TY - JOUR
TI - TRAINABILITY OF ReLU NETWORKS AND DATA-DEPENDENT INITIALIZATION
AU - Shin, Yeonjong
AU - Karniadakis, George Em
T2 - Journal of Machine Learning for Modeling and Computing
AB - In this paper we study the trainability of rectified linear unit (ReLU) networks at initialization. A ReLU neuron is said to be dead if it only outputs a constant for any input. Two death states of neurons are introduced−tentative and permanent death. A network is then said to be trainable if the number of permanently dead neurons is sufficiently small for a learning task. We refer to the probability of a randomly initialized network being trainable as trainability. We show that a network being trainable is a necessary condition for successful training, and the trainability serves as an upper bound of training success rates. In order to quantify the trainability, we study the probability distribution of the number of active neurons at initialization. In many applications, overspecified or overparameterized neural networks are successfully employed and shown to be trained effectively. With the notion of trainability, we show that overparameterization is both a necessary and a sufficient condition for achieving a zero training loss. Furthermore, we propose a data-dependent initialization method in an overparameterized setting. Numerical examples are provided to demonstrate the effectiveness of the method and our theoretical findings.
DA - 2020///
PY - 2020///
DO - 10.1615/jmachlearnmodelcomput.2020034126
VL - 1
IS - 1
SP - 39-74
UR - http://dx.doi.org/10.1615/jmachlearnmodelcomput.2020034126
ER -
TY - JOUR
TI - On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
AU - Shin, Yeonjong
AU - Darbon, J.
AU - Karniadakis, G. E.
T2 - Communications in Computational Physics
AB - Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encounted in computational science and engineering. Guided by data and physical laws, PINNs find a neural network that approximates the solution to a system of PDEs. Such a neural network is obtained by minimizing a loss function in which any prior knowledge of PDEs and data are encoded. Despite its remarkable empirical success in one, two or three dimensional problems, there is little theoretical justification for PINNs. As the number of data grows, PINNs generate a sequence of minimizers which correspond to a sequence of neural networks. We want to answer the question: Does the sequence of minimizers converge to the solution to the PDE? We consider two classes of PDEs: linear second-order elliptic and parabolic. By adapting the Schauder approach and the maximum principle, we show that the sequence of minimizers strongly converges to the PDE solution in $C^0$. Furthermore, we show that if each minimizer satisfies the initial/boundary conditions, the convergence mode becomes $H^1$. Computational examples are provided to illustrate our theoretical findings. To the best of our knowledge, this is the first theoretical work that shows the consistency of PINNs.
DA - 2020/6//
PY - 2020/6//
DO - 10.4208/cicp.oa-2020-0193
VL - 28
IS - 5
SP - 2042–2074
SN - 1815-2406 1991-7120
UR - http://dx.doi.org/10.4208/cicp.oa-2020-0193
ER -
TY - JOUR
TI - Dying ReLU and Initialization: Theory and Numerical Examples
AU - Lu, Lu
AU - Shin, Y.
AU - Su, Y.
AU - Karniadakis, G. E.
T2 - Communications in Computational Physics
AB - Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically resolved by the rectified linear unit (ReLU) activation. However, here we show that even for such activation, deep and narrow neural networks (NNs) will converge to erroneous mean or median states of the target function depending on the loss with high probability. Deep and narrow NNs are encountered in solving partial differential equations with high-order derivatives. We demonstrate this collapse of such NNs both numerically and theoretically, and provide estimates of the probability of collapse. We also construct a diagram of a safe region for designing NNs that avoid the collapse to erroneous states. Finally, we examine different ways of initialization and normalization that may avoid the collapse problem. Asymmetric initializations may reduce the probability of collapse but do not totally eliminate it.
DA - 2020/6//
PY - 2020/6//
DO - 10.4208/cicp.oa-2020-0165
VL - 28
IS - 5
SP - 1671–1706
SN - 1815-2406 1991-7120
UR - http://dx.doi.org/10.4208/cicp.oa-2020-0165
ER -
TY - JOUR
TI - A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data
AU - Le, Thuy Thi Thu
AU - Nguyen, Loc Hoang
T2 - Journal of Inverse and Ill-posed Problems
AB - Abstract We propose a new numerical method for the solution of the problem of the reconstruction of the initial condition of a quasilinear parabolic equation from the measurements of both Dirichlet and Neumann data on the boundary of a bounded domain. Although this problem is highly nonlinear, we do not require an initial guess of the true solution. The key in our method is the derivation of a boundary value problem for a system of coupled quasilinear elliptic equations whose solution is the vector function of the spatially dependent Fourier coefficients of the solution to the governing parabolic equation. We solve this problem by an iterative method. The global convergence of the system is rigorously established using a Carleman estimate. Numerical examples are presented.
DA - 2020/5//
PY - 2020/5//
DO - 10.1515/jiip-2020-0028
VL - 0
IS - 0
ER -
TY - JOUR
TI - Numerical solution of a linearized travel time tomography problem with incomplete data
AU - Klibanov, Michael V.
AU - Le, Thuy T.
AU - Nguyen, Loc H.
T2 - SIAM Journal on Scientific Computing
AB - Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 13 November 2019Accepted: 08 July 2020Published online: 23 September 2020Keywordslinearization, inverse kinematic problem, travel time tomography, numerical solution, convergenceAMS Subject Headings35R25, 35R30Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Publisher: Society for Industrial and Applied MathematicsCODEN: sjoce3
DA - 2020///
PY - 2020///
DO - 10.1137/19M1299487
VL - 42
IS - 5
SP - B1173-B1192
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85093113145&partnerID=MN8TOARS
ER -
TY - RPRT
TI - Scalable spatio-temporal modeling using a fast multipole method for 3D tracer concentration breakthrough data with magnetic resonance imaging.
AU - Lee, Jonghyun
AU - Chen, Chao
AU - Toru, Takahashi
AU - Darve, Eric
AU - Yoon, Hongkyu
A3 - Sandia National Lab.(SNL-NM), Albuquerque, NM (United States)
DA - 2020///
PY - 2020///
PB - Sandia National Lab.(SNL-NM), Albuquerque, NM (United States)
ER -
TY - JOUR
TI - Parallelization of the inverse fast multipole method with an application to boundary element method
AU - Takahashi, Toru
AU - Chen, Chao
AU - Darve, Eric
T2 - Computer Physics Communications
AB - We present an algorithm to parallelize the inverse fast multipole method (IFMM), which is an approximate direct solver for dense linear systems. The parallel scheme is based on a greedy coloring algorithm, where two nodes in the hierarchy with the same color are separated by at least σ nodes. We proved that when σ≥6, the workload associated with one color is embarrassingly parallel. However, the number of nodes in a group (color) may be small when σ=6. Therefore, we also explored σ=3, where a small fraction of the algorithm needs to be serialized, and the overall parallel efficiency was improved. We implemented the parallel IFMM using OpenMP for shared-memory machines. Successively, we applied it to a fast-multipole accelerated boundary element method (FMBEM) as a preconditioner, and compared its efficiency with (a) the original IFMM parallelized by linking a multi-threaded linear algebra library and (b) the commonly used parallel block-diagonal preconditioner. Our results showed that our parallel IFMM achieved at most 4× and 11× speedups over the reference method (a) and (b), respectively, in realistic examples involving more than one million variables.
DA - 2020/2//
PY - 2020/2//
DO - 10.1016/j.cpc.2019.106975
VL - 247
SP - 106975
J2 - Computer Physics Communications
LA - en
OP -
SN - 0010-4655
UR - http://dx.doi.org/10.1016/j.cpc.2019.106975
DB - Crossref
ER -
TY - JOUR
TI - An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations
AU - Cambier, Léopold
AU - Chen, Chao
AU - Boman, Erik G.
AU - Rajamanickam, Sivasankaran
AU - Tuminaro, Raymond S.
AU - Darve, Eric
T2 - SIAM Journal on Matrix Analysis and Applications
AB - We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection, sparsification, and low-rank compression. After eliminating all interiors at a given level of the elimination tree, the algorithm sparsifies all separators corresponding to the interiors. This operation reduces the size of the separators by eliminating some degrees of freedom but without introducing any fill-in. This is done at the expense of a small and controllable approximation error. The result is an approximate factorization that can be used as an efficient preconditioner. We then perform several numerical experiments to evaluate this algorithm. We demonstrate that a version using orthogonal factorization and block-diagonal scaling takes fewer CG iterations to converge than previous similar algorithms on various kinds of problems. Furthermore, this algorithm is provably guaranteed to never break down and the matrix stays symmetric positive-definite throughout the process. We evaluate the algorithm on some large problems show it exhibits near-linear scaling. The factorization time is roughly $\mathcal{O}$(N), and the number of iterations grows slowly with N.
DA - 2020/1//
PY - 2020/1//
DO - 10.1137/19m123806X
VL - 41
IS - 2
SP - 715-746
J2 - SIAM J. Matrix Anal. Appl.
LA - en
OP -
SN - 0895-4798 1095-7162
UR - http://dx.doi.org/10.1137/19m123806x
DB - Crossref
ER -
TY - CONF
TI - A preconditioner based on sparsified nested dissection and low-rank approximation
AU - Boman, Erik G
AU - Cambier, Leopold
AU - Chen, Chao
AU - Darve, Eric
AU - Rajamanickam, Siva
AU - Tuminaro, Ray S
C2 - 2020///
C3 - XXI Householder Symposium on Numerical Linear Algebra
DA - 2020///
SP - 128
ER -
TY - JOUR
TI - Stability of thin film flowing down the outer surface of a rotating non-uniformly heated vertical cylinder
AU - Mukhopadhyay, Anandamoy
AU - Chattopadhyay, Souradip
AU - Barua, Amlan K.
T2 - Nonlinear Dynamics
DA - 2020/4/14/
PY - 2020/4/14/
DO - 10.1007/s11071-020-05558-x
VL - 100
IS - 2
SP - 1143-1172
UR - https://doi.org/10.1007/s11071-020-05558-x
ER -
TY - CHAP
TI - Central-upwind scheme for a non-hydrostatic Saint-Venant
system
AU - Chertock, Alina
AU - Kurganov, Alexander
AU - Miller, Jason
AU - Yan, Jun
T2 - Hyperbolic problems: theory, numerics, applications
PY - 2020///
VL - 10
SP - 25-41
PB - Am. Inst. Math. Sci. (AIMS), Springfield, MO
ER -
TY - JOUR
TI - Physics-integrated machine learning: embedding a neural network in the Navier-Stokes equations. Part I
T2 - ArXiv
DA - 2020///
PY - 2020///
UR - https://publons.com/wos-op/publon/58758828/
ER -
TY - JOUR
TI - EFFECTIVE
*l
*^{2
DECOUPLING FOR THE PARABOLA
AU - Li, Zane Kun
T2 - Mathematika
AB - We make effective l 2 L p decoupling for the parabola in the range 4 < p < 6 . In an appendix joint with Jean Bourgain, we apply the main theorem to prove the conjectural bound for the sixth-order correlation of the integer solutions of the equation x 2 + y 2 = m in an extremal case. This proves unconditionally a result that was proven in Bombieri and Bourgain [Int. Math. Res. Not. IMRN 2015(11), 3343–3407] under the hypotheses of the Birch and Swinnerton–Dyer conjecture and the Riemann Hypothesis for L-functions of elliptic curves over Q.
DA - 2020/5/4/
PY - 2020/5/4/
DO - 10.1112/mtk.12038
VL - 66
IS - 3
SP - 681-712
J2 - Mathematika
LA - en
OP -
SN - 0025-5793 2041-7942
UR - http://dx.doi.org/10.1112/mtk.12038
DB - Crossref
ER -
TY - JOUR
TI - Nonlinear power-like and SVD-like iterative schemes with applications to entangled bipartite rank-1 approximation
AU - Chu, M.T.
AU - Lin, M.W.
T2 - SIAM Journal on Scientific Computing
AB - Nonlinear Power-Like and SVD-Like Iterative Schemes with Applications to Entangled Bipartite Rank-1 Approximation
DA - 2020///
PY - 2020///
DO - 10.1137/20M1336059
SP - S448-S474
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85113342436&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Theory for undercompressive shocks in tears of wine
AU - Dukler, Yonatan
AU - Ji, Hangjie
AU - Falcon, Claudia
AU - Bertozzi, Andrea L.
T2 - Physical Review Fluids
AB - Tears of wine, in which a thin layer of a water-ethanol mixture travel up an inclined surface against gravity and then fall down in the form of tears, have been observed in wine glasses for centuries. It has been modeled with a conservation law with a nonconvex flux and higher order diffusion due to the bulk surface tension. The resulting nonclassical ``undercompressive'' shock solutions are the main driver of the destabilizing front forming the ``wine tears''. Prior modeling did not address the wine tears but rather the behavior of the film at earlier stages and the behavior of the meniscus.
DA - 2020/3/17/
PY - 2020/3/17/
DO - 10.1103/PhysRevFluids.5.034002
VL - 5
IS - 3
J2 - Phys. Rev. Fluids
LA - en
OP -
SN - 2469-990X
UR - http://dx.doi.org/10.1103/physrevfluids.5.034002
DB - Crossref
ER -
TY - JOUR
TI - Steady states and dynamics of a thin-film-type equation with non-conserved mass
AU - HANGJIE, JI
AU - WITELSKI, THOMAS P.
T2 - European Journal of Applied Mathematics
AB - We study the steady states and dynamics of a thin-film-type equation with non-conserved mass in one dimension. The evolution equation is a non-linear fourth-order degenerate parabolic partial differential equation (PDE) motivated by a model of volatile viscous fluid films allowing for condensation or evaporation. We show that by changing the sign of the non-conserved flux and breaking from a gradient flow structure, the problem can exhibit novel behaviours including having two distinct classes of co-existing steady-state solutions. Detailed analysis of the bifurcation structure for these steady states and their stability reveals several possibilities for the dynamics. For some parameter regimes, solutions can lead to finite-time rupture singularities. Interestingly, we also show that a finite-amplitude limit cycle can occur as a singular perturbation in the nearly conserved limit.
DA - 2020/12/22/
PY - 2020/12/22/
DO - 10.1017/S0956792519000330
VL - 11
SP - 1-34
UR - https://doi.org/10.1017/S0956792519000330
ER -
TY - JOUR
TI - Modelling film flows down a fibre influenced by nozzle geometry
AU - Ji, H.
AU - Sadeghpour, A.
AU - Ju, Y. S.
AU - Bertozzi, A. L.
T2 - Journal of Fluid Mechanics
AB - Abstract
DA - 2020/8/28/
PY - 2020/8/28/
DO - 10.1017/jfm.2020.605
VL - 901
J2 - J. Fluid Mech.
LA - en
OP -
SN - 0022-1120 1469-7645
UR - http://dx.doi.org/10.1017/jfm.2020.605
DB - Crossref
ER -
TY - CONF
TI - Crystal for Stable Grothendieck Polynomials
AU - Morse, J.
AU - Pan, J.
AU - Poh, W.
AU - Schilling, A.
T2 - 32nd Conference on Formal Power Series and Algebraic Combinatorics
C2 - 2020///
C3 - Proceedings of of the 32nd Conference on Formal Power Series and Algebraic Combinatorics
CY - Ramat Gan, Israel
DA - 2020///
PY - 2020/7/13/
ER -
TY - JOUR
TI - A Crystal on Decreasing Factorizations in the 0-Hecke Monoid
AU - Morse, Jennifer
AU - Pan, Jianping
AU - Poh, Wencin
AU - Schilling, Anne
T2 - The Electronic Journal of Combinatorics
AB - We introduce a type $A$ crystal structure on decreasing factorizations of fully-commu\-tative elements in the 0-Hecke monoid which we call $\star$-crystal. This crystal is a $K$-theoretic generalization of the crystal on decreasing factorizations in the symmetric group of the first and last author. We prove that under the residue map the $\star$-crystal intertwines with the crystal on set-valued tableaux recently introduced by Monical, Pechenik and Scrimshaw. We also define a new insertion from decreasing factorization to pairs of semistandard Young tableaux and prove several properties, such as its relation to the Hecke insertion and the uncrowding algorithm. The new insertion also intertwines with the crystal operators.
DA - 2020/5/29/
PY - 2020/5/29/
DO - 10.37236/9168
VL - 27
IS - 2
J2 - Electron. J. Combin.
OP -
SN - 1077-8926
UR - http://dx.doi.org/10.37236/9168
DB - Crossref
ER -
TY - JOUR
TI - A functional analysis approach to the static replication of European options
AU - Bossu, Sébastien
AU - Carr, Peter
AU - Papanicolaou, Andrew
T2 - Quantitative Finance
AB - The replication of any European contingent claim by a static portfolio of calls and puts with strikes forming a continuum, formally proven by Carr and Madan [Towards a theory of volatility trading. In Volatility: New Estimation Techniques for Pricing Derivatives, edited by R.A. Jarrow, Vol. 29, pp. 417–427, 1998 (Risk books)], is part of the more general theory of integral equations. We use spectral decomposition techniques to show that exact payoff replication may be achieved with a discrete portfolio of special options. We discuss applications for fast pricing of vanilla options that may be suitable for large option books or high frequency option trading, and for model pricing when the characteristic function of the underlying asset price is known.
DA - 2020/11/4/
PY - 2020/11/4/
DO - 10.1080/14697688.2020.1810857
VL - 21
IS - 4
SP - 637-655
J2 - Quantitative Finance
LA - en
OP -
SN - 1469-7688 1469-7696
UR - http://dx.doi.org/10.1080/14697688.2020.1810857
DB - Crossref
KW - Derivatives
KW - Options
KW - Static replication
KW - Payoff
KW - Integral equation
KW - Functional analysis
KW - Spectral theorem
KW - Breeden-Litzenberger formula
KW - Implied distribution
ER -
TY - JOUR
TI - PCA for Implied Volatility Surfaces
AU - Avellaneda, Marco
AU - Healy, Brian
AU - Papanicolaou, Andrew
AU - Papanicolaou, George
T2 - The Journal of Financial Data Science
AB - Principal component analysis (PCA) is a useful tool when trying to construct factor models from historical asset returns. For the implied volatilities of US equities, there is a PCA-based model with a principal eigenportfolio whose return time series lies close to that of an overarching market factor. The authors show that this market factor is the index resulting from the daily compounding of a weighted average of implied-volatility returns, with weights based on the options’ open interest and Vega. The authors also analyze the singular vectors derived from the tensor structure of the implied volatilities of S&P 500 constituents and find evidence indicating that some type of open interest- and Vega-weighted index should be one of at least two significant factors in this market. TOPICS:Statistical methods, simulations, big data/machine learning Key Findings • Principal component analysis of a comprehensive dataset of implied volatility surfaces from options on US equities shows that their collective behavior is captured by just nine factors, whereas the effective spatial dimension of the residuals is closer to 500 than to the nominal dimension of 28,000, revealing the large redundancy in the data. • Portfolios of implied volatility surface returns, weighed suitably by open interest and Vega, track the principal eigenportfolio associated with a market portfolio of options, in analogy to equity portfolios. • Retention of the tensor structure in the eigenportfolio analysis improves the tracking between the open interest–Vega weighted (tensor) implied volatility surface returns portfolio and the (tensor) eigenportfolio, indicating that data structure matters.
DA - 2020/3/24/
PY - 2020/3/24/
DO - 10.3905/jfds.2020.1.032
VL - 2
IS - 2
SP - 85-109
J2 - JFDS
LA - en
OP -
SN - 2640-3943
UR - http://dx.doi.org/10.3905/jfds.2020.1.032
DB - Crossref
ER -
TY - JOUR
TI - Physics-integrated machine learning: Embedding a neural network in the navier-stokes equations. Part II
AU - Iskhakov, A.S.
AU - Dinh, N.T.
T2 - arXiv
DA - 2020///
PY - 2020///
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85108266968&partnerID=MN8TOARS
ER -
TY - CHAP
TI - Khovanov Link Homology
AU - Sazdanovic, R.
T2 - Encyclopedia of Knot Theory
A2 - Adams, C.
A2 - Flapan, E.
A2 - Henrich, A.
A2 - Kauffman, L.H.
A2 - Ludwig, L.D.
A2 - Nelson, S.
PY - 2020/12/29/
SP - Chapter 70
PB - Chapman & Hall
SN - 9781138297845
ER -
TY - JOUR
TI - A Method for Dimensionally Adaptive Sparse Trigonometric Interpolation of Periodic Functions
AU - Morrow, Zachary
AU - Stoyanov, Miroslav
T2 - SIAM Journal on Scientific Computing
AB - We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved and the precise anisotropy is not known a priori. To the authors' knowledge, this is the first instance of a dimensionally adaptive sparse interpolation algorithm that uses a trigonometric interpolation basis. The motivating application behind this work is the adaptive approximation of a multi-input model for a molecular potential energy surface (PES) where each input represents an angle of rotation. Our method is based on an anisotropic quasi-optimal estimate for the decay rate of the Fourier coefficients of the model; a least-squares fit to the coefficients of the interpolant is used to estimate the anisotropy. Thus, our adaptive approximation strategy begins with a coarse isotropic interpolant, which is gradually refined using the estimated anisotropic rates. The procedure takes several iterations where ever-more accurate interpolants are used to generate ever-improving anisotropy rates. We present several numerical examples of our algorithm where the adaptive procedure successfully recovers the theoretical “best” convergence rate, including an application to a periodic PES approximation. An open-source implementation of our algorithm resides in the Tasmanian UQ library developed at Oak Ridge National Laboratory.
DA - 2020/1//
PY - 2020/1//
DO - 10.1137/19M1283483
VL - 42
IS - 4
SP - A2436-A2460
UR - https://doi.org/10.1137/19M1283483
KW - sparse interpolation
KW - trigonometric interpolation
KW - adaptive refinement
KW - periodicity-preserving approximation
ER -
TY - JOUR
TI - Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis
AU - Cang, Zixuan
AU - Munch, Elizabeth
AU - Wei, Guo-Wei
T2 - Journal of Applied and Computational Topology
AB - While the spatial topological persistence is naturally constructed from a radius-based filtration, it has hardly been derived from a temporal filtration. Most topological models are designed for the global topology of a given object as a whole. There is no method reported in the literature for the topology of an individual component in an object to the best of our knowledge. For many problems in science and engineering, the topology of an individual component is important for describing its properties. We propose evolutionary homology (EH) constructed via a time evolution-based filtration and topological persistence. Our approach couples a set of dynamical systems or chaotic oscillators by the interactions of a physical system, such as a macromolecule. The interactions are approximated by weighted graph Laplacians. Simplices, simplicial complexes, algebraic groups and topological persistence are defined on the coupled trajectories of the chaotic oscillators. The resulting EH gives rise to time-dependent topological invariants or evolutionary barcodes for an individual component of the physical system, revealing its topology-function relationship. In conjunction with Wasserstein metrics, the proposed EH is applied to protein flexibility analysis, an important problem in computational biophysics. Numerical results for the B-factor prediction of a benchmark set of 364 proteins indicate that the proposed EH outperforms all the other state-of-the-art methods in the field.
DA - 2020/12//
PY - 2020/12//
DO - 10.1007/s41468-020-00057-9
VL - 4
IS - 4
SP - 481-507
UR - http://dx.doi.org/10.1007/s41468-020-00057-9
ER -
TY - JOUR
TI - Defining Epidermal Basal Cell States during Skin Homeostasis and Wound Healing Using Single-Cell Transcriptomics
AU - Haensel, Daniel
AU - Jin, Suoqin
AU - Sun, Peng
AU - Cinco, Rachel
AU - Dragan, Morgan
AU - Nguyen, Quy
AU - Cang, Zixuan
AU - Gong, Yanwen
AU - Vu, Remy
AU - MacLean, Adam L.
AU - Kessenbrock, Kai
AU - Gratton, Enrico
AU - Nie, Qing
AU - Dai, Xing
T2 - Cell Reports
AB - Our knowledge of transcriptional heterogeneities in epithelial stem and progenitor cell compartments is limited. Epidermal basal cells sustain cutaneous tissue maintenance and drive wound healing. Previous studies have probed basal cell heterogeneity in stem and progenitor potential, but a comprehensive dissection of basal cell dynamics during differentiation is lacking. Using single-cell RNA sequencing coupled with RNAScope and fluorescence lifetime imaging, we identify three non-proliferative and one proliferative basal cell state in homeostatic skin that differ in metabolic preference and become spatially partitioned during wound re-epithelialization. Pseudotemporal trajectory and RNA velocity analyses predict a quasi-linear differentiation hierarchy where basal cells progress from Col17a1Hi/Trp63Hi state to early-response state, proliferate at the juncture of these two states, or become growth arrested before differentiating into spinous cells. Wound healing induces plasticity manifested by dynamic basal-spinous interconversions at multiple basal transcriptional states. Our study provides a systematic view of epidermal cellular dynamics, supporting a revised “hierarchical-lineage” model of homeostasis.
DA - 2020/3//
PY - 2020/3//
DO - 10.1016/j.celrep.2020.02.091
VL - 30
IS - 11
SP - 3932-3947.e6
UR - http://dx.doi.org/10.1016/j.celrep.2020.02.091
ER -
TY - JOUR
TI - Structural cavities are critical to balancing stability and activity of a membrane-integral enzyme
AU - Guo, Ruiqiong
AU - Cang, Zixuan
AU - Yao, Jiaqi
AU - Kim, Miyeon
AU - Deans, Erin
AU - Wei, Guowei
AU - Kang, Seung-gu
AU - Hong, Heedeok
T2 - Proceedings of the National Academy of Sciences
AB - Significance The physical principles of membrane protein folding are not well understood. Because of the lack of water inside the cell membrane, the hydrophobic effect cannot drive the folding of membrane-embedded structural elements. Therefore, van der Waals packing interaction becomes a crucial driving force, which may imply that the membrane protein interior is tightly packed. Paradoxically, membrane proteins such as channels, transporters, receptors, and enzymes require cavities (i.e., voids, pockets, and pores) for function. Then, how do membrane proteins achieve the stability carrying out function? Using experiment and molecular dynamics simulation, we show that cavities in membrane proteins can be stabilized by favorable interaction with surrounding lipid molecules and play a pivotal role in balancing stability and flexibility for function.
DA - 2020/9/8/
PY - 2020/9/8/
DO - 10.1073/pnas.1917770117
VL - 117
IS - 36
SP - 22146-22156
UR - https://doi.org/10.1073/pnas.1917770117
KW - membrane protein stability
KW - cavity
KW - packing
KW - GIpG
KW - steric trapping
ER -
TY - JOUR
TI - Persistent Cohomology for Data With Multicomponent Heterogeneous Information
AU - Cang, Zixuan
AU - Wei, Guo-Wei
T2 - SIAM Journal on Mathematics of Data Science
AB - Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and reveal certain interaction patterns in terms of topological invariants. However, in addition to the geometric information, there is a wide variety of nongeometric information of molecular structures, such as element types, atomic partial charges, atomic pairwise interactions, and electrostatic potential functions, that is not described by persistent homology. Although element-specific homology and electrostatic persistent homology can encode some nongeometric information into geometry based topological invariants, it is desirable to have a mathematical paradigm to systematically embed both geometric and nongeometric information, i.e., multicomponent heterogeneous information, into unified topological representations. To this end, we propose a persistent cohomology based framework for the enriched representation of data. In our framework, nongeometric information can either be distributed globally or reside locally on the datasets in the geometric sense and can be properly defined on topological spaces, i.e., simplicial complexes. Using the proposed persistent cohomology based framework, enriched barcodes are extracted from datasets to represent heterogeneous information. We consider a variety of datasets to validate the present formulation and illustrate the usefulness of the proposed method based on persistent cohomology. It is found that the proposed framework outperforms or at least matches the state-of-the-art methods in the protein-ligand binding affinity prediction from massive biomolecular datasets without resorting to any deep learning formulation.
DA - 2020/1//
PY - 2020/1//
DO - 10.1137/19M1272226
VL - 2
IS - 2
SP - 396-418
UR - https://doi.org/10.1137/19M1272226
KW - topological data analysis
KW - machine learning
KW - biophysics
KW - drug design
ER -
TY - JOUR
TI - Inferring spatial and signaling relationships between cells from single cell transcriptomic data
AU - Cang, Zixuan
AU - Nie, Qing
T2 - Nature Communications
AB - Abstract Single-cell RNA sequencing (scRNA-seq) provides details for individual cells; however, crucial spatial information is often lost. We present SpaOTsc, a method relying on structured optimal transport to recover spatial properties of scRNA-seq data by utilizing spatial measurements of a relatively small number of genes. A spatial metric for individual cells in scRNA-seq data is first established based on a map connecting it with the spatial measurements. The cell–cell communications are then obtained by “optimally transporting” signal senders to target signal receivers in space. Using partial information decomposition, we next compute the intercellular gene–gene information flow to estimate the spatial regulations between genes across cells. Four datasets are employed for cross-validation of spatial gene expression prediction and comparison to known cell–cell communications. SpaOTsc has broader applications, both in integrating non-spatial single-cell measurements with spatial data, and directly in spatial single-cell transcriptomics data to reconstruct spatial cellular dynamics in tissues.
DA - 2020/4/29/
PY - 2020/4/29/
DO - 10.1038/s41467-020-15968-5
UR - https://doi.org/10.1038/s41467-020-15968-5
ER -
TY - JOUR
TI - A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation
AU - Wang, Menglun
AU - Cang, Zixuan
AU - Wei, Guo-Wei
T2 - Nature Machine Intelligence
AB - The ability to predict protein‚Äìprotein interactions is crucial to our understanding of a wide range of biological activities and functions in the human body, and for guiding drug discovery. Despite considerable efforts to develop suitable computational methods, predicting protein‚Äìprotein interaction binding affinity changes following mutation (ŒîŒîG) remains a severe challenge. Algebraic topology, a champion in recent worldwide competitions for protein‚Äìligand binding affinity predictions, is a promising approach to simplifying the complexity of biological structures. Here we introduce element- and site-specific persistent homology (a new branch of algebraic topology) to simplify the structural complexity of protein‚Äìprotein complexes and embed crucial biological information into topological invariants. We also propose a new deep learning algorithm called NetTree to take advantage of convolutional neural networks and gradient-boosting trees. A topology-based network tree is constructed by integrating the topological representation and NetTree for predicting protein‚Äìprotein interaction ŒîŒîG. Tests on major benchmark datasets indicate that the proposed topology-based network tree is an important improvement over the current state of the art in predicting ŒîŒîG. Persistent homology provides an efficient approach to simplifying the complexity of protein structure. Wang et al. combine this approach with convolutional neural networks and gradient-boosting trees to improve predictions of protein‚Äìprotein interactions.
DA - 2020/2/14/
PY - 2020/2/14/
DO - 10.1038/s42256-020-0149-6
UR - https://doi.org/10.1038/s42256-020-0149-6
ER -
TY - JOUR
TI - A review of mathematical representations of biomolecular data
AU - Nguyen, Duc Duy
AU - Cang, Zixuan
AU - Wei, Guo-Wei
T2 - Physical Chemistry Chemical Physics
AB - Recently, machine learning (ML) has established itself in various worldwide benchmarking competitions in computational biology, including Critical Assessment of Structure Prediction (CASP) and Drug Design Data Resource (D3R) Grand Challenges. However, the intricate structural complexity and high ML dimensionality of biomolecular datasets obstruct the efficient application of ML algorithms in the field. In addition to data and algorithm, an efficient ML machinery for biomolecular predictions must include structural representation as an indispensable component. Mathematical representations that simplify the biomolecular structural complexity and reduce ML dimensionality have emerged as a prime winner in D3R Grand Challenges. This review is devoted to the recent advances in developing low-dimensional and scalable mathematical representations of biomolecules in our laboratory. We discuss three classes of mathematical approaches, including algebraic topology, differential geometry, and graph theory. We elucidate how the physical and biological challenges have guided the evolution and development of these mathematical apparatuses for massive and diverse biomolecular data. We focus the performance analysis on protein-ligand binding predictions in this review although these methods have had tremendous success in many other applications, such as protein classification, virtual screening, and the predictions of solubility, solvation free energies, toxicity, partition coefficients, protein folding stability changes upon mutation, etc.
DA - 2020///
PY - 2020///
DO - 10.1039/C9CP06554G
UR - https://doi.org/10.1039/C9CP06554G
ER -
TY - JOUR
TI - Multi-Linear Population Analysis (MLPA) of LFP Data Using Tensor Decompositions
AU - Geddes, Justen
AU - Einevol, Gaute T.
AU - Acar, Evrim
AU - Stasik, Alexander J.
T2 - FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS
AB - The local field potential (LFP) is the low frequency part of the extracellular electrical potential in the brain and reflects synaptic activity onto thousands of neurons around each recording contact. Nowadays, LFPs can be measured at several hundred locations simultaneously. The measured LFP is in general a superposition of contributions from many underlying neural populations which makes interpretation of LFP measurements in terms of the underlying neural activity challenging. Classical statistical analyses of LFPs rely on matrix decomposition-based methods such as PCA (Principal Component Analysis) and ICA (Independent Component Analysis), which require additional constraints on spatial and/or temporal patterns of populations. In this work, we instead explore the multi-fold data structure of LFP recordings, e.g., multiple trials, multi-channel time series, arrange the signals as a higher-order tensor (i.e., multiway array), and study how a specific tensor decomposition approach, namely canonical polyadic (CP) decomposition, can be used to reveal the underlying neural populations. Essential for interpretation, the CP model provides uniqueness without imposing constraints on patterns of underlying populations. Here, we first define a neural network model and based on its dynamics, compute LFPs. We run multiple trials with this network, and LFPs are then analysed simultaneously using the CP model. More specifically, we design \Note{feed-forward population rate neuron models} to match the structure of state-of-the-art, large-scale LFP simulations, but downscale them to allow easy inspection and interpretation. We demonstrate that our feed-forward model matches the mathematical structure assumed in the CP model, and CP successfully reveals temporal and spatial patterns as well as variations over trials of underlying populations when compared with the ground truth from the model. We also discuss the use of diagnostic approaches for CP to guide the analysis when there is no ground truth information. In comparison with classical methods, we discuss the advantages of using tensor decompositions for analyzing LFP recordings as well as their limitations.
DA - 2020/9/8/
PY - 2020/9/8/
DO - 10.3389/fams.2020.00041
VL - 6
SP -
SN - 2297-4687
KW - tensor decompositions
KW - neuroscience
KW - local field potential (LFP)
KW - population rate model
KW - CANDECOMP
KW - PARAFAC
KW - independent component analysis (ICA)
KW - principal component analysis (PCA)
ER -
TY - JOUR
TI - A Note on Sparse Polynomial Interpolation in Dickson Polynomial Basis
AU - Imamoglu, Erdal
AU - Kaltofen, Erich L.
T2 - ACM COMMUNICATIONS IN COMPUTER ALGEBRA
AB - research-article A note on sparse polynomial interpolation in Dickson polynomial basis Share on Authors: Erdal Imamoglu Kirklareli University, Kirklareli, Turkey Kirklareli University, Kirklareli, TurkeyView Profile , Erich L. Kaltofen North Carolina State University, Raleigh, North Carolina and Duke University, Durham, North Carolina North Carolina State University, Raleigh, North Carolina and Duke University, Durham, North CarolinaView Profile Authors Info & Claims ACM Communications in Computer AlgebraVolume 54Issue 4December 2020 pp 125–128https://doi.org/10.1145/3465002.3465003Online:10 May 2021Publication History 0citation29DownloadsMetricsTotal Citations0Total Downloads29Last 12 Months29Last 6 weeks3 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access
DA - 2020/12//
PY - 2020/12//
DO - 10.1145/3465002.3465003
VL - 54
IS - 4
SP - 125-128
SN - 1932-2240
ER -
TY - JOUR
TI - Operator splitting based central-upwind schemes for shallow water equations with moving bottom topography
AU - Chertock, Alina
AU - Kurganov, Alexander
AU - Wu, Tong
T2 - Communications in Mathematical Sciences
DA - 2020///
PY - 2020///
DO - 10.4310/cms.2020.v18.n8.a3
VL - 18
IS - 8
SP - 2149-2168
ER -
TY - CONF
TI - On Khovanov Homology and Related Invariants
AU - Caprau, C.
AU - Gonzalez, N.
AU - Lee, Christine Ruey Shan
AU - Lowrance, A.
AU - Sazdanovic, R.
AU - Zhang, M.
C2 - 2020/2/12/
C3 - Proceedings of the Research Collaboration Conference of the Women in Symplectic and Contact Geometry and Topology
DA - 2020/2/12/
PB - Springer
ER -
TY - JOUR
TI - Smooth Points on Semi-algebraic Sets
AU - Harris, Katherine
AU - Hauenstein, Jonathan D.
AU - Szanto, Agnes
T2 - ACM COMMUNICATIONS IN COMPUTER ALGEBRA
AB - Many algorithms for determining properties of semi-algebraic sets rely upon the ability to compute smooth points [1]. We present a simple procedure based on computing the critical points of some well-chosen function that guarantees the computation of smooth points in each connected bounded component of a real atomic semi-algebraic set. Our technique is intuitive in principal, performs well on previously difficult examples, and is straightforward to implement using existing numerical algebraic geometry software. The practical efficiency of our approach is demonstrated by solving a conjecture on the number of equilibria of the Kuramoto model for the n = 4 case. We also apply our method to design an efficient algorithm to compute the real dimension of algebraic sets, the original motivation for this research.
DA - 2020/9//
PY - 2020/9//
DO - 10.1145/3457341.3457347
VL - 54
IS - 3
SP - 105-108
SN - 1932-2240
ER -
TY - RPRT
TI - Extremal Khovanov homology and the girth of a knot
AU - Sazdanovic, R.
AU - Scofield, D.
DA - 2020/3/11/
PY - 2020/3/11/
M1 - 2003.05074
M3 - arXiv
SN - 2003.05074
ER -
TY - RPRT
TI - Bilinear pairings on two-dimensional cobordisms and generalizations of the Deligne category
AU - Khovanov, M.
AU - Sazdanovic, R.
DA - 2020/7/24/
PY - 2020/7/24/
M1 - 2007.11640
M3 - arXiv
SN - 2007.11640
ER -
TY - JOUR
TI - A numerical integration-based Kalman filter for moderately nonlinear systems
AU - King, Sarah A.
AU - Ito, Kazufumi
AU - Hodyss, Daniel
T2 - TELLUS SERIES A-DYNAMIC METEOROLOGY AND OCEANOGRAPHY
AB - This paper introduces a computationally efficient data assimilation scheme based on Gaussian quadrature filtering that potentially outperforms current methods in data assimilation for moderately nonlinear systems. Moderately nonlinear systems, in this case, are systems with numerical models with small fourth and higher derivative terms. Gaussian quadrature filters are a family of filters that make simplifying Gaussian assumptions about filtering pdfs in order to numerically evaluate the integrals found in Bayesian data assimilation. These filters are differentiated by the varying quadrature rules to evaluate the arising integrals. The approach we present, denoted by Assumed Gaussian Reduced (AGR) filter, uses a reduced order version of the polynomial quadrature first proposed in Ito and Xiong [2000. Gaussian filters for nonlinear filtering problems. IEEE Trans. Automat. Control. 45, 910–927]. This quadrature uses the properties of Gaussian distributions to form an effectively higher order method increasing its efficiency. To construct the AGR filter, this quadrature is used to form a reduced order square-root filter, which will reduce computational costs and improve numerical robustness. For cases of sufficiently small fourth derivatives of the nonlinear model, we demonstrate that the AGR filter outperforms ensemble Kalman filters (EnKFs) for a Korteweg-de Vries model and a Boussinesq model.
DA - 2020/1/1/
PY - 2020/1/1/
DO - 10.1080/16000870.2020.1712938
VL - 72
IS - 1
SP -
SN - 1600-0870
KW - data assimilation
KW - Bayesian filtering
KW - Kalman filtering
KW - numerical integration
ER -
TY - JOUR
TI - Supply chain coordination under financial constraints and yield uncertainty
AU - Peng, Hongjun
AU - Pang, Tao
T2 - EUROPEAN JOURNAL OF INDUSTRIAL ENGINEERING
AB - A coordination problem for a supply chain with capital constraints and yield uncertainty is considered in this paper. In order to improve the supply chain, a buyback and risk sharing (BBRS) mechanism is proposed, in which the distributor shares the supplier's yield uncertainty risk by purchasing the overproduced products or waiving the shortage penalty, and the supplier shares the distributor's demand uncertainty risk by buying back the unsold products. The results indicate that, the profits and the strategies under the BBRS are the same with those under the centralised case. In addition, the proposed BBRS mechanism has a built-in mechanism to allocate the spillover profit between the supplier and the distributor. The results also show that the BBRS can increase the production quantity. Finally, we derive the bankruptcy probabilities for both the supplier and the distributor, and the probabilities depend on their initial capitals. [Received 4 August 2018; Accepted 18 January 2020]
DA - 2020///
PY - 2020///
DO - 10.1504/EJIE.2020.112493
VL - 14
IS - 6
SP - 782-812
SN - 1751-5262
KW - supply chain finance
KW - capital constraint
KW - yield uncertainty
KW - buyback
KW - risk sharing
ER -
TY - JOUR
TI - Efficacy and Spatial Extent of Yard-Scale Control of Aedes (Stegomyia) albopictus (Diptera: Culicidae) Using Barrier Sprays and Larval Habitat Management
AU - Hollingsworth, B.
AU - Hawkins, P.
AU - Lloyd, A. L.
AU - Reiskind, M. H.
T2 - J. Med. Entomol.
DA - 2020/2/13/
PY - 2020/2/13/
VL - 57
SP - 1104–-1110
ER -
TY - JOUR
TI - Gene Drive Dynamics in Natural Populations: The Importance of Density Dependence, Space, and Sex
AU - Dhole, Sumit
AU - Lloyd, Alun L.
AU - Gould, Fred
T2 - ANNUAL REVIEW OF ECOLOGY, EVOLUTION, AND SYSTEMATICS, VOL 51, 2020
AB - The spread of synthetic gene drives is often discussed in the context of panmictic populations connected by gene flow and described with simple deterministic models. Under such assumptions, an entire species could be altered by releasing a single individual carrying an invasive gene drive, such as a standard homing drive. While this remains a theoretical possibility, gene drive spread in natural populations is more complex and merits a more realistic assessment. The fate of any gene drive released in a population would be inextricably linked to the population's ecology. Given the uncertainty often involved in ecological assessment of natural populations, understanding the sensitivity of gene drive spread to important ecological factors is critical. Here we review how different forms of density dependence, spatial heterogeneity, and mating behaviors can impact the spread of self-sustaining gene drives. We highlight specific aspects of gene drive dynamics and the target populations that need further research.
DA - 2020///
PY - 2020///
DO - 10.1146/annurev-ecolsys-031120-101013
VL - 51
IS - 1
SP - 505-531
SN - 1545-2069
KW - genetic pest management
KW - underdominance
KW - CRISPR
KW - spatial dynamics
KW - density dependence
KW - population alteration
ER -
TY - CHAP
TI - Prediction in Cancer Genomics Using Topological Signatures and Machine Learning
AU - Gonzalez, Georgina
AU - Ushakova, Arina
AU - Sazdanovic, Radmila
AU - Arsuaga, Javier
T2 - Topological Data Analysis
AB - Copy Number Aberrations, gains and losses of genomic regions, are a hallmark of cancer and can be experimentally detected using microarray comparative genomic hybridization (aCGH). In previous works, we developed a topology based method to analyze aCGH data whose output are regions of the genome where copy number is altered in patients with a predetermined cancer phenotype. We call this method Topological Analysis of array CGH (TAaCGH). Here we combine TAaCGH with machine learning techniques to build classifiers using copy number aberrations. We chose logistic regression on two different binary phenotypes related to breast cancer to illustrate this approach. The first case consists of patients with over-expression of the ERBB2 gene. Over-expression of ERBB2 is commonly regulated by a copy number gain in chromosome arm 17q. TAaCGH found the region 17q11-q22 associated with the phenotype and using logistic regression we reduced this region to 17q12-q21.31 correctly classifying 78% of the ERBB2 positive individuals (sensitivity) in a validation data set. We also analyzed over-expression in Estrogen Receptor (ER), a second phenotype commonly observed in breast cancer patients and found that the region 5p14.3-12 together with six full arms were associated with the phenotype. Our method identified 4p, 6p and 16q as the strongest predictors correctly classifying 76% of ER positives in our validation data set. However, for this set there was a significant increase in the false positive rate (specificity). We suggest that topological and machine learning methods can be combined for prediction of phenotypes using genetic data.
PY - 2020///
DO - 10.1007/978-3-030-43408-3_10
SP - 247-276
OP -
PB - Springer International Publishing
SN - 9783030434076 9783030434083
UR - http://dx.doi.org/10.1007/978-3-030-43408-3_10
DB - Crossref
ER -
TY - JOUR
TI - On homotopy types of Vietoris–Rips complexes of metric gluings
AU - Adamaszek, Michał
AU - Adams, Henry
AU - Gasparovic, Ellen
AU - Gommel, Maria
AU - Purvine, Emilie
AU - Sazdanovic, Radmila
AU - Wang, Bei
AU - Wang, Yusu
AU - Ziegelmeier, Lori
T2 - Journal of Applied and Computational Topology
AB - Given a sample of points $X$ in a metric space $M$ and a scale $r>0$, the Vietoris-Rips simplicial complex $\mathrm{VR}(X;r)$ is a standard construction to attempt to recover $M$ from $X$ up to homotopy type. A deficiency of this approach is that $\mathrm{VR}(X;r)$ is not metrizable if it is not locally finite, and thus does not recover metric information about $M$. We attempt to remedy this shortcoming by defining a metric space thickening of $X$, which we call the \emph{Vietoris-Rips thickening} $\mathrm{VR}^m(X;r)$, via the theory of optimal transport. When $M$ is a complete Riemannian manifold, or alternatively a compact Hadamard space, we show that the the Vietoris-Rips thickening satisfies Hausmann's theorem ($\mathrm{VR}^m(M;r)\simeq M$ for $r$ sufficiently small) with a simpler proof: homotopy equivalence $\mathrm{VR}^m(M;r)\to M$ is canonically defined as a center of mass map, and its homotopy inverse is the (now continuous) inclusion map $M\hookrightarrow\mathrm{VR}^m(M;r)$. Furthermore, we describe the homotopy type of the Vietoris-Rips thickening of the $n$-sphere at the first positive scale parameter $r$ where the homotopy type changes.
DA - 2020/5/20/
PY - 2020/5/20/
DO - 10.1007/s41468-020-00054-y
VL - 4
IS - 3
SP - 425-454
J2 - J Appl. and Comput. Topology
LA - en
OP -
SN - 2367-1726 2367-1734
UR - http://dx.doi.org/10.1007/s41468-020-00054-y
DB - Crossref
ER -
TY - JOUR
TI - Bregman Forward-Backward Operator Splitting
AU - Bui, Minh N.
AU - Combettes, Patrick L.
T2 - SET-VALUED AND VARIATIONAL ANALYSIS
AB - We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far been proved only in the case of minimization problems. The proposed framework features Bregman distances that vary over the iterations and a novel assumption on the single-valued operator that captures various properties scattered in the literature. In the minimization setting, we obtain rates that are sharper than existing ones.
DA - 2020///
PY - 2020///
DO - 10.1007/s11228-020-00563-z
KW - Banach space
KW - Bregman distance
KW - Forward-backward splitting
KW - Legendre function
KW - Monotone operator
ER -
TY - JOUR
TI - Representations of Quantum Affine Algebras in their R-Matrix Realization
AU - Jing, Naihuan
AU - Liu, Ming
AU - Molev, Alexander
T2 - SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
AB - We use the isomorphisms between the $R$-matrix and Drinfeld presentations of the quantum affine algebras in types $B$, $C$ and $D$ produced in our previous work to describe finite-dimensional irreducible representations in the $R$-matrix realization. We also review the isomorphisms for the Yangians of these types and use Gauss decomposition to establish an equivalence of the descriptions of the representations in the $R$-matrix and Drinfeld presentations of the Yangians.
DA - 2020///
PY - 2020///
DO - 10.3842/SIGMA.2020.145
VL - 16
SP -
SN - 1815-0659
KW - R-matrix presentation
KW - Drinfeld polynomials
KW - highest weight representation
KW - Gauss decomposition
ER -
TY - JOUR
TI - Scattering Fans
AU - Reading, Nathan
T2 - INTERNATIONAL MATHEMATICS RESEARCH NOTICES
AB - Abstract Scattering diagrams arose in the context of mirror symmetry, Donaldson–Thomas theory, and integrable systems. We show that a consistent scattering diagram with minimal support cuts the ambient space into a complete fan. A special class of scattering diagrams, the cluster scattering diagrams, is closely related to cluster algebras. We show that the cluster scattering fan associated to an exchange matrix $B$ refines the mutation fan for $B$ (a complete fan that encodes the geometry of mutations of $B$). We conjecture that, when $B$ is $n\times n$ for $n>2$, these two fans coincide if and only if $B$ is of finite mutation type.
DA - 2020/11//
PY - 2020/11//
DO - 10.1093/imrn/rny260
VL - 2020
IS - 23
SP - 9640-9673
SN - 1687-0247
ER -
TY - JOUR
TI - Biologically-informed neural networks guide mechanistic modeling from sparse experimental data
AU - Lagergren, John H.
AU - Nardini, John T.
AU - Baker, Ruth E.
AU - Simpson, Matthew J.
AU - Flores, Kevin B.
T2 - PLOS COMPUTATIONAL BIOLOGY
AB - Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks [1], are introduced and used to discover the underlying dynamics of biological systems from sparse experimental data. In the present work, BINNs are trained in a supervised learning framework to approximate in vitro cell biology assay experiments while respecting a generalized form of the governing reaction-diffusion partial differential equation (PDE). By allowing the diffusion and reaction terms to be multilayer perceptrons (MLPs), the nonlinear forms of these terms can be learned while simultaneously converging to the solution of the governing PDE. Further, the trained MLPs are used to guide the selection of biologically interpretable mechanistic forms of the PDE terms which provides new insights into the biological and physical mechanisms that govern the dynamics of the observed system. The method is evaluated on sparse real-world data from wound healing assays with varying initial cell densities [2].
DA - 2020/12//
PY - 2020/12//
DO - 10.1371/journal.pcbi.1008462
VL - 16
IS - 12
SP -
SN - 1553-7358
ER -
TY - JOUR
TI - Chiral Versus Classical Operad
AU - Bakalov, Bojko
AU - De Sole, Alberto
AU - Heluani, Reimundo
AU - Kac, Victor G.
T2 - INTERNATIONAL MATHEMATICS RESEARCH NOTICES
AB - We establish an explicit isomorphism between the associated graded of the filtered chiral operad and the classical operad, which is useful for computing the cohomology of vertex algebras.
DA - 2020/10//
PY - 2020/10//
DO - 10.1093/imrn/rnz373
VL - 2020
IS - 19
SP - 6463-6488
SN - 1687-0247
ER -
TY - JOUR
TI - Complete Genome Sequences of Six Lactobacilli Isolated from American Quarter Horses
AU - Meinders, Rachael I.
AU - Mendoza, Mary
AU - Dickey, Allison N.
AU - Scholl, Elizabeth H.
AU - Hassan, Hosni M.
T2 - MICROBIOLOGY RESOURCE ANNOUNCEMENTS
AB - We report the complete circular genome sequences of six Lactobacillus strains and their plasmids, if any, from the fecal material of quarter horses at different ages.
DA - 2020/11//
PY - 2020/11//
DO - 10.1128/MRA.00997-20
VL - 9
IS - 47
SP -
SN - 2576-098X
ER -
TY - JOUR
TI - SBV regularity for Burgers-Poisson equation
DA - 2020/12/15/
PY - 2020/12/15/
ER -
TY - JOUR
TI - Metric entropy for Hamilton-Jacobi equation with uniformly directionally convex Hamiltonian
DA - 2020/12/19/
PY - 2020/12/19/
ER -
TY - JOUR
TI - Weak Convergence of a Collection of Random Functions Defined by the Eigenvectors of Large Dimensional Random Matrices
DA - 2020/12/23/
PY - 2020/12/23/
ER -
TY - JOUR
TI - Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation
AU - Paun, L. Mihaela
AU - Colebank, Mitchel J.
AU - Olufsen, Mette S.
AU - Hill, Nicholas A.
AU - Husmeier, Dirk
T2 - Journal of The Royal Society Interface
AB - This study uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. We emphasize an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called ‘model mismatch’). We demonstrate that minimizing the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method allowing for model mismatch, which we represent with Gaussian processes, corrects the bias. Additionally, we compare a linear and a nonlinear wall model, as well as models with different vessel stiffness relations. We use formal model selection analysis based on the Watanabe Akaike information criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the nonlinear pressure–area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse.
DA - 2020/12//
PY - 2020/12//
DO - 10.1098/rsif.2020.0886
VL - 17
IS - 173
SP - 20200886
UR - https://doi.org/10.1098/rsif.2020.0886
KW - uncertainty quantification
KW - model mismatch
KW - model selection
KW - MCMC
KW - Gaussian processes
KW - pulmonary circulation
ER -
TY - JOUR
TI - DRINFELD-TYPE PRESENTATIONS OF LOOP ALGEBRAS
AU - Chen, Fulin
AU - Jing, Naihuan
AU - Kong, Fei
AU - Tan, Shaobin
T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
AB - Let g \mathfrak {g} be the derived subalgebra of a Kac-Moody Lie algebra of finite-type or affine-type, let μ \mu be a diagram automorphism of g \mathfrak {g} , and let L ( g , μ ) \mathcal {L}(\mathfrak {g},\mu ) be the loop algebra of g \mathfrak {g} associated to μ \mu . In this paper, by using the vertex algebra technique, we provide a general construction of current-type presentations for the universal central extension g ^ [ μ ] \widehat {\mathfrak {g}}[\mu ] of L ( g , μ ) \mathcal {L}(\mathfrak {g},\mu ) . The construction contains the classical limit of Drinfeld’s new realization for (twisted and untwisted) quantum affine algebras [Soviet Math. Dokl. 36 (1988), pp. 212–216] and the Moody-Rao-Yokonuma presentation for toroidal Lie algebras [Geom. Dedicata 35 (1990), pp. 283–307] as special examples. As an application, when g \mathfrak {g} is of simply-laced-type, we prove that the classical limit of the μ \mu -twisted quantum affinization of the quantum Kac-Moody algebra associated to g \mathfrak {g} introduced in [J. Math. Phys. 59 (2018), 081701] is the universal enveloping algebra of g ^ [ μ ] \widehat {\mathfrak {g}}[\mu ] .
DA - 2020/11//
PY - 2020/11//
DO - 10.1090/tran/8120
VL - 373
IS - 11
SP - 7713-7753
SN - 1088-6850
KW - Drinfeld-type presentation
KW - loop algebra
KW - universal central extension
KW - extended affine Lie algebra
KW - twisted quantum affinization
KW - Gamma-vertex algebra
ER -
TY - JOUR
TI - Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations
AU - Sunseri, Isaac
AU - Hart, Joseph
AU - Bloemen Waanders, Bart
AU - Alexanderian, Alen
T2 - INVERSE PROBLEMS
AB - High fidelity models used in many science and engineering applications couple multiple physical states and parameters. Inverse problems arise when a model parameter cannot be determined directly, but rather is estimated using (typically sparse and noisy) measurements of the states. The data is usually not sufficient to simultaneously inform all of the parameters. Consequently, the governing model typically contains parameters which are uncertain but must be specified for a complete model characterization necessary to invert for the parameters of interest. We refer to the combination of the additional model parameters (those which are not inverted for) and the measured data states as the "complementary parameters". We seek to quantify the relative importance of these complementary parameters to the solution of the inverse problem. To address this, we present a framework based on hyper-differential sensitivity analysis (HDSA). HDSA computes the derivative of the solution of an inverse problem with respect to complementary parameters. We present a mathematical framework for HDSA in large-scale PDE-constrained inverse problems and show how HDSA can be interpreted to give insight about the inverse problem. We demonstrate the effectiveness of the method on an inverse problem by estimating a permeability field, using pressure and concentration measurements, in a porous medium flow application with uncertainty in the boundary conditions, source injection, and diffusion coefficient.
DA - 2020/12//
PY - 2020/12//
DO - 10.1088/1361-6420/abaf63
VL - 36
IS - 12
SP -
SN - 1361-6420
KW - inverse problems
KW - sensitivity analysis
KW - design of experiments
KW - subsurface flow
KW - model uncertainty
ER -
TY - JOUR
TI - Bases for Second Order Linear ODEs
AU - McGrath, Peter
T2 - AMERICAN MATHEMATICAL MONTHLY
AB - The usual analysis of the constant coefficient ODE ay″+by′+cy=0 —which concludes that ert is a solution when r=(−b±b2−4ac)/(2a) —fails to produce a basis for the solution space when b2−4ac=0 . Redu...
DA - 2020/10/20/
PY - 2020/10/20/
DO - 10.1080/00029890.2020.1803626
VL - 127
IS - 9
SP - 849-849
SN - 1930-0972
KW - MSC
ER -
TY - JOUR
TI - Clonal Analysis of Gliogenesis in the Cerebral Cortex Reveals Stochastic Expansion of Glia and Cell Autonomous Responses to Egfr Dosage
AU - Zhang, Xuying
AU - Mennicke, Christine V.
AU - Xiao, Guanxi
AU - Beattie, Robert
AU - Haider, Mansoor A
AU - Hippenmeyer, Simon
AU - Ghashghaei, Troy
T2 - Cells
AB - Development of the nervous system undergoes important transitions, including one from neurogenesis to gliogenesis which occurs late during embryonic gestation. Here we report on clonal analysis of gliogenesis in mice using Mosaic Analysis with Double Markers (MADM) with quantitative and computational methods. Results reveal that developmental gliogenesis in the cerebral cortex occurs in a fraction of earlier neurogenic clones, accelerating around E16.5, and giving rise to both astrocytes and oligodendrocytes. Moreover, MADM-based genetic deletion of the epidermal growth factor receptor (Egfr) in gliogenic clones revealed that Egfr is cell autonomously required for gliogenesis in the mouse dorsolateral cortices. A broad range in the proliferation capacity, symmetry of clones, and competitive advantage of MADM cells was evident in clones that contained one cellular lineage with double dosage of Egfr relative to their environment, while their sibling Egfr-null cells failed to generate glia. Remarkably, the total numbers of glia in MADM clones balance out regardless of significant alterations in clonal symmetries. The variability in glial clones shows stochastic patterns that we define mathematically, which are different from the deterministic patterns in neuronal clones. This study sets a foundation for studying the biological significance of stochastic and deterministic clonal principles underlying tissue development, and identifying mechanisms that differentiate between neurogenesis and gliogenesis.
DA - 2020/12//
PY - 2020/12//
DO - 10.3390/cells9122662
VL - 9
IS - 12
SP - 2662
UR - https://www.mdpi.com/2073-4409/9/12/2662
KW - cerebral cortex
KW - clonal analysis
KW - neurogenesis
KW - gliogenesis
KW - Egfr
KW - astrocyte
KW - oligodendrocyte MADM
KW - stochastic
KW - deterministic
ER -
TY - JOUR
TI - The future-climate, current-policy framework: towards an approach linking climate science to sector policy development
AU - Evans, Barbara E.
AU - Rowell, David P.
AU - Semazzi, Frederick H. M.
T2 - ENVIRONMENTAL RESEARCH LETTERS
AB - Abstract That global climate is being altered by human activities is well-established; for specific locations, however, the details of how and when many aspects of the changes will become manifest remains somewhat uncertain. For many policy makers there is a gap between recognising a long-term change and implementing short-term practical responses; therefore many countries are failing to implement changes needed for long-term adaptation. Traditional planning approaches are often closely aligned with near- term political cycles and perform poorly in terms of prioritising interventions that address multi-decadal climate impacts. We propose a novel approach that builds on adaptive planning and lessons from the business sector. The Future-Climate, Current-Policy (FCCP) Framework is based on plausible medium-term future climate scenarios, linked ‘backwards’ to identify short-term ‘no regrets’ actions. The approach was designed by a team of climate scientists and policy practitioners in East Africa and tested in national and regional fora. Initial trials of the FCCP Framework has proved it to be popular and effective as a way of linking climate science with policy. Its use shows promise as a way of initiating discussions that can enable long-term climate change information to feed effectively into the policy and planning process.
DA - 2020/11//
PY - 2020/11//
DO - 10.1088/1748-9326/abbeb9
VL - 15
IS - 11
SP -
SN - 1748-9326
KW - climate change
KW - policy
KW - east Africa
KW - planning
KW - sanitation
KW - agriculture
KW - water
ER -
TY - JOUR
TI - Disease control across urban–rural gradients
AU - Wells, Konstans
AU - Lurgi, Miguel
AU - Collins, Brendan
AU - Lucini, Biagio
AU - Kao, Rowland R.
AU - Lloyd, Alun L.
AU - Frost, Simon D. W.
AU - Gravenor, Mike B.
T2 - Journal of The Royal Society Interface
AB - Controlling the regional re-emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) after its initial spread in ever-changing personal contact networks and disease landscapes is a challenging task. In a landscape context, contact opportunities within and between populations are changing rapidly as lockdown measures are relaxed and a number of social activities re-activated. Using an individual-based metapopulation model, we explored the efficacy of different control strategies across an urban–rural gradient in Wales, UK. Our model shows that isolation of symptomatic cases or regional lockdowns in response to local outbreaks have limited efficacy unless the overall transmission rate is kept persistently low. Additional isolation of non-symptomatic infected individuals, who may be detected by effective test-and-trace strategies, is pivotal to reducing the overall epidemic size over a wider range of transmission scenarios. We define an ‘urban–rural gradient in epidemic size' as a correlation between regional epidemic size and connectivity within the region, with more highly connected urban populations experiencing relatively larger outbreaks. For interventions focused on regional lockdowns, the strength of such gradients in epidemic size increased with higher travel frequencies, indicating a reduced efficacy of the control measure in the urban regions under these conditions. When both non-symptomatic and symptomatic individuals are isolated or regional lockdown strategies are enforced, we further found the strongest urban–rural epidemic gradients at high transmission rates. This effect was reversed for strategies targeted at symptomatic individuals only. Our results emphasize the importance of test-and-trace strategies and maintaining low transmission rates for efficiently controlling SARS-CoV-2 spread, both at landscape scale and in urban areas.
DA - 2020/12//
PY - 2020/12//
DO - 10.1098/rsif.2020.0775
VL - 17
IS - 173
SP - 20200775
UR - https://doi.org/10.1098/rsif.2020.0775
KW - disease spread
KW - epidemiological metapopulation dynamics
KW - pandemic control
KW - source-sink dynamics
ER -
TY - JOUR
TI - A Distributed Active Subspace Method for Scalable Surrogate Modeling of Function Valued Outputs
AU - Guy, Hayley
AU - Alexanderian, Alen
AU - Yu, Meilin
T2 - JOURNAL OF SCIENTIFIC COMPUTING
AB - We present a distributed active subspace method for training surrogate models of complex physical processes with high-dimensional inputs and function valued outputs. Specifically, we represent the model output with a truncated Karhunen–Loève (KL) expansion, screen the structure of the input space with respect to each KL mode via the active subspace method, and finally form an overall surrogate model of the output by combining surrogates of individual output KL modes. To ensure scalable computation of the gradients of the output KL modes, needed in active subspace discovery, we rely on adjoint-based gradient computation. The proposed method combines benefits of active subspace methods for input dimension reduction and KL expansions used for spectral representation of the output field. We provide a mathematical framework for the proposed method and conduct an error analysis of the mixed KL active subspace approach. Specifically, we provide an error estimate that quantifies errors due to active subspace projection and truncated KL expansion of the output. We demonstrate the numerical performance of the surrogate modeling approach with an application example from biotransport.
DA - 2020/10/24/
PY - 2020/10/24/
DO - 10.1007/s10915-020-01346-2
VL - 85
IS - 2
SP -
SN - 1573-7691
KW - Distributed active subspace
KW - Karhunen–
KW - Loè
KW - ve expansion
KW - Dimension reduction
KW - Function valued outputs
KW - Porous medium flow
KW - Biotransport
ER -
TY - JOUR
TI - Characterization of Blood Pressure and Heart Rate Oscillations of POTS Patients via Uniform Phase Empirical Mode Decomposition
AU - Geddes, Justen
AU - Mehlsen, Jesper
AU - Olufsen, Mette S.
T2 - IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING
AB - Objective: Postural Orthostatic Tachycardia Syndrome (POTS) is associated with the onset of tachycardia upon postural change. The current diagnosis involves the measurement of heart rate (HR) and blood pressure (BP) during head-up tilt (HUT) or active standing test. A positive diagnosis is made if HR changes with more than 30 bpm (40 bpm in patients aged 12-19 years), ignoring all of the BP and most of the HR signals. This study examines 0.1 Hz oscillations in systolic arterial blood pressure (SBP) and HR signals providing additional metrics characterizing the dynamics of the baroreflex. Methods: We analyze data from 28 control subjects and 28 POTS patients who underwent HUT. We extract beat-to-beat HR and SBP during a 10 min interval including 5 minutes of baseline and 5 minutes of HUT. We employ Uniform Phase Empirical Mode Decomposition (UPEMD) to extract 0.1 Hz stationary modes from both signals and use random forest machine learning and k-means clustering to analyze the outcomes. Results show that the amplitude of the 0.1 Hz oscillations is higher in POTS patients and that the phase response between the two signals is shorter (p <; 0.005). Conclusion: POTS is associated with an increase in the amplitude of SBP and HR 0.1 Hz oscillation and shortening of the phase between the two signals. Significance: The 0.1 Hz phase response and oscillation amplitude metrics provide new markers that can improve POTS diagnostic augmenting the existing diagnosis protocol only analyzing the change in HR.
DA - 2020/11//
PY - 2020/11//
DO - 10.1109/TBME.2020.2974095
VL - 67
IS - 11
SP - 3016-3025
SN - 1558-2531
KW - Heart rate
KW - Oscillators
KW - Baroreflex
KW - Blood pressure
KW - Empirical mode decomposition
KW - Measurement
KW - Aging
KW - Empirical mode decomposition (EMD)
KW - head-up tilt (HUT)
KW - postural orthostatic tachycardia syndrome (POTS)
KW - uniform phase empirical mode decomposition (UPEMD)
KW - clustering
ER -
TY - JOUR
TI - Probabilistic Error Analysis for Inner Products
AU - Ipsen, Ilse C. F.
AU - Zhou, Hua
T2 - SIAM Journal on Matrix Analysis and Applications
AB - Probabilistic models are proposed for bounding the forward error in the numerically computed inner product (dot product, scalar product) between two real $n$-vectors. We derive probabilistic perturbation bounds as well as probabilistic roundoff error bounds for the sequential accumulation of the inner product. These bounds are nonasymptotic, explicit, with minimal assumptions, and with a clear relationship between failure probability and relative error. The roundoffs are represented as bounded, zero-mean random variables that are independent or have conditionally independent means. Our probabilistic bounds are based on Azuma's inequality and its associated martingale, which mirrors the sequential order of computations. The derivation of forward error bounds “from first principles” has the advantage of producing condition numbers that are customized for the probabilistic bounds. Numerical experiments confirm that our bounds are more informative, often by several orders of magnitude, than traditional deterministic bounds---even for small vector dimensions $n$ and very stringent success probabilities. In particular the probabilistic roundoff error bounds are functions of $\sqrt{n}$ rather than $n$, thus giving a quantitative confirmation of Wilkinson's intuition. The paper concludes with a critical assessment of the probabilistic approach.
DA - 2020/1//
PY - 2020/1//
DO - 10.1137/19M1270434
VL - 41
IS - 4
SP - 1726-1741
UR - https://doi.org/10.1137/19M1270434
KW - roundoff errors
KW - random variables
KW - concentration bounds
KW - martingale
KW - Azuma's inequality
ER -
TY - CONF
TI - Certified Hermite Matrices from Approximate Roots - Univariate Case
AU - Ayyildiz Akoglu, Tulay
AU - Szanto, Agnes
C2 - 2020///
C3 - Mathematical Aspects of Computer and Information Sciences
DA - 2020///
DO - 0.1007/978-3-030-43120-4_1
SP - 3-9
PB - Springer International Publishing
ER -
TY - JOUR
TI - Local Convergence of an AMP Variant to the LASSO Solution in Finite Dimensions
DA - 2020/7/18/
PY - 2020/7/18/
ER -
TY - JOUR
TI - Smooth Points on Semi-algebraic Sets
DA - 2020/2/11/
PY - 2020/2/11/
ER -
TY - CONF
TI - Punctual Hilbert scheme and certified approximate singularities
AU - Mantzaflaris, Angelos
AU - Mourrain, Bernard
AU - Szanto, Agnes
AB - In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root and we compute its multiplicity structure. More precisely, given a polynomial system f = (f1, ..., fN) ∈ C[x1, ..., xn]N, we present a Newton iteration on an extended deflated system that locally converges, under regularity conditions, to a small deformation of f such that this deformed system has an exact singular root. The iteration simultaneously converges to the coordinates of the singular root and the coefficients of the so-called inverse system that describes the multiplicity structure at the root. We use α-theory test to certify the quadratic convergence, and to give bounds on the size of the deformation and on the approximation error. The approach relies on an analysis of the punctual Hilbert scheme, for which we provide a new description. We show in particular that some of its strata can be rationally parametrized and exploit these parametrizations in the certification. We show in numerical experimentation how the approximate inverse system can be computed as a starting point of the Newton iterations and the fast numerical convergence to the singular root with its multiplicity structure, certified by our criteria.
C2 - 2020/7/20/
C3 - Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation
DA - 2020/7/20/
DO - 10.1145/3373207.3404024
PB - ACM
UR - http://dx.doi.org/10.1145/3373207.3404024
ER -
TY - CONF
TI - Certified Hermite Matrices from Approximate Roots - Univariate Case
AU - Akoglu, Tulay Ayyildiz
AU - Szanto, Agnes
AB - Let \(f_1, \ldots , f_m\) be univariate polynomials with rational coefficients and \(\mathcal {I}:=\langle f_1, \ldots , f_m\rangle \subset {\mathbb Q}[x]\) be the ideal they generate. Assume that we are given approximations \(\{z_1, \ldots , z_k\}\subset \mathbb {Q}[i]\) for the common roots \(\{\xi _1, \ldots , \xi _k\}=V(\mathcal {I})\subseteq {\mathbb C}\). In this study, we describe a symbolic-numeric algorithm to construct a rational matrix, called Hermite matrix, from the approximate roots \(\{z_1, \ldots , z_k\}\) and certify that this matrix is the true Hermite matrix corresponding to the roots \(V({\mathcal I})\). Applications of Hermite matrices include counting and locating real roots of the polynomials and certifying their existence.
C2 - 2020///
C3 - Mathematical Aspects of Computer and Information Sciences
DA - 2020///
DO - 10.1007/978-3-030-43120-4_1
SP - 3-9
PB - Springer International Publishing
UR - http://dx.doi.org/10.1007/978-3-030-43120-4_1
ER -
TY - JOUR
TI - MULTISCALE ANALYSIS OF ACCELERATED GRADIENT METHODS
AU - Farazmand, Mohammad
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow. Using geometric singular perturbation theory, we show that, under certain conditions, the accelerated gradient flow possesses an attracting invariant slow manifold to which the trajectories of the flow converge asymptotically. We obtain a general explicit expression in the form of functional series expansions that approximates the slow manifold to any arbitrary order of accuracy. To the leading order, the accelerated gradient flow reduced to this slow manifold coincides with the usual gradient descent. We illustrate the implications of our results on three examples.
DA - 2020///
PY - 2020///
DO - 10.1137/18M1203997
VL - 30
IS - 3
SP - 2337-2354
SN - 1095-7189
UR - https://doi.org/10.1137/18M1203997
KW - convex optimization
KW - accelerated gradient methods
KW - invariant manifolds
KW - singular perturbation theory
ER -
TY - JOUR
TI - Deep learning-enabled analysis reveals distinct neuronal phenotypes induced by aging and cold-shock
AU - Saberi-Bosari, Sahand
AU - Flores, Kevin B.
AU - San-Miguel, Adriana
T2 - BMC BIOLOGY
AB - Abstract Background Access to quantitative information is crucial to obtain a deeper understanding of biological systems. In addition to being low-throughput, traditional image-based analysis is mostly limited to error-prone qualitative or semi-quantitative assessment of phenotypes, particularly for complex subcellular morphologies. The PVD neuron in Caenorhabditis elegans , which is responsible for harsh touch and thermosensation, undergoes structural degeneration as nematodes age characterized by the appearance of dendritic protrusions. Analysis of these neurodegenerative patterns is labor-intensive and limited to qualitative assessment. Results In this work, we apply deep learning to perform quantitative image-based analysis of complex neurodegeneration patterns exhibited by the PVD neuron in C. elegans . We apply a convolutional neural network algorithm (Mask R-CNN) to identify neurodegenerative subcellular protrusions that appear after cold-shock or as a result of aging. A multiparametric phenotypic profile captures the unique morphological changes induced by each perturbation. We identify that acute cold-shock-induced neurodegeneration is reversible and depends on rearing temperature and, importantly, that aging and cold-shock induce distinct neuronal beading patterns. Conclusion The results of this work indicate that implementing deep learning for challenging image segmentation of PVD neurodegeneration enables quantitatively tracking subtle morphological changes in an unbiased manner. This analysis revealed that distinct patterns of morphological alteration are induced by aging and cold-shock, suggesting different mechanisms at play. This approach can be used to identify the molecular components involved in orchestrating neurodegeneration and to characterize the effect of other stressors on PVD degeneration.
DA - 2020/9/23/
PY - 2020/9/23/
DO - 10.1186/s12915-020-00861-w
VL - 18
IS - 1
SP -
SN - 1741-7007
KW - Deep learning
KW - Convolutional neural networks
KW - Neurodegeneration
KW - Neuronal beading
KW - Aging
KW - Machine learning
KW - Phenotyping
KW - C
KW - elegans
ER -
TY - JOUR
TI - Classification of some subclasses of 6-dimensional nilpotent Leibniz algebras
AU - Demir, Ismail
T2 - TURKISH JOURNAL OF MATHEMATICS
AB - This article is a contribution to the improvement of classification theory in Leibniz algebras. We extend the method of congruence classes of matrices of bilinear forms that was used to classify complex nilpotent Leibniz algebras with one dimensional derived algebra. In this work we focus on applying this method to the classification of 6-dimensional complex nilpotent Leibniz algebras with two dimensional derived algebra.
DA - 2020///
PY - 2020///
DO - 10.3906/mat-2002-69
VL - 44
IS - 5
SP - 1925-1940
SN - 1303-6149
KW - Leibniz algebra
KW - nilpotency
KW - classification
ER -
TY - JOUR
TI - SHARP 2-NORM ERROR BOUNDS FOR LSQR AND THE CONJUGATE GRADIENT METHOD
AU - Hallman, Eric
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - We consider the iterative method LSQR for solving $\min_x |Ax-b|_2$. LSQR is based on the Golub--Kahan bidiagonalization process and at every step produces an iterate that minimizes the norm of the residual vector over a Krylov subspace $\mathcal{K}_k$. The 2-norm of the error is known to decrease monotonically, although it is not minimized over $\mathcal{K}_k$. Given a lower bound on the smallest singular value of $A$, we show that in exact arithmetic the solution lies in the interior of a certain ellipsoid and that the LSQR iterate lies on the boundary of this ellipsoid. We use this result to derive new 2-norm error bounds for LSQR. Although our bounds are not much smaller than the existing ones, we show that they are sharp in the following sense: if the only information we use is our lower bound on $\sigma_{\min}(A)$ plus the information gained by running $k$ steps of LSQR, then our bounds cannot be improved. We also show how to choose a point with an error bound smaller than our corresponding bound for the LSQR error, although its true error is not necessarily smaller than the true LSQR error. As LSQR is formally equivalent to the conjugate gradient (CG) method applied to the normal equations $A{^T} Ax = A{^T} b$, we derive analogous error bounds for CG. Our bounds for CG apply to any system $Ax=b$ where $A$ is symmetric positive definite.
DA - 2020///
PY - 2020///
DO - 10.1137/19M1272822
VL - 41
IS - 3
SP - 1183-1207
SN - 1095-7162
KW - LSQR
KW - least-squares problem
KW - sparse matrix
KW - Krylov subspace method
KW - Golub-Kahan process
KW - conjugate gradient method
KW - stopping criteria
KW - iterative method
ER -
TY - JOUR
TI - Radiation Source Localization Using Surrogate Models Constructed from 3-D Monte Carlo Transport Physics Simulations
AU - Miles, Paul R.
AU - Cook, Jared A.
AU - Angers, Zoey V.
AU - Swenson, Christopher J.
AU - Kiedrowski, Brian C.
AU - Mattingly, John
AU - Smith, Ralph
T2 - NUCLEAR TECHNOLOGY
AB - Recent research has focused on the development of surrogate models for radiation source localization in a simulated urban domain. We employ the Monte Carlo N-Particle (MCNP) code to provide high-fidelity simulations of radiation transport within an urban domain. The model is constructed to employ a source location (x,y,z) as input and return the estimated count rate for a set of specified detector locations. Because MCNP simulations are computationally expensive, we develop efficient and accurate surrogate models of the detector responses. We construct surrogate models using Gaussian processes and neural networks that we train and verify using the MCNP simulations. The trained surrogate models provide an efficient framework for Bayesian inference and experimental design. We employ Delayed Rejection Adaptive Metropolis (DRAM), a Markov Chain Monte Carlo algorithm, to infer the location and intensity of an unknown source. The DRAM results yield a posterior probability distribution for the source’s location conditioned on the observed detector count rates. The posterior distribution exhibits regions of high and low probability within the simulated environment identifying potential source locations. In this manner, we can quantify the source location to within at least one of these regions of high probability in the considered cases. Employing these methods, we are able to reduce the space of potential source locations by at least 60%.
DA - 2020///
PY - 2020///
DO - 10.1080/00295450.2020.1738796
KW - Radiation detection
KW - inverse problem
KW - Bayesian inference
KW - MCNP
KW - surrogate modeling
ER -
TY - JOUR
TI - After the honeymoon, the divorce: Unexpected outcomes of disease control measures against endemic infections
AU - Hollingsworth, Brandon
AU - Okamoto, Kenichi W.
AU - Lloyd, Alun L.
T2 - PLOS Computational Biology
AB - The lack of effective vaccines for many endemic diseases often forces policymakers to rely on non-immunizing control measures, such as vector control, to reduce the massive burden of these diseases. Controls can have well-known counterintuitive effects on endemic infections, including the honeymoon effect, in which partially effective controls cause not only a greater initial reduction in infection than expected, but also large outbreaks during control resulting from accumulation of susceptibles. Unfortunately, many control measures cannot be maintained indefinitely, and the results of cessation are poorly understood. Here, we examine the results of stopped or failed non-immunizing control measures in endemic settings. By using a mathematical model to compare the cumulative number of cases expected with and without control, we show that deployment of control can lead to a larger total number of infections, counting from the time that control started, than without any control–the divorce effect. This result is directly related to the population-level loss of immunity resulting from non-immunizing controls and is seen in a variety of models when non-immunizing controls are used against an infection that confers immunity. Finally, we examine three control plans for minimizing the magnitude of the divorce effect in seasonal infections and show that they are incapable of eliminating the divorce effect. While we do not suggest stopping control programs that rely on non-immunizing controls, our results strongly argue that the accumulation of susceptibility should be considered before deploying such controls against endemic infections when indefinite use of the control is unlikely. We highlight that our results are particularly germane to endemic mosquito-borne infections, such as dengue virus, both for routine management involving vector control and for field trials of novel control approaches, and in the context of non-pharmaceutical interventions aimed at COVID-19.
DA - 2020/10/19/
PY - 2020/10/19/
DO - 10.1371/journal.pcbi.1008292
VL - 16
IS - 10
SP - e1008292
UR - https://doi.org/10.1371/journal.pcbi.1008292
ER -
TY - JOUR
TI - Nonzero-Sum Stochastic Differential Reinsurance Games with Jump-Diffusion Processes
AU - Medhin, Negash
AU - Xu, Chuan
T2 - JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
DA - 2020/11//
PY - 2020/11//
DO - 10.1007/s10957-020-01756-0
VL - 187
IS - 2
SP - 566-584
SN - 1573-2878
KW - Hamilton-Jacobi-Bellman equation
KW - Stochastic differential game
KW - Nonzero-sum reinsurance game
KW - Jump-diffusion process
ER -
TY - JOUR
TI - Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation
AU - Aceves-Sanchez, P.
AU - Degond, P.
AU - Keaveny, E. E.
AU - Manhart, A.
AU - Merino-Aceituno, S.
AU - Peurichard, D.
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
AB - Abstract We model and study the patterns created through the interaction of collectively moving self-propelled particles (SPPs) and elastically tethered obstacles. Simulations of an individual-based model reveal at least three distinct large-scale patterns: travelling bands, trails and moving clusters. This motivates the derivation of a macroscopic partial differential equations model for the interactions between the self-propelled particles and the obstacles, for which we assume large tether stiffness. The result is a coupled system of nonlinear, non-local partial differential equations. Linear stability analysis shows that patterning is expected if the interactions are strong enough and allows for the predictions of pattern size from model parameters. The macroscopic equations reveal that the obstacle interactions induce short-ranged SPP aggregation, irrespective of whether obstacles and SPPs are attractive or repulsive.
DA - 2020/9/25/
PY - 2020/9/25/
DO - 10.1007/s11538-020-00805-z
VL - 82
IS - 10
SP -
SN - 1522-9602
KW - Self-propelled particles
KW - Hydrodynamic limit
KW - Pattern formation
KW - Stability analysis
KW - Gradient flow
KW - Non-local interactions
ER -
TY - JOUR
TI - Rademacher type and Enflo type coincide
AU - Ivanisvili, Paata
AU - Handel, Ramon
AU - Volberg, Alexander
T2 - ANNALS OF MATHEMATICS
AB - A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure. We prove that Rademacher type and Enflo type coincide, settling a long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the discrete cube.
DA - 2020/9//
PY - 2020/9//
DO - 10.4007/annals.2020.192.2.8
VL - 192
IS - 2
SP - 665-678
SN - 1939-8980
KW - Rademacher type
KW - Enflo type
KW - Pisier's inequality
KW - Banach spaces
ER -
TY - JOUR
TI - Lifelong Analysis of Key Aging Genes as Determinants of Lifespan in C. elegans
AU - San Miguel, Adriana
AU - Ramirez, Javier
AU - Flores, Kevin
T2 - FASEB JOURNAL
AB - Aging is an integrative phenotype subject to a complex interplay of genetic, environmental, and life history factors, and a key risk factor for a multitude of human diseases. Research in model organisms has enabled the identification of key evolutionary conserved genetic pathways that play a role in aging. In particular, research on the model organism Caenorhabditis elegans has been crucial in our current understanding of the genetic and environmental regulation of lifespan. Although a multitude of pathways are known to affect longevity, how these pathways jointly respond to upstream stimuli, and how they integrate this information to drive lifespan is far from understood. A major limitation to answer this question is the technical difficulty associated with studying the spatiotemporal activity of multiple pathways throughout lifespan, and under a variety of environmental conditions. In this work, we present a system that enables in vivo tracking the endogenous spatiotemporal activity of key aging genes throughout C. elegans lifespan. This system hinges on an integrative experimental platform based on microfluidics, computer vision, and tagging of endogenous genes via CRISPR/Cas9 genetic engineering approaches. In contrast to traditional transgene expression, CRISPR/Cas9 enables insertion of a tag at precise genomic locations. This results in fluorescent protein levels representative of the endogenously expressed genes, and where all isoforms can be analyzed. Studying endogenous protein levels, however, poses a significant challenge, as these reporters are extremely dim in comparison to traditional multi‐copy insertion transgenes. To address this limitation, we have developed computer vision approaches to quantitatively determine the spatial location and levels of said proteins, which can be used as a metric for gene activity. Furthermore, the use of microfluidic devices enables culture, stimulation, and longitudinal high‐resolution imaging of animal populations under precise environmental conditions. Taking advantage of our computer vision algorithms, we can quantify protein levels, cellular compartmentalization, and tissue localization. Using this approach, we have studied the key transcription factor, DAF‐16/FOXO, the main regulator of Insulin/Insulin‐like Signaling in C. elegans . Under a variety of exposures to dietary restriction, a well‐known regulator of lifespan that acts through DAF‐16, we have observed patterns of activity that have not been identified with traditional transgenes. Integrating lifespan measurements under varied environmental conditions with quantitative analysis from DAF‐16 lifelong spatiotemporal activity, we are exploring the predictive power of this key transcription factor at the tissue‐level, using statistical and mathematical models. We are working on expanding our analysis to additional lifespan regulators to better understand how these interact in driving lifespan. Support or Funding Information This work was supported in part by grants NIH R21AG059099 and NSF 1838314
DA - 2020/4//
PY - 2020/4//
DO - 10.1096/fasebj.2020.34.s1.00160
VL - 34
SP -
SN - 1530-6860
ER -
TY - JOUR
TI - Regular potential games
AU - Swenson, Brian
AU - Murray, Ryan
AU - Kar, Soummya
T2 - Games and Economic Behavior
AB - Abstract A fundamental problem with the Nash equilibrium concept is the existence of certain “structurally deficient” equilibria that (i) lack fundamental robustness properties, and (ii) are difficult to analyze. The notion of a “regular” Nash equilibrium was introduced by Harsanyi. Such equilibria are isolated, highly robust, and relatively simple to analyze. A game is said to be regular if all equilibria in the game are regular. In this paper it is shown that almost all potential games are regular. That is, except for a closed subset with Lebesgue measure zero, all potential games are regular. As an immediate consequence of this, the paper also proves an oddness result for potential games: In almost all potential games, the number of Nash equilibrium strategies is finite and odd. Specialized results are given for weighted potential games, exact potential games, and games with identical payoffs. Applications of the results to game-theoretic learning are discussed.
DA - 2020/11//
PY - 2020/11//
DO - 10.1016/j.geb.2020.09.005
VL - 124
SP - 432-453
UR - https://doi.org/10.1016/j.geb.2020.09.005
KW - Game theory
KW - Potential games
KW - Generic games
KW - Regular equilibria
KW - Multi-agent systems
ER -
TY - JOUR
TI - Learning Equations from Biological Data with Limited Time Samples
AU - Nardini, John T.
AU - Lagergren, John H.
AU - Hawkins-Daarud, Andrea
AU - Curtin, Lee
AU - Morris, Bethan
AU - Rutter, Erica M.
AU - Swanson, Kristin R.
AU - Flores, Kevin B.
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
AB - Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets; however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data are sampled over a time interval exhibiting both linear and nonlinear dynamics. Our findings suggest that equation learning methods can be used for model discovery and selection in many areas of biology when an informative dataset is used. We focus on glioblastoma multiforme modeling as a case study in this work to highlight how these results are informative for data-driven modeling-based tumor invasion predictions.
DA - 2020/9/9/
PY - 2020/9/9/
DO - 10.1007/s11538-020-00794-z
VL - 82
IS - 9
SP -
SN - 1522-9602
KW - Equation learning
KW - Numerical differentiation
KW - Sparse regression
KW - Model selection
KW - Partial differential equations
KW - Parameter estimation
KW - Population dynamics
KW - Glioblastoma multiforme
ER -
TY - JOUR
TI - AN FE-FD METHOD FOR ANISOTROPIC ELLIPTIC INTERFACE PROBLEMS
AU - Dong, Baiying
AU - Feng, Xiufang
AU - Li, Zhilin
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - Anisotropic elliptic interface problems are important but hard to solve either analytically or numerically. There is limited literature on numerical methods based on structured meshes. Finite element methods are often used, but the usual average error estimates cannot guarantee accuracy of the solution near or at the interface. For finite difference methods, it is challenging to discretize mixed derivatives and carry out the convergence analysis. In this paper, a new finite element-finite difference (FE-FD) method that combines a finite element discretization (away from the interface) whose coefficient matrix is a symmetric semipositive definite, with a finite difference discretization (near or on the interface) whose coefficient matrix part has properties of an M-matrix, is developed. An interpolation scheme based on the immersed interface method is also applied to compute the normal derivative of solution (or gradient) accurately from each side of the interface. Error analysis and numerical experiments are also presented.
DA - 2020///
PY - 2020///
DO - 10.1137/19M1291030
VL - 42
IS - 4
SP - B1041-B1066
SN - 1095-7197
KW - anisotropic elliptic interface problem
KW - finite element and finite difference method
KW - maximum principle preserving scheme
KW - normal derivative computation
KW - scaling technique
KW - error analysis
ER -
TY - JOUR
TI - The value of green energy under regulation uncertainty
AU - Detemple, Jerome
AU - Kitapbayev, Yerkin
T2 - ENERGY ECONOMICS
AB - We examine investments in power generation projects under policy uncertainty, when the investor has the choice between two alternative technologies, a gas-fired plant and a wind plant. Increased likelihood of subsidy withdrawal reduces the payoff from and postpones investments in the wind technology. Simultaneously, it accelerates investments in gas, thereby eliminating or further postponing investments in wind capacity. We show that this substitution phenomenon can be of first order importance: it can have a significant impact on the timing of investment, the wind premium, and the probability of investing in the wind technology. Our results provide new insights about the scope and impact of green energy regulation.
DA - 2020/6//
PY - 2020/6//
DO - 10.1016/j.eneco.2020.104807
VL - 89
SP -
SN - 1873-6181
KW - Wind plant
KW - Gas-fired plant
KW - Real options
KW - Subsidy
KW - Regulation uncertainty
ER -
TY - JOUR
TI - On the global controllability of scalar conservation laws with boundary and source controls
DA - 2020/9/17/
PY - 2020/9/17/
ER -
TY - JOUR
TI - Markovian Solutions to Discontinuous ODEs
DA - 2020/9/11/
PY - 2020/9/11/
ER -
TY - JOUR
TI - Key questions for modelling COVID-19 exit strategies
AU - Thompson, Robin N.
AU - Hollingsworth, T. Deirdre
AU - Isham, Valerie
AU - Arribas-Bel, Daniel
AU - Ashby, Ben
AU - Britton, Tom
AU - Challenor, Peter
AU - Chappell, Lauren H. K.
AU - Clapham, Hannah
AU - Cunniffe, Nik J.
AU - Dawid, A. Philip
AU - Donnelly, Christl A.
AU - Eggo, Rosalind M.
AU - Funk, Sebastian
AU - Gilbert, Nigel
AU - Glendinning, Paul
AU - Gog, Julia R.
AU - Hart, William S.
AU - Heesterbeek, Hans
AU - House, Thomas
AU - Keeling, Matt
AU - Kiss, Istvan Z.
AU - Kretzschmar, Mirjam E.
AU - Lloyd, Alun L.
AU - McBryde, Emma S.
AU - McCaw, James M.
AU - McKinley, Trevelyan J.
AU - Miller, Joel C.
AU - Morris, Martina
AU - Philip D. O'Neill,
AU - Parag, Kris V
AU - Pearson, Carl A. B.
AU - Pellis, Lorenzo
AU - Pulliam, Juliet R. C.
AU - Ross, Joshua V
AU - Tomba, Gianpaolo Scalia
AU - Silverman, Bernard W.
AU - Struchiner, Claudio J.
AU - Tildesley, Michael J.
AU - Trapman, Pieter
AU - Webb, Cerian R.
AU - Mollison, Denis
AU - Restif, Olivier
T2 - PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES
AB - Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute ‘Models for an exit strategy’ workshop (11–15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.
DA - 2020/8/12/
PY - 2020/8/12/
DO - 10.1098/rspb.2020.1405
VL - 287
IS - 1932
SP -
SN - 1471-2954
KW - COVID-19
KW - SARS-CoV-2
KW - exit strategy
KW - mathematical modelling
KW - epidemic control
KW - uncertainty
ER -
TY - JOUR
TI - Short-term effects of specific humidity and temperature on COVID-19 morbidity in select US cities
AU - Runkle, Jennifer D.
AU - Sugg, Margaret M.
AU - Leeper, Ronald D.
AU - Rao, Yuhan
AU - Matthews, Jessica L.
AU - Rennie, Jared J.
T2 - SCIENCE OF THE TOTAL ENVIRONMENT
AB - Little is known about the environmental conditions that drive the spatiotemporal patterns of SARS-CoV-2. Preliminary research suggests an association with meteorological parameters. However, the relationship with temperature and humidity is not yet apparent for COVID-19 cases in US cities first impacted. The objective of this study is to evaluate the association between COVID-19 cases and meteorological parameters in select US cities. A case-crossover design with a distributed lag nonlinear model was used to evaluate the contribution of ambient temperature and specific humidity on COVID-19 cases in select US cities. The case-crossover examines each COVID case as its own control at different time periods (before and after transmission occurred). We modeled the effect of temperature and humidity on COVID-19 transmission using a lag period of 7 days. A subset of 8 cities were evaluated for the relationship with meteorological parameters and 5 cities were evaluated in detail. Short-term exposure to humidity was positively associated with COVID-19 transmission in 4 cities. The associations were small with 3 out of 4 cities exhibiting higher COVID19 transmission with specific humidity that ranged from 6 to 9 g/kg. Our results suggest that weather should be considered in infectious disease modeling efforts. Future work is needed over a longer time period and across different locations to clearly establish the weather-COVID19 relationship.
DA - 2020/10/20/
PY - 2020/10/20/
DO - 10.1016/j.scitotenv.2020.140093
VL - 740
SP -
SN - 1879-1026
KW - COVID-19 morbidity
KW - Distributed lag non-linear model
KW - Time-stratified case-crossover
KW - Weather
KW - Seasonality
ER -
TY - JOUR
TI - y A Maximum Principle Argument for the Uniform Convergence of Graph Laplacian Regressors
AU - Trillos, Nicolas Garcia
AU - Murray, Ryan W.
T2 - SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE
AB - This paper investigates the use of methods from partial differential equations and the calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for capturing local and global geometry in many classes of learning problems, and the techniques developed in this paper help to broaden the methodology of studying such problems. In particular, we develop the use of maximum principle arguments to establish asymptotic consistency guarantees within the context of noise corrupted, nonparametric regression with samples living on an unknown manifold embedded in $\mathbb{R}^d$. The maximum principle arguments provide a new technical tool which informs parameter selection by giving concrete error estimates in terms of various regularization parameters. A review of learning algorithms which utilize graph Laplacians, as well as previous developments in the use of differential equation and variational techniques to study those algorithms, is given. In addition, new connections are drawn between Laplacian methods and other machine learning techniques, such as kernel regression and $k$-nearest neighbor methods.
DA - 2020///
PY - 2020///
DO - 10.1137/19M1245372
VL - 2
IS - 3
SP - 705-739
SN - 2577-0187
UR - https://doi.org/10.1137/19M1245372
KW - empirical risk minimization
KW - graph Laplacian
KW - discrete to continuum
KW - nonparametric regression
ER -
TY - JOUR
TI - COVID-19 control across urban-rural gradients
AU - Wells, Konstans
AU - Lurgi, Miguel
AU - Collins, Brendan
AU - Lucini, Biagio
AU - Kao, Rowland R.
AU - Lloyd, Alun L.
AU - Frost, Simon D.W.
AU - Gravenor, Mike B.
AB - Abstract Controlling the regional re-emergence of SARS-CoV-2 after its initial spread in ever-changing personal contact networks and disease landscapes is a challenging task. In a landscape context, contact opportunities within and between populations are changing rapidly as lockdown measures are relaxed and a number of social activities re-activated. Using an individual-based metapopulation model, we explored the efficacy of different control strategies across an urban-rural gradient in Wales, UK. Our model shows that isolation of symptomatic cases, or regional lockdowns in response to local outbreaks, have limited efficacy unless the overall transmission rate is kept persistently low. Additional isolation of non-symptomatic infected individuals, who may be detected by effective test and trace strategies, is pivotal to reduce the overall epidemic size over a wider range of transmission scenarios. We define an ‘urban-rural gradient in epidemic size’ as a correlation between regional epidemic size and connectivity within the region, with more highly connected urban populations experiencing relatively larger outbreaks. For interventions focused on regional lockdowns, the strength of such gradients in epidemic size increased with higher travel frequencies, indicating a reduced efficacy of the control measure in the urban regions under these conditions. When both non-symptomatic and symptomatic individuals are isolated or regional lockdown strategies are enforced, we further found the strongest urban-rural epidemic gradients at high transmission rates. This effect was reversed for strategies targeted at symptomatics only. Our results emphasise the importance of test-and-tracing strategies and maintaining low transmission rates for efficiently controlling COVID19 spread, both at landscape scale and in urban areas. Author summary The spread of infectious diseases is the outcome of contact patterns and involves source-sink dynamics of how infectious individuals spread the disease through pools of susceptible individuals. Control strategies that aim to reduce disease spread often need to accept ongoing transmission chains and therefore, may not work equally well in different scenarios of how individuals and populations are connected to each other. To understand the efficacy of different control strategies to contain the spread of COVID19 across gradients of urban and rural populations, we simulated a large range of different control strategies in response to regional COVID19 outbreaks, involving regional lockdown and the isolation individuals that express symptoms and those that developed not symptoms but may contribute to disease transmission. Our results suggest that isolation of asymptomatic individuals through intensive test-and-tracing is important for efficiently reducing the epidemic size. Regional lockdowns and the isolation of symptomatic cases only are of limited efficacy for reducing the epidemic size, unless overall transmission rate is kept persistently low. Moreover, we found high overall transmission rates to result in relatively larger epidemics in urban than in rural communities for these control strategies, emphasising the importance of keeping transmission rates constantly low in addition to regional measures to avoid the disease spread at large scale.
DA - 2020/9/9/
PY - 2020/9/9/
DO - 10.1101/2020.09.07.20189597
VL - 9
UR - https://doi.org/10.1101/2020.09.07.20189597
ER -
TY - JOUR
TI - Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators
AU - Combettes, Patrick L.
AU - Pesquet, Jean-Christophe
T2 - SIAM Journal on Mathematics of Data Science
AB - Obtaining sharp Lipschitz constants for feed-forward neural networks is essential to assess their robustness in the face of perturbations of their inputs. We derive such constants in the context of a general layered network model involving compositions of nonexpansive averaged operators and affine operators. By exploiting this architecture, our analysis finely captures the interactions between the layers, yielding tighter Lipschitz constants than those resulting from the product of individual bounds for groups of layers. The proposed framework is shown to cover in particular many practical instances encountered in feed-forward neural networks. Our Lipschitz constant estimates are further improved in the case of structures employing scalar nonlinear functions, which include standard convolutional networks as special cases.
DA - 2020/1//
PY - 2020/1//
DO - 10.1137/19m1272780
VL - 2
IS - 2
SP - 529-557
SN - 2577-0187
UR - http://dx.doi.org/10.1137/19m1272780
KW - activation function
KW - neural network
KW - nonexpansive operator
KW - averaged operator
KW - stability
KW - layered network
ER -
TY - JOUR
TI - Regression Models for Compositional Data: General Log-Contrast Formulations, Proximal Optimization, and Microbiome Data Applications
AU - Combettes, Patrick L.
AU - Müller, Christian L.
T2 - Statistics in Biosciences
AB - Abstract Compositional data sets are ubiquitous in science, including geology, ecology, and microbiology. In microbiome research, compositional data primarily arise from high-throughput sequence-based profiling experiments. These data comprise microbial compositions in their natural habitat and are often paired with covariate measurements that characterize physicochemical habitat properties or the physiology of the host. Inferring parsimonious statistical associations between microbial compositions and habitat- or host-specific covariate data is an important step in exploratory data analysis. A standard statistical model linking compositional covariates to continuous outcomes is the linear log-contrast model. This model describes the response as a linear combination of log-ratios of the original compositions and has been extended to the high-dimensional setting via regularization. In this contribution, we propose a general convex optimization model for linear log-contrast regression which includes many previous proposals as special cases. We introduce a proximal algorithm that solves the resulting constrained optimization problem exactly with rigorous convergence guarantees. We illustrate the versatility of our approach by investigating the performance of several model instances on soil and gut microbiome data analysis tasks.
DA - 2020/6/19/
PY - 2020/6/19/
DO - 10.1007/s12561-020-09283-2
VL - 6
J2 - Stat Biosci
LA - en
OP -
SN - 1867-1764 1867-1772
UR - http://dx.doi.org/10.1007/s12561-020-09283-2
DB - Crossref
KW - Compositional data
KW - Convex optimization
KW - Log-contrast model
KW - Microbiome
KW - Perspective function
KW - Proximal algorithm
ER -
TY - JOUR
TI - Genomic analyses of a livestock pest, the New World screwworm, find potential targets for genetic control programs
AU - Scott, Maxwell J.
AU - Benoit, Joshua B.
AU - Davis, Rebecca J.
AU - Bailey, Samuel T.
AU - Varga, Virag
AU - Martinson, Ellen O.
AU - Hickner, Paul V
AU - Syed, Zainulabeuddin
AU - Cardoso, Gisele A.
AU - Torres, Tatiana T.
AU - Weirauch, Matthew T.
AU - Scholl, Elizabeth H.
AU - Phillippy, Adam M.
AU - Sagel, Agustin
AU - Vasquez, Mario
AU - Quintero, Gladys
AU - Skoda, Steven R.
T2 - COMMUNICATIONS BIOLOGY
AB - Abstract The New World Screwworm fly, Cochliomyia hominivorax , is a major pest of livestock in South America and Caribbean. However, few genomic resources have been available for this species. A genome of 534 Mb was assembled from long read PacBio DNA sequencing of DNA from a highly inbred strain. Analysis of molecular evolution identified 40 genes that are likely under positive selection. Developmental RNA-seq analysis identified specific genes associated with each stage. We identify and analyze the expression of genes that are likely important for host-seeking behavior (chemosensory), development of larvae in open wounds in warm-blooded animals (heat shock protein, immune response) and for building transgenic strains for genetic control programs including gene drive (sex determination, germline). This study will underpin future experiments aimed at understanding the parasitic lifestyle of the screwworm fly and greatly facilitate future development of strains for efficient systems for genetic control of screwworm.
DA - 2020/8/4/
PY - 2020/8/4/
DO - 10.1038/s42003-020-01152-4
VL - 3
IS - 1
SP -
SN - 2399-3642
ER -
TY - JOUR
TI - Correlation functions of charged free boson and fermion systems
AU - Jing, Naihuan
AU - Li, Zhijun
AU - Cai, Tommy Wuxing
T2 - JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
AB - Using the idea of the quantum inverse scattering method, we introduce the operators $\mathbf{B}(x), \mathbf{C}(x)$ and $\mathbf{\tilde{B}}(x), \mathbf{\tilde{C}}(x)$ corresponding to the off-diagonal entries of the monodromy matrix $T$ for the phase model and $i$-boson model in terms of bc fermions and neutral fermions respectively, thus giving alternative treatment of the KP and BKP hierarchies. We also introduce analogous operators $\mathbf{B}^{*}(x)$ and $\mathbf{C}^{*}(x)$ for the charged free boson system and show that they are in complete analogy to those of $bc$ fermionic fields. It is proved that the correlation function $\langle 0|\mathbf{C}(x_N)\cdots\mathbf{C}(x_1)\mathbf{B}(y_1)\cdots $ $\mathbf{B}(y_N)|0\rangle$ in the $bc$ fermionic fields is the inverse of the correlation function $\langle 0|\mathbf{C}^{*}(x_N)\cdots\mathbf{C}^{*}(x_1)\mathbf{B}^{*}(y_1)\cdots \mathbf{B}^{*}(y_N)|0\rangle$ in the charged free bosons.
DA - 2020/8//
PY - 2020/8//
DO - 10.1088/1742-5468/aba0aa
VL - 2020
IS - 8
SP -
SN - 1742-5468
KW - correlation functions
KW - quantum integrability (Bethe ansatz)
KW - algebraic structures of integrable models
KW - bosonisation
ER -
TY - JOUR
TI - Structural and hemodynamic properties of murine pulmonary arterial networks under hypoxia-induced pulmonary hypertension
AU - Chambers, Megan J.
AU - Colebank, Mitchel J.
AU - Qureshi, M. Umar
AU - Clipp, Rachel
AU - Olufsen, Mette S.
T2 - PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART H-JOURNAL OF ENGINEERING IN MEDICINE
AB - Detection and monitoring of patients with pulmonary hypertension, defined as a mean blood pressure in the main pulmonary artery above 25 mmHg, requires a combination of imaging and hemodynamic measurements. This study demonstrates how to combine imaging data from microcomputed tomography images with hemodynamic pressure and flow waveforms from control and hypertensive mice. Specific attention is devoted to developing a tool that processes computed tomography images, generating subject-specific arterial networks in which one-dimensional fluid dynamics modeling is used to predict blood pressure and flow. Each arterial network is modeled as a directed graph representing vessels along the principal pathway to ensure perfusion of all lobes. The one-dimensional model couples these networks with structured tree boundary conditions representing the small arteries and arterioles. Fluid dynamics equations are solved in this network and compared to measurements of pressure in the main pulmonary artery. Analysis of microcomputed tomography images reveals that the branching ratio is the same in the control and hypertensive animals, but that the vessel length-to-radius ratio is significantly lower in the hypertensive animals. Fluid dynamics predictions show that in addition to changed network geometry, vessel stiffness is higher in the hypertensive animal models than in the control models.
DA - 2020/11//
PY - 2020/11//
DO - 10.1177/0954411920944110
VL - 234
IS - 11
SP - 1312-1329
SN - 2041-3033
UR - https://doi.org/10.1177/0954411920944110
KW - Pulmonary hypertension
KW - fractal networks
KW - image segmentation
KW - center line extraction
KW - one-dimensional fluid dynamics
KW - Navier-Stokes equations
ER -
TY - JOUR
TI - Mechanistic model of hormonal contraception
AU - Wright, A. Armean
AU - Fayad, Ghassan N.
AU - Selgrade, James F.
AU - Olufsen, Mette S.
T2 - PLOS COMPUTATIONAL BIOLOGY
AB - Contraceptive drugs intended for family planning are used by the majority of married or in-union women in almost all regions of the world. The two most prevalent types of hormones associated with contraception are synthetic estrogens and progestins. Hormonal based contraceptives contain a dose of a synthetic progesterone (progestin) or a combination of a progestin and a synthetic estrogen. In this study we use mathematical modeling to understand better how these contraceptive paradigms prevent ovulation, special focus is on understanding how changes in dose impact hormonal cycling. To explain this phenomenon, we added two autocrine mechanisms essential to achieve contraception within our previous menstrual cycle models. This new model predicts mean daily blood concentrations of key hormones during a contraceptive state achieved by administering progestins, synthetic estrogens, or a combined treatment. Model outputs are compared with data from two clinical trials: one for a progestin only treatment and one for a combined hormonal treatment. Results show that contraception can be achieved with synthetic estrogen, with progestin, and by combining the two hormones. An advantage of the combined treatment is that a contraceptive state can be obtained at a lower dose of each hormone. The model studied here is qualitative in nature, but can be coupled with a pharmacokinetic/pharamacodynamic (PKPD) model providing the ability to fit exogenous inputs to specific bioavailability and affinity. A model of this type may allow insight into a specific drug's effects, which has potential to be useful in the pre-clinical trial stage identifying the lowest dose required to achieve contraception.
DA - 2020/6//
PY - 2020/6//
DO - 10.1371/journal.pcbi.1007848
VL - 16
IS - 6
SP -
SN - 1553-7358
ER -
TY - JOUR
TI - Deep Neural Network Structures Solving Variational Inequalities
AU - Combettes, Patrick L.
AU - Pesquet, Jean-Christophe
T2 - Set-Valued and Variational Analysis
AB - Motivated by structures that appear in deep neural networks, we investigate nonlinear composite models alternating proximity and affine operators defined on different spaces. We first show that a wide range of activation operators used in neural networks are actually proximity operators. We then establish conditions for the averagedness of the proposed composite constructs and investigate their asymptotic properties. It is shown that the limit of the resulting process solves a variational inequality which, in general, does not derive from a minimization problem. The analysis relies on tools from monotone operator theory and sheds some light on a class of neural networks structures with so far elusive asymptotic properties.
DA - 2020/2/13/
PY - 2020/2/13/
DO - 10.1007/s11228-019-00526-z
VL - 28
IS - 3
SP - 491-518
J2 - Set-Valued Var. Anal
LA - en
OP -
SN - 1877-0533 1877-0541
UR - http://dx.doi.org/10.1007/s11228-019-00526-z
DB - Crossref
KW - Averaged operator
KW - Deep neural network
KW - Monotone operator
KW - Nonexpansive operator
KW - Proximity operator
KW - Variational inequality
ER -
TY - JOUR
TI - Tau functions of the charged free bosons
AU - Jing, Naihuan
AU - Li, Zhijun
T2 - SCIENCE CHINA-MATHEMATICS
AB - We study bosonic tau functions in relation with the charged free bosonic fields. It is proved that up to a constant the only tau function in the Fock space M is the vacuum vector, and some tau functions were given in the completion of M using Schur functions. We also give a new proof of Borchardt's identity and obtain several q-series identities by using the boson-boson correspondence.
DA - 2020/11//
PY - 2020/11//
DO - 10.1007/s11425-019-1735-4
VL - 63
IS - 11
SP - 2157-2176
SN - 1869-1862
KW - tau functions
KW - boson-boson correspondence
KW - vertex operator algebras
KW - symmetric functions
ER -
TY - JOUR
TI - Efficient Krylov subspace methods for uncertainty quantification in large Bayesian linear inverse problems
AU - Saibaba, Arvind K.
AU - Chung, Julianne
AU - Petroske, Katrina
T2 - NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
AB - Summary Uncertainty quantification for linear inverse problems remains a challenging task, especially for problems with a very large number of unknown parameters (e.g., dynamic inverse problems) and for problems where computation of the square root and inverse of the prior covariance matrix are not feasible. This work exploits Krylov subspace methods to develop and analyze new techniques for large‐scale uncertainty quantification in inverse problems. In this work, we assume that generalized Golub‐Kahan‐based methods have been used to compute an estimate of the solution, and we describe efficient methods to explore the posterior distribution. In particular, we use the generalized Golub‐Kahan bidiagonalization to derive an approximation of the posterior covariance matrix, and we provide theoretical results that quantify the accuracy of the approximate posterior covariance matrix and of the resulting posterior distribution. Then, we describe efficient methods that use the approximation to compute measures of uncertainty, including the Kullback‐Liebler divergence. We present two methods that use the preconditioned Lanczos algorithm to efficiently generate samples from the posterior distribution. Numerical examples from dynamic photoacoustic tomography demonstrate the effectiveness of the described approaches.
DA - 2020/10//
PY - 2020/10//
DO - 10.1002/nla.2325
VL - 27
IS - 5
SP -
SN - 1099-1506
KW - generalized Golub-Kahan
KW - preconditioned iterative methods
KW - Bayesian inverse problems
KW - uncertainty measures
KW - Krylov subspace samplers
ER -
TY - JOUR
TI - Warped proximal iterations for monotone inclusions
AU - Bùi, Minh N.
AU - Combettes, Patrick L.
T2 - Journal of Mathematical Analysis and Applications
AB - Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion, called warped resolvent, which is constructed with the help of an auxiliary operator. The properties of warped resolvents are investigated and connections are made with existing notions. Abstract weak and strong convergence principles based on warped resolvents are proposed and shown to not only provide a synthetic view of splitting algorithms but to also constitute an effective device to produce new solution methods for challenging inclusion problems.
DA - 2020/11//
PY - 2020/11//
DO - 10.1016/j.jmaa.2020.124315
VL - 491
IS - 1
SP - 124315
J2 - Journal of Mathematical Analysis and Applications
LA - en
OP -
SN - 0022-247X
UR - http://dx.doi.org/10.1016/j.jmaa.2020.124315
DB - Crossref
KW - Monotone inclusion
KW - Operator splitting
KW - Strong convergence
KW - Warped resolvent
KW - Warped proximal iterations
ER -
TY - JOUR
TI - RANDOMIZATION AND REWEIGHTED l(1)-MINIMIZATION FOR A-OPTIMAL DESIGN OF LINEAR INVERSE PROBLEMS
AU - Herman, Elizabeth
AU - Alexanderian, Alen
AU - Saibaba, Arvind K.
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the posterior covariance operator. We propose using structure exploiting randomized methods to compute the A-optimal objective function and its gradient, and we provide a detailed analysis of the error for the proposed estimators. To ensure sparse and binary design vectors, we develop a novel reweighted $\ell_1$-minimization algorithm. We also introduce a modified A-optimal criterion and present randomized estimators for its efficient computation. We present numerical results illustrating the proposed methods on a model contaminant source identification problem, where the inverse problem seeks to recover the initial state of a contaminant plume using discrete measurements of the contaminant in space and time.
DA - 2020///
PY - 2020///
DO - 10.1137/19M1267362
VL - 42
IS - 3
SP - A1714-A1740
SN - 1095-7197
KW - Bayesian inversion
KW - A-optimal experimental design
KW - large-scale ill-posed inverse problems
KW - randomized matrix methods
KW - reweighted l(1) minimization
KW - uncertainty quantification
ER -
TY - JOUR
TI - A tutorial review of mathematical techniques for quantifying tumor heterogeneity
AU - Everett, Rebecca
AU - Flores, Kevin B.
AU - Henscheid, Nick
AU - Lagergren, John
AU - Larripa, Kamila
AU - Li, Ding
AU - Nardini, John T.
AU - Nguyen, Phuong T. T.
AU - Pitman, E. Bruce
AU - Rutter, Erica M.
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - https://github.com/jtnardin/Tumor-Heterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018–2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.]]>
DA - 2020///
PY - 2020///
DO - 10.3934/mbe.2020207
VL - 17
IS - 4
SP - 3660-3709
SN - 1551-0018
KW - cancer heterogeneity
KW - mathematical oncology
KW - tumor growth
KW - glioblastoma multiforme
KW - virtual populations
KW - nonlinear mixed effects
KW - spatiotemporal data
KW - Bayesian estimation
KW - generative
KW - adversarial networks
KW - non-parametric estimation
KW - variational autoencoders
KW - machine learning
ER -
TY - JOUR
TI - Perspective maximum likelihood-type estimation via proximal decomposition
AU - Combettes, Patrick L.
AU - Müller, Christian L.
T2 - Electronic Journal of Statistics
AB - We introduce a flexible optimization model for maximum likelihood-type estimation (M-estimation) that encompasses and generalizes a large class of existing statistical models, including Huber’s concomitant M-estimator, Owen’s Huber/Berhu concomitant estimator, the scaled lasso, support vector machine regression, and penalized estimation with structured sparsity. The model, termed perspective M-estimation, leverages the observation that convex M-estimators with concomitant scale as well as various regularizers are instances of perspective functions, a construction that extends a convex function to a jointly convex one in terms of an additional scale variable. These nonsmooth functions are shown to be amenable to proximal analysis, which leads to principled and provably convergent optimization algorithms via proximal splitting. We derive novel proximity operators for several perspective functions of interest via a geometrical approach based on duality. We then devise a new proximal splitting algorithm to solve the proposed M-estimation problem and establish the convergence of both the scale and regression iterates it produces to a solution. Numerical experiments on synthetic and real-world data illustrate the broad applicability of the proposed framework.
DA - 2020///
PY - 2020///
DO - 10.1214/19-EJS1662
VL - 14
IS - 1
SP - 207-238
J2 - Electron. J. Statist.
LA - en
OP -
SN - 1935-7524
UR - http://dx.doi.org/10.1214/19-ejs1662
DB - Crossref
KW - Convex optimization
KW - heteroscedastic model
KW - concomitant M-estimator
KW - perspective function
KW - proximal algorithm
KW - robust regression
ER -
TY - JOUR
TI - Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs
AU - Koval, Karina
AU - Alexanderian, Alen
AU - Stadler, Georg
T2 - INVERSE PROBLEMS
AB - We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the model that exist in addition to the parameters in the inverse problem, and that cannot be reduced through observations. Specifically, given a statistical distribution for the model uncertainties, we compute the optimal design that minimizes the expected value of the posterior covariance trace. The expected value is discretized using Monte Carlo leading to an objective function consisting of a sum of trace operators and a binary-inducing penalty. Minimization of this objective requires a large number of PDE solves in each step. To make this problem computationally tractable, we construct a composite low-rank basis using a randomized range finder algorithm to eliminate forward and adjoint PDE solves. We also present a novel formulation of the A-optimal design objective that requires the trace of an operator in the observation rather than the parameter space. The binary structure is enforced using a weighted regularized $\ell_0$-sparsification approach. We present numerical results for inference of the initial condition in a subsurface flow problem with inherent uncertainty in the flow fields and in the initial times.
DA - 2020/7//
PY - 2020/7//
DO - 10.1088/1361-6420/ab89c5
VL - 36
IS - 7
SP -
SN - 1361-6420
KW - optimal design
KW - inverse problems
KW - model uncertainty
KW - optimization under uncertainty
KW - model reduction
KW - subsurface flow
ER -
TY - JOUR
TI - Computation of cohomology of Lie conformal and Poisson vertex algebras
AU - Bakalov, Bojko
AU - De Sole, Alberto
AU - Kac, Victor G.
T2 - SELECTA MATHEMATICA-NEW SERIES
AB - We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as for the universal affine and Virasoro Poisson vertex algebras. We establish finite dimensionality of this cohomology for conformal Poisson vertex (super)algebras that are finitely and freely generated by elements of positive conformal weight.
DA - 2020/7/10/
PY - 2020/7/10/
DO - 10.1007/s00029-020-00578-2
VL - 26
IS - 4
SP -
SN - 1420-9020
KW - Lie conformal (super)algebras
KW - Poisson vertex (super)algebras
KW - Affine Lie algebras
KW - Virasoro algebra
KW - Basic cohomology
KW - LCA cohomology
KW - Variational PVA cohomology
KW - Energy operator
ER -
TY - JOUR
TI - The Douglas--Rachford Algorithm Converges Only Weakly
AU - Bùi, Minh N.
AU - Combettes, Patrick L.
T2 - SIAM Journal on Control and Optimization
AB - We show that the weak convergence of the Douglas--Rachford algorithm for finding a zero of the sum of two maximally monotone operators cannot be improved to strong convergence. Likewise, we show that strong convergence can fail for the method of partial inverses.
DA - 2020/1//
PY - 2020/1//
DO - 10.1137/19M1308451
VL - 58
IS - 2
SP - 1118-1120
J2 - SIAM J. Control Optim.
LA - en
OP -
SN - 0363-0129 1095-7138
UR - http://dx.doi.org/10.1137/19m1308451
DB - Crossref
KW - Douglas-Rachford algorithm
KW - method of partial inverses
KW - monotone operator
KW - operator splitting
KW - strong convergence
ER -
TY - JOUR
TI - Deep phenotyping of cardiac function in heart transplant patients using cardiovascular system models
AU - Colunga, Amanda L.
AU - Kim, Karam G.
AU - Woodall, N. Payton
AU - Dardas, Todd F.
AU - Gennari, John H.
AU - Olufsen, Mette S.
AU - Carlson, Brian E.
T2 - JOURNAL OF PHYSIOLOGY-LONDON
AB - Key points Right heart catheterization data from clinical records of heart transplant patients are used to identify patient‐specific models of the cardiovascular system. These patient‐specific cardiovascular models represent a snapshot of cardiovascular function at a given post‐transplant recovery time point. This approach is used to describe cardiac function in 10 heart transplant patients, five of which had multiple right heart catheterizations allowing an assessment of cardiac function over time. These patient‐specific models are used to predict cardiovascular function in the form of right and left ventricular pressure‐volume loops and ventricular power, an important metric in the clinical assessment of cardiac function. Outcomes for the longitudinally tracked patients show that our approach was able to identify the one patient from the group of five that exhibited post‐transplant cardiovascular complications. Abstract Heart transplant patients are followed with periodic right heart catheterizations (RHCs) to identify post‐transplant complications and guide treatment. Post‐transplant positive outcomes are associated with a steady reduction of right ventricular and pulmonary arterial pressures, toward normal levels of right‐side pressure (about 20 mmHg) measured by RHC. This study shows that more information about patient progression is obtained by combining standard RHC measures with mechanistic computational cardiovascular system models. The purpose of this study is twofold: to understand how cardiovascular system models can be used to represent a patient's cardiovascular state, and to use these models to track post‐transplant recovery and outcome. To obtain reliable parameter estimates comparable within and across datasets, we use sensitivity analysis, parameter subset selection, and optimization to determine patient‐specific mechanistic parameters that can be reliably extracted from the RHC data. Patient‐specific models are identified for 10 patients from their first post‐transplant RHC, and longitudinal analysis is carried out for five patients. Results of the sensitivity analysis and subset selection show that we can reliably estimate seven non‐measurable quantities; namely, ventricular diastolic relaxation, systemic resistance, pulmonary venous elastance, pulmonary resistance, pulmonary arterial elastance, pulmonary valve resistance and systemic arterial elastance. Changes in parameters and predicted cardiovascular function post‐transplant are used to evaluate the cardiovascular state during recovery of five patients. Of these five patients, only one showed inconsistent trends during recovery in ventricular pressure–volume relationships and power output. At the four‐year post‐transplant time point this patient exhibited biventricular failure along with graft dysfunction while the remaining four exhibited no cardiovascular complications.
DA - 2020/8//
PY - 2020/8//
DO - 10.1113/JP279393
VL - 598
IS - 15
SP - 3203-3222
SN - 1469-7793
KW - computational physiology
KW - heart transplant
KW - patient-specific modeling
KW - right heart catheterization
ER -
TY - JOUR
TI - Uncertainty relations based on Wigner-Yanase skew information
AU - Huang, Xiaofen
AU - Zhang, Tinggui
AU - Jing, Naihuan
T2 - COMMUNICATIONS IN THEORETICAL PHYSICS
AB - In this paper, we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information. First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous lower bounds. We then propose new weighted uncertainty relations for two noncompatible observables. Two separable criteria via skew information are also obtained.
DA - 2020/7/1/
PY - 2020/7/1/
DO - 10.1088/1572-9494/ab892f
VL - 72
IS - 7
SP -
SN - 1572-9494
KW - uncertainty relations
KW - skew information
KW - entanglement
ER -
TY - JOUR
TI - A Sustainable Quantitative Stock Selection Strategy Based on Dynamic Factor Adjustment
AU - Fu, Yi
AU - Cao, Shuai
AU - Pang, Tao
T2 - SUSTAINABILITY
AB - In this paper, we consider a sustainable quantitative stock selection strategy using some machine learning techniques. In particular, we use a random forest model to dynamically select factors for the training set in each period to ensure that the factors that can be selected in each period are the optimal factors in the current period. At the same time, the classification probability prediction (CPP) of stock returns is performed. Historical back-testing using Chinese stock market data shows that the proposed CPP quantitative stock selection strategy performs better than the traditional machine learning stock selection methods, and it can outperform the market index over the same period in most back-testing periods. Moreover, this strategy is sustainable in all market conditions, such as a bull market, a bear market, or a volatile market.
DA - 2020/5//
PY - 2020/5//
DO - 10.3390/su12103978
VL - 12
IS - 10
SP -
SN - 2071-1050
KW - stock selection
KW - machine learning
KW - classification probability prediction
KW - back-testing
ER -
TY - JOUR
TI - ON WEAKLY NONLINEAR BOUNDARY VALUE PROBLEMS ON INFINITE INTERVALS
AU - Freedman, Benjamin
AU - Rodriguez, Jesus
T2 - DIFFERENTIAL EQUATIONS & APPLICATIONS
DA - 2020/5//
PY - 2020/5//
DO - 10.7153/dea-202-12-12
VL - 12
IS - 2
SP - 185-200
ER -
TY - JOUR
TI - Global Identifiability of Differential Models
AU - Hong, Hoon
AU - Ovchinnikov, Alexey
AU - Pogudin, Gleb
AU - Yap, Chee
T2 - COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
AB - Many real‐world processes and phenomena are modeled using systems of ordinary differential equations with parameters. Given such a system, we say that a parameter is globally identifiable if it can be uniquely recovered from input and output data. The main contribution of this paper is to provide theory, an algorithm, and software for deciding global identifiability. First, we rigorously derive an algebraic criterion for global identifiability (this is an analytic property), which yields a deterministic algorithm. Second, we improve the efficiency by randomizing the algorithm while guaranteeing the probability of correctness. With our new algorithm, we can tackle problems that could not be tackled before. A software based on the algorithm (called SIAN) is available at https://github.com/pogudingleb/SIAN . © 2020 Wiley Periodicals LLC
DA - 2020/9//
PY - 2020/9//
DO - 10.1002/cpa.21921
VL - 73
IS - 9
SP - 1831-1879
SN - 1097-0312
UR - http://dx.doi.org/10.1002/cpa.21921
ER -
TY - JOUR
TI - Subresultants of (x - alpha)(m) and (x - beta)(n), Jacobipolynomials and complexity
AU - Bostan, A.
AU - Krick, T.
AU - Szanto, A.
AU - Valdettaro, M.
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - In an earlier article (Bostan et al., 2017), with Carlos D'Andrea, we described explicit expressions for the coefficients of the order-d polynomial subresultant of (x−α)m and (x−β)n with respect to Bernstein's set of polynomials {(x−α)j(x−β)d−j, 0≤j≤d}, for 0≤dR}, and (ii) in a neighborhood of the points where the solution exhibits a spiraling vortex singularity. The outer solution is obtained as the fixed point of a contractive transformation, based on the Biot-Savart formula and integration along characteristics. The inner solution is constructed using a system of adapted coordinates, following the approach of V. Elling (2016) [17].
DA - 2020/9/5/
PY - 2020/9/5/
DO - 10.1016/j.jde.2020.04.005
VL - 269
IS - 6
SP - 5142-5203
SN - 1090-2732
ER -
TY - JOUR
TI - Method of Difference Potentials for Evolution Equations with Lacunas
AU - Petropavlovsky, S. V.
AU - Tsynkov, S. V.
T2 - COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
DA - 2020/4//
PY - 2020/4//
DO - 10.1134/S0965542520040144
VL - 60
IS - 4
SP - 711-722
SN - 1555-6662
KW - method of difference potentials
KW - Huygens principle
KW - lacunas
KW - wave equation
ER -
TY - JOUR
TI - Deformation of Cayley's hyperdeterminants
AU - Cai, Tommy Wuxing
AU - Jing, Naihuan
T2 - ELECTRONIC JOURNAL OF COMBINATORICS
AB - We introduce a deformation of Cayley's second hyperdeterminant for even-dimensional hypermatrices. As an application, we obtain a generalization of Jacobi-Trudi formula for Macdonald functions of rectangular shapes generalizing Matsumoto's formula for Jack functions.
DA - 2020/6/12/
PY - 2020/6/12/
DO - 10.37236/8091
VL - 27
IS - 2
SP -
SN - 1077-8926
ER -
TY - JOUR
TI - Mitigation of tipping point transitions by time-delay feedback control
AU - Farazmand, Mohammad
T2 - CHAOS
AB - In stochastic multistable systems driven by the gradient of a potential, transitions between equilibria are possible because of noise. We study the ability of linear delay feedback control to mitigate these transitions, ensuring that the system stays near a desirable equilibrium. For small delays, we show that the control term has two effects: (i) a stabilizing effect by deepening the potential well around the desirable equilibrium and (ii) a destabilizing effect by intensifying the noise by a factor of (1−τα)−1/2, where τ and α denote the delay and the control gain, respectively. As a result, successful mitigation depends on the competition between these two factors. We also derive analytical results that elucidate the choice of the appropriate control gain and delay that ensure successful mitigations. These results eliminate the need for any Monte Carlo simulations of the stochastic differential equations and, therefore, significantly reduce the computational cost of determining the suitable control parameters. We demonstrate the application of our results on two examples.
DA - 2020/1//
PY - 2020/1//
DO - 10.1063/1.5137825
VL - 30
IS - 1
SP -
SN - 1089-7682
UR - https://doi.org/10.1063/1.5137825
ER -
TY - JOUR
TI - Minimizing drag in a moving boundary fluid-elasticity interaction
AU - Bociu, L.
AU - Castle, L.
AU - Lasiecka, I
AU - Tuffaha, A.
T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
AB - Our goal is to minimize the fluid vorticity in the case of an elastic body moving and deforming inside the fluid, using a distributed control. This translates into analyzing an optimal control problem subject to a moving boundary fluid–structure interaction (FSI). The FSI is described by the coupling of Navier–Stokes and wave equations. The control is inherently a nonlinear control, acting as feedback on the moving frame. Its action depends on the flow map of the domain, which is itself defined through the dynamics of the problem. A key ingredient in the optimal control problem is represented by the long time behavior of the forced dynamics, which was an open problem in the field. Our main results include existence of solutions for all times with small distributed sources and small initial data, as well as existence of optimal control for the problem of minimization of drag in the fluid.
DA - 2020/8//
PY - 2020/8//
DO - 10.1016/j.na.2020.111837
VL - 197
SP -
SN - 1873-5215
KW - Control problem
KW - Minimization of drag
KW - Moving boundary
KW - Fluid-structure interaction
ER -
TY - JOUR
TI - Gradient-induced droplet motion over soft solids
AU - Bardall, Aaron
AU - Chen, Shih-Yuan
AU - Daniels, Karen E.
AU - Shearer, Michael
T2 - IMA Journal of Applied Mathematics
AB - Abstract Fluid droplets can be induced to move over rigid or flexible surfaces under external or body forces. We describe the effect of variations in material properties of a flexible substrate as a mechanism for motion. In this paper, we consider a droplet placed on a substrate with either a stiffness or surface energy gradient and consider its potential for motion via coupling to elastic deformations of the substrate. In order to clarify the role of contact angles and to obtain a tractable model, we consider a 2D droplet. The gradients in substrate material properties give rise to asymmetric solid deformation and to unequal contact angles, thereby producing a force on the droplet. We then use a dynamic viscoelastic model to predict the resulting dynamics of droplets. Numerical results quantifying the effect of the gradients establish that it is more feasible to induce droplet motion with a gradient in surface energy. The results show that the magnitude of elastic modulus gradient needed to induce droplet motion exceeds experimentally feasible limits in the production of soft solids and is therefore unlikely as a passive mechanism for cell motion. In both cases, of surface energy or elastic modulus, the threshold to initiate motion is achieved at lower mean values of the material properties.
DA - 2020/6//
PY - 2020/6//
DO - 10.1093/imamat/hxaa015
VL - 85
IS - 3
SP - 495–512
KW - droplet motion soft solids
ER -
TY - JOUR
TI - Isomorphism between the R-Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types B and D
AU - Jing, Naihuan
AU - Liu, Ming
AU - Molev, Alexander
T2 - SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
AB - Following the approach of Ding and Frenkel [Comm. Math. Phys. 156 (1993), 277-300] for type $A$, we showed in our previous work [J. Math. Phys. 61 (2020), 031701, 41 pages] that the Gauss decomposition of the generator matrix in the $R$-matrix presentation of the quantum affine algebra yields the Drinfeld generators in all classical types. Complete details for type $C$ were given therein, while the present paper deals with types $B$ and $D$. The arguments for all classical types are quite similar so we mostly concentrate on necessary additional details specific to the underlying orthogonal Lie algebras.
DA - 2020///
PY - 2020///
DO - 10.3842/SIGMA.2020.043
VL - 16
SP -
SN - 1815-0659
KW - R-matrix presentation
KW - Drinfeld new presentation
KW - universal R-matrix
KW - Gauss decomposition
ER -
TY - JOUR
TI - Randomized Discrete Empirical Interpolation Method for Nonlinear Model Reduction
T2 - SIAM Journal on Scientific Computing
AB - The discrete empirical interpolation method (DEIM) is a popular technique for nonlinear model reduction, and it has two main ingredients: an interpolating basis that is computed from a collection of snapshots of the solution, and a set of indices which determine the nonlinear components to be simulated. The computation of these two ingredients dominates the overall cost of the DEIM algorithm. To specifically address these two issues, we present randomized versions of the DEIM algorithm. There are three main contributions of this paper. First, we use randomized range finding algorithms to efficiently find an approximate DEIM basis. Second, we develop randomized subset selection tools, based on leverage scores, to efficiently select the nonlinear components. Third, we develop several theoretical results that quantify the accuracy of the randomization on the DEIM approximation. We also present numerical experiments that demonstrate the benefits of the proposed algorithms.
DA - 2020/1//
PY - 2020/1//
DO - 10.1137/19m1243270
UR - http://dx.doi.org/10.1137/19m1243270
KW - model reduction
KW - randomized algorithms
KW - discrete empirical interpolation method
KW - subset selection
KW - subspace iteration
ER -
TY - JOUR
TI - Randomized Algorithms for Low-Rank Tensor Decompositions in the Tucker Format
AU - Minster, Rachel
AU - Saibaba, Arvind K.
AU - Kilmer, Misha E.
T2 - SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE
AB - Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 17 May 2019Accepted: 05 December 2019Published online: 25 February 2020Keywordsrandomized algorithms, tensors, Tucker decompositions, low-rank, multilinear algebra, structure-preservingAMS Subject Headings65F99, 15A69, 15A18, 15B52, 68W20, 65F15Publication DataISSN (online): 2577-0187Publisher: Society for Industrial and Applied MathematicsCODEN: sjmdaq
DA - 2020///
PY - 2020///
DO - 10.1137/19m1261043
VL - 2
IS - 1
SP - 189-215
SN - 2577-0187
UR - http://dx.doi.org/10.1137/19m1261043
KW - randomized algorithms
KW - tensors
KW - Tucker decompositions
KW - low-rank
KW - multilinear algebra
KW - structure-preserving
ER -
TY - JOUR
TI - Poincare Series of Relative Symmetric Invariants for SLn(C)
AU - Jing, Naihuan
AU - Wang, Danxia
AU - Zhang, Honglian
T2 - ALGEBRAS AND REPRESENTATION THEORY
AB - Let (N, G), where N is a normal subgroup of G[1]}, the aggregate nature of the data was ignored. In this paper, we embrace this aspect of the experiment and *correctly* model the data as aggregate data, comparing the results to the previous approach. We discuss cases in which the approach may provide similar results as well as cases in which there is a clear difference in the resulting fit to the data.
DA - 2020///
PY - 2020///
DO - 10.3934/mbe.2020091
VL - 17
IS - 2
SP - 1743-1756
SN - 1551-0018
KW - plant-insect interactions
KW - inverse problems
KW - hypothesis testing and standard errors in dynamical models
KW - aggregate data
KW - Prohorov metric
ER -
TY - JOUR
TI - Finite-Volume-Particle Methods for the Two-Component Camassa-Holm System
AU - Chertock, Alina
AU - Kurganov, Alexander
AU - Liu, Yongle
T2 - COMMUNICATIONS IN COMPUTATIONAL PHYSICS
DA - 2020/2//
PY - 2020/2//
DO - 10.4208/cicp.OA-2018-0325
VL - 27
IS - 2
SP - 480-502
SN - 1991-7120
KW - Two-component Camassa-Holm system
KW - finite-volume method
KW - deterministic particle method
KW - finite-volume-particle method
KW - central-upwind scheme
ER -
TY - JOUR
TI - Parameter estimation using aggregate data
AU - Banks, H. . T.
AU - Meade, Annabel E.
AU - Schacht, Celia
AU - Catenacci, Jared
AU - Thompson, W. Clayton
AU - Abate-Daga, Daniel
AU - Enderling, Heiko
T2 - APPLIED MATHEMATICS LETTERS
AB - In biomedical/physiological/ecological experiments, it is common for measurements in time series data to be collected from multiple subjects. Often it is the case that a subject cannot be measured or identified at multiple time points (often referred to as aggregate population data). Due to a lack of alternative methods, this form of data is typically treated as if it is collected from a single individual. As we show by examples, this assumption leads to an overconfidence in model parameter (means, variances) values and model based predictions. We discuss these issues in the context of a mathematical model to determine T-cell behavior with cancer chimeric antigen receptor (CAR) therapies where during the collection of data cancerous mice are sacrificed at each measurement time.
DA - 2020/2//
PY - 2020/2//
DO - 10.1016/j.aml.2019.105999
VL - 100
SP -
SN - 0893-9659
KW - Uncertainty quantification
KW - Parameter estimation
KW - CAR T cancer therapy
ER -
TY - JOUR
TI - P-partition generating function equivalence of naturally labeled posets
AU - Liu, Ricky Ini
AU - Weselcouch, Michael
T2 - JOURNAL OF COMBINATORIAL THEORY SERIES A
AB - The P-partition generating function of a (naturally labeled) poset P is a quasisymmetric function enumerating order-preserving maps from P to Z+. Using the Hopf algebra of posets, we give necessary conditions for two posets to have the same generating function. In particular, we show that they must have the same number of antichains of each size, as well as the same shape (as defined by Greene). We also discuss which shapes guarantee uniqueness of the P-partition generating function and give a method of constructing pairs of non-isomorphic posets with the same generating function.
DA - 2020/2//
PY - 2020/2//
DO - 10.1016/j.jcta.2019.105136
VL - 170
SP -
SN - 1096-0899
KW - P-Partition
KW - Quasisymmetric function
KW - Combinatorial hopf algebra
ER -
TY - JOUR
TI - How to obtain an accurate gradient for interface problems?
AU - Tong, Fenghua
AU - Wang, Weilong
AU - Feng, Xinlong
AU - Zhao, Jianping
AU - Li, Zhilin
T2 - Journal of Computational Physics
AB - It is well-known that the Immersed Interface Method (IIM) is second order accurate for interface problems. But the accuracy of the first order derivatives, or gradients for short, is not so clear and is often assumed to be first order accurate. In this paper, new strategies based on IIM are proposed for elliptic interface problems to compute the gradient at grid points both regular and irregular, and at the interface from each side of the interface. Second order in 1D, or nearly second order (except a factor of |logh|) convergence in 2D of the computed gradient is obtained with almost no extra cost, and has been explained in intuition and verified by non-trivial numerical tests. Numerical examples in one, two dimensions, radial and axis-symmetric cases in polar and spherical coordinates are presented to validate the numerical methods and analysis.
DA - 2020/3//
PY - 2020/3//
DO - 10.1016/j.jcp.2019.109070
VL - 405
SP - 109070
UR - https://doi.org/10.1016/j.jcp.2019.109070
KW - Accuracy of derivatives
KW - Elliptic interface problems
KW - Discontinuous coefficient
KW - Discrete Green functions
KW - IIM
ER -
TY - JOUR
TI - Modelling the effects of field spatial scale and natural enemy colonization behaviour on pest suppression in diversified agroecosystems
AU - Banks, John E.
AU - Laubmeier, Amanda N.
AU - Banks, H. Thomas
T2 - AGRICULTURAL AND FOREST ENTOMOLOGY
AB - Abstract Diversifying agroecosystems by establishing or retaining natural vegetation in and around crop areas has long been recognized as a potentially effective means of bolstering pest control as a result of attracting more numerous and diverse natural enemies, although outcomes are inconsistent across species. Little is known about the underlying mechanisms driving such differences in species responses, creating challenges for determining how best to manage landscapes for maximizing environmental services such as biological control. The present study addresses gaps in our understanding of the link between noncrop vegetation in field margins and pest suppression by using a system of partial differential equations to model population‐level predator–prey interactions, as well as spatial processes, aiming to capture the dynamics of crop plants, herbivores and two generalist predators. We focus on differences in how two predators (a carabid and a ladybird beetle) colonize crop fields where they forage for prey, examining differences in how they move into the fields from adjacent vegetation as a potential driver of differences in overall pest suppression. The results obtained demonstrate that predator colonization behaviour and spatial scale are important factors with respect to determining the effectiveness of biological control.
DA - 2020/2//
PY - 2020/2//
DO - 10.1111/afe.12354
VL - 22
IS - 1
SP - 30-40
SN - 1461-9563
KW - Beetle
KW - differential equation
KW - diffusion
KW - dispersal
KW - habitat heterogeneity
ER -