zaikun
T2 - SIAM Journal on Scientific Computing
AB - We propose and analyze a smoothing direct search algorithm for finding a minimizer of a nonsmooth nonconvex function over a box constraint set, where the objective function values cannot be computed directly but are approximated by Monte Carlo simulation. In the algorithm, we adjust the stencil size, the sample size, and the smoothing parameter simultaneously so that the stencil size goes to zero faster than the smoothing parameter and the square root of the sample size goes to infinity faster than the reciprocal of the stencil size. We prove that with probability one any accumulation point of the sequence generated by the algorithm is a Clarke stationary point. We report on numerical results from statistics and financial applications.
DA - 2018/1//
PY - 2018/1//
DO - 10.1137/17M1116714
VL - 40
IS - 4
SP - A2174-A2199
J2 - SIAM J. Sci. Comput.
LA - en
OP -
SN - 1064-8275 1095-7197
UR - http://dx.doi.org/10.1137/17M1116714
DB - Crossref
KW - sampling methods
KW - direct search algorithm
KW - Monte Carlo simulation
KW - nonsmooth optimization
KW - smoothing functions
KW - Clarke stationarity
ER -
TY - BOOK
TI - Reaction kinetics: Exercises, programs and theorems: Mathematica for deterministic and stochastic kinetics
AU - Tóth, J.
AU - Nagy, A.L.
AU - Papp, D.
DA - 2018///
PY - 2018///
DO - 10.1007/978-1-4939-8643-9
SE - 1-469
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85061518011&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Automated Object Tracing for Biomedical Image Segmentation Using a Deep Convolutional Neural Network
AU - Rutter, Erica M.
AU - Lagergren, John H.
AU - Flores, Kevin B.
T2 - MEDICAL IMAGE COMPUTING AND COMPUTER ASSISTED INTERVENTION - MICCAI 2018, PT IV
AB - Convolutional neural networks (CNNs) have been used for fast and accurate segmentation of medical images. In this paper, we present a novel methodology that uses CNNs for segmentation by mimicking the human task of tracing object boundaries. The architecture takes as input a patch of an image with an overlay of previously traced pixels and the output predicts the coordinates of the next m pixels to be traced. We also consider a CNN architecture that leverages the output from another semantic segmentation CNN, e.g., U-net, as an auxiliary image channel. To initialize the trace path in an image, we use either locations identified as object boundaries with high confidence from a semantic segmentation CNN or a short manually traced path. By iterating the CNN output, our method continues the trace until it intersects with the beginning of the path. We show that our network is more accurate than the state-of-the-art semantic segmentation CNN on microscopy images from the ISBI cell tracking challenge. Moreover, our methodology provides a natural platform for performing human-in-the-loop segmentation that is more accurate than CNNs alone and orders of magnitude faster than manual segmentation.
DA - 2018///
PY - 2018///
DO - 10.1007/978-3-030-00937-3_78
VL - 11073
SP - 686-694
SN - 1611-3349
ER -
TY - JOUR
TI - The equivalence of two Seiberg-Witten Floer homologies
AU - Lidman, T.
AU - Manolescu, C.
T2 - Astérisque
DA - 2018///
PY - 2018///
VL - 399
ER -
TY - JOUR
TI - Hemodynamic assessment of pulmonary hypertension in mice: a model-based analysis of the disease mechanism
AU - Qureshi, M. Umar
AU - Colebank, Mitchel J.
AU - Paun, L. Mihaela
AU - Ellwein Fix, Laura
AU - Chesler, Naomi
AU - Haider, Mansoor A.
AU - Hill, Nicholas A.
AU - Husmeier, Dirk
AU - Olufsen, Mette S.
T2 - Biomechanics and Modeling in Mechanobiology
AB - This study uses a one-dimensional fluid dynamics arterial network model to infer changes in hemodynamic quantities associated with pulmonary hypertension in mice. Data for this study include blood flow and pressure measurements from the main pulmonary artery for 7 control mice with normal pulmonary function and 5 mice with hypoxia-induced pulmonary hypertension. Arterial dimensions for a 21-vessel network are extracted from micro-CT images of lungs from a representative control and hypertensive mouse. Each vessel is represented by its length and radius. Fluid dynamic computations are done assuming that the flow is Newtonian, viscous, laminar, and has no swirl. The system of equations is closed by a constitutive equation relating pressure and area, using a linear model derived from stress–strain deformation in the circumferential direction assuming that the arterial walls are thin, and also an empirical nonlinear model. For each dataset, an inflow waveform is extracted from the data, and nominal parameters specifying the outflow boundary conditions are computed from mean values and characteristic timescales extracted from the data. The model is calibrated for each mouse by estimating parameters that minimize the least squares error between measured and computed waveforms. Optimized parameters are compared across the control and the hypertensive groups to characterize vascular remodeling with disease. Results show that pulmonary hypertension is associated with stiffer and less compliant proximal and distal vasculature with augmented wave reflections, and that elastic nonlinearities are insignificant in the hypertensive animal.
DA - 2018/10/3/
PY - 2018/10/3/
DO - 10.1007/s10237-018-1078-8
VL - 18
IS - 1
SP - 219-243
J2 - Biomech Model Mechanobiol
LA - en
OP -
SN - 1617-7959 1617-7940
UR - http://dx.doi.org/10.1007/s10237-018-1078-8
DB - Crossref
KW - Pulmonary hypertension
KW - 1D fluid dynamics model
KW - Linear and nonlinear wall model
KW - Parameter estimation
KW - Statistical model selection
KW - Wave intensity analysis
KW - Impedance analysis
ER -
TY - JOUR
TI - Eigenvector Continuation with Subspace Learning
AU - Frame, Dillon
AU - He, Rongzheng
AU - Ipsen, Ilse
AU - Lee, Daniel
AU - Lee, Dean
AU - Rrapaj, Ermal
T2 - Physical Review Letters
AB - A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous efficient methods developed for this task, but they generally fail when some control parameter in the Hamiltonian matrix exceeds some threshold value. In this Letter we present a new technique called eigenvector continuation that can extend the reach of these methods. The key insight is that while an eigenvector resides in a linear space with enormous dimensions, the eigenvector trajectory generated by smooth changes of the Hamiltonian matrix is well approximated by a very low-dimensional manifold. We prove this statement using analytic function theory and propose an algorithm to solve for the extremal eigenvectors. We benchmark the method using several examples from quantum many-body theory.Received 13 April 2018DOI:https://doi.org/10.1103/PhysRevLett.121.032501© 2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear bindingNuclear many-body theoryTechniquesQuantum Monte CarloNuclear Physics
DA - 2018/7/17/
PY - 2018/7/17/
DO - 10.1103/physrevlett.121.032501
VL - 121
IS - 3
J2 - Phys. Rev. Lett.
LA - en
OP -
SN - 0031-9007 1079-7114
UR - http://dx.doi.org/10.1103/physrevlett.121.032501
DB - Crossref
ER -
TY - JOUR
TI - A Generalization of an Integrability Theorem of Darboux
AU - Benfield, Michael
AU - Jenssen, Helge Kristian
AU - Kogan, Irina A.
T2 - The Journal of Geometric Analysis
AB - In his monograph “Systemes Orthogonaux” (Darboux, in Lecons sur les systemes orthogonaux et les coordonnees curvilignes, Gauthier-Villars, Paris, 1910) Darboux stated three theorems providing local existence and uniqueness of solutions to first-order systems of the type $$\begin{aligned} \partial _{x_i} u_\alpha (x)=f^\alpha _i(x,u(x)), \quad i\in I_\alpha \subseteq \{1,\dots ,n\}. \end{aligned}$$For a given point $${\bar{x}}\in \mathbb {R}^n$$ it is assumed that the values of the unknown $$u_\alpha $$ are given locally near $${\bar{x}}$$ along $$\{x\,|\, x_i={\bar{x}}_i \, \text {for each}\, i\in I_\alpha \}$$. The more general of the theorems, Theoreme III, was proved by Darboux only for the cases $$n=2$$ and 3. In this work we formulate and prove a generalization of Darboux’s Theoreme III which applies to systems of the form $$\begin{aligned} {{\mathbf {r}}}_i(u_\alpha )\big |_x = f_i^\alpha (x, u(x)), \quad i\in I_\alpha \subseteq \{1,\dots ,n\} \end{aligned}$$where $${\mathcal {R}}=\{{{\mathbf {r}}}_i\}_{i=1}^n$$ is a fixed local frame of vector fields near $${\bar{x}}$$. The data for $$u_\alpha $$ are prescribed along a manifold $$\Xi _\alpha $$ containing $${\bar{x}}$$ and transverse to the vector fields $$\{{{\mathbf {r}}}_i\,|\, i\in I_\alpha \}$$. We identify a certain Stable Configuration Condition (SCC). This is a geometric condition that depends on both the frame $${\mathcal {R}}$$ and on the manifolds $$\Xi _\alpha $$; it is automatically met in the case considered by Darboux. Assuming the SCC and the relevant integrability conditions are satisfied, we establish local existence and uniqueness of a $$C^1$$-solution via Picard iteration for any number of independent variables n.
DA - 2018/11/28/
PY - 2018/11/28/
DO - 10.1007/s12220-018-00119-6
VL - 11
J2 - J Geom Anal
LA - en
OP -
SN - 1050-6926 1559-002X
UR - http://dx.doi.org/10.1007/s12220-018-00119-6
DB - Crossref
KW - Overdetermined systems of PDEs
KW - Integrability theorems
KW - Systems of first order PDEs
KW - Local existence
KW - Picard iteration
ER -
TY -
ER -
TY - JOUR
TI - Detection of Bladder Contractions From the Activity of the External Urethral Sphincter in Rats Using Sparse Regression
AU - Rutter, Erica M.
AU - Langdale, Christopher L.
AU - Hokanson, James A.
AU - Hamilton, Franz
AU - Tran, Hien
AU - Grill, Warren M.
AU - Flores, Kevin B.
T2 - IEEE Transactions on Neural Systems and Rehabilitation Engineering
AB - Bladder overactivity and incontinence and dysfunction can be mitigated by electrical stimulation of the pudendal nerve applied at the onset of a bladder contraction. Thus, it is important to predict accurately both bladder pressure and the onset of bladder contractions. We propose a novel method for prediction of bladder pressure using a time-dependent spectrogram representation of external urethral sphincter electromyographic (EUS EMG) activity and a least absolute shrinkage and selection operator regression model. There was a statistically significant improvement in prediction of bladder pressure compared with methods based on the firing rate of EUS EMG activity. This approach enabled prediction of the onset of bladder contractions with 91% specificity and 96% sensitivity and may be suitable for closed-loop control of bladder continence.
DA - 2018/8//
PY - 2018/8//
DO - 10.1109/tnsre.2018.2854675
VL - 26
IS - 8
SP - 1636-1644
J2 - IEEE Trans. Neural Syst. Rehabil. Eng.
OP -
SN - 1534-4320 1558-0210
UR - http://dx.doi.org/10.1109/tnsre.2018.2854675
DB - Crossref
KW - LASSO
KW - neural stimulation
KW - bladder dysfunction
KW - spectrogram
ER -
TY - JOUR
TI - Khovanov homology and torsion
AU - Sazdanovic, Radmila
T2 - NEW DIRECTIONS IN GEOMETRIC AND APPLIED KNOT THEORY
AB - The present chapter gives an overview on results for discrete knot energies. These discrete energies are designed to make swift numerical computations and thus open the field to computational methods. Additionally, they provide an independent, geometrically pleasing and consistent discrete model that behaves similarly to the original model. We will focus on Mobius energy, integral Menger curvature and thickness.
DA - 2018///
PY - 2018///
DO - 10.1515/9783110571493-005
SP - 125-137
KW - Knot theory
KW - Jones polynomial
KW - Khovanov homology
KW - torsion
KW - categorification
ER -
TY - JOUR
TI - MCMC methods for inference in a mathematical model of pulmonary circulation
AU - Păun, L. Mihaela
AU - Qureshi, M. Umar
AU - Colebank, Mitchel
AU - Hill, Nicholas A.
AU - Olufsen, Mette S.
AU - Haider, Mansoor A.
AU - Husmeier, Dirk
T2 - Statistica Neerlandica
AB - This study performs parameter inference in a partial differential equations system of pulmonary circulation. We use a fluid dynamics network model that takes selected parameter values and mimics the behaviour of the pulmonary haemodynamics under normal physiological and pathological conditions. This is of medical interest as it enables tracking the progression of pulmonary hypertension. We show how we make the fluids model tractable by reducing the parameter dimension from a 55D to a 5D problem. The Delayed Rejection Adaptive Metropolis algorithm, coupled with constraint non-linear optimization, is successfully used to learn the parameter values and quantify the uncertainty in the parameter estimates. To accommodate for different magnitudes of the parameter values, we introduce an improved parameter scaling technique in the Delayed Rejection Adaptive Metropolis algorithm. Formal convergence diagnostics are employed to check for convergence of the Markov chains. Additionally, we perform model selection using different information criteria, including Watanabe Akaike Information Criteria.
DA - 2018/4/20/
PY - 2018/4/20/
DO - 10.1111/stan.12132
VL - 72
IS - 3
SP - 306-338
J2 - Statistica Neerlandica
LA - en
OP -
SN - 0039-0402
UR - http://dx.doi.org/10.1111/stan.12132
DB - Crossref
KW - constraint non-linear optimization
KW - delayed rejection adaptive metropolis
KW - pulmonary hypertension
KW - parameter inference
KW - partial differential equations
KW - Windkessel model
ER -
TY - JOUR
TI - Universal Geometric Coefficients for the Four-Punctured Sphere
AU - Barnard, Emily
AU - Meehan, Emily
AU - Reading, Nathan
AU - Viel, Shira
T2 - Annals of Combinatorics
AB - We construct universal geometric coefficients for the cluster algebra associated to the four-punctured sphere and obtain, as a by-product, the g-vectors of cluster variables. We also construct the rational part of the mutation fan. These constructions rely on a classification of the allowable curves (the curves which can appear in quasi-laminations). The classification allows us to prove the Null Tangle Property for the four-punctured sphere, thus adding this surface to a short list of surfaces for which this property is known. The Null Tangle Property then implies that the shear coordinates of allowable curves are the universal coefficients. We compute shear coordinates explicitly to obtain universal geometric coefficients.
DA - 2018/2/5/
PY - 2018/2/5/
DO - 10.1007/s00026-018-0378-0
VL - 22
IS - 1
SP - 1-44
J2 - Ann. Comb.
LA - en
OP -
SN - 0218-0006 0219-3094
UR - http://dx.doi.org/10.1007/s00026-018-0378-0
DB - Crossref
ER -
TY - CHAP
TI - Bayesian Approaches to Uncertainty Quantification and Structure Refinement from X-Ray Diffraction
AU - Paterson, Alisa R.
AU - Reich, Brian J.
AU - Smith, Ralph C.
AU - Wilson, Alyson G.
AU - Jones, Jacob L.
T2 - Materials Discovery and Design
AB - This chapter introduces classical frequentist and Bayesian inference applied to analyzing diffraction profiles, and the methods are compared and contrasted. The methods are applied to both the modelling of single diffraction profiles and the full profile refinement of crystallographic structures. In the Bayesian method, Markov chain Monte Carlo algorithms are used to sample the distribution of model parameters, allowing for the construction of posterior probability distributions, which provide both parameter estimates and quantifiable uncertainties. We present the application of this method to single peak fitting in lead zirconate titanate, and the crystal structure refinement of a National Institute of Standards and Technology silicon standard reference material.
PY - 2018///
DO - 10.1007/978-3-319-99465-9_4
SP - 81-102
OP -
PB - Springer International Publishing
SN - 9783319994642 9783319994659
UR - http://dx.doi.org/10.1007/978-3-319-99465-9_4
DB - Crossref
ER -
TY - JOUR
TI - Analysis of a multi-axial quantum-informed ferroelectric continuum model: Part 2—sensitivity analysis
AU - Leon, Lider
AU - Smith, Ralph C
AU - Oates, William S
AU - Miles, Paul
T2 - Journal of Intelligent Material Systems and Structures
AB - We illustrate the use of global sensitivity analysis, and a parameter subset selection algorithm based on local sensitivity analysis, to quantify the relative influence of parameters in polarization and electrostrictive energy relations for a quantum-informed, single-domain, ferroelectric material model. A motivating objective is to determine which parameters are identifiable or influential in the sense that they are uniquely determined by density functional theory–generated data. Noninfluential parameters will be fixed at nominal values for subsequent Bayesian inference, uncertainty propagation, and material design since variations in these parameters are minimally reflected in responses. Whereas global sensitivity analysis is typically based on the assumption of mutually independent, uniformly distributed parameters, we demonstrate that inherent parameter correlations must be accommodated to achieve correct interpretations of parameter influence. For the considered energy functionals, we demonstrate that all of the parameters are influential and will be informed by density functional theory–simulated data.
DA - 2018/7/10/
PY - 2018/7/10/
DO - 10.1177/1045389x18781024
VL - 29
IS - 13
SP - 2840-2860
J2 - Journal of Intelligent Material Systems and Structures
LA - en
OP -
SN - 1045-389X 1530-8138
UR - http://dx.doi.org/10.1177/1045389x18781024
DB - Crossref
KW - Ferroelectric
KW - density functional theory
KW - Landau energy
KW - sensitivity analysis
ER -
TY -
ER -
TY - JOUR
TI - Identifiability of Phylogenetic Parameters from k-mer Data Under the Coalescent
AU - Durden, Chris
AU - Sullivant, Seth
T2 - Bulletin of Mathematical Biology
AB - Distances between sequences based on their k-mer frequency counts can be used to reconstruct phylogenies without first computing a sequence alignment. Past work has shown that effective use of k-mer methods depends on (1) model-based corrections to distances based on k-mers and (2) breaking long sequences into blocks to obtain repeated trials from the sequence-generating process. Good performance of such methods is based on having many high-quality blocks with many homologous sites, which can be problematic to guarantee a priori. Nature provides natural blocks of sequences into homologous regions-namely, the genes. However, directly using past work in this setting is problematic because of possible discordance between different gene trees and the underlying species tree. Using the multispecies coalescent model as a basis, we derive model-based moment formulas that involve the species divergence times and the coalescent parameters. From this setting, we prove identifiability results for the tree and branch length parameters under the Jukes-Cantor model of sequence mutations.
DA - 2018/2/1/
PY - 2018/2/1/
DO - 10.1007/s11538-018-0399-1
VL - 81
IS - 2
SP - 431-451
J2 - Bull Math Biol
LA - en
OP -
SN - 0092-8240 1522-9602
UR - http://dx.doi.org/10.1007/s11538-018-0399-1
DB - Crossref
KW - k-mer method
KW - Coalescent
KW - Algebraic geometry
ER -
TY - JOUR
TI - Covering numbers for bounded variation functions
AU - Dutta, Prerona
AU - Nguyen, Khai T.
T2 - Journal of Mathematical Analysis and Applications
AB - In this paper, we provide upper and lower estimates for the minimal number of functions needed to represent a bounded variation function with an accuracy of epsilon with respect to L1-distance.
DA - 2018/12//
PY - 2018/12//
DO - 10.1016/j.jmaa.2018.08.062
VL - 468
IS - 2
SP - 1131-1143
J2 - Journal of Mathematical Analysis and Applications
LA - en
OP -
SN - 0022-247X
UR - http://dx.doi.org/10.1016/j.jmaa.2018.08.062
DB - Crossref
KW - The epsilon-entropy
KW - Bounded variation functions
ER -
TY - JOUR
TI - Biographical Memoir and Publications of Paul F. Zweifel
AU - McCormick, Norman J.
AU - Garcia, Roberto D. M.
AU - Siewert, Charles E.
T2 - JOURNAL OF COMPUTATIONAL AND THEORETICAL TRANSPORT
AB - Paul Zweifel served as the founding editor of the Transport Theory and Statistical Physics journal from 1971 to 1981. An overview of his professional life gives a detailed list of his publications,...
DA - 2018/4/16/
PY - 2018/4/16/
DO - 10.1080/23324309.2018.1508474
VL - 47
IS - 1-3
SP - 187-208
SN - 2332-4325
KW - Paul Zweifel
KW - reactor physics
KW - neutron scattering
KW - transport theory
KW - mathematical physics
KW - statistical physics
KW - mathematics of music
ER -
TY - JOUR
TI - Sparse Polynomial Interpolation With Arbitrary Orthogonal Polynomial Bases
AU - Imamoglu, Erdal
AU - Kaltofen, Erich L.
AU - Yang, Zhengfeng
T2 - ISSAC'18: PROCEEDINGS OF THE 2018 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION
AB - An algorithm for interpolating a polynomial f from evaluation points whose running time depends on the sparsity t of the polynomial when it is represented as a sum of t Chebyshev Polynomials of the First Kind with non-zero scalar coefficients is given by Lakshman Y. N. and Saunders [SIAM J. Comput., vol. 24, nr. 2 (1995)]; Kaltofen and Lee [JSC, vol. 36, nr. 3--4 (2003)] analyze a randomized early termination version which computes the sparsity t. Those algorithms mirror Prony's algorithm for the standard power basis to the Chebyshev Basis of the First Kind. An alternate algorithm by Arnold's and Kaltofen's [Proc. ISSAC 2015, Sec. 4] uses Prony's original algorithm for standard power terms. Here we give sparse interpolation algorithms for generalized Chebyshev polynomials, which include the Chebyshev Bases of the Second, Third and Fourth Kind. Our algorithms also reduce to Prony's algorithm. If given on input a bound B >= t for the sparsity, our new algorithms deterministically recover the sparse representation in the First, Second, Third and Fourth Kind Chebyshev representation from exactly t + B evaluations. Finally, we generalize our algorithms to bases whose Chebyshev recurrences have parametric scalars. We also show how to compute those parameter values which optimize the sparsity of the representation in the corresponding basis, similar to computing a sparsest shift.
DA - 2018///
PY - 2018///
DO - 10.1145/3208976.3208999
SP - 223-230
ER -
TY - JOUR
TI - Irredundant Triangular Decomposition
AU - Pogudin, Gleb
AU - Szanto, Agnes
T2 - ISSAC'18: PROCEEDINGS OF THE 2018 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION
AB - Triangular decomposition is a classic, widely used and well-developed way to represent algebraic varieties with many applications. In particular, there exist sharp degree bounds for a single triangular set in terms of intrinsic data of the variety it represents, and powerful randomized algorithms for computing triangular decompositions using Hensel lifting in the zero-dimensional case and for irreducible varieties. However, in the general case, most of the algorithms computing triangular decompositions produce embedded components, which makes it impossible to directly apply the intrinsic degree bounds. This, in turn, is an obstacle for efficiently applying Hensel lifting due to the higher degrees of the output polynomials and the lower probability of success. In this paper, we give an algorithm to compute an irredundant triangular decomposition of an arbitrary algebraic set $W$ defined by a set of polynomials in C[x_1, x_2, ..., x_n]. Using this irredundant triangular decomposition, we were able to give intrinsic degree bounds for the polynomials appearing in the triangular sets and apply Hensel lifting techniques. Our decomposition algorithm is randomized, and we analyze the probability of success.
DA - 2018///
PY - 2018///
DO - 10.1145/3208976.3208996
SP - 311-318
UR - http://dx.doi.org/10.1145/3208976.3208996
ER -
TY - JOUR
TI - Personalized mathematical model of endotoxin-induced inflammatory responses in young men and associated changes in heart rate variability
AU - Brady, R.
AU - Frank-Ito, D.O.
AU - Tran, H.T.
AU - Janum, S.
AU - Møller, K.
AU - Brix, S.
AU - Ottesen, J.T.
AU - Mehlsen, J.
AU - Olufsen, M.S.
T2 - Mathematical Modelling of Natural Phenomena
AB - The objective of this study was to develop a personalized inflammatory model and estimate subject-specific parameters that could be related to changes in heart rate variability (HRV), a measure that can be obtained non-invasively in real time. An inflammatory model was developed and calibrated to measurements of interleukin-6 (IL-6), tumor necrosis factor (TNF-alpha), interleukin-8 (IL-8) and interleukin-10 (IL-10) over 8 hours in 20 subjects administered a low dose of lipopolysaccharide. For this model, we estimated 11 subject-specific parameters for all 20 subjects. Estimated parameters were correlated with changes in HRV, computed from ECG measurements using a built-in HRV module available in Labchart. Results revealed that patients could be separated into two groups expressing normal and abnormal responses to endotoxin. Abnormal responders exhibited increased HRV, most likely as a result of increased vagal firing. The observed correlation between the inflammatory response and HRV brings us a step further towards understanding if HRV predictions can be used as a marker for inflammation. Analyzing HRV parameters provides an easy, non-invasively obtained measure that can be used to assess the state of the subject, potentially translating to identifying a non-invasive marker that can be used to detect the onset of sepsis.
DA - 2018///
PY - 2018///
DO - 10.1051/mmnp/2018031
VL - 13
IS - 5
SP - 42
J2 - Math. Model. Nat. Phenom.
OP -
SN - 0973-5348 1760-6101
UR - http://dx.doi.org/10.1051/mmnp/2018031
DB - Crossref
KW - Acute inflammation
KW - mathematical modeling
KW - heart rate variability
KW - parameter estimation
ER -
TY - JOUR
TI - Log-Concave Polynomials, Entropy, and a Deterministic Approximation Algorithm for Counting Bases of Matroids
AU - Anari, Nima
AU - Gharan, Shayan Oveis
AU - Vinzant, Cynthia
T2 - 2018 IEEE 59TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS)
AB - We give a deterministic polynomial time 2^O(r)-approximation algorithm for the number of bases of a given matroid of rank r and the number of common bases of any two matroids of rank r. To the best of our knowledge, this is the first nontrivial deterministic approximation algorithm that works for arbitrary matroids. Based on a lower bound of Azar, Broder, and Frieze this is almost the best possible assuming oracle access to independent sets of the matroid. There are two main ingredients in our result: For the first, we build upon recent results of Adiprasito, Huh, and Katz and Huh and Wang on combinatorial hodge theory to derive a connection between matroids and log-concave polynomials. We expect that several new applications in approximation algorithms will be derived from this connection in future. Formally, we prove that the multivariate generating polynomial of the bases of any matroid is log-concave as a function over the positive orthant. For the second ingredient, we develop a general framework for approximate counting in discrete problems, based on convex optimization. The connection goes through subadditivity of the entropy. For matroids, we prove that an approximate superadditivity of the entropy holds by relying on the log-concavity of the corresponding polynomials.
DA - 2018///
PY - 2018///
DO - 10.1109/FOCS.2018.00013
SP - 35-46
SN - 0272-5428
KW - matroid
KW - deterministic counting
KW - entropy
KW - log-concave polynomial
ER -
TY - JOUR
TI - Improving the generation and selection of virtual populations in quantitative systems pharmacology models
AU - Rieger, Theodore R.
AU - Allen, Richard J.
AU - Bystricky, Lukas
AU - Chen, Yuzhou
AU - Colopy, Glen Wright
AU - Cui, Yifan
AU - Gonzalez, Angelica
AU - Liu, Yifei
AU - White, R. D.
AU - Everett, R. A.
AU - Banks, H. T.
AU - Musante, Cynthia J.
T2 - PROGRESS IN BIOPHYSICS & MOLECULAR BIOLOGY
AB - Quantitative systems pharmacology (QSP) models aim to describe mechanistically the pathophysiology of disease and predict the effects of therapies on that disease. For most drug development applications, it is important to predict not only the mean response to an intervention but also the distribution of responses, due to inter-patient variability. Given the necessary complexity of QSP models, and the sparsity of relevant human data, the parameters of QSP models are often not well determined. One approach to overcome these limitations is to develop alternative virtual patients (VPs) and virtual populations (Vpops), which allow for the exploration of parametric uncertainty and reproduce inter-patient variability in response to perturbation. Here we evaluated approaches to improve the efficiency of generating Vpops. We aimed to generate Vpops without sacrificing diversity of the VPs' pathophysiologies and phenotypes. To do this, we built upon a previously published approach (Allen et al., 2016) by (a) incorporating alternative optimization algorithms (genetic algorithm and Metropolis-Hastings) or alternatively (b) augmenting the optimized objective function. Each method improved the baseline algorithm by requiring significantly fewer plausible patients (precursors to VPs) to create a reasonable Vpop.
DA - 2018/11//
PY - 2018/11//
DO - 10.1016/j.pbiomolbio.2018.06.002
VL - 139
SP - 15-22
SN - 0079-6107
KW - Global optimization
KW - Acceptance rejection sampling
KW - Mathematical modeling
KW - Ordinary differential equations
KW - Genetic algorithm
KW - Metropolis-Hastings
ER -
TY - JOUR
TI - Variation in cell-associated unspliced HIV RNA on antiretroviral therapy is associated with the circadian regulator brain-and-muscle-ARNT-like-1
AU - Chang, Christina C.
AU - Naranbhai, Vivek
AU - Stern, Jared
AU - Roche, Michael
AU - Dantanarayana, Ashanti
AU - Ke, Ruian
AU - Tennakoon, Surekha
AU - Solomon, Ajantha
AU - Hoh, Rebecca
AU - Hartogensis, Wendy
AU - Hecht, Frederick M.
AU - Sikaris, Ken
AU - Price, David J.
AU - Elliott, Julian H.
AU - Deeks, Steven G.
AU - Churchill, Melissa
AU - Cameron, Paul U.
AU - Hengartner, Nicolas
AU - Perelson, Alan S.
AU - Lewin, Sharon R.
T2 - AIDS
AB - Objective(s): To determine whether variation in cell-associated unspliced (CA-US) HIV RNA in HIV-infected individuals on antiretroviral therapy (ART) has a circadian basis. Methods: Prospective observational study of HIV-infected individuals on ART. Blood was collected on three occasions and CA-US HIV RNA and mRNA of the circadian-locomotor-output-cycles-kaput (CLOCK)-associated genes quantified by real time PCR. CLOCK-associated proteins were over-expressed in a cell line stably transfected with an HIV long-terminal repeat (LTR) luciferase reporter. Results: Using a mixed effects model, there was a significant increase in log-CA-US RNA at the third visit compared with the first visit (effect size of 0.619 with standard error (SE) of 0.098, P < 0.001) and an independent effect of time of blood draw (effect size 0.051 (SE 0.025), P = 0.040). The CLOCK-associated gene, brain-and-muscle-ARNT-like-1 (BMAL-1) had a significant relationship with log CA-US HIV RNA (effect size 8.508 (SE 3.777), P = 0.028) and also with time (P = 0.045). Over expression of BMAL-1 and CLOCK in a cell line stably transfected with an HIV-LTR luciferase reporter resulted in an increase in luciferase expression and this was reduced following mutation of the second E-box in the HIV-LTR. Conclusion: The basal level of HIV transcription on ART can vary significantly and is modulated by the circadian regulator BMAL-1, amongst other factors.
DA - 2018/9/24/
PY - 2018/9/24/
DO - 10.1097/QAD.0000000000001937
VL - 32
IS - 15
SP - 2119-2128
SN - 1473-5571
KW - brain-and-muscle-ARNT-like-1
KW - circadian rhythm
KW - HIV
KW - HIV latency
KW - HIV transcription
KW - stress
KW - unspliced RNA
ER -
TY - JOUR
TI - SVD-BASED ALGORITHMS FOR THE BEST RANK-1 APPROXIMATION OF A SYMMETRIC TENSOR
AU - Guan, Yu
AU - Chu, Moody T.
AU - Chu, Delin
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - This paper revisits the problem of finding the best rank-1 approximation to a symmetric tensor and makes three contributions. First, in contrast to the many long and lingering arguments in the lite...
DA - 2018///
PY - 2018///
DO - 10.1137/17M1136699
VL - 39
IS - 3
SP - 1095-1115
SN - 1095-7162
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85048210526&partnerID=MN8TOARS
KW - symmetric tensor
KW - best rank-1 approximation
KW - singular value decomposition
KW - convergence analysis
ER -
TY - JOUR
TI - A PROBABILISTIC SUBSPACE BOUND WITH APPLICATION TO ACTIVE SUBSPACES
AU - Holodnak, John T.
AU - Ipsen, Ilse C. F.
AU - Smith, Ralph C.
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - Given a real symmetric positive semidefinite matrix $E$, and an approximation $S$ that is a sum of $n$ independent matrix-valued random variables, we present bounds on the relative error in $S$ due to randomization. The bounds do not depend on the matrix dimensions but only on the numerical rank (intrinsic dimension) of $E$. Our approach resembles the low-rank approximation of kernel matrices from random features, but our accuracy measures are more stringent. In the context of parameter selection based on active subspaces, where $S$ is computed via Monte Carlo sampling, we present a bound on the number of samples so that with high probability the angle between the dominant subspaces of $E$ and $S$ is less than a user-specified tolerance. This is a substantial improvement over existing work, as it is a nonasymptotic and fully explicit bound on the sampling amount $n$, and it allows the user to tune the success probability. It also suggests that Monte Carlo sampling can be efficient in the presence of many parameters, as long as the underlying function $f$ is sufficiently smooth.
DA - 2018///
PY - 2018///
DO - 10.1137/17M1141503
VL - 39
IS - 3
SP - 1208-1220
SN - 1095-7162
UR - https://doi.org/10.1137/17M1141503
KW - positive semidefinite matrices
KW - principal angles
KW - eigenvalue decomposition
KW - eigen-value gaps
KW - matrix concentration inequality
KW - intrinsic dimension
KW - Monte Carlo sampling
KW - active sub-spaces
ER -
TY - JOUR
TI - THE DISCRETE EMPIRICAL INTERPOLATION METHOD: CANONICAL STRUCTURE AND FORMULATION IN WEIGHTED INNER PRODUCT SPACES
AU - Drmac, Zlatko
AU - Saibaba, Arvind Krishna
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - New contributions are offered to the theory and numerical implementation of the discrete empirical interpolation method (DEIM). A substantial tightening of the error bound for the DEIM oblique projection is achieved by index selection via a strong rank revealing QR factorization. This removes the exponential factor in the dimension of the search space from the DEIM projection error and allows sharper a priori error bounds. A well-known canonical structure of pairs of projections is used to reveal canonical structure of DEIM. Further, the DEIM approximation is formulated in weighted inner product defined by a real symmetric positive-definite matrix $W$. The weighted DEIM ($W$-DEIM) can be interpreted as a numerical implementation of the generalized empirical interpolation method (GEIM) and the more general parametrized-background data-weak (PBDW) approach. Also, it can be naturally deployed in the framework when the POD Galerkin projection is formulated in a discretization of a suitable energy (weighted) inner product such that the projection preserves important physical properties, e.g., stability. While the theoretical foundations of weighted POD and the GEIM are available in the more general setting of function spaces, this paper focuses to the gap between sound functional analysis and the core numerical linear algebra. The new proposed algorithms allow different forms of $W$-DEIM for pointwise and generalized interpolation. For the generalized interpolation, our bounds show that the condition number of $W$ does not affect the accuracy, and for pointwise interpolation the condition number of the weight matrix $W$ enters the bound essentially as $\sqrt{\min_{D={diag}}\kappa_2(DWD)}$, where $\kappa_2(W)=\|W\|_2 \|W^{-1}\|_2$ is the spectral condition number.
DA - 2018///
PY - 2018///
DO - 10.1137/17M1129635
VL - 39
IS - 3
SP - 1152-1180
SN - 1095-7162
KW - empirical interpolation
KW - Galerkin projection
KW - generalized empirical interpolation
KW - nonlinear model reduction
KW - oblique projection
KW - proper orthogonal decomposition
KW - parametrized-background data-weak approach
KW - rank revealing QR factorization
KW - weighted inner product
ER -
TY - JOUR
TI - ON MULTISCALE ADI METHODS FOR PARABOLIC PDEs WITH A DISCONTINUOUS COEFFICIENT
AU - Li, Zhilin
AU - Chen, Xiaohong
AU - Zhang, Zhengru
T2 - MULTISCALE MODELING & SIMULATION
AB - Alternating direction implicit (ADI) method is one of the most efficient methods in solving parabolic PDEs of initial and boundary value problems. However, it is challenging to develop efficient AD...
DA - 2018///
PY - 2018///
DO - 10.1137/17M1151985
VL - 16
IS - 4
SP - 1623-1647
SN - 1540-3467
KW - ADI method
KW - interface problems
KW - discontinuous coefficient
KW - multiscale
KW - jump conditions
KW - augmented variable
KW - stability
ER -
TY - JOUR
TI - A Mutual Subsidy Mechanism for a Seasonal Product Supply Chain Channel Under Double Price Regulation
AU - Peng, Hongjun
AU - Pang, Tao
AU - Cao, Fuliang
AU - Zhao, Juan
T2 - ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH
AB - In this paper, we consider the decision-making and coordination mechanism of a seasonal product supply chain channel over a period consisting of a low season and a high season, where the price of the final product is strictly regulated, and the raw material is subject to a price cap regulation during the high season. The optimal decisions and profits under decentralized and centralized cases are derived for the low season and the high season. Our research indicates that, under the double price regulation, the manufacturer’s raw material order in the channel usually is not completely fulfilled during the high season and the order during the low season is usually small. Based on the results, we propose a mutual subsidy mechanism, in order to encourage the supplier to supply more raw material during the high season and to encourage the manufacturer to order more raw material during the low season.The theoretical results indicate that the mutual subsidy mechanism can effectively coordinate the seasonal product supply chain channel under the double price regulation, which is further verified by a numerical example. Moreover, the negotiation skills of the supplier and the manufacturer are also considered under the mutual subsidy mechanism, so that the spillover profit can be allocated on a win–win basis for both sides.
DA - 2018/12//
PY - 2018/12//
DO - 10.1142/S0217595918500471
VL - 35
IS - 6
SP -
SN - 1793-7019
KW - Supply chain channel
KW - mutual subsidy mechanism
KW - price regulation
KW - seasonal product
ER -
TY - JOUR
TI - A numerical algorithm for constructing an individual mathematical model of HIV dynamics at cellular level
AU - Banks, H. Thomas
AU - Kabanikhin, Sergey I
AU - Krivorotko, Olga I
AU - Yermolenko, Darya V
T2 - JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
AB - Abstract In this paper a problem of specifying HIV-infection parameters and immune response using additional measurements of the concentrations of the T-lymphocytes, the free virus and the immune effectors at fixed times for a mathematical model of HIV dynamics is investigated numerically. The problem of the parameter specifying of the mathematical model (an inverse problem) is reduced to a problem of minimizing an objective function describing the deviation of the simulation results from the experimental data. A genetic algorithm for solving the least squares function minimization problem is implemented and investigated. The results of a numerical solution of the inverse problem are analyzed.
DA - 2018/12//
PY - 2018/12//
DO - 10.1515/jiip-2018-0019
VL - 26
IS - 6
SP - 859-873
SN - 1569-3945
KW - Mathematical model of HIV dynamics
KW - parameter specification problem
KW - inverse problem
KW - optimization approach
KW - genetic algorithm
KW - confidence intervals
ER -
TY - JOUR
TI - A note on concordance properties of fibers in Seifert homology spheres
AU - Lidman, Tye
AU - Tweedy, Eamonn
T2 - CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
AB - Abstract In this note, we collect various properties of Seifert homology spheres from the viewpoint of Dehn surgery along a Seifert fiber. We expect that many of these are known to various experts, but include them in one place, which we hope will be useful in the study of concordance and homology cobordism.
DA - 2018/12//
PY - 2018/12//
DO - 10.4153/CMB-2017-081-9
VL - 61
IS - 4
SP - 754-767
SN - 1496-4287
KW - Seifert fibered
KW - homology sphere
KW - 3-manifold
KW - concordance
KW - cobordism
KW - Heegaard Floer
ER -
TY - JOUR
TI - Estimating intratumoral heterogeneity from spatiotemporal data
AU - Rutter, E. M.
AU - Banks, H. T.
AU - Flores, K. B.
T2 - JOURNAL OF MATHEMATICAL BIOLOGY
AB - Glioblastoma multiforme (GBM) is a malignant brain cancer with a tendency to both migrate and proliferate. We propose modeling GBM with heterogeneity in cell phenotypes using a random differential equation version of the reaction–diffusion equation, where the parameters describing diffusion (D) and proliferation ( $$\rho $$ ) are random variables. We investigate the ability to perform the inverse problem to recover the probability distributions of D and $$\rho $$ using the Prohorov metric, for a variety of probability distribution functions. We test the ability to perform the inverse problem for noisy synthetic data. We then examine the predicted effect of treatment, specifically, chemotherapy, when assuming such a heterogeneous population and compare with predictions from a homogeneous cell population model.
DA - 2018/12//
PY - 2018/12//
DO - 10.1007/s00285-018-1238-6
VL - 77
IS - 6-7
SP - 1999-2022
SN - 1432-1416
KW - Glioblastoma multiforme
KW - Random differential equation
KW - Parameter estimation
ER -
TY - JOUR
TI - AN APPROXIMATION THEORETIC PERSPECTIVE OF SOBOL' INDICES WITH DEPENDENT VARIABLES
AU - Hart, J. L.
AU - Gremaud, P. A.
T2 - INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION
AB - The Sobol' indices are a recognized tool in global sensitivity analysis. When the uncertain variables in a model are statistically independent, the Sobol' indices may be easily interpreted and utilized. However, their interpretation and utility is more challenging with statistically dependent variables. This article develops an approximation theoretic perspective to interpret Sobol' indices in the presence of variable dependencies. The value of this perspective is demonstrated in the context of dimension reduction, a common application of the Sobol' indices. Theoretical analysis and illustrative examples are provided.
DA - 2018///
PY - 2018///
DO - 10.1615/Int.J.UncertaintyQuantification.2018026498
VL - 8
IS - 6
SP - 483-493
SN - 2152-5099
KW - global sensitivity analysis
KW - Sobol' indices
KW - dependent variables
ER -
TY - JOUR
TI - Automated Defect Detection in Spent Nuclear Fuel Using Combined Cerenkov Radiation and Gamma Emission Tomography Data
AU - Brayfindley, Eva
AU - Smith, Ralph C.
AU - Mattingly, John
AU - Brigantic, Robert
T2 - Nuclear Technology
AB - Spent fuel monitoring and characterization has been central to safeguards and nuclear facility monitoring for many years. The Digital Cerenkov Viewing Device (DCVD) has been used since the 1980s as a method of defect detection in spent fuel. In recent years, the accounting for large quantities of spent fuel before storage has renewed interest in this relatively quick and inexpensive method. This has an impact not only in safeguards, but also for nuclear power facilities, as accounting can be a long, arduous, and costly process. Additionally, the DCVD demonstrates limited accuracy in more complex cases such as substitution of a fuel rod with steel or a partial defect detection. A second method, gamma emission tomography (GET) has been explored as an improved defect detection method, but is much more expensive and invasive than DCVD. The present investigation identifies deficiencies in both methods and proposes a combination of data gathered from each method to address these deficiencies for improved spent fuel characterization. Initial results are promising, showing 97% detection of a single missing fuel rod when the data types are combined, versus approximately 50% and 70%, respectively, for DCVD and GET data on their own. These classification results are obtained with algorithms derived from facial recognition and applied to this problem, yielding unique accuracy in near real time while also maintaining the information barrier between output and measurement desired in safeguards.
DA - 2018/8//
PY - 2018/8//
DO - 10.1080/00295450.2018.1490123
VL - 204
IS - 3
SP - 343-353
J2 - Nuclear Technology
LA - en
OP -
SN - 0029-5450 1943-7471
UR - http://dx.doi.org/10.1080/00295450.2018.1490123
DB - Crossref
KW - Digital Cerenkov Viewing Device
KW - tomography
KW - image analysis
KW - spent fuel characterization
ER -
TY - JOUR
TI - PERTURBATION RESULTS AND THE FORWARD ORDER LAW FOR THE MOORE-PENROSE INVERSE OF A PRODUCT
AU - Castro-Gonzalez, Nieves
AU - Hartwig, Robert E.
T2 - ELECTRONIC JOURNAL OF LINEAR ALGEBRA
DA - 2018///
PY - 2018///
DO - 10.13001/1081-3810,1537-9582.3365
VL - 34
SP - 514-525
ER -
TY - JOUR
TI - RANDOM DELAY DIFFERENTIAL EQUATIONS AND INVERSE PROBLEMS FOR AGGREGATE DATA PROBLEMS
AU - Banks, H. T.
AU - Thompson, W. C.
T2 - EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS
DA - 2018///
PY - 2018///
DO - 10.32523/2306-6172-2018-6-4-4-16
VL - 6
IS - 4
SP - 4-16
SN - 2308-9822
KW - Inverse problems
KW - random delay differential equations
KW - aggregate data
KW - approximation and consistency of estimators
ER -
TY - JOUR
TI - A MULTISCALE METHOD FOR COMPUTING EFFECTIVE PARAMETERS OF COMPOSITE ELECTROMAGNETIC MATERIALS WITH MEMORY EFFECTS
AU - Bokil, V. A.
AU - Banks, H. T.
AU - Cioranescu, D.
AU - Griso, G.
T2 - QUARTERLY OF APPLIED MATHEMATICS
AB - We consider the problem of computing (macroscopic) effective properties of composite materials that are mixtures of complex dispersive dielectrics described by polarization and magnetization laws. We assume that the micro-structure of the composite material is described by spatially periodic and deterministic parameters. Mathematically, the problem is to homogenize Maxwell’s equations along with constitutive laws that describe the material response of the micro-structure comprising the mixture, to obtain an equivalent effective model for the composite material with constant effective parameters. The novel contribution of this paper is the homogenization of a hybrid model consisting of the Maxwell partial differential equations along with ordinary (auxiliary) differential equations modeling the evolution of the polarization and magnetization, as a model for the complex dielectric material. This is in contrast to our previous work (2006) in which we employed a convolution in time of a susceptibility kernel with the electric field to model the delayed polarization effects in the dispersive material. In this paper, we describe the auxiliary differential equation approach to modeling material responses in the composite material and use the periodic unfolding method to construct a homogenized model.
DA - 2018/12//
PY - 2018/12//
DO - 10.1090/qam/1503
VL - 76
IS - 4
SP - 713-738
SN - 1552-4485
KW - Maxwell's equations
KW - periodic unfolding
KW - homogenization
KW - dispersive media
KW - auxiliary differential equation
ER -
TY - JOUR
TI - Coordination contracts for a supply chain with yield uncertainty and low-carbon preference
AU - Peng, Hongjun
AU - Pang, Tao
AU - Cong, Jing
T2 - JOURNAL OF CLEANER PRODUCTION
AB - We consider a supply chain consisting of a supplier and a manufacturer under the carbon emission cap-and-trade scheme, where the manufacturer faces yield uncertainty. A Stackelberg model is adopted to investigate the production, price and carbon emission reduction decisions for the decentralized and centralized supply chain. We analyze the popular quantity discount contract and the revenue sharing contract for the supply chain. Our results indicate that the quantity discount contract can efficiently coordinate the low-carbon supply chain, but the revenue-sharing contract cannot. We then design a new contract of revenue-sharing with subsidy on emission reduction (RSS) to coordinate the supply chain. We have showed that the proposed RSS contract can coordinate the low-carbon supply chain with yield uncertainty perfectly and the carbon emission reduction level can achieve the level under the centralized case.
DA - 2018/12/20/
PY - 2018/12/20/
DO - 10.1016/j.jclepro.2018.09.038
VL - 205
SP - 291-302
SN - 1879-1786
KW - Low-carbon
KW - Cap-and-trade
KW - Quantity discount
KW - Revenue sharing
KW - Emission reduction subsidy
ER -
TY - JOUR
TI - EFFICIENT D-OPTIMAL DESIGN OF EXPERIMENTS FOR INFINITE-DIMENSIONAL BAYESIAN LINEAR INVERSE PROBLEMS
AU - Alexanderian, Alen
AU - Saibaba, Arvind K.
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the infinite-dimensional limit. The optimal design is obtained by solving an optimization problem that involves repeated evaluation of the log-determinant of high-dimensional operators along with their derivatives. Forming and manipulating these operators is computationally prohibitive for large-scale problems. Our methods exploit the low-rank structure in the inverse problem in three different ways, yielding efficient algorithms. Specifically, we propose three approaches for computing the D-optimal criterion, its gradient, and the Kullback--Leibler (KL) divergence from the posterior to prior. The first approach is based on truncated spectral decomposition of the prior-preconditioned data misfit Hessian, the second approach uses randomized matrix methods, and the third approach uses a fixed low-rank approximation of the prior-preconditioned forward operator. Detailed error analysis is provided for each of the methods, and their effectiveness is demonstrated on a model sensor placement problem for initial state reconstruction in a time-dependent advection-diffusion equation in two space dimensions.
DA - 2018///
PY - 2018///
DO - 10.1137/17M115712X
VL - 40
IS - 5
SP - A2956-A2985
SN - 1095-7197
KW - Bayesian inversion
KW - D-optimal experimental design
KW - large-scale ill-posed inverse problems
KW - randomized matrix methods
KW - low-rank approximation
KW - uncertainty quantification
ER -
TY - JOUR
TI - Determinants of the efficacy of HIV latency-reversing agents and implications for drug and treatment design
AU - Ke, Ruian
AU - Conway, Jessica M.
AU - Margolis, David M.
AU - Perelson, Alan S.
T2 - JCI INSIGHT
AB - HIV eradication studies have focused on developing latency-reversing agents (LRAs). However, it is not understood how the rate of latent reservoir reduction is affected by different steps in the process of latency reversal. Furthermore, as current LRAs are host-directed, LRA treatment is likely to be intermittent to avoid host toxicities. Few careful studies of the serial effects of pulsatile LRA treatment have yet been done. This lack of clarity makes it difficult to evaluate the efficacy of candidate LRAs or predict long-term treatment outcomes. We constructed a mathematical model that describes the dynamics of latently infected cells under LRA treatment. Model analysis showed that, in addition to increasing the immune recognition and clearance of infected cells, the duration of HIV antigen expression (i.e., the period of vulnerability) plays an important role in determining the efficacy of LRAs, especially if effective clearance is achieved. Patients may benefit from pulsatile LRA exposures compared with continuous LRA exposures if the period of vulnerability is long and the clearance rate is high, both in the presence and absence of an LRA. Overall, the model framework serves as a useful tool to evaluate the efficacy and the rational design of LRAs and combination strategies.
DA - 2018/10/18/
PY - 2018/10/18/
DO - 10.1172/jci.insight.123052
VL - 3
IS - 20
SP -
SN - 2379-3708
ER -
TY - JOUR
TI - Modeling Nondilute Species Transport Using the Thermodynamically Constrained Averaging Theory
AU - Weigand, T. M.
AU - Schultz, P. B.
AU - Giffen, D. H.
AU - Farthing, M. W.
AU - Crockett, A.
AU - Kelley, C. T.
AU - Gray, W. G.
AU - Miller, C. T.
T2 - Water Resources Research
AB - Nondilute transport in porous media results in fronts that are much sharper in space and time than the corresponding transport of a conservative, nonreactive dilute species. A thermodynamically constrained averaging theory model for such situations is developed. A novel closure scheme is formulated, which is cross-coupled between flow and transport in its most general form. Experiments are performed to investigate the effects of density, viscosity, and chemical activity. An adaptive numerical approximation method is developed to efficiently solve the formulated model. Parameter estimation is performed, and excellent agreement between laboratory data and model simulations is obtained. Accurate prediction of experimental data not used to estimate model parameters is found. It is also shown that chemical activity effects contribute to asymmetric breakthrough curves for nondilute transport in porous medium systems.
DA - 2018/9//
PY - 2018/9//
DO - 10.1029/2017WR022471
VL - 54
IS - 9
SP - 6656-6682
J2 - Water Resour. Res.
LA - en
OP -
SN - 0043-1397
UR - http://dx.doi.org/10.1029/2017WR022471
DB - Crossref
ER -
TY - JOUR
TI - A randomized tensor singular value decomposition based on the t-product
AU - Zhang, Jiani
AU - Saibaba, Arvind K.
AU - Kilmer, Misha E.
AU - Aeron, Shuchin
T2 - NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
AB - The tensor SVD (t-SVD) for third-order tensors, previously proposed in the literature, has been applied successfully in many fields, such as computed tomography, facial recognition, and video completion. In this paper, we propose a method that extends a well-known randomized matrix method to the t-SVD. This method can produce a factorization with similar properties to the t-SVD, but it is more computationally efficient on very large data sets. We present details of the algorithms and theoretical results and provide numerical results that show the promise of our approach for compressing and analyzing image-based data sets. We also present an improved analysis of the randomized and simultaneous iteration for matrices, which may be of independent interest to the scientific community. We also use these new results to address the convergence properties of the new and randomized tensor method as well.
DA - 2018/10//
PY - 2018/10//
DO - 10.1002/nla.2179
VL - 25
IS - 5
SP -
SN - 1099-1506
KW - randomized SVD
KW - singular value decomposition
KW - t-product
KW - tensor
KW - truncated SVD
ER -
TY - JOUR
TI - Decentralized Observer-Based Reliable Control for a Class of Interconnected Markov Jumped Time-Delay System Subject to Actuator Saturation and Failure
AU - Chen, Zhaohui
AU - Cao, Zhong
AU - Huang, Qi
AU - Campbell, Stephen L.
T2 - CIRCUITS SYSTEMS AND SIGNAL PROCESSING
DA - 2018/11//
PY - 2018/11//
DO - 10.1007/s00034-018-0795-7
VL - 37
IS - 11
SP - 4728-4752
SN - 1531-5878
KW - Interconnected systems
KW - Time-delay systems
KW - Actuator saturation
KW - Actuator failure
KW - Decentralized observer-based stabilization
ER -
TY - JOUR
TI - THE ROLE OF STRUCTURAL VISCOELASTICITY IN DEFORMABLE POROUS MEDIA WITH INCOMPRESSIBLE CONSTITUENTS: APPLICATIONS IN BIOMECHANICS
AU - Verri, Maurizio
AU - Guidoboni, Giovanna
AU - Bociu, Lorena
AU - Sacco, Riccardo
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in external applied loads. Models of deformable porous media with incompressible constituents are often utilized to describe the behavior of biological tissues, such as cartilages, bones and engineered tissue scaffolds, where viscoelastic properties may change with age, disease or by design. Here, for the first time, we show that the fluid velocity within the medium could increase tremendously, even up to infinity, should the external applied load experience sudden changes in time and the structural viscoelasticity be too small. In particular, we consider a one-dimensional poro-visco-elastic model for which we derive explicit solutions in the cases where the external applied load is characterized by a step pulse or a trapezoidal pulse in time. By means of dimensional analysis, we identify some dimensionless parameters that can aid the design of structural properties and/or experimental conditions as to ensure that the fluid velocity within the medium remains bounded below a certain given threshold, thereby preventing potential tissue damage. The application to confined compression tests for biological tissues is discussed in detail. Interestingly, the loss of viscoelastic tissue properties has been associated with various disease conditions, such as atherosclerosis, Alzheimer’s disease and glaucoma. Thus, the findings of this work may be relevant to many applications in biology and medicine.
DA - 2018/8//
PY - 2018/8//
DO - 10.3934/mbe.2018042
VL - 15
IS - 4
SP - 933-959
SN - 1551-0018
KW - Deformable porous media flow
KW - incompressible constituents
KW - viscoelasticity
KW - explicit solution
KW - velocity blow-up
KW - confined compression
ER -
TY - JOUR
TI - OPTIMAL DESIGN FOR DYNAMICAL MODELING OF PEST POPULATIONS
AU - Banks, H. T.
AU - Everett, R. A.
AU - Murad, Neha
AU - White, R. D.
AU - Banks, J. E.
AU - Cass, Bodil N.
AU - Rosenheim, Jay A.
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - We apply SE-optimal design methodology to investigate optimal data collection procedures as a first step in investigating information content in ecoinformatics data sets. To illustrate ideas we use a simple phenomenological citrus red mite population model for pest dynamics. First the optimal sampling distributions for a varying number of data points are determined. We then analyze these optimal distributions by comparing the standard errors of parameter estimates corresponding to each distribution. This allows us to investigate how many data are required to have confidence in model parameter estimates in order to employ dynamical modeling to infer population dynamics. Our results suggest that a field researcher should collect at least 12 data points at the optimal times. Data collected according to this procedure along with dynamical modeling will allow us to estimate population dynamics from presence/absence-based data sets through the development of a scaling relationship. These Likert-type data sets are commonly collected by agricultural pest management consultants and are increasingly being used in ecoinformatics studies. By applying mathematical modeling with the relationship scale from the new data, we can then explore important integrated pest management questions using past and future presence/absence data sets.
DA - 2018/8//
PY - 2018/8//
DO - 10.3934/mbe.2018044
VL - 15
IS - 4
SP - 993-1010
SN - 1551-0018
KW - Dynamic modeling
KW - pest management
KW - optimal experimental design
KW - constrained optimization
KW - ecoinformatics
ER -
TY - JOUR
TI - Acetosyringone treatment duration affects large T-DNA molecule transfer to rice callus
AU - Xi, Jing
AU - Patel, Minesh
AU - Dong, Shujie
AU - Que, Qiudeng
AU - Qu, Rongda
T2 - BMC BIOTECHNOLOGY
AB - Large T-DNA fragment transfer has long been a problem for Agrobacterium-mediated transformation. Although vector systems, such as the BIBAC series, were successfully developed for the purpose, low transformation efficiencies were consistently observed.To gain insights of this problem in monocot transformation, we investigated the T-strand accumulation of various size of T-DNA in two kinds of binary vectors (one copy vs. multi-copy) upon acetosyringone (AS) induction and explored ways to improve the efficiency of the large T-DNA fragment transfer in Agrobacterium-mediated rice transformation. By performing immuno-precipitation of VirD2-T-strands and quantitative real-time PCR assays, we monitored the accumulation of the T-strands in Agrobacterium tumeficiens after AS induction. We further demonstrated that extension of AS induction time highly significantly improved large-size T-DNA transfer to rice cells.Our data provide valuable information of the T-strand dynamics and its impact on large T-DNA transfer in monocots, and likely dicots as well.
DA - 2018/8/9/
PY - 2018/8/9/
DO - 10.1186/s12896-018-0459-5
VL - 18
SP -
SN - 1472-6750
KW - Agrobacterium
KW - BIBAC
KW - Immuno-precipitation
KW - Large T-DNA
KW - Monocot transformation
ER -
TY - JOUR
TI - Goal-oriented optimal design of experiments for large-scale Bayesian linear inverse problems
AU - Attia, Ahmed
AU - Alexanderian, Alen
AU - Saibaba, Arvind K.
T2 - INVERSE PROBLEMS
AB - We develop a framework for goal-oriented optimal design of experiments (GOODE) for large-scale Bayesian linear inverse problems governed by PDEs. This framework differs from classical Bayesian optimal design of experiments (ODE) in the following sense: we seek experimental designs that minimize the posterior uncertainty in the experiment end-goal, e.g., a quantity of interest (QoI), rather than the estimated parameter itself. This is suitable for scenarios in which the solution of an inverse problem is an intermediate step and the estimated parameter is then used to compute a QoI. In such problems, a GOODE approach has two benefits: the designs can avoid wastage of experimental resources by a targeted collection of data, and the resulting design criteria are computationally easier to evaluate due to the often low-dimensionality of the QoIs. We present two modified design criteria, A-GOODE and D-GOODE, which are natural analogues of classical Bayesian A- and D-optimal criteria. We analyze the connections to other ODE criteria, and provide interpretations for the GOODE criteria by using tools from information theory. Then, we develop an efficient gradient-based optimization framework for solving the GOODE optimization problems. Additionally, we present comprehensive numerical experiments testing the various aspects of the presented approach. The driving application is the optimal placement of sensors to identify the source of contaminants in a diffusion and transport problem. We enforce sparsity of the sensor placements using an $\ell_1$-norm penalty approach, and propose a practical strategy for specifying the associated penalty parameter.
DA - 2018/9//
PY - 2018/9//
DO - 10.1088/1361-6420/aad210
VL - 34
IS - 9
SP -
SN - 1361-6420
KW - design of experiments
KW - inverse problems
KW - sensor placement
KW - data assimilation
ER -
TY - JOUR
TI - Number of common roots and resultant of two tropical univariate polynomials
AU - Hong, Hoon
AU - Rafael Sendra, J.
T2 - JOURNAL OF ALGEBRA
AB - Abstract It is well known that for two univariate polynomials over the complex number field the number of their common roots is equal to the order of their resultant. In this paper, we show that this fundamental relationship still holds for the tropical polynomials under suitable adaptation of the notion of order, if the roots are simple and non-zero.
DA - 2018/10/1/
PY - 2018/10/1/
DO - 10.1016/j.jalgebra.2018.06.027
VL - 511
SP - 420-439
SN - 1090-266X
UR - http://dx.doi.org/10.1016/j.jalgebra.2018.06.027
KW - Tropical semifield
KW - Tropical resultant
KW - Common roots
ER -
TY - JOUR
TI - Convergence analysis of an SVD-based algorithm for the best rank-1 tensor approximation
AU - Guan, Yu
AU - Chu, Moody T.
AU - Chu, Delin
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - This paper revisits the classical problem of finding the best rank-1 approximation to a generic tensor. The main focus is on providing a mathematical proof for the convergence of the iterates of an SVD-based algorithm. In contrast to the conventional approach by the so called alternating least squares (ALS) method that works to adjust one factor a time, the SVD-based algorithms improve two factors simultaneously. The ALS method is easy to implement, but suffers from slow convergence and easy stagnation at a local solution. It has been suggested recently that the SVD-algorithm might have a better limiting behavior leading to better approximations, yet a theory of convergence has been elusive in the literature. This note proposes a simple tactic to partially close that gap.
DA - 2018/10/15/
PY - 2018/10/15/
DO - 10.1016/j.laa.2018.06.006
VL - 555
SP - 53-69
SN - 1873-1856
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85048228789&partnerID=MN8TOARS
KW - Best rank-1 tensor approximation
KW - Singular value decomposition
ER -
TY - JOUR
TI - An approach to periodic, time-varying parameter estimation using nonlinear filtering
AU - Arnold, Andrea
AU - Lloyd, Alun L
T2 - Inverse Problems
AB - Many systems arising in biological applications are subject to periodic forcing. In these systems the forcing parameter is not only time-varying but also known to have a periodic structure. We present an approach to estimating periodic, time-varying parameters that imposes periodic structure by treating the time-varying parameter as a piecewise function with unknown coefficients. This method allows the resulting parameter estimate more flexibility in shape than prescribing a specific functional form (e.g., sinusoidal) to model its behavior, while still maintaining periodicity. We employ nonlinear filtering, more specifically, a version of the augmented ensemble Kalman filter (EnKF), to estimate the unknown coefficients comprising the piecewise approximation of the periodic, time-varying parameter. This allows for straightforward comparison of the proposed method with an EnKF-based parameter tracking algorithm, where periodicity is not guaranteed. We demonstrate the effectiveness of the proposed approach on two biological examples: a synthetic example with data generated from the nonlinear FitzHugh-Nagumo system, modeling the excitability of a nerve cell, to estimate the external voltage parameter, and a case study using reported measles incidence data from three locations during the pre-vaccine era to estimate the seasonal transmission parameter. The formulation of the proposed approach also allows for simultaneous estimation of initial conditions and other static system parameters, such as the reporting probability of measles cases, which is vital for predicting under-reported incidence data.
DA - 2018/8/3/
PY - 2018/8/3/
DO - 10.1088/1361-6420/aad3e0
VL - 34
IS - 10
SP - 105005
J2 - Inverse Problems
OP -
SN - 0266-5611 1361-6420
UR - http://dx.doi.org/10.1088/1361-6420/aad3e0
DB - Crossref
KW - time-varying parameter estimation
KW - periodic structure
KW - nonlinear filtering
KW - ensemble Kalman filter (EnKF)
KW - FitzHugh-Nagumo
KW - measles transmission
ER -
TY - JOUR
TI - A direct IIM approach for two-phase Stokes equations with discontinuous viscosity on staggered grids
AU - Chen, Xiaohong
AU - Li, Zhilin
AU - Ruiz Alvarez, Juan
T2 - COMPUTERS & FLUIDS
AB - In this paper, a direct immersed interface method (IIM) is proposed to solve two-phase incompressible Stokes equations with an interface and a piecewise constant viscosity on staggered grids. The velocity components and the pressure are placed in different grid points and the Marker and Cell (MAC) scheme is used for discretizing the momentum and continuity equations at regular grid points. At irregular grid points, correction terms are added to the finite difference scheme to offset the discontinuities. The correction terms are determined directly by an interpolation scheme using the values of both the velocity and pressure at nearby grid points. The resulted linear system of equations is rank-one deficient and is solved by the Uzawa iterative method. In each Uzawa iteration, an inner GMRES solver is used and preconditioned by the discrete Laplacian. The computed numerical solutions are second order accurate in the L∞ norm for both the velocity and pressure, which is demonstrated in numerical tests. Compared with the augmented interface method (AIIM), one of advantages of this approach is that it avoids the costs for introducing augmented variables and difficulties in solving them from the corresponding Schur complement system. Hence, this new method is easier to implement and computationally more efficient.
DA - 2018/8/30/
PY - 2018/8/30/
DO - 10.1016/j.compfluid.2018.03.038
VL - 172
SP - 549-563
SN - 1879-0747
UR - https://doi.org/10.1016/j.compfluid.2018.03.038
KW - Incompressible Stokes equations
KW - Interface problem
KW - Discontinuous viscosity
KW - Marker and cell scheme
KW - Staggered mesh
KW - Uzawa method
KW - Immersed interface method
KW - Finite difference method
ER -
TY - JOUR
TI - Uncertainty-enabled design of electromagnetic reflectors with integrated shape control
AU - Haque, Samiul
AU - Kindrat, Laszlo P.
AU - Zhang, Li
AU - Mikheev, Vikenty
AU - Kim, Daewa
AU - Liu, Sijing
AU - Chung, Jooyeon
AU - Kuian, Mykhailo
AU - Massad, Jordan E.
AU - Smith, Ralph C.
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES XII
AB - We implemented a computationally efficient model for a corner-supported, thin, rectangular, orthotropic polyvinylidene fluoride (PVDF) laminate membrane, actuated by a two-dimensional array of segmented electrodes. The laminate can be used as shape-controlled electromagnetic reflector and the model estimates the reflector’s shape given an array of control voltages. In this paper, we describe a model to determine the shape of the laminate for a given distribution of control voltages. Then, we investigate the surface shape error and its sensitivity to the model parameters. Subsequently, we analyze the simulated deflection of the actuated bimorph using a Zernike polynomial decomposition. Finally, we provide a probabilistic description of reflector performance using statistical methods to quantify uncertainty. We make design recommendations for nominal parameter values and their tolerances based on optimization under uncertainty using multiple methods.
DA - 2018///
PY - 2018///
DO - 10.1117/12.2300396
VL - 10596
SP -
SN - 1996-756X
KW - Bimorph membrane
KW - Zernike polynomials
KW - PVDF
KW - Sensitivity analysis
KW - Uncertainty Quantification
ER -
TY - JOUR
TI - Fractional Viscoelasticity of Soft Elastomers and Auxetic Foams
AU - Solheim, Hannah
AU - Stanisauskis, Eugenia
AU - Miles, Paul
AU - Oates, William
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES XII
AB - Dielectric elastomers are commonly implemented in adaptive structures due to their unique capabilities for real time control of a structure’s shape, stiffness, and damping. These active polymers are often used in applications where actuator control or dynamic tunability are important, making an accurate understanding of the viscoelastic behavior critical. This challenge is complicated as these elastomers often operate over a broad range of deformation rates. Whereas research has demonstrated success in applying a nonlinear viscoelastic constitutive model to characterize the behavior of Very High Bond (VHB) 4910, robust predictions of the viscoelastic response over the entire range of time scales is still a significant challenge. An alternative formulation for viscoelastic modeling using fractional order calculus has shown significant improvement in predictive capabilities. While fractional calculus has been explored theoretically in the field of linear viscoelasticity, limited experimental validation and statistical evaluation of the underlying phenomena have been considered. In the present study, predictions across several orders of magnitude in deformation rates are validated against data using a single set of model parameters. Moreover, we illustrate the fractional order is material dependent by running complementary experiments and parameter estimation on the elastomer VHB 4949 as well as an auxetic foam. All results are statistically validated using Bayesian uncertainty methods to obtain posterior densities for the fractional order as well as the hyperelastic parameters.
DA - 2018///
PY - 2018///
DO - 10.1117/12.2296666
VL - 10596
SP -
SN - 1996-756X
KW - Dielectric Elastomers
KW - Auxetic Foams
KW - Parameter Estimation
KW - Fractional Order Calculus
ER -
TY - JOUR
TI - Practical identifiability and uncertainty quantification of a pulsatile cardiovascular model
AU - Marquis, Andrew D.
AU - Arnold, Andrea
AU - Dean-Bernhoft, Caron
AU - Carlson, Brian E.
AU - Olufsen, Mette S.
T2 - MATHEMATICAL BIOSCIENCES
AB - Mathematical models are essential tools to study how the cardiovascular system maintains homeostasis. The utility of such models is limited by the accuracy of their predictions, which can be determined by uncertainty quantification (UQ). A challenge associated with the use of UQ is that many published methods assume that the underlying model is identifiable (e.g. that a one-to-one mapping exists from the parameter space to the model output). In this study we present a novel workflow to calibrate a lumped-parameter model to left ventricular pressure and volume time series data. Key steps include using (1) literature and available data to determine nominal parameter values; (2) sensitivity analysis and subset selection to determine a set of identifiable parameters; (3) optimization to find a point estimate for identifiable parameters; and (4) frequentist and Bayesian UQ calculations to assess the predictive capability of the model. Our results show that it is possible to determine 5 identifiable model parameters that can be estimated to our experimental data from three rats, and that computed UQ intervals capture the measurement and model error.
DA - 2018/10//
PY - 2018/10//
DO - 10.1016/j.mbs.2018.07.001
VL - 304
SP - 9-24
SN - 1879-3134
KW - Cardiovascular dynamics
KW - Modeling
KW - Parameter estimation
KW - Uncertainty quantification
KW - Patient-specific modeling
ER -
TY - JOUR
TI - Active Subspace Uncertainty Quantification for a Polydomain Ferroelectric Phase-Field Model
AU - Leon, Lider S.
AU - Smith, Ralph C.
AU - Miles, Paul
AU - Oates, William S.
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES XII
AB - Quantum-informed ferroelectric phase field models capable of predicting material behavior, are necessary for facilitating the development and production of many adaptive structures and intelligent systems. Uncertainty is present in these models, given the quantum scale at which calculations take place. A necessary analysis is to determine how the uncertainty in the response can be attributed to the uncertainty in the model inputs or parameters. A second analysis is to identify active subspaces within the original parameter space, which quantify directions in which the model response varies most dominantly, thus reducing sampling effort and computational cost. In this investigation, we identify an active subspace for a poly-domain ferroelectric phase-field model. Using the active variables as our independent variables, we then construct a surrogate model and perform Bayesian inference. Once we quantify the uncertainties in the active variables, we obtain uncertainties for the original parameters via an inverse mapping. The analysis provides insight into how active subspace methodologies can be used to reduce computational power needed to perform Bayesian inference on model parameters informed by experimental or simulated data.
DA - 2018///
PY - 2018///
DO - 10.1117/12.2297207
VL - 10596
SP -
SN - 1996-756X
KW - Ferroelectric materials
KW - ferroelectricity
KW - active subspaces
KW - surrogate model
KW - uncertainty quantification
KW - Bayesian inference
ER -
TY - JOUR
TI - Polyphasic characterization of four soil-derived phenanthrene-degrading Acidovorax strains and proposal of Acidovorax carolinensis sp nov.
AU - Singleton, David R.
AU - Lee, Janice
AU - Dickey, Allison N.
AU - Stroud, Aaron
AU - Scholl, Elizabeth H.
AU - Wright, Fred A.
AU - Aitken, Michael D.
T2 - SYSTEMATIC AND APPLIED MICROBIOLOGY
AB - Four bacterial strains identified as members of the Acidovorax genus were isolated from two geographically distinct but similarly contaminated soils in North Carolina, USA, characterized, and their genomes sequenced. Their 16S rRNA genes were highly similar to those previously recovered during stable-isotope probing (SIP) of one of the soils with the polycyclic aromatic hydrocarbon (PAH) phenanthrene. Heterotrophic growth of all strains occurred with a number of organic acids, as well as phenanthrene, but no other tested PAHs. Optimal growth occurred aerobically under mesophilic temperature, neutral pH, and low salinity conditions. Predominant fatty acids were C16:1ω7c/C16:1ω6c, C16:0, and C18:1ω7c, and were consistent with the genus. Genomic G+C contents ranged from 63.6 to 64.2%. A combination of whole genome comparisons and physiological analyses indicated that these four strains likely represent a single species within the Acidovorax genus. Chromosomal genes for phenanthrene degradation to phthalate were nearly identical to highly conserved regions in phenanthrene-degrading Delftia, Burkholderia, Alcaligenes, and Massilia species in regions flanked by transposable or extrachromosomal elements. The lower degradation pathway for phenanthrene metabolism was inferred by comparisons to described genes and proteins. The novel species Acidovorax carolinensis sp. nov. is proposed, comprising the four strains described in this study with strain NA3T as the type strain (=LMG 30136, =DSM 105008).
DA - 2018/9//
PY - 2018/9//
DO - 10.1016/j.syapm.2018.06.001
VL - 41
IS - 5
SP - 460-472
SN - 0723-2020
KW - Acidovorax
KW - Phenanthrene
KW - Polycyclic aromatic hydrocarbons
ER -
TY - JOUR
TI - Multipartite Separability of Density Matrices of Graphs
AU - Zhao, Hui
AU - Zhao, Jing-Yun
AU - Jing, Naihuan
T2 - INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
AB - A new layers method is presented for multipartite separability of density matrices from simple graphs. Full separability of tripartite states is studied for graphs on degree symmetric premise. The models are generalized to multipartite systems by presenting a class of fully separable states arising from partially symmetric graphs.
DA - 2018/10//
PY - 2018/10//
DO - 10.1007/s10773-018-3829-9
VL - 57
IS - 10
SP - 3112-3126
SN - 1572-9575
UR - https://doi.org/10.1007/s10773-018-3829-9
KW - Laplacian matrices
KW - Partially symmetric
KW - Degree symmetric
KW - Separability
ER -
TY - JOUR
TI - Tissue self-organization underlies morphogenesis of the notochord
AU - Norman, James
AU - Sorrell, Emma L.
AU - Hu, Yi
AU - Siripurapu, Vaishnavi
AU - Garcia, Jamie
AU - Bagwell, Jennifer
AU - Charbonneau, Patrick
AU - Lubkin, Sharon R.
AU - Bagnat, Michel
T2 - PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES
AB - The notochord is a conserved axial structure that in vertebrates serves as a hydrostatic scaffold for embryonic axis elongation and, later on, for proper spine assembly. It consists of a core of large fluid-filled vacuolated cells surrounded by an epithelial sheath that is encased in extracellular matrix. During morphogenesis, the vacuolated cells inflate their vacuole and arrange in a stereotypical staircase pattern. We investigated the origin of this pattern and found that it can be achieved purely by simple physical principles. We are able to model the arrangement of vacuolated cells within the zebrafish notochord using a physical model composed of silicone tubes and water-absorbing polymer beads. The biological structure and the physical model can be accurately described by the theory developed for the packing of spheres and foams in cylinders. Our experiments with physical models and numerical simulations generated several predictions on key features of notochord organization that we documented and tested experimentally in zebrafish. Altogether, our data reveal that the organization of the vertebrate notochord is governed by the density of the osmotically swelling vacuolated cells and the aspect ratio of the notochord rod. We therefore conclude that self-organization underlies morphogenesis of the vertebrate notochord. This article is part of the Theo Murphy meeting issue on ‘Mechanics of development’.
DA - 2018/11/5/
PY - 2018/11/5/
DO - 10.1098/rstb.2017.0320
VL - 373
IS - 1759
SP -
SN - 1471-2970
UR - https://doi.org/10.1098/rstb.2017.0320
KW - zebrafish
KW - notochord
KW - vacuolated cells
KW - packing
KW - self-organization
ER -
TY - JOUR
TI - Low-Rank Independence Samplers in Hierarchical Bayesian Inverse Problems
AU - Brown, D. Andrew
AU - Saibaba, Arvind
AU - Vallelian, Sarah
T2 - SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
AB - In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In fully Bayesian approaches in which prior parameters are assigned hyperpriors, Markov chain Monte Carlo algorithms often are used to draw samples from the posterior distribution. However, implementations of such algorithms can be computationally expensive. We present a computationally efficient scheme for sampling high-dimensional Gaussian distributions in ill-posed Bayesian linear inverse problems. Our approach uses Metropolis--Hastings independence sampling with a proposal distribution based on a low-rank approximation of the prior-preconditioned Hessian. We show the dependence of the acceptance rate on the number of eigenvalues retained and discuss conditions under which the acceptance rate is high. We demonstrate our proposed sampler by using it with Metropolis--Hastings-within-Gibbs sampling in numerical experiments in image deblurring, computerized tomography, and NMR relaxometry.
DA - 2018///
PY - 2018///
DO - 10.1137/17M1137218
VL - 6
IS - 3
SP - 1076-1100
SN - 2166-2525
KW - computerized tomography
KW - image deblurring
KW - low-rank approximation
KW - Metropolis-Hastings independence sampler
KW - prior-preconditioned Hessian
ER -
TY - JOUR
TI - The group inverse of the nivellateur
AU - Hartwig, R. E.
AU - Patricio, P.
T2 - LINEAR & MULTILINEAR ALGEBRA
AB - We shall derive necessary and sufficient conditions for the nivellateur to have a group inverse over an algebraically closed field. We then extend these results to arbitrary fields.
DA - 2018///
PY - 2018///
DO - 10.1080/03081087.2017.1397092
VL - 66
IS - 12
SP - 2409-2420
SN - 1563-5139
KW - Nivellateur
KW - group inverse
KW - matrices over a field
ER -
TY - JOUR
TI - Uncertainty Quantification for PZT Bimorph Actuators
AU - Bravo, Nikolas
AU - Smith, Ralph C.
AU - Crews, John
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES XII
AB - In this paper, we discuss the development of a high fidelity model for a PZT bimorph actuator used for micro-air vehicles, which includes the Robobee. We developed a high-fidelity model for the actuator using the homogenized energy model (HEM) framework, which quantifies the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. We then discussed an inverse problem on the model. We included local and global sensitivity analysis of the parameters in the high-fidelity model. Finally, we will discuss the results of Bayesian inference and uncertainty quantification on the HEM.
DA - 2018///
PY - 2018///
DO - 10.1117/12.2297148
VL - 10596
SP -
SN - 1996-756X
KW - Uncertainty Quantification
KW - PZT Bimorph
KW - Modeling
KW - Surrogate
KW - Homogenized Energy Model
ER -
TY - JOUR
TI - ON THE SOLVABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS SUBJECT TO GENERALIZED BOUNDARY CONDITIONS
AU - Freedman, Benjamin
AU - Rodriguez, Jesus
T2 - DIFFERENTIAL EQUATIONS & APPLICATIONS
AB - In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability of a large number of nonlinear scalar boundary value problems. We begin by giving our general strategy which involves the reformulation of our boundary value problem as an operator equation. We then proceed to establish our results and compare them to closely related previous work.
DA - 2018/8//
PY - 2018/8//
DO - 10.7153/dea-2018-10-22
VL - 10
IS - 3
SP - 317-327
SN - 1848-9605
KW - Boundary value problems
KW - ordinary differential equation
KW - nonlinear equations
KW - fixed-point theorems
ER -
TY - JOUR
TI - The effect of pore size and density on ultrasonic attenuation in porous structures with mono-disperse random pore distribution: A two-dimensional in-silico study
AU - Yousefian, Omid
AU - White, R. D.
AU - Karbalaeisadegh, Yasamin
AU - Banks, H. T.
AU - Muller, Marie
T2 - JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
AB - This work proposes a power law model to describe the attenuation of ultrasonic waves in non-absorbing heterogeneous media with randomly distributed scatterers, mimicking a simplified structure of cortical bone. This paper models the propagation in heterogeneous structures with controlled porosity using a two-dimensional finite-difference time domain numerical simulation in order to measure the frequency dependent attenuation. The paper then fits a phenomenological model to the simulated frequency dependent attenuation by optimizing parameters under an ordinary least squares framework. Local sensitivity analysis is then performed on the resulting parameter estimates in order to determine to which estimates the model is most sensitive. This paper finds that the sensitivity of the model to various parameter estimates depends on the micro-architectural parameters, pore diameter (ϕ) and pore density (ρ). In order to get a sense for how confidently model parameters are able to be estimated, 95% confidence intervals for these estimates are calculated. In doing so, the ability to estimate model-sensitive parameters with a high degree of confidence is established. In the future, being able to accurately estimate model parameters from which micro-architectural ones could be inferred will allow pore density and diameter to be estimated via an inverse problem given real or simulated ultrasonic data to be determined.
DA - 2018/8//
PY - 2018/8//
DO - 10.1121/1.5049782
VL - 144
IS - 2
SP - 709-719
SN - 1520-8524
ER -
TY - JOUR
TI - no blokes Is Essential for Male Viability and X Chromosome Gene Expression in the Australian Sheep Blowfly
AU - Davis, Rebecca J.
AU - Belikoff, Esther J.
AU - Scholl, Elizabeth H.
AU - Li, Fang
AU - Scott, Maxwell J.
T2 - CURRENT BIOLOGY
AB - It has been hypothesized that the Drosophila 4th chromosome is derived from an ancient X chromosome [1Vicoso B. Bachtrog D. Reversal of an ancient sex chromosome to an autosome in Drosophila.Nature. 2013; 499: 332-335Crossref PubMed Scopus (131) Google Scholar]. In the Australian sheep blowfly, Lucilia cuprina, the heterochromatic X chromosome contains few active genes and orthologs of Drosophila X-linked genes are autosomal. Of 8 X-linked genes identified previously in L. cuprina, 6 were orthologs of Drosophila 4th-chromosome genes [2Linger R.J. Belikoff E.J. Scott M.J. Dosage compensation of X-linked Muller element F genes but not X-linked transgenes in the Australian sheep blowfly.PLoS ONE. 2015; 10: e0141544Crossref PubMed Scopus (14) Google Scholar]. The X-linked genes were expressed equally in males and females. Here we identify an additional 51 X-linked genes and show that most are dosage compensated. Orthologs of 49 of the 59 X-linked genes are on the 4th chromosome in D. melanogaster. Because painting of fourth (Pof) is important for expression of Drosophila 4th-chromosome genes [3Johansson A.M. Stenberg P. Allgardsson A. Larsson J. POF regulates the expression of genes on the fourth chromosome in Drosophila melanogaster by binding to nascent RNA.Mol. Cell. Biol. 2012; 32: 2121-2134Crossref PubMed Scopus (27) Google Scholar], we used Cas9 to make a loss-of-function knockin mutation in an L. cuprina Pof ortholog we call no blokes (nbl). Homozygous nbl males derived from homozygous nbl mothers die at the late pupal stage. Homozygous nbl females are viable, fertile, and live longer than heterozygous nbl females. RNA expression of most X-linked genes was reduced in homozygous nbl male pupae and to a lesser extent in nbl females compared to heterozygous siblings. The results suggest that NBL could be important for X chromosome dosage compensation in L. cuprina. NBL may also facilitate gene expression in the heterochromatic environment of the X chromosome in both sexes. This study supports the hypothesis on the origin of the Drosophila 4th chromosome and that a POF-like protein was required for normal gene expression on the ancient X chromosome.
DA - 2018/6/18/
PY - 2018/6/18/
DO - 10.1016/j.cub.2018.05.005
VL - 28
IS - 12
SP - 1987-+
SN - 1879-0445
ER -
TY - JOUR
TI - Reliable H-infinity control on saturated linear Markov jump system with uncertain transition rates and asynchronous jumped actuator failure
AU - Chen, Zhaohui
AU - Cao, Zhong
AU - Huang, Qi
AU - Campbell, Stephen L.
T2 - JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
AB - This paper is concerned with reliable H∞ control for saturated linear Markov jump systems with uncertain transition rates and asynchronous jumped actuator failure. The actuator failures are assumed to occur randomly under the Markov process with a different jumping mode from the system jumping mode. In considering the mixed-mode-dependent state feedback controller, both H∞ stochastic stability analysis for closed-loop system with completely accessible transition rates and uncertain transition rates are investigated. Moreover, based on the obtained stability conditions, the H∞ control problems are investigated, and the controller gains can be obtained by solving a convex optimization problem with minimizing H∞ performance as objective and linear matrix inequalities (LMIs) as constraints. The problem of designing state feedback controllers such that the estimate of the domain of attraction is enlarged is also formulated and solved as an optimization problem with LMI constraints. Simulation results are presented to illustrate the effectiveness of the proposed results.
DA - 2018/6//
PY - 2018/6//
DO - 10.1016/j.jfranklin.2018.02.029
VL - 355
IS - 9
SP - 3853-3872
SN - 1879-2693
ER -
TY - JOUR
TI - Perspective Functions: Properties, Constructions, and Examples
AU - Combettes, Patrick L.
T2 - SET-VALUED AND VARIATIONAL ANALYSIS
AB - Many functions encountered in applied mathematics and in statistical data analysis can be expressed in terms of perspective functions. One of the earliest examples is the Fisher information, which appeared in statistics in the 1920s. We analyze various algebraic and convex-analytical properties of perspective functions and provide general schemes to construct lower semicontinuous convex functions from them. Several new examples are presented and existing instances are featured as special cases.
DA - 2018/6//
PY - 2018/6//
DO - 10.1007/s11228-017-0407-x
VL - 26
IS - 2
SP - 247-264
SN - 1877-0541
KW - Berhu function
KW - Convex function
KW - Convex optimization
KW - Huber function
KW - Integral functional
KW - Perspective function
KW - Statistical divergence
ER -
TY - JOUR
TI - Error analysis of the immersed interface method for Stokes equations with an interface
AU - Hu, Rui
AU - Li, Zhilin
T2 - APPLIED MATHEMATICS LETTERS
AB - The immersed interface method using the three Poisson equation approach has been successfully developed to solve incompressible Stokes equations with interfaces (Li, 2015 and Li and Ito, 2006). While the numerical results show second order convergence for both velocity and pressure, rigorous error analysis is still missing. Based on recent theoretical development, particularly the error analysis by Beale and Layton (2006), second order convergence has been shown in this paper for both pressure and velocity under some assumptions.
DA - 2018/9//
PY - 2018/9//
DO - 10.1016/j.aml.2018.03.034
VL - 83
SP - 207-211
SN - 0893-9659
UR - https://doi.org/10.1016/j.aml.2018.03.034
KW - Stokes equations
KW - Error analysis
KW - Finite difference method
KW - Immersed interface method
KW - Divergence-free
ER -
TY - JOUR
TI - Efficacy of Aedes aegypti control by indoor Ultra Low Volume (ULV) insecticide spraying in Iquitos, Peru
AU - Gunning, Christian E.
AU - Okamoto, Kenichi W.
AU - Astete, Helvio
AU - Vasquez, Gissella M.
AU - Erhardt, Erik
AU - Del Aguila, Clara
AU - Pinedo, Raul
AU - Cardenas, Roldan
AU - Pacheco, Carlos
AU - Chalco, Enrique
AU - Rodriguez-Ferruci, Hugo
AU - Scott, Thomas W.
AU - Lloyd, Alun L.
AU - Gould, Fred
AU - Morrison, Amy C.
T2 - PLOS Neglected Tropical Diseases
AB - Background Aedes aegypti is a primary vector of dengue, chikungunya, Zika, and urban yellow fever viruses. Indoor, ultra low volume (ULV) space spraying with pyrethroid insecticides is the main approach used for Ae. aegypti emergency control in many countries. Given the widespread use of this method, the lack of large-scale experiments or detailed evaluations of municipal spray programs is problematic. Methodology/Principal findings Two experimental evaluations of non-residual, indoor ULV pyrethroid spraying were conducted in Iquitos, Peru. In each, a central sprayed sector was surrounded by an unsprayed buffer sector. In 2013, spray and buffer sectors included 398 and 765 houses, respectively. Spraying reduced the mean number of adults captured per house by ~83 percent relative to the pre-spray baseline survey. In the 2014 experiment, sprayed and buffer sectors included 1,117 and 1,049 houses, respectively. Here, the sprayed sector’s number of adults per house was reduced ~64 percent relative to baseline. Parity surveys in the sprayed sector during the 2014 spray period indicated an increase in the proportion of very young females. We also evaluated impacts of a 2014 citywide spray program by the local Ministry of Health, which reduced adult populations by ~60 percent. In all cases, adult densities returned to near-baseline levels within one month. Conclusions/Significance Our results demonstrate that densities of adult Ae. aegypti can be reduced by experimental and municipal spraying programs. The finding that adult densities return to approximately pre-spray densities in less than a month is similar to results from previous, smaller scale experiments. Our results demonstrate that ULV spraying is best viewed as having a short-term entomological effect. The epidemiological impact of ULV spraying will need evaluation in future trials that measure capacity of insecticide spraying to reduce human infection or disease.
DA - 2018/4/6/
PY - 2018/4/6/
DO - 10.1371/journal.pntd.0006378
VL - 12
IS - 4
SP - e0006378
J2 - PLoS Negl Trop Dis
LA - en
OP -
SN - 1935-2735
UR - http://dx.doi.org/10.1371/journal.pntd.0006378
DB - Crossref
ER -
TY - JOUR
TI - Differential Faraday Rotation and Polarimetric SAR
AU - Gilman, Mikhail
AU - Tsynkov, Semyon
T2 - SIAM Journal on Applied Mathematics
AB - The propagation of linearly polarized electromagnetic waves through the Earth's ionosphere is accompanied by Faraday rotation (FR), which is due to gyrotropy of the ionospheric plasma in the magnetic field of the Earth. FR may cause distortions of the images taken by spaceborne polarimetric synthetic aperture radar (SAR). We show that the mechanism of those distortions is related to the variation of the FR angle within the bandwidth of the interrogating signals sent by the radar. This effect has not been analyzed previously in the context of SAR imaging. We also propose a special matched filter that we call the polarimetric matched filter (PMF). The PMF helps correct the FR-induced distortions and provides a provably superior SAR performance compared to the case of the traditional polarimetric SAR signal processing.
DA - 2018/1//
PY - 2018/1//
DO - 10.1137/17m114042x
VL - 78
IS - 3
SP - 1422-1449
J2 - SIAM J. Appl. Math.
LA - en
OP -
SN - 0036-1399 1095-712X
UR - http://dx.doi.org/10.1137/17M114042X
DB - Crossref
KW - inverse scattering
KW - scattering matrix
KW - gyrotropy
KW - electromagnetic waves
KW - polarization
KW - rotation of polarization plane
KW - radar signal bandwidth
KW - radar ambiguity theory
KW - polarimetric matched filter
KW - Earth's ionosphere
KW - magnetic field of the Earth
ER -
TY - BOOK
TI - Numerical solution of differential equations: Introduction to finite difference and finite element methods
AU - Li, Z.
AU - Zhonghua, Q.
AU - Tang, T.
DA - 2018///
PY - 2018///
PB - New York: Cambridge University Press
ER -
TY - CONF
TI - Network analysis of virus-innate immune interaction within a host
AU - Huang, Y. F.
AU - Dai, M.
AU - Zhang, Z. H.
AU - Ke, R. A.
AB - Viruses invade a host through infecting and spreading among host cells. Initial virus replication and transmission are counteracted by the host innate immune response, in particular the interferon response. Although the virus-innate immune interaction has been studied in laboratory for a long time, a theoretical understanding of how the interferon response impacts on viral spread is lacking. In this work, we model this interaction as a competition process between the virus spreading and the interferon response on a two-layer multiplex network with virus and interferon spread on the two layers separately. We specifically explore how the overlap between the two layers impacts on the threshold and the final size of virus spread. A mean-field method and a general homogeneous multiplex network are adopted to approximate and analyze the behavior of system. We find that interferon response can effectively stop the spread of the virus or reduce the final size of viral infection when the two networks largely overlap each other. This is true especially when the interferon response is strong. The results provide insights about how the innate immune response counteracts viral invasion and spread. It may also have implications for designing strategies for risk mitigation in computer or social networks.
C2 - 2018///
C3 - 2018 52nd Annual Conference on Information Sciences and Systems (CISS)
DA - 2018///
DO - 10.1109/ciss.2018.8362278
ER -
TY - JOUR
TI - Locating and Counting Equilibria of the Kuramoto Model with Rank-One Coupling
AU - Coss, Owen
AU - Hauenstein, Jonathan D.
AU - Hong, Hoon
AU - Molzahn, Daniel K.
T2 - SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY
AB - The Kuramoto model describes synchronization behavior among coupled oscillators and enjoys successful application in a wide variety of fields. Many of these applications seek phase-coherent solutions, i.e., equilibria of the model. Historically, research has focused on situations where the number of oscillators, $n$, is extremely large and can be treated as being infinite. More recently, however, applications have arisen in areas such as electrical engineering with more modest values of $n$. For these, the equilibria can be located by finding the real solutions of a system of polynomial equations utilizing techniques from algebraic geometry. However, typical methods for solving such systems locate all complex solutions even though only the real solutions give equilibria. In this paper, we present an algorithm to locate only the real solutions of the model, thereby shortening computation time by several orders of magnitude in certain situations. This is accomplished by choosing specific equilibria representatives and the consequent algebraic decoupling of the system. The correctness of the algorithm (that it finds only and all the equilibria) is proved rigorously. Additionally, the algorithm can be implemented using interval methods, so that the equilibria can be approximated up to any given precision without significantly more computational effort. We also compare this solution approach to other computational algebraic geometric methods. Furthermore, analyzing this approach allows us to prove, asymptotically, that the maximum number of equilibria grows at the same rate as the number of complex solutions of a corresponding polynomial system. Finally, we conjecture an upper bound on the maximum number of equilibria for any number of oscillators, which generalizes the known cases and is obtained on a range of explicitly provided natural frequencies.
DA - 2018///
PY - 2018///
DO - 10.1137/17m1128198
VL - 2
IS - 1
SP - 45-71
SN - 2470-6566
UR - http://dx.doi.org/10.1137/17m1128198
KW - Kuramoto model
KW - equilibria
KW - univariate solving
KW - homotopy continuation
KW - numerical algebraic geometry
ER -
TY - JOUR
TI - Gromov's theorem in n-symplectic geometry on LRn
AU - Norris, L. K.
T2 - JOURNAL OF MATHEMATICAL PHYSICS
AB - If M is an n-dimensional manifold, then the associated bundle of linear frames LM of M supports the canonically defined Rn-valued soldering 1-form θ^. The pair (LM,dθ^) is an n-symplectic manifold, where dθ^ is the n-symplectic 2-form. We adapt the proofs of de Gosson and McDuff and Salamon of Gromov’s non-squeezing theorem on R2n to give a proof of Gromov’s theorem for affine n-symplectomorphisms on LRn.
DA - 2018/5//
PY - 2018/5//
DO - 10.1063/1.5029474
VL - 59
IS - 5
SP -
SN - 1089-7658
ER -
TY - JOUR
TI - Forecasting and Uncertainty Quantification Using a Hybrid of Mechanistic and Non-mechanistic Models for an Age-Structured Population Model
AU - Lagergren, John
AU - Reeder, Amanda
AU - Hamilton, Franz
AU - Smith, Ralph C.
AU - Flores, Kevin B.
T2 - Bulletin of Mathematical Biology
AB - In this paper, we present a new method for the prediction and uncertainty quantification of data-driven multivariate systems. Traditionally, either mechanistic or non-mechanistic modeling methodologies have been used for prediction; however, it is uncommon for the two to be incorporated together. We compare the forecast accuracy of mechanistic modeling, using Bayesian inference, a non-mechanistic modeling approach based on state space reconstruction, and a novel hybrid methodology composed of the two for an age-structured population data set. The data come from cannibalistic flour beetles, in which it is observed that the adults preying on the eggs and pupae result in non-equilibrium population dynamics. Uncertainty quantification methods for the hybrid models are outlined and illustrated for these data. We perform an analysis of the results from Bayesian inference for the mechanistic model and hybrid models to suggest reasons why hybrid modeling methodology may enable more accurate forecasts of multivariate systems than traditional approaches.
DA - 2018/4/2/
PY - 2018/4/2/
DO - 10.1007/s11538-018-0421-7
VL - 80
IS - 6
SP - 1578-1595
J2 - Bull Math Biol
LA - en
OP -
SN - 0092-8240 1522-9602
UR - http://dx.doi.org/10.1007/s11538-018-0421-7
DB - Crossref
KW - State space reconstruction
KW - Uncertainty quantification
KW - Structured population model
KW - Forecasting
ER -
TY - JOUR
TI - Floer homology and covering spaces
AU - Lidman, Tye
AU - Manolescu, Ciprian
T2 - GEOMETRY & TOPOLOGY
AB - We prove a Smith-type inequality for regular covering spaces in monopole Floer homology. Using the monopole Floer / Heegaard Floer correspondence, we deduce that if a 3-manifold Y admits a p^n-sheeted regular cover that is a Z/pZ-L-space (for p prime), then Y is a Z/pZ-L-space. Further, we obtain constraints on surgeries on a knot being regular covers over other surgeries on the same knot, and over surgeries on other knots.
DA - 2018///
PY - 2018///
DO - 10.2140/gt.2018.22.2817
VL - 22
IS - 5
SP - 2817-2838
SN - 1364-0380
ER -
TY - JOUR
TI - Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource
AU - Li, H. Q.
AU - Jing, Naihuan
AU - Tang, X. L.
T2 - Quantum Information Processing
AB - Recently, the method that using an entanglement as a resource to distinguish orthogonal product states by local operations and classical communication (LOCC) has brought into focus. Zhang et al. (Sci Rep 6:30493, 2016) presented protocols which use an entanglement to distinguish some classes of orthogonal product states in $$\mathbb {C}^m\otimes \mathbb {C}^n$$ . In this paper, we mainly study the local distinguishability of multipartite product states. For the class of locally indistinguishable multipartite product states constructed by Wang et al. (Quantum Inf Process 16:5, 2017), we present a protocol that distinguishes perfectly these quantum states by LOCC using an entangled state as a resource for implementing quantum measurements.
DA - 2018///
PY - 2018///
DO - 10.1007/s11128-018-1962-2
VL - 17
IS - 8
ER -
TY - JOUR
TI - AN ASYMPTOTIC PRESERVING SCHEME FOR KINETIC MODELS WITH SINGULAR LIMIT
AU - Chertock, Alina
AU - Tan, Changhui
AU - Yan, Bokai
T2 - KINETIC AND RELATED MODELS
AB - We propose a new class of asymptotic preserving schemes to solve kinetic equations with mono-kinetic singular limit. The main idea to deal with the singularity is to transform the equations by appropriate scalings in velocity. In particular, we study two biologically related kinetic systems. We derive the scaling factors and prove that the rescaled solution does not have a singular limit, under appropriate spatial non-oscillatory assumptions, which can be verified numerically by a newly developed asymptotic preserving scheme. We set up a few numerical experiments to demonstrate the accuracy, stability, efficiency and asymptotic preserving property of the schemes.
DA - 2018/8//
PY - 2018/8//
DO - 10.3934/krm.2018030
VL - 11
IS - 4
SP - 735-756
SN - 1937-5077
UR - https://doi-org.prox.lib.ncsu.edu/10.3934/krm.2018030
KW - Kinetic models
KW - singular limit
KW - asymptotic-preserving schemes
KW - velocity scaling
KW - aggregation equation
KW - flocking phenomena
ER -
TY - JOUR
TI - A method of boundary equations for unsteady hyperbolic problems in 3D
AU - Petropavlovsky, S.
AU - Tsynkov, S.
AU - Turkel, E.
T2 - Journal of Computational Physics
AB - We consider interior and exterior initial boundary value problems for the three-dimensional wave (d'Alembert) equation. First, we reduce a given problem to an equivalent operator equation with respect to unknown sources defined only at the boundary of the original domain. In doing so, the Huygens' principle enables us to obtain the operator equation in a form that involves only finite and non-increasing pre-history of the solution in time. Next, we discretize the resulting boundary equation and solve it efficiently by the method of difference potentials (MDP). The overall numerical algorithm handles boundaries of general shape using regular structured grids with no deterioration of accuracy. For long simulation times it offers sub-linear complexity with respect to the grid dimension, i.e., is asymptotically cheaper than the cost of a typical explicit scheme. In addition, our algorithm allows one to share the computational cost between multiple similar problems. On multi-processor (multi-core) platforms, it benefits from what can be considered an effective parallelization in time.
DA - 2018/7//
PY - 2018/7//
DO - 10.1016/j.jcp.2018.03.039
VL - 365
SP - 294-323
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2018.03.039
DB - Crossref
KW - Time-dependent wave equation
KW - Calderon's boundary equation
KW - The Huygens' principle
KW - Method of difference potentials (MDP)
KW - Sub-linear complexity
KW - Parallelization in time
ER -
TY - JOUR
TI - A high-order source removal finite element method for a class of elliptic interface problems
AU - Ji, Haifeng
AU - Chen, Jinru
AU - Li, Zhilin
T2 - APPLIED NUMERICAL MATHEMATICS
AB - A high-order finite element method based on unfitted meshes for solving a class of elliptic interface problems whose solution and its normal derivative have finite jumps across an interface is proposed in this paper. The idea of the method is based on the source removal technique first introduced in the immersed interface method (IIM). The strategy is to use the level set representation of the interface and extend the jump conditions that are defined along the interface to a neighborhood of the interface. In our numerical method, the jump conditions only need to be extended to the Lagrange points of elements intersecting with the interface. Optimal error estimates of the method in the broken H1 and L2 norms are rigorously proven. Numerical examples presented in this paper also confirm our theoretical analysis.
DA - 2018/8//
PY - 2018/8//
DO - 10.1016/j.apnum.2018.03.017
VL - 130
SP - 112-130
SN - 1873-5460
KW - Interface problem
KW - Level set function
KW - Source removal technique
KW - Immersed interface
ER -
TY - JOUR
TI - Times from Infection to Disease-Induced Death and their Influence on Final Population Sizes After Epidemic Outbreaks
AU - Farrell, Alex P.
AU - Collins, James P.
AU - Greer, Amy L.
AU - Thieme, Horst R.
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
DA - 2018/7//
PY - 2018/7//
DO - 10.1007/s11538-018-0446-y
VL - 80
IS - 7
SP - 1937-1961
SN - 1522-9602
KW - Host extinction
KW - Infection age
KW - Incidence function
KW - Lognormal distribution
KW - Tiger salamander
KW - Functional equation
ER -
TY - JOUR
TI - Special Issue - Devoted to the 60th birthday of J. H. Przytycki; Guest Editors: M. K. Dabkowski, V. Harizanov, L. H. Kauffman, J. H. Przytycki, R. Sazdanovic and A. Sikora Preface
AU - Dabkowski, M. K.
AU - Harizanov, V.
AU - Kauffman, L. H.
AU - Przytycki, J. H.
AU - Sazdanovic, R.
AU - Sikora, A.
T2 - Journal of Knot Theory and its Ramifications
DA - 2018///
PY - 2018///
VL - 27
IS - 3
ER -
TY - JOUR
TI - STRUCTURAL CONVERGENCE RESULTS FOR APPROXIMATION OF DOMINANT SUBSPACES FROM BLOCK KRYLOV SPACES
AU - Drineas, Petros
AU - Ipsen, Ilse C. F.
AU - Kontopoulou, Eugenia-Maria
AU - Magdon-Ismail, Malik
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - This paper is concerned with approximating the dominant left singular vector space of a real matrix $A$ of arbitrary dimension, from block Krylov spaces generated by the matrix ${A}{A}^T$ and the block vector $A{X}$. Two classes of results are presented. First are bounds on the distance, in the two- and Frobenius norms, between the Krylov space and the target space. The distance is expressed in terms of principal angles. Second are bounds for the low-rank approximation computed from the Krylov space compared to the best low-rank approximation, in the two- and Frobenius norms. For starting guesses ${X}$ of full column-rank, the bounds depend on the tangent of the principal angles between ${X}$ and the dominant right singular vector space of ${A}$. The results presented here form the structural foundation for the analysis of randomized Krylov space methods. The innovative feature is a combination of traditional Lanczos convergence analysis with optimal approximations via least squares problems.
DA - 2018///
PY - 2018///
DO - 10.1137/16m1091745
VL - 39
IS - 2
SP - 567-586
SN - 1095-7162
UR - https://doi.org/10.1137/16M1091745
KW - singular value decomposition
KW - least squares
KW - principal angles
KW - gap-amplifying polynomials
KW - random matrices
ER -
TY - JOUR
TI - Patterns in Khovanov link and chromatic graph homology
AU - Sazdanovic, Radmila
AU - Scofield, Daniel
T2 - JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
AB - Khovanov homology of a link and chromatic graph homology are known to be isomorphic in a range of homological gradings that depend on the girth of a graph. We discuss patterns shared by these two homology theories. In particular, we improve the bounds for the homological span of chromatic homology by Helme–Guizon, Przytycki and Rong. An explicit formula for the rank of the third chromatic homology group on the main diagonal is given and used to compute the corresponding Khovanov homology group and the fourth coefficient of the Jones polynomial for links with certain diagrams.
DA - 2018/3//
PY - 2018/3//
DO - 10.1142/s0218216518400072
VL - 27
IS - 3
SP -
SN - 1793-6527
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85044463913&partnerID=MN8TOARS
KW - Categorification
KW - chromatic graph homology
KW - Jones polynomial
KW - Khovanov homology
ER -
TY - JOUR
TI - Lattice structure of Weyl groups via representation theory of preprojective algebras
AU - Iyama, Osamu
AU - Reading, Nathan
AU - Reiten, Idun
AU - Thomas, Hugh
T2 - COMPOSITIO MATHEMATICA
AB - This paper studies the combinatorics of lattice congruences of the weak order on a finite Weyl group $W$, using representation theory of the corresponding preprojective algebra $\Pi$. Natural bijections are constructed between important objects including join-irreducible congruences, join-irreducible (respectively, meet-irreducible) elements of $W$, indecomposable $\tau$-rigid (respectively, $\tau^-$-rigid) modules and layers of $\Pi$. The lattice-theoretically natural labeling of the Hasse quiver by join-irreducible elements of $W$ is shown to coincide with the algebraically natural labelling by layers of $\Pi$. We show that layers of $\Pi$ are nothing but bricks (or equivalently stones, or 2-spherical modules). The forcing order on join-irreducible elements of $W$ (arising from the study of lattice congruences) is described algebraically in terms of the doubleton extension order. We give a combinatorial description of indecomposable $\tau^-$-rigid modules for type $A$ and $D$.
DA - 2018/6//
PY - 2018/6//
DO - 10.1112/s0010437x18007078
VL - 154
IS - 6
SP - 1269-1305
SN - 1570-5846
UR - https://doi.org/10.1112/s0010437x18007078
KW - preprojective algebra
KW - Weyl group
KW - weak order
KW - tau-tilting theory
KW - brick
KW - join-irreducible element
KW - lattice congruence
ER -
TY - JOUR
TI - Invasion and migration of spatially self-limiting gene drives: A comparative analysis
AU - Dhole, Sumit
AU - Vella, Michael R.
AU - Lloyd, Alun L.
AU - Gould, Fred
T2 - Evolutionary Applications
AB - Recent advances in research on gene drives have produced genetic constructs that could theoretically spread a desired gene (payload) into all populations of a species, with a single release in one place. This attribute has advantages, but also comes with risks and ethical concerns. There has been a call for research on gene drive systems that are spatially and/or temporally self-limiting. Here, we use a population genetics model to compare the expected characteristics of three spatially self-limiting gene drive systems: one-locus underdominance, two-locus underdominance and daisy-chain drives. We find large differences between these gene drives in the minimum release size required for successfully driving a payload into a population. The daisy-chain system is the most efficient, requiring the smallest release, followed by the two-locus underdominance system, and then the one-locus underdominance system. However, when the target population exchanges migrants with a nontarget population, the gene drives requiring smaller releases suffer from higher risks of unintended spread. For payloads that incur relatively low fitness costs (up to 30%), a simple daisy-chain drive is practically incapable of remaining localized, even with migration rates as low as 0.5% per generation. The two-locus underdominance system can achieve localized spread under a broader range of migration rates and of payload fitness costs, while the one-locus underdominance system largely remains localized. We also find differences in the extent of population alteration and in the permanence of the alteration achieved by the three gene drives. The two-locus underdominance system does not always spread the payload to fixation, even after successful drive, while the daisy-chain system can, for a small set of parameter values, achieve a temporally limited spread of the payload. These differences could affect the suitability of each gene drive for specific applications.
DA - 2018/1/4/
PY - 2018/1/4/
DO - 10.1111/eva.12583
VL - 11
IS - 5
SP - 794-808
J2 - Evol Appl
LA - en
OP -
SN - 1752-4571
UR - http://dx.doi.org/10.1111/eva.12583
DB - Crossref
KW - Cas9
KW - CRISPR
KW - daisy-chain drive
KW - gene drive
KW - population alteration
KW - underdominance
ER -
TY - JOUR
TI - Contributions from the silent majority dominate dengue virus transmission
AU - ten Bosch, Quirine A.
AU - Clapham, Hannah E.
AU - Lambrechts, Louis
AU - Duong, Veasna
AU - Buchy, Philippe
AU - Althouse, Benjamin M.
AU - Lloyd, Alun L.
AU - Waller, Lance A.
AU - Morrison, Amy C.
AU - Kitron, Uriel
AU - Vazquez-Prokopec, Gonzalo M.
AU - Scott, Thomas W.
AU - Perkins, T. Alex
T2 - PLOS Pathogens
AB - Despite estimates that, each year, as many as 300 million dengue virus (DENV) infections result in either no perceptible symptoms (asymptomatic) or symptoms that are sufficiently mild to go undetected by surveillance systems (inapparent), it has been assumed that these infections contribute little to onward transmission. However, recent blood-feeding experiments with Aedes aegypti mosquitoes showed that people with asymptomatic and pre-symptomatic DENV infections are capable of infecting mosquitoes. To place those findings into context, we used models of within-host viral dynamics and human demographic projections to (1) quantify the net infectiousness of individuals across the spectrum of DENV infection severity and (2) estimate the fraction of transmission attributable to people with different severities of disease. Our results indicate that net infectiousness of people with asymptomatic infections is 80% (median) that of people with apparent or inapparent symptomatic infections (95% credible interval (CI): 0–146%). Due to their numerical prominence in the infectious reservoir, clinically inapparent infections in total could account for 84% (CI: 82–86%) of DENV transmission. Of infections that ultimately result in any level of symptoms, we estimate that 24% (95% CI: 0–79%) of onward transmission results from mosquitoes biting individuals during the pre-symptomatic phase of their infection. Only 1% (95% CI: 0.8–1.1%) of DENV transmission is attributable to people with clinically detected infections after they have developed symptoms. These findings emphasize the need to (1) reorient current practices for outbreak response to adoption of pre-emptive strategies that account for contributions of undetected infections and (2) apply methodologies that account for undetected infections in surveillance programs, when assessing intervention impact, and when modeling mosquito-borne virus transmission.
DA - 2018/5/3/
PY - 2018/5/3/
DO - 10.1371/journal.ppat.1006965
VL - 14
IS - 5
SP - e1006965
J2 - PLoS Pathog
LA - en
OP -
SN - 1553-7374
UR - http://dx.doi.org/10.1371/journal.ppat.1006965
DB - Crossref
ER -
TY - JOUR
TI - Acquisition War-Gaming Technique for Acquiring Future Complex Systems: Modeling and Simulation Results for Cost Plus Incentive Fee Contract
AU - Nguyen, Tien
AU - Tran, Hien
AU - Guillen, Andy
AU - Bui, Tung
AU - Matsunaga, Sumner
T2 - Mathematics
AB - This paper provides a high-level discussion and propositions of frameworks and models for acquisition strategy of complex systems. In particular, it presents an innovative system engineering approach to model the Department of Defense (DoD) acquisition process and offers several optimization modules including simulation models using game theory and war-gaming concepts. Our frameworks employ Advanced Game-based Mathematical Framework (AGMF) and Unified Game-based Acquisition Framework (UGAF), and related advanced simulation and mathematical models that include a set of War-Gaming Engines (WGEs) implemented in MATLAB statistical optimization models. WGEs are defined as a set of algorithms, characterizing the Program and Technical Baseline (PTB), technology enablers, architectural solutions, contract type, contract parameters and associated incentives, and industry bidding position. As a proof of concept, Aerospace, in collaboration with the North Carolina State University (NCSU) and University of Hawaii (UH), successfully applied and extended the proposed frameworks and decision models to determine the optimum contract parameters and incentives for a Cost Plus Incentive Fee (CPIF) contract. As a result, we can suggest a set of acquisition strategies that ensure the optimization of the PTB.
DA - 2018/3/14/
PY - 2018/3/14/
DO - 10.3390/math6030043
VL - 6
IS - 3
SP - 43
J2 - Mathematics
LA - en
OP -
SN - 2227-7390
UR - http://dx.doi.org/10.3390/math6030043
DB - Crossref
KW - game theory
KW - Bayesian games
KW - incentives
KW - contract parameters
KW - Cost plus Incentive Fee (CPIF)
KW - mathematical modelling
KW - simulation
KW - program and technical baseline (PTB)
KW - acquisition strategy
KW - space systems
ER -
TY - JOUR
TI - A SCALAR CONSERVATION LAW FOR PLUME MIGRATION IN CARBON SEQUESTRATION
AU - Brown, Elisabeth
AU - Shearer, Michael
T2 - SIAM JOURNAL ON APPLIED MATHEMATICS
AB - A quasi-linear hyperbolic partial differential equation with a discontinuous flux models geologic carbon dioxide (CO$_2$) migration and storage [M. Hesse, F. Orr, and H. Tchelepi, Fluid Mech., 611 (2008), pp. 35--60]. Two flux functions characterize the model, giving rise to flux discontinuities. One convex flux describes the invasion of the plume into pore space, and the other captures the flow as the plume leaves CO$_2$ bubbles behind, which are then trapped in the pore space. We investigate the method of characteristics, the structure of shock and rarefaction waves, and the result of binary wave interactions. The dual flux property introduces unexpected differences between the structure of these solutions and those of a scalar conservation law with a convex flux. During our analysis, we introduce a new construction of cross-hatch characteristics in regions of the space-time plane where the solution is constant, and there are two characteristic speeds. This construction is used to generalize the notion of the Lax entropy condition for admissible shocks and is crucial to continuing the propagation of a shock wave if its speed becomes characteristic.
DA - 2018///
PY - 2018///
DO - 10.1137/17m1127089
VL - 78
IS - 3
SP - 1823-1841
SN - 1095-712X
KW - hyperbolic PDE
KW - discontinuous flux
KW - method of characteristics
KW - shocks and rarefactions
KW - residual trapping
ER -
TY - JOUR
TI - A High Order Compact Time/Space Finite Difference Scheme for the Wave Equation with Variable Speed of Sound
AU - Britt, Steven
AU - Turkel, Eli
AU - Tsynkov, Semyon
T2 - Journal of Scientific Computing
DA - 2018/1/17/
PY - 2018/1/17/
DO - 10.1007/s10915-017-0639-9
VL - 76
IS - 2
SP - 777-811
J2 - J Sci Comput
LA - en
OP -
SN - 0885-7474 1573-7691
UR - http://dx.doi.org/10.1007/s10915-017-0639-9
DB - Crossref
KW - Compact finite differences
KW - Wave equation
KW - Variable coefficients
KW - High order accuracy
ER -
TY - JOUR
TI - On the nature of the generating series of walks in the quarter plane
AU - Dreyfus, Thomas
AU - Hardouin, Charlotte
AU - Roques, Julien
AU - Singer, Michael F.
T2 - INVENTIONES MATHEMATICAE
AB - In the present paper, we introduce a new approach, relying on the Galois theory of difference equations, to study the nature of the generating series of walks in the quarter plane. Using this approach, we are not only able to recover many of the recent results about these series, but also to go beyond them. For instance, we give for the first time hypertranscendency results, i.e., we prove that certain of these generating series do not satisfy any nontrivial nonlinear algebraic differential equation with rational function coefficients.
DA - 2018/7//
PY - 2018/7//
DO - 10.1007/s00222-018-0787-z
VL - 213
IS - 1
SP - 139-203
SN - 1432-1297
ER -
TY - JOUR
TI - Numerical methods for nonlinear equations
AU - Kelley, C. T.
T2 - Acta Numerica
AB - This article is about numerical methods for the solution of nonlinear equations. We consider both the fixed-point form $\mathbf{x}=\mathbf{G}(\mathbf{x})$ and the equations form $\mathbf{F}(\mathbf{x})=0$ and explain why both versions are necessary to understand the solvers. We include the classical methods to make the presentation complete and discuss less familiar topics such as Anderson acceleration, semi-smooth Newton’s method, and pseudo-arclength and pseudo-transient continuation methods.
DA - 2018/5/1/
PY - 2018/5/1/
DO - 10.1017/s0962492917000113
VL - 27
SP - 207-287
J2 - Acta Numerica
LA - en
OP -
SN - 0962-4929 1474-0508
UR - http://dx.doi.org/10.1017/S0962492917000113
DB - Crossref
ER -
TY - JOUR
TI - Nonlocal rheology of dense granular flow in annular shear experiments
AU - Tang, Zhu
AU - Brzinski, Theodore A.
AU - Shearer, Michael
AU - Daniels, Karen E.
T2 - Soft Matter
AB - Experimental measurements of boundary stresses and flow fields of a quasi-2D granular material under steady shear validate two nonlocal rheological models.
DA - 2018///
PY - 2018///
DO - 10.1039/c8sm00047f
VL - 14
IS - 16
SP - 3040-3048
J2 - Soft Matter
LA - en
OP -
SN - 1744-683X 1744-6848
UR - http://dx.doi.org/10.1039/c8sm00047f
DB - Crossref
ER -
TY - JOUR
TI - Nonlocal PDF methods for Langevin equations with colored noise
AU - Maltba, Tyler
AU - Gremaud, Pierre A.
AU - Tartakoysky, Daniel M.
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - Langevin equations describe systems driven by internally generated or externally imposed random excitations. If these excitations correspond to Gaussian white noise, it is relatively straightforward to derive a closed form equation for the joint probability density function (PDF) of state variables. Many natural phenomena present however correlated (colored) excitations. For such problems, a full probabilistic characterization through the resolution of a PDF equation can be obtained through two levels of approximations: first, mixed ensemble moments have to be approximated to lead to a closed system of equations and, second, the resulting nonlocal equations should be at least partially localized to ensure computational efficiency. We propose a new semi-local formulation based on a modified large-eddy diffusivity (LED) approach; the formulation retains most of the accuracy of a fully nonlocal approach while presenting the same order of algorithmic complexity as the standard LED approach. The accuracy of the approach is successfully tested against Monte Carlo simulations.
DA - 2018/8/15/
PY - 2018/8/15/
DO - 10.1016/j.jcp.2018.04.023
VL - 367
SP - 87-101
SN - 1090-2716
KW - PDF method
KW - Nonlocal
KW - Langevin equation
KW - Colored noise
KW - Stochastic
KW - Random
KW - Uncertainty quantification
ER -
TY - JOUR
TI - Monotone operator theory in convex optimization
AU - Combettes, Patrick L.
T2 - MATHEMATICAL PROGRAMMING
AB - Several aspects of the interplay between monotone operator theory and convex optimization are presented. The crucial role played by monotone operators in the analysis and the numerical solution of convex minimization problems is emphasized. We review the properties of subdifferentials as maximally monotone operators and, in tandem, investigate those of proximity operators as resolvents. In particular, we study new transformations which map proximity operators to proximity operators, and establish connections with self-dual classes of firmly nonexpansive operators. In addition, new insights and developments are proposed on the algorithmic front.
DA - 2018/7//
PY - 2018/7//
DO - 10.1007/s10107-018-1303-3
VL - 170
IS - 1
SP - 177-206
SN - 1436-4646
KW - Firmly nonexpansive operator
KW - Monotone operator
KW - Operator splitting
KW - Proximal algorithm
KW - Proximity operator
KW - Proximity-preserving transformation
KW - Self-dual class
KW - Subdifferential
ER -
TY - JOUR
TI - Kronecker coefficients and noncommutative super Schur functions
AU - Blasiak, Jonah
AU - Liu, Ricky Ini
T2 - Journal of Combinatorial Theory, Series A
AB - Abstract The theory of noncommutative Schur functions can be used to obtain positive combinatorial formulae for the Schur expansion of various classes of symmetric functions, as shown by Fomin and Greene [11] . We develop a theory of noncommutative super Schur functions and use it to prove a positive combinatorial rule for the Kronecker coefficients g λ μ ν where one of the partitions is a hook, recovering previous results of the two authors [7] , [22] . This method also gives a precise connection between this rule and a heuristic for Kronecker coefficients first investigated by Lascoux [19] .
DA - 2018/8//
PY - 2018/8//
DO - 10.1016/j.jcta.2018.02.007
VL - 158
SP - 315-361
J2 - Journal of Combinatorial Theory, Series A
LA - en
OP -
SN - 0097-3165
UR - http://dx.doi.org/10.1016/j.jcta.2018.02.007
DB - Crossref
KW - Kronecker coefficients
KW - Noncommutative Schur functions
KW - Super Schur functions
KW - Colored tableaux
ER -
TY - JOUR
TI - Information content in data sets: A review of methods for interrogation and model comparison
AU - Banks, H. Thomas
AU - Joyner, Michele L.
T2 - JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
AB - Abstract In this review we discuss methodology to ascertain the amount of information in given data sets with respect to determination of model parameters with desired levels of uncertainty. We do this in the context of least squares (ordinary, weighted, iterative reweighted weighted or “generalized”, etc.) based inverse problem formulations. The ideas are illustrated with several examples of interest in the biological and environmental sciences.
DA - 2018/6//
PY - 2018/6//
DO - 10.1515/jiip-2017-0096
VL - 26
IS - 3
SP - 423-452
SN - 1569-3945
KW - Information content
KW - weighted least squares
KW - sensitivity
KW - model comparison techniques
KW - Akaike Information Criterion
ER -
TY - JOUR
TI - Global attractors of some predator-prey reaction-diffusion systems with density-dependent diffusion and time-delays
AU - Pao, C. V.
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - This paper deals with a two-species and a three-species predator–prey reaction diffusion systems where the diffusion coefficients are density dependent and time-delays are involved in the reaction functions. The diffusion terms are of porous medium type which are degenerate and the boundary conditions are of Neumann type. The aim of the paper is to investigate the asymptotic behavior of the time-dependent solution in relation to various steady-state solutions of the system. This includes the existence of a unique positive classical solution, global attraction of a steady-state solution, and stability or instability of various semitrivial solutions and the positive steady-state solution.
DA - 2018/8/1/
PY - 2018/8/1/
DO - 10.1016/j.jmaa.2018.03.076
VL - 464
IS - 1
SP - 164-187
SN - 1096-0813
KW - Predator-prey models
KW - Quasi-linear reaction diffusion
KW - Time-delay
KW - Global attractor
KW - Upper and lower solutions
ER -
TY - JOUR
TI - From theory to experimental design-Quantifying a trait-based theory of predator-prey dynamics
AU - Laubmeier, A. N.
AU - Wootton, K.
AU - Banks, J. E.
AU - Bommarco, R.
AU - Curtsdotter, A.
AU - Jonsson, T.
AU - Roslin, T.
AU - Banks, H. T.
T2 - PLoS One
DA - 2018///
PY - 2018///
VL - 13
IS - 4
ER -
TY - JOUR
TI - FEEDBACK STABILIZATION OF A LINEAR HYDRO-ELASTIC SYSTEM
AU - Bociu, Lorena
AU - Derochers, Steven
AU - Toundykov, Daniel
T2 - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
AB - It is known that the linear Stokes-Lamé system can be stabilized by a boundary feedback in the form of a dissipative velocity matching on the common interface [5]. Here we consider feedback stabilization for a generalized linear fluid-elasticity interaction, where the matching conditions on the interface incorporate the curvature of the common boundary and thus take into account the geometry of the problem. Such a coupled system is semigroup well-posed on the natural finite energy space [13], however, the system is not dissipative to begin with, which represents a key departure from the feedback control analysis in [5]. We prove that a damped version of the general linear hydro-elasticity model is exponentially stable. First, such a result is given for boundary dissipation of the form used in [5]. This proof resolves a more complex version, compared to the classical case, of the weighted energy methods, and addresses the lack of over-determination in the associated unique continuation result. The second theorem demonstrates how assumptions can be relaxed if a viscous damping is added in the interior of the solid.
DA - 2018/5//
PY - 2018/5//
DO - 10.3934/dcdsb.2018144
VL - 23
IS - 3
SP - 1107-1132
SN - 1553-524X
KW - Fluid-structure
KW - free boundary
KW - moving boundary
KW - linearization
KW - boundary damping
KW - stability
ER -
TY - JOUR
TI - EXISTENCE THEORY FOR NONLINEAR STURM-LIOUVILLE PROBLEMS WITH NON-LOCAL BOUNDARY CONDITIONS
AU - Maroncelli, Daniel
AU - Rodriguez, Jesus
T2 - DIFFERENTIAL EQUATIONS & APPLICATIONS
DA - 2018/5//
PY - 2018/5//
DO - 10.7153/dea-2018-10-09
VL - 10
IS - 2
SP - 147-161
SN - 1848-9605
KW - Existence theory
KW - Sturm-Liouville problem
KW - boundary conditions
ER -
TY - JOUR
TI - Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras
AU - Stitzinger, Ernie
AU - White, Ashley
T2 - ALGEBRAS AND REPRESENTATION THEORY
AB - We extend conjugacy results from Lie algebras to their Leibniz algebra generalizations. The proofs in the Lie case depend on anti-commutativity. Thus it is necessary to find other paths in the Leibniz case. Some of these results involve Cartan subalgebras. Our results can be used to extend other results on Cartan subalgebras. We show an example here and others will be shown in future work.
DA - 2018/6//
PY - 2018/6//
DO - 10.1007/s10468-017-9731-y
VL - 21
IS - 3
SP - 627-633
SN - 1572-9079
KW - Leibniz algebras
KW - Conjugacy
KW - Cartan subalgebras
KW - Maximal subalgebras
ER -
TY - JOUR
TI - A least squares augmented immersed interface method for solving Navier-Stokes and Darcy coupling equations
AU - Li, Zhilin
AU - Lai, Ming-Chih
AU - Peng, Xiaofei
AU - Zhang, Zhiyue
T2 - COMPUTERS & FLUIDS
AB - A new finite difference method based on Cartesian meshes and fast Poisson/Helmholtz solvers is proposed to solve the coupling of a fluid flow modeled by the incompressible Navier–Stokes equations and a porous media modeled by the Darcy’s law. The finite difference discretization in time is based on the pressure Poisson equation formulation. At each time step, several augmented variables along the interface between the fluid flow and the porous media are introduced so that the coupled equations can be decoupled into several Poisson/Helmholtz equations with those augmented variables acting as jumps of the unknown solution and some directional derivatives. The augmented variables should be chosen so that the Beavers–Joseph–Saffman (BJS) or Beavers–Joseph (BJ) and other interface conditions are satisfied. It has been tested that a direct extension of the augmented idea in [27] does not work well when the fluid flow is modeled by the Navier–Stokes equations. One of the new ideas of this paper is to enforce the divergence free condition at the interface from the fluid side. In this way, the Schur complement matrix for the augmented variables is over-determined and the least squares solution is used for the coupling problem. The new augmented approach enables us to solve the Navier–Stokes and Darcy coupling efficiently with second order accurate velocity and pressure in the L∞ norm for tested problems. The proposed new idea in enforcing the divergence free condition at the interface from the fluid side has also been utilized to solve the Stokes and Darcy coupling equations and shown to outperform the original method in [27]. In additional to the detailed accuracy check for the present method, some interesting numerical simulations for Navier–Stokes and Darcy coupling have been conducted in this paper as well.
DA - 2018/5/15/
PY - 2018/5/15/
DO - 10.1016/j.compfluid.2018.03.032
VL - 167
SP - 384-399
SN - 1879-0747
UR - https://doi.org/10.1016/j.compfluid.2018.03.032
KW - Navier-Stokes and Darcy coupling
KW - Coupled fluid flow with porous media
KW - Least squares augmented IIM
KW - Fast Poisson/Helmholtz solver
KW - Analytic solution for Navier-Stokes and
KW - Darcy coupling
KW - Interface relations
ER -
TY - JOUR
TI - Rank My Update, Please
AU - Meyer, Carl D.
T2 - AMERICAN MATHEMATICAL MONTHLY
AB - Updating a given a matrix Am × n by a rank-one matrix B = cdT, where c and d are appropriately sized column vectors, is a common practice throughout all applied areas of mathematics, science, and e...
DA - 2018///
PY - 2018///
DO - 10.1080/00029890.2017.1389199
VL - 125
IS - 1
SP - 61-64
SN - 1930-0972
ER -
TY - JOUR
TI - Consistent learning by composite proximal thresholding
AU - Combettes, Patrick L.
AU - Salzo, Saverio
AU - Villa, Silvia
T2 - MATHEMATICAL PROGRAMMING
AB - We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite dictionary of functions. We propose a novel flexible composite regularization model, which makes it possible to incorporate various priors on the coefficients of the prediction function, including sparsity and hard constraints. We show that the estimators obtained by minimizing the regularized empirical risk are consistent in a statistical sense, and we design an error-tolerant composite proximal thresholding algorithm for computing such estimators. New results on the asymptotic behavior of the proximal forward–backward splitting method are derived and exploited to establish the convergence properties of the proposed algorithm. In particular, our method features a o(1 / m) convergence rate in objective values.
DA - 2018/1//
PY - 2018/1//
DO - 10.1007/s10107-017-1133-8
VL - 167
IS - 1
SP - 99-127
SN - 1436-4646
KW - Consistent estimator
KW - Convex optimization
KW - Forward-backward splitting
KW - Proximal algorithm
KW - Sparse data representation
ER -
TY - JOUR
TI - Characteristic impedance: frequency or time domain approach?
AU - Qureshi, M Umar
AU - Colebank, Mitchel J
AU - Schreier, David A
AU - Tabima, Diana M
AU - Haider, Mansoor A
AU - Chesler, Naomi C
AU - Olufsen, Mette S
T2 - Physiological Measurement
AB - Objective: Characteristic impedance (Zc) is an important component in the theory of hemodynamics. It is a commonly used metric of proximal arterial stiffness and pulse wave velocity. Calculated using simultaneously measured dynamic pressure and flow data, estimates of characteristic impedance can be obtained using methods based on frequency or time domain analysis. Applications of these methods under different physiological and pathological conditions in species with different body sizes and heart rates show that the two approaches do not always agree. In this study, we have investigated the discrepancies between frequency and time domain estimates accounting for uncertainties associated with experimental processes and physiological conditions. Approach: We have used published data measured in different species including humans, dogs, and mice to investigate: (a) the effects of time delay and signal noise in the pressure-flow data, (b) uncertainties about the blood flow conditions, (c) periodicity of the cardiac cycle versus the breathing cycle, on the frequency and time domain estimates of Zc, and (d) if discrepancies observed under different hemodynamic conditions can be eliminated. Main results and Significance: We have shown that the frequency and time domain estimates are not equally sensitive to certain characteristics of hemodynamic signals including phase lag between pressure and flow, signal to noise ratio and the end of systole retrograde flow. The discrepancies between two types of estimates are inherent due to their intrinsically different mathematical expressions and therefore it is impossible to define a criterion to resolve such discrepancies. Considering the interpretation and role of Zc as an important hemodynamic parameter, we suggest that the frequency and time domain estimates should be further assessed as two different hemodynamic parameters in a future study.
DA - 2018/1/31/
PY - 2018/1/31/
DO - 10.1088/1361-6579/aa9d60
VL - 39
IS - 1
SP - 014004
J2 - Physiol. Meas.
OP -
SN - 1361-6579
UR - http://dx.doi.org/10.1088/1361-6579/aa9d60
DB - Crossref
KW - characteristic impedance
KW - blood pressure and flow
KW - pulse wave analysis
KW - impedance analysis
KW - time domain analysis
KW - Fourier methods
KW - large arteries
ER -
TY - JOUR
TI - Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes
AU - Chertock, Alina
AU - Cui, Shumo
AU - Kurganov, Alexander
AU - Ozcan, Seyma Nur
AU - Tadmor, Eitan
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium variables combined with a well-balanced central-upwind evolution in time, which is adapted to reduce the amount of numerical viscosity when the flow is at (near) steady-state regime. We show the performance of our newly developed central-upwind scheme and demonstrate importance of perfect balance between the fluxes and gravitational forces in a series of one- and two-dimensional examples.
DA - 2018/4/1/
PY - 2018/4/1/
DO - 10.1016/j.jcp.2017.12.026
VL - 358
SP - 36-52
SN - 1090-2716
UR - https://doi-org.prox.lib.ncsu.edu/10.1016/j.jcp.2017.12.026
KW - Euler equations of gas dynamics with gravitation
KW - Well-balanced scheme
KW - Equilibrium variables
KW - Central-upwind scheme
KW - Piecewise linear reconstruction
ER -
TY - JOUR
TI - Variational Gaussian approximation for Poisson data
AU - Arridge, Simon R.
AU - Ito, Kazufumi
AU - Jin, Bangti
AU - Zhang, Chen
T2 - INVERSE PROBLEMS
AB - The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.
DA - 2018/2//
PY - 2018/2//
DO - 10.1088/1361-6420/aaa0ab
VL - 34
IS - 2
SP -
SN - 1361-6420
KW - variational Gaussian approximation
KW - Poisson data
KW - hierarchical modeling
KW - Kullback-Leibler divergence
KW - alternating direction maximization
ER -
TY - JOUR
TI - Stability of combustion waves in a simplified gas-solid combustion model in porous media
AU - Ozbag, Fatih
AU - Schecter, Stephen
T2 - PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
AB - We study the stability of the combustion waves that occur in a simplified model for injection of air into a porous medium that initially contains some solid fuel. We determine the essential spectrum of the linearized system at a travelling wave. For certain waves, we are able to use a weight function to stabilize the essential spectrum. We perform a numerical computation of the Evans function to show that some of these waves have no unstable discrete spectrum. The system is partly parabolic, so the linearized operator is not sectorial, and the weight function decays at one end. We use an extension of a recent result about partly parabolic systems that are stabilized by such weight functions to show nonlinear stability. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.
DA - 2018/4/13/
PY - 2018/4/13/
DO - 10.1098/rsta.2017.0185
VL - 376
IS - 2117
SP -
SN - 1471-2962
KW - travelling wave
KW - stability
KW - combustion waves
KW - porous media
ER -
TY - JOUR
TI - Probabilistic modeling and global sensitivity analysis for CO2 storage in geological formations: a spectral approach
AU - Saad, Bilal M.
AU - Alexanderian, Alen
AU - Prudhomme, Serge
AU - Knio, Omar M.
T2 - APPLIED MATHEMATICAL MODELLING
AB - This work focuses on the simulation of CO2 storage in deep underground formations under uncertainty and seeks to understand the impact of uncertainties in reservoir properties on CO2 leakage. To simulate the process, a non-isothermal two-phase two-component flow system with equilibrium phase exchange is used. Since model evaluations are computationally intensive, instead of traditional Monte Carlo methods, we rely on polynomial chaos (PC) expansions for representation of the stochastic model response. A non-intrusive approach is used to determine the PC coefficients. We establish the accuracy of the PC representations within a reasonable error threshold through systematic convergence studies. In addition to characterizing the distributions of model observables, we compute probabilities of excess CO2 leakage. Moreover, we consider the injection rate as a design parameter and compute an optimum injection rate that ensures that the risk of excess pressure buildup at the leaky well remains below acceptable levels. We also provide a comprehensive analysis of sensitivities of CO2 leakage, where we compute the contributions of the random parameters, and their interactions, to the variance by computing first, second, and total order Sobol’ indices.
DA - 2018/1//
PY - 2018/1//
DO - 10.1016/j.apm.2017.09.016
VL - 53
SP - 584-601
SN - 1872-8480
KW - Carbon sequestration
KW - Multiphase flow
KW - Risk assessment
KW - Parametric uncertainty
KW - Polynomial chaos
KW - Sensitivity analysis
ER -
TY - JOUR
TI - High-order positivity-preserving hybrid finite-volume-finite-difference methods for chemotaxis systems
AU - Chertock, Alina
AU - Epshteyn, Yekaterina
AU - Hu, Hengrui
AU - Kurganov, Alexander
T2 - ADVANCES IN COMPUTATIONAL MATHEMATICS
DA - 2018/2//
PY - 2018/2//
DO - 10.1007/s10444-017-9545-9
VL - 44
IS - 1
SP - 327-350
SN - 1572-9044
UR - https://doi-org.prox.lib.ncsu.edu/10.1007/s10444-017-9545-9
KW - Patlak-Keller-Segel chemotaxis system
KW - Advection-diffusion-reaction systems
KW - High-order finite-difference
KW - Finite-volume methods
KW - Positivity-preserving algorithms
ER -
TY - JOUR
TI - Efficient generalized Golub-Kahan based methods for dynamic inverse problems
AU - Chung, J.
AU - Saibaba, Arvind
AU - Brown, M.
AU - Westman, E.
T2 - Inverse Problems
AB - We consider efficient methods for computing solutions to and estimating uncertainties in dynamic inverse problems, where the parameters of interest may change during the measurement procedure. Compared to static inverse problems, incorporating prior information in both space and time in a Bayesian framework can become computationally intensive, in part, due to the large number of unknown parameters. In these problems, explicit computation of the square root and/or inverse of the prior covariance matrix is not possible, so we consider efficient, iterative, matrix-free methods based on the generalized Golub–Kahan bidiagonalization that allow automatic regularization parameter and variance estimation. We demonstrate that these methods for dynamic inversion can be more flexible than standard methods and develop efficient implementations that can exploit structure in the prior, as well as possible structure in the forward model. Numerical examples from photoacoustic tomography, space-time deblurring, and passive seismic tomography demonstrate the range of applicability and effectiveness of the described approaches. Specifically, in passive seismic tomography, we demonstrate our approach on both synthetic and real data. To demonstrate the scalability of our algorithm, we solve a dynamic inverse problem with approximately measurements and 7.8 million unknowns in under 40 s on a standard desktop.
DA - 2018///
PY - 2018///
DO - 10.1088/1361-6420/aaa0e1
VL - 34
IS - 2
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85041011795&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Center of the quantum affine vertex algebra in type A
AU - Jing, Naihuan
AU - Kozic, Slaven
AU - Molev, Alexander
AU - Yang, Fan
T2 - JOURNAL OF ALGEBRA
AB - We consider the quantum vertex algebra associated with the double Yangian in type A as defined by Etingof and Kazhdan. We show that its center is a commutative associative algebra and construct algebraically independent families of topological generators of the center at the critical level.
DA - 2018/2/15/
PY - 2018/2/15/
DO - 10.1016/j.jalgebra.2017.10.020
VL - 496
SP - 138-186
SN - 1090-266X
KW - Quantum vertex algebra
KW - Double Yangian
KW - Center at the critical level
ER -
TY - JOUR
TI - A second-order finite-difference method for compressible
fluids in domains with moving boundaries
AU - Chertock, Alina
AU - Coco, Armando
AU - Kurganov, Alexander
AU - Russo, Giovanni
T2 - Commun. Comput. Phys.
DA - 2018///
PY - 2018///
VL - 23
IS - 1
SP - 230-263
ER -
TY - JOUR
TI - Tissue geometry may govern lung branching mode selection
AU - George, Uduak Z.
AU - Lubkin, Sharon R.
T2 - JOURNAL OF THEORETICAL BIOLOGY
AB - Lung branching morphogenesis proceeds in three stereotyped modes (domain, planar, and orthogonal branching). Much is known about the molecular players, including growth factors such as fibroblast growth factor 10 but it is unknown how these signals could actuate the different branching patterns. With the aim of identifying mechanisms that may determine the different branching modes, we developed a computational model of the epithelial lung bud and its surrounding mesenchyme. We studied transport of morphogens and localization of morphogen flux at lobe surfaces and lobe edges. We find that a single simple mechanism is theoretically capable of directing an epithelial tubule to elongate, bend, flatten, or bifurcate, depending solely on geometric ratios of the tissues in the vicinity of a growing tubule tip. Furthermore, the same simple mechanism is capable of generating orthogonal or planar branching, depending only on the same geometric ratios.
DA - 2018/4/7/
PY - 2018/4/7/
DO - 10.1016/j.jtbi.2017.12.031
VL - 442
SP - 22-30
SN - 1095-8541
ER -
TY - JOUR
TI - Stability of Feedback Solutions for Infinite Horizon Noncooperative Differential Games
AU - Bressan, Alberto
AU - Nguyen, Khai T.
T2 - DYNAMIC GAMES AND APPLICATIONS
DA - 2018/3//
PY - 2018/3//
DO - 10.1007/s13235-016-0206-2
VL - 8
IS - 1
SP - 42-78
SN - 2153-0793
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85042207992&partnerID=MN8TOARS
KW - Noncooperative differential games
KW - Nash equilibrium
KW - Infinite horizon
ER -
TY - JOUR
TI - Population genetic diversity in zebrafish lines
AU - Balik-Meisner, Michele
AU - Truong, Lisa
AU - Scholl, Elizabeth H.
AU - Tanguay, Robert L.
AU - Reif, David M.
T2 - MAMMALIAN GENOME
AB - Toxicological and pharmacological researchers have seized upon the many benefits of zebrafish, including the short generation time, well-characterized development, and early maturation as clear embryos. A major difference from many model organisms is that standard husbandry practices in zebrafish are designed to maintain population diversity. While this diversity is attractive for translational applications in human and ecological health, it raises critical questions on how interindividual genetic variation might contribute to chemical exposure or disease susceptibility differences. Findings from pooled samples of zebrafish support this supposition of diversity yet cannot directly measure allele frequencies for reference versus alternate alleles. Using the Tanguay lab Tropical 5D zebrafish line (T5D), we performed whole genome sequencing on a large group (n = 276) of individual zebrafish embryos. Paired-end reads were collected on an Illumina 3000HT, then aligned to the most recent zebrafish reference genome (GRCz10). These data were used to compare observed population genetic variation across species (humans, mice, zebrafish), then across lines within zebrafish. We found more single nucleotide polymorphisms (SNPs) in T5D than have been reported in SNP databases for any of the WIK, TU, TL, or AB lines. We theorize that some subset of the novel SNPs may be shared with other zebrafish lines but have not been identified in other studies due to the limitations of capturing population diversity in pooled sequencing strategies. We establish T5D as a model that is representative of diversity levels within laboratory zebrafish lines and demonstrate that experimental design and analysis can exert major effects when characterizing genetic diversity in heterogeneous populations.
DA - 2018/2//
PY - 2018/2//
DO - 10.1007/s00335-018-9735-x
VL - 29
IS - 1-2
SP - 90-100
SN - 1432-1777
ER -
TY - JOUR
TI - Plasmodium knowlesi invasion following spread by infected mosquitoes, macaques and humans
AU - Yakob, Laith
AU - Lloyd, Alun L.
AU - Kao, Rowland R.
AU - Ferguson, Heather M.
AU - Brock, Patrick M.
AU - Drakeley, Chris
AU - Bonsall, Michael B.
T2 - PARASITOLOGY
AB - Plasmodium knowlesi is increasingly recognized as a major cause of malaria in Southeast Asia. Anopheles leucosphyrous group mosquitoes transmit the parasite and natural hosts include long-tailed and pig-tailed macaques. Despite early laboratory experiments demonstrating successful passage of infection between humans, the true role that humans play in P. knowlesi epidemiology remains unclear. The threat posed by its introduction into immunologically naïve populations is unknown despite being a public health priority for this region. A two-host species mathematical model was constructed to analyse this threat. Global sensitivity analysis using Monte Carlo methods highlighted the biological processes of greatest influence to transmission. These included parameters known to be influential in classic mosquito-borne disease models (e.g. vector longevity); however, interesting ecological components that are specific to this system were also highlighted: while local vectors likely have intrinsic preferences for certain host species, how plastic these preferences are, and how this is shaped by local conditions, are key determinants of parasite transmission potential. Invasion analysis demonstrates that this behavioural plasticity can qualitatively impact the probability of an epidemic sparked by imported infection. Identifying key vector sub/species and studying their biting behaviours constitute important next steps before models can better assist in strategizing disease control.
DA - 2018/1//
PY - 2018/1//
DO - 10.1017/s0031182016002456
VL - 145
IS - 1
SP - 101-110
SN - 1469-8161
KW - invasion analysis
KW - Plasmodium knowlesi
KW - vector-borne disease
KW - mathematical model
KW - vector behaviour
ER -
TY - JOUR
TI - Coxeter-biCatalan combinatorics
AU - Barnard, Emily
AU - Reading, Nathan
T2 - JOURNAL OF ALGEBRAIC COMBINATORICS
AB - We pose counting problems related to the various settings for Coxeter-Catalan combinatorics (noncrossing, nonnesting, clusters, Cambrian). Each problem is to count “twin” pairs of objects from a corresponding problem in Coxeter-Catalan combinatorics. We show that the problems all have the same answer, and, for a given finite Coxeter group W, we call the common solution to these problems the W-biCatalan number. We compute the W-biCatalan number for all W and take the first steps in the study of Coxeter-biCatalan combinatorics.
DA - 2018/3//
PY - 2018/3//
DO - 10.1007/s10801-017-0775-1
VL - 47
IS - 2
SP - 241-300
SN - 1572-9192
UR - https://doi.org/10.1007/s10801-017-0775-1
KW - Alternating arc diagram
KW - Coxeter-Catalan combinatorics
KW - Doubled root poset
KW - Twin clusters
KW - Twin noncrossing partitions
KW - Twin nonnesting partitions
KW - Twin sortable elements
ER -
TY - JOUR
TI - Capelli identity on multiparameter quantum linear groups
AU - Jing, Naihuan
AU - Zhang, Jian
T2 - SCIENCE CHINA-MATHEMATICS
AB - A quantum Capelli identity is given on the multiparameter quantum general linear group based on the (p ij , u)-condition. The multiparameter quantum Pfaffan of the (p ij , u)-quantum group is also introduced and the transformation under the congruent action is given. Generalization to the multiparameter hyper-Pfaffan and relationship with the quantum minors are also investigated.
DA - 2018/2//
PY - 2018/2//
DO - 10.1007/s11425-017-9216-x
VL - 61
IS - 2
SP - 253-268
SN - 1869-1862
KW - multiparameter quantum groups
KW - q-determinants
KW - quasi-center
KW - Capelli identity
KW - q-Pfaffians
KW - q-hyper-Pfaffians
ER -
TY - JOUR
TI - Bosonic vertex representations of the toroidal superalgebras in type D(m, n)
AU - Jing, Naihuan
AU - Xu, Chongbin
T2 - JOURNAL OF ALGEBRA AND ITS APPLICATIONS
AB - In this paper, vertex representations of the 2-toroidal Lie superalgebras of type [Formula: see text] are constructed using both bosonic fields and vertex operators based on their loop algebraic presentation.
DA - 2018/3//
PY - 2018/3//
DO - 10.1142/s0219498818500573
VL - 17
IS - 3
SP -
SN - 1793-6829
KW - Toroidal Lie superalgebra
KW - vertex operators
KW - free fields
ER -
TY - JOUR
TI - A closed-form solution of the Black-Litterman model with conditional value at risk
AU - Pang, Tao
AU - Karan, Cagatay
T2 - OPERATIONS RESEARCH LETTERS
AB - We consider a portfolio optimization problem of the Black–Litterman type, in which we use the conditional value-at-risk (CVaR) as the risk measure and we use the multi-variate elliptical distributions, instead of the multi-variate normal distribution, to model the financial asset returns. We propose an approximation algorithm and establish the convergence results. Based on the approximation algorithm, we derive a closed-form solution of the portfolio optimization problems of the Black–Litterman type with CVaR.
DA - 2018/1//
PY - 2018/1//
DO - 10.1016/j.orl.2017.11.014
VL - 46
IS - 1
SP - 103-108
SN - 1872-7468
KW - Black-Litterman model
KW - Portfolio optimization
KW - CVaR
KW - Elliptical distribution
ER -
TY - JOUR
TI - Well-balanced schemes for the shallow water equations with Coriolis forces
AU - Chertock, Alina
AU - Dudzinski, Michael
AU - Kurganov, Alexander
AU - Lukacova-Medvid'ova, Maria
T2 - NUMERISCHE MATHEMATIK
DA - 2018/4//
PY - 2018/4//
DO - 10.1007/s00211-017-0928-0
VL - 138
IS - 4
SP - 939-973
SN - 0945-3245
UR - https://doi-org.prox.lib.ncsu.edu/10.1007/s00211-017-0928-0
ER -
TY - JOUR
TI - INITIAL-SEED RECURSIONS AND DUALITIES FOR d-VECTORS
AU - Reading, Nathan
AU - Stella, Salvatore
T2 - PACIFIC JOURNAL OF MATHEMATICS
AB - We present an initial-seed-mutation formula for d-vectors of cluster variables in a cluster algebra. We also give two rephrasings of this recursion: one as a duality formula for d-vectors in the style of the g-vectors/c-vectors dualities of Nakanishi and Zelevinsky, and one as a formula expressing the highest powers in the Laurent expansion of a cluster variable in terms of the d-vectors of any cluster containing it. We prove that the initial-seed-mutation recursion holds in a varied collection of cluster algebras, but not in general. We conjecture further that the formula holds for source-sink moves on the initial seed in an arbitrary cluster algebra, and we prove this conjecture in the case of surfaces.
DA - 2018/3//
PY - 2018/3//
DO - 10.2140/pjm.2018.293.179
VL - 293
IS - 1
SP - 179-206
SN - 0030-8730
UR - https://doi.org/10.2140/pjm.2018.293.179
KW - cluster algebra
KW - denominator vector
KW - initial-seed recursion
KW - marked surface
ER -
TY - JOUR
TI - Criteria for solvability and supersolvability in Leibniz algebras
AU - Misra, Kailash C.
AU - Stitzinger, Ernie
AU - Turner, Bethany
T2 - COMMUNICATIONS IN ALGEBRA
AB - ABSTRACTLeibniz algebras are certain generalization of Lie algebras. Recently, analyzing the structure of subalgebras, David Towers gave some criteria for the solvability and supersolvability of Li...
DA - 2018///
PY - 2018///
DO - 10.1080/00927872.2017.1372455
VL - 46
IS - 5
SP - 2083-2088
SN - 1532-4125
KW - Leibniz algebra
KW - solvable
KW - subalgebras
KW - supersolvable
ER -
TY - JOUR
TI - A NOTE ON SURGERY OBSTRUCTIONS AND HYPERBOLIC INTEGER HOMOLOGY SPHERES
AU - Hom, Jennifer
AU - Lidman, Tye
T2 - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
AB - Auckly gave two examples of irreducible integer homology spheres (one toroidal and one hyperbolic) which are not surgery on a knot in the three-sphere. Using Heegaard Floer homology, the authors and Karakurt provided infinitely many small Seifert fibered examples. In this note, we extend those results to give infinitely many hyperbolic examples, as well as infinitely many examples with arbitrary JSJ decomposition.
DA - 2018/3//
PY - 2018/3//
DO - 10.1090/proc/13925
VL - 146
IS - 3
SP - 1363-1365
SN - 1088-6826
ER -
TY - JOUR
TI - Stationary Expansion Shocks for a Regularized Boussinesq System
AU - El, Gennady A.
AU - Hoefer, Mark A.
AU - Shearer, Michael
T2 - STUDIES IN APPLIED MATHEMATICS
AB - Stationary expansion shocks have been recently identified as a new type of solution to hyperbolic conservation laws regularized by non-local dispersive terms that naturally arise in shallow-water theory. These expansion shocks were studied in (El, Hoefer, Shearer 2016) for the Benjamin-Bona-Mahony equation using matched asymptotic expansions. In this paper, we extend the analysis of (El, Hoefer, Shearer 2016) to the regularized Boussinesq system by using Riemann invariants of the underlying dispersionless shallow water equations. The extension for a system is non-trivial, requiring a combination of small amplitude, long-wave expansions with high order matched asymptotics. The constructed asymptotic solution is shown to be in excellent agreement with accurate numerical simulations of the Boussinesq system for a range of appropriately smoothed Riemann data.
DA - 2018/1//
PY - 2018/1//
DO - 10.1111/sapm.12191
VL - 140
IS - 1
SP - 27-47
SN - 1467-9590
ER -
TY - JOUR
TI - Perspective functions: Proximal calculus and applications in high-dimensional statistics
AU - Combettes, Patrick L.
AU - Muller, Christian L.
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - Perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis. To date, no systematic strategy is available to solve the associated, typically nonsmooth, optimization problems. In this paper, we fill this gap by showing that proximal methods provide an efficient framework to model and solve problems involving perspective functions. We study the construction of the proximity operator of a perspective function under general assumptions and present important instances in which the proximity operator can be computed explicitly or via straightforward numerical operations. These results constitute central building blocks in the design of proximal optimization algorithms. We showcase the versatility of the framework by designing novel proximal algorithms for state-of-the-art regression and variable selection schemes in high-dimensional statistics.
DA - 2018/1/15/
PY - 2018/1/15/
DO - 10.1016/j.jmaa.2016.12.021
VL - 457
IS - 2
SP - 1283-1306
SN - 1096-0813
KW - Convex function
KW - Perspective function
KW - Proximal algorithm
KW - Proximity operator
KW - Statistics
ER -
TY - JOUR
TI - Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit
AU - Gaddy, Melissa R.
AU - Yildiz, Sercan
AU - Unkelbach, Jan
AU - Papp, David
T2 - PHYSICS IN MEDICINE AND BIOLOGY
AB - Spatiotemporal fractionation schemes, that is, treatments delivering different dose distributions in different fractions, can potentially lower treatment side effects without compromising tumor control. This can be achieved by hypofractionating parts of the tumor while delivering approximately uniformly fractionated doses to the surrounding tissue. Plan optimization for such treatments is based on biologically effective dose (BED); however, this leads to computationally challenging nonconvex optimization problems. Optimization methods that are in current use yield only locally optimal solutions, and it has hitherto been unclear whether these plans are close to the global optimum. We present an optimization framework to compute rigorous bounds on the maximum achievable normal tissue BED reduction for spatiotemporal plans. The approach is demonstrated on liver tumors, where the primary goal is to reduce mean liver BED without compromising any other treatment objective. The BED-based treatment plan optimization problems are formulated as quadratically constrained quadratic programming (QCQP) problems. First, a conventional, uniformly fractionated reference plan is computed using convex optimization. Then, a second, nonconvex, QCQP model is solved to local optimality to compute a spatiotemporally fractionated plan that minimizes mean liver BED, subject to the constraints that the plan is no worse than the reference plan with respect to all other planning goals. Finally, we derive a convex relaxation of the second model in the form of a semidefinite programming problem, which provides a rigorous lower bound on the lowest achievable mean liver BED. The method is presented on five cases with distinct geometries. The computed spatiotemporal plans achieve 12-35% mean liver BED reduction over the optimal uniformly fractionated plans. This reduction corresponds to 79-97% of the gap between the mean liver BED of the uniform reference plans and our lower bounds on the lowest achievable mean liver BED. The results indicate that spatiotemporal treatments can achieve substantial reductions in normal tissue dose and BED, and that local optimization techniques provide high-quality plans that are close to realizing the maximum potential normal tissue dose reduction.
DA - 2018/1//
PY - 2018/1//
DO - 10.1088/1361-6560/aa9975
VL - 63
IS - 1
SP -
SN - 1361-6560
UR - http://dx.doi.org/10.1088/1361-6560/aa9975
KW - treatment planning
KW - optimization
KW - spatiotemporal fractionation
ER -
TY - JOUR
TI - Improving root separation bounds
AU - Herman, Aaron
AU - Hong, Hoon
AU - Tsigaridas, Elias
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - Let f be a polynomial (or polynomial system) with all simple roots. The root separation of f is the minimum of the pair-wise distances between the complex roots. A root separation bound is a lower bound on the root separation. Finding a root separation bound is a fundamental problem, arising in numerous disciplines. We present two new root separation bounds: one univariate bound, and one multivariate bound. The new bounds improve on the old bounds in two ways: The new bounds are usually significantly bigger (hence better) than the previous bounds. The new bounds scale correctly, unlike the previous bounds.
DA - 2018///
PY - 2018///
DO - 10.1016/j.jsc.2017.03.001
VL - 84
SP - 25-56
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2017.03.001
KW - Root separation bounds
KW - Polynomial roots
KW - Polynomial systems
ER -
TY - JOUR
TI - Certifying solutions to overdetermined and singular polynomial systems over Q
AU - Akoglu, Tulay Ayyildiz
AU - Hauenstein, Jonathan D.
AU - Szanto, Agnes
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - This paper is concerned with certifying that a given point is near an exact root of an overdetermined or singular polynomial system with rational coefficients. The difficulty lies in the fact that consistency of overdetermined systems is not a continuous property. Our certification is based on hybrid symbolic-numeric methods to compute an exact rational univariate representation (RUR) of a component of the input system from approximate roots. For overdetermined polynomial systems with simple roots, we compute an initial RUR from approximate roots. The accuracy of the RUR is increased via Newton iterations until the exact RUR is found, which we certify using exact arithmetic. Since the RUR is well-constrained, we can use it to certify the given approximate roots using α-theory. To certify isolated singular roots, we use a determinantal form of the isosingular deflation, which adds new polynomials to the original system without introducing new variables. The resulting polynomial system is overdetermined, but the roots are now simple, thereby reducing the problem to the overdetermined case. We prove that our algorithms have complexity that are polynomial in the input plus the output size upon successful convergence, and we use worst case upper bounds for termination when our iteration does not converge to an exact RUR. Examples are included to demonstrate the approach.
DA - 2018///
PY - 2018///
DO - 10.1016/j.jsc.2017.03.004
VL - 84
SP - 147-171
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2017.03.004
KW - Overdetermined
KW - Polynomial system
KW - Singular solutions
KW - Certification
KW - Rational univariate representation
KW - Isosingular deflation
ER -
TY - JOUR
TI - Regularized learning schemes in feature Banach spaces
AU - Combettes, Patrick L.
AU - Salzo, Saverio
AU - Villa, Silvia
T2 - ANALYSIS AND APPLICATIONS
AB - This paper proposes a unified framework for the investigation of constrained learning theory in reflexive Banach spaces of features via regularized empirical risk minimization. The focus is placed on Tikhonov-like regularization with totally convex functions. This broad class of regularizers provides a flexible model for various priors on the features, including, in particular, hard constraints and powers of Banach norms. In such context, the main results establish a new general form of the representer theorem and the consistency of the corresponding learning schemes under general conditions on the loss function, the geometry of the feature space, and the modulus of total convexity of the regularizer. In addition, the proposed analysis gives new insight into basic tools such as reproducing Banach spaces, feature maps, and universality. Even when specialized to Hilbert spaces, this framework yields new results that extend the state of the art.
DA - 2018/1//
PY - 2018/1//
DO - 10.1142/s0219530516500202
VL - 16
IS - 1
SP - 1-54
SN - 1793-6861
KW - Consistency
KW - Banach spaces
KW - empirical risk
KW - feature map
KW - reproducing kernel
KW - regularization
KW - representer theorem
KW - statistical learning
KW - totally convex function
ER -
TY - JOUR
TI - Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials
AU - Britt, S.
AU - Tsynkov, S.
AU - Turkel, E.
T2 - Journal of Computational Physics
AB - We solve the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time. This is accomplished using an implicit finite difference (FD) scheme for the wave equation and solving an elliptic (modified Helmholtz) equation at each time step with fourth order spatial accuracy by the method of difference potentials (MDP). High-order MDP utilizes compact FD schemes on regular structured grids to efficiently solve problems on nonconforming domains while maintaining the design convergence rate of the underlying FD scheme. Asymptotically, the computational complexity of high-order MDP scales the same as that for FD.
DA - 2018/2//
PY - 2018/2//
DO - 10.1016/j.jcp.2017.10.049
VL - 354
SP - 26-42
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2017.10.049
DB - Crossref
KW - Method of difference potentials (MDP)
KW - Compact finite difference scheme
KW - Implicit scheme
KW - Regular structured grid
KW - Nonconforming boundary
KW - High-order accuracy
KW - High-order MDP
ER -
TY - JOUR
TI - Nonlinear Kalman filtering for censored observations
AU - Arthur, Joseph
AU - Attarian, Adam
AU - Hamilton, Franz
AU - Tran, Hien
T2 - Applied Mathematics and Computation
AB - The use of Kalman filtering, as well as its nonlinear extensions, for the estimation of system variables and parameters has played a pivotal role in many fields of scientific inquiry where observations of the system are restricted to a subset of variables. However in the case of censored observations, where measurements of the system beyond a certain detection point are impossible, the estimation problem is complicated. Without appropriate consideration, censored observations can lead to inaccurate estimates. Motivated by previous work on censored filtering in linear systems, we develop a modified version of the extended Kalman filter to handle the case of censored observations in nonlinear systems. We validate this methodology in a simple oscillator system first, showing its ability to accurately reconstruct state variables and track system parameters when observations are censored. Finally, we utilize the nonlinear censored filter to analyze censored datasets from patients with hepatitis C and human immunodeficiency virus.
DA - 2018/1//
PY - 2018/1//
DO - 10.1016/j.amc.2017.08.002
VL - 316
SP - 155-166
J2 - Applied Mathematics and Computation
LA - en
OP -
SN - 0096-3003
UR - http://dx.doi.org/10.1016/j.amc.2017.08.002
DB - Crossref
KW - Extended Kalman filter
KW - Censored observation
KW - Parameter estimation
KW - Hepatitis C virus (HCV)
KW - Human immunodeficiency virus (HIV)
ER -
TY - JOUR
TI - A categorification of the chromatic symmetric function
AU - Sazdanovic, Radmila
AU - Yip, Martha
T2 - Journal of Combinatorial Theory, Series A
AB - The Stanley chromatic symmetric function XG of a graph G is a symmetric function generalization of the chromatic polynomial and has interesting combinatorial properties. We apply the ideas from Khovanov homology to construct a homology theory of graded Sn-modules, whose graded Frobenius series FrobG(q,t) specializes to the chromatic symmetric function at q=t=1. This homology theory can be thought of as a categorification of the chromatic symmetric function, and it satisfies homological analogues of several familiar properties of XG. In particular, the decomposition formula for XG discovered recently by Orellana, Scott, and independently by Guay-Paquet, is lifted to a long exact sequence in homology.
DA - 2018/2//
PY - 2018/2//
DO - 10.1016/j.jcta.2017.08.014
VL - 154
SP - 218-246
J2 - Journal of Combinatorial Theory, Series A
LA - en
OP -
SN - 0097-3165
UR - http://dx.doi.org/10.1016/j.jcta.2017.08.014
DB - Crossref
KW - Symmetric functions
KW - Chromatic polynomial
KW - Khovanov homology
KW - Representations
KW - Frobenius series
KW - Graph coloring
ER -
TY - JOUR
TI - The maximum likelihood threshold of a graph
AU - Gross, Elizabeth
AU - Sullivant, Seth
T2 - BERNOULLI
AB - The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph parameter is connected to the theory of combinatorial rigidity. In particular, if the edge set of a graph $G$ is an independent set in the $(n-1)$-dimensional generic rigidity matroid, then the maximum likelihood threshold of $G$ is less than or equal to $n$. This connection allows us to prove many results about the maximum likelihood threshold. We conclude by showing that these methods give exact bounds on the number of observations needed for the score matching estimator to exist with probability one.
DA - 2018/2//
PY - 2018/2//
DO - 10.3150/16-bej881
VL - 24
IS - 1
SP - 386-407
SN - 1573-9759
KW - algebraic matroids
KW - Gaussian graphical models
KW - matrix completion
KW - maximum likelihood estimation
KW - maximum likelihood threshold
KW - rigidity theory
KW - score matching estimator
KW - weak maximum likelihood threshold
ER -
TY - JOUR
TI - Deformation of an elastic substrate due to a resting sessile droplet
AU - Bardall, Aaron
AU - Daniels, Karen E.
AU - Shearer, Michael
T2 - EUROPEAN JOURNAL OF APPLIED MATHEMATICS
AB - On a sufficiently soft substrate, a resting fluid droplet will cause significant deformation of the substrate. This deformation is driven by a combination of capillary forces at the contact line and the fluid pressure at the solid surface. These forces are balanced at the surface by the solid traction stress induced by the substrate deformation. Young's Law, which predicts the equilibrium contact angle of the droplet, also indicates an a priori radial force balance for rigid substrates, but not necessarily for soft substrates that deform under loading. It remains an open question whether the contact line transmits a non-zero force tangent to the substrate surface in addition to the conventional normal (vertical) force. We present an analytic Fourier transform solution technique that includes general interfacial energy conditions, which govern the contact angle of a 2D droplet. This includes evaluating the effect of gravity on the droplet shape in order to determine the correct fluid pressure at the substrate surface for larger droplets. Importantly, we find that in order to avoid a strain singularity at the contact line under a non-zero tangential contact line force, it is necessary to include a previously neglected horizontal traction boundary condition. To quantify the effects of the contact line and identify key quantities that will be experimentally accessible for testing the model, we evaluate solutions for the substrate surface displacement field as a function of Poisson's ratio and zero/non-zero tangential contact line forces.
DA - 2018/4//
PY - 2018/4//
DO - 10.1017/s0956792517000134
VL - 29
IS - 2
SP - 281-300
SN - 1469-4425
KW - PDEs in Connection with Mechanics of Deformable Solids
KW - Transform Methods
KW - Classical Linear Elasticity
KW - Numerical Approximation of Solutions
KW - Fluid-Solid Interactions
ER -