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Discretized Fast-Slow Systems with Canard Points in Two DimensionsJul 15 2019We study the behaviour of slow manifolds for two different discretization schemes of fast-slow systems with canard fold points. The analysis uses the blow-up method to deal with the loss of normal hyperbolicity at the canard point. While the Euler method ... More
Where did the tumor start? An inverse solver with sparse localization for tumor growth modelsJul 15 2019We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation (PDE) for ... More
Out-of-core singular value decompositionJul 15 2019Singular value decomposition (SVD) is a standard matrix factorization technique that produces optimal low-rank approximations of matrices. It has diverse applications, including machine learning, data science and signal processing. However, many common ... More
On the Correlation of Critical Points and Angular Trispectrum for Random Spherical HarmonicsJul 12 2019We prove a Central Limit Theorem for the Critical Points of Random Spherical Harmonics, in the High-Energy Limit. The result is a consequence of a deeper characterizations of the total number of critical points, which are shown to be asymptotically fully ... More
Convergent discretisation schemes for transition path theory for diffusion processesJul 12 2019In the analysis of metastable diffusion processes, Transition Path Theory (TPT) provides a way to quantify the probability of observing a given transition between two disjoint metastable subsets of state space. However, many TPT-based methods for diffusion ... More
Global Stabilization of 2D Forced Viscous Burgers' Equation Around Nonconstant Steady State Solution by Nonlinear Neumann Boundary Feedback Control:Theory and Finite Element AnalysisJul 11 2019Global stabilization of viscous Burgers' equation around constant steady state solution has been discussed in the literature. The main objective of this paper is to show global stabilization results for the 2D forced viscous Burgers' equation around a ... More
Vertex-Fault Tolerant Complete Matching in Bipartite graphs: the Biregular CaseJul 10 2019Given a family $\mathcal{H}$ of graphs and a positive integer $k$, a graph $G$ is called vertex $k$-fault-tolerant with respect to $\mathcal{H}$, denoted by $k$-FT$(\mathcal{H})$, if $G-S$ contains some $H\in\mathcal{H}$ as a subgraph, for every $S\subset ... More
Deformation classes of real Cayley M-octadsJul 10 2019We study 8-point configurations in the real projective space forming an intersection locus of three quadrics and containing no coplanar quadruples. We found that there exists precisely 8 mirror-pairs of deformation classes of such configurations. We describe ... More
Identifying Linear Models in Multi-Resolution Population Data using Minimum Description Length Principle to Predict Household IncomeJul 10 2019One shirt size cannot fit everybody, while we cannot make a unique shirt that fits perfectly for everyone because of resource limitation. This analogy is true for the policy making. Policy makers cannot establish a single policy to solve all problems ... More
Shock Capturing by Bernstein Polynomials for Scalar Conservation LawsJul 09 2019A main disadvantage of many high-order methods for hyperbolic conservation laws lies in the famous Gibbs-Wilbraham phenomenon, once discontinuities appear in the solution. Due to the Gibbs-Wilbraham phenomenon, the numerical approximation will be polluted ... More
Error analysis of finite difference/collocation method for the nonlinear coupled parabolic free boundary problem modeling plaque growth in the arteryJul 09 2019The main target of this paper is to present a new and efficient method to solve a nonlinear free boundary mathematical model of atherosclerosis. This model consists of three parabolics, one elliptic and one ordinary differential equations that are coupled ... More
Multirate PWM balance method for the efficient field-circuit coupled simulation of power convertersJul 08 2019The field-circuit coupled simulation of switch-mode power converters with conventional time discretization is computationally expensive since very small time steps are needed to appropriately account for steep transients occurring inside the converter, ... More
A generic finite element framework on parallel tree-based adaptive meshesJul 08 2019We present highly scalable parallel distributed-memory algorithms and associated data structures for a generic finite element framework that supports $h$-adaptivity on computational domains represented as multiple connected adaptive trees, thus providing ... More
Analogue of a Fock-type integral arising from electromagnetism and its applications in number theoryJul 08 2019Closed-form evaluations of certain integrals of $J_{0}(\xi)$, the Bessel function of the first kind, have been crucial in the studies on the electromagnetic field of alternating current in a circuit with two groundings, as can be seen from the works of ... More
Deep splitting method for parabolic PDEsJul 08 2019In this paper we introduce a numerical method for parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational graph for each of the ... More
The energy of a simplicial complexJul 07 2019A finite abstract simplicial complex G defines a matrix L, where L(x,y)=1 if two simplicies x,y in G intersect and where L(x,y)=0 if they don't. This matrix is always unimodular so that the inverse g of L has integer entries g(x,y). In analogy to Laplacians ... More
Entropy stable numerical approximations for the isothermal and polytropic Euler equationsJul 07 2019In this work we analyze the entropic properties of the Euler equations when the system is closed with the assumption of a polytropic gas. In this case, the pressure solely depends upon the density of the fluid and the energy equation is not necessary ... More
Finding classes of delta-matroids closed under handle slidesJul 07 2019In this work, we study the operations of handle slides introduced recently for delta-matroids by Iain Moffatt and Eunice Mphako-Banda. We then prove that the class of binary delta-matroids is the only class of delta-matroids closed under handle slides. ... More
Pseudo random number generators: attention for a newly proposed generatorJul 07 2019Xorshift128+ is a newly proposed pseudo random number generator (PRNG), which is now the standard PRNG in a number of platforms. We point out some flaws of such generators, propose a little slower replacements tiny Mersenne Twisters (tinyMTs), and argue ... More
Average Gromov hyperbolicity and the Parisi ansatzJul 06 2019Jul 10 2019Gromov hyperbolicity of a metric space measures the distance of the space from a perfect tree-like structure. The measure has a "worst-case" aspect to it, in the sense that it detects a region in the space which sees the maximum deviation from tree-like ... More
Average Gromov hyperbolicity and the Parisi ansatzJul 06 2019Gromov hyperbolicity of a metric space measures the distance of the space from a perfect tree-like structure. The measure has a "worst-case'' aspect to it, in the sense that it detects a region in the space which sees the maximum deviation from tree-like ... More
Average Gromov hyperbolicity and the Parisi ansatzJul 06 2019Jul 11 2019Gromov hyperbolicity of a metric space measures the distance of the space from a perfect tree-like structure. The measure has a "worst-case" aspect to it, in the sense that it detects a region in the space which sees the maximum deviation from tree-like ... More
Optimizing Xeon Phi for Interactive Data AnalysisJul 06 2019The Intel Xeon Phi manycore processor is designed to provide high performance matrix computations of the type often performed in data analysis. Common data analysis environments include Matlab, GNU Octave, Julia, Python, and R. Achieving optimal performance ... More
Symmetries of Spatial Graphs in Homology SpheresJul 06 2019This paper explores the relationship between symmetries of spatial graphs in $S^3$ and symmetries of spatial graphs in homology $3$-spheres and other $3$-manifolds. We prove that for any $3$-connected graph $G$, an automorphism $\sigma$ is induced by ... More
A constrained pressure-temperature residual (CPTR) method for non-isothermal multiphase flow in porous mediaJul 05 2019In petroleum reservoir simulation, the standard preconditioner, the Constrained Pressure Residual (CPR) method, is a two-stage process which involves solving a restricted pressure system. Initially designed for isothermal models, this approach is often ... More
Exponential integrators for semi-linear parabolic problems with linear constraintsJul 05 2019This paper is devoted to the construction of exponential integrators of first and second order for the time discretization of constrained parabolic systems. For this extend, we combine well-known exponential integrators for unconstrained systems with ... More
A note on optimal $H^1$-error estimates for Crank-Nicolson approximations to the nonlinear Schrödinger equationJul 05 2019In this paper we consider a mass- and energy--conserving Crank-Nicolson time discretization for a general class of nonlinear Schr\"odinger equations. This scheme, which enjoys popularity in the physics community due to its conservation properties, was ... More
Automatic Generation of Efficient Linear Algebra ProgramsJul 05 2019The level of abstraction at which application experts reason about linear algebra computations and the level of abstraction used by developers of high-performance numerical linear algebra libraries do not match. The former is conveniently captured by ... More
A-priori error analysis of local incremental minimization schemes for rate-independent evolutionsJul 05 2019This paper is concerned with a priori error estimates for the local incremental minimization scheme, which is an implicit time discretization method for the approximation of rate-independent systems with non-convex energies. We first show by means of ... More
On The Structure of Dyck LanguagesJul 04 2019We prove that the closure of the one-sided Dyck language in a free monoid is a two-sided Dyck language.
A statistical framework for generating microstructures of two-phase random materials: application to fatigue analysisJul 04 2019Random microstructures of heterogeneous materials play a crucial role in the material macroscopic behavior and in predictions of its effective properties. A common approach to modeling random multiphase materials is to develop so-called surrogate models ... More
An $hr$-Adaptive Method for the Cubic Nonlinear Schrödinger EquationJul 04 2019The nonlinear Schr\"{o}dinger equation (NLSE) is one of the most important equations in quantum mechanics, and appears in a wide range of applications including optical fibre communications, plasma physics and biomolecule dynamics. It is a notoriously ... More
Tent pitching and Trefftz-DG method for the acoustic wave equationJul 04 2019We present a space-time Trefftz discontinuous Galerkin method for approximating the acoustic wave equation semi-explicitly on tent pitched meshes. DG Trefftz methods use discontinuous test and trial functions, which solve the wave equation locally. Tent ... More
Borel invariant for Zimmer cocycles of 3-manifold groupsJul 04 2019Let $\Gamma$ be a non-uniform lattice of $\text{PSL}(2,\mathbb{C})$. Given any representation $\rho:\Gamma \rightarrow \text{PSL}(n,\mathbb{C})$ we can define a numerical invariant $\beta_n(\rho)$, called Borel invariant, which remains constant along ... More
A stabilized second order exponential time differencing multistep method for thin film growth model without slope selectionJul 04 2019In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. An artificial stabilizing term $A\tau^2\frac{\partial\Delta^2 u}{\partial t}$ is ... More
Toward Fairness in AI for People with Disabilities: A Research RoadmapJul 04 2019AI technologies have the potential to dramatically impact the lives of people with disabilities (PWD). Indeed, improving the lives of PWD is a motivator for many state-of-the-art AI systems, such as automated speech recognition tools that can caption ... More
Linearly implicit local and global energy-preserving methods for Hamiltonian PDEsJul 03 2019We present linearly implicit methods that preserve discrete approximations to local and global energy conservation laws for multi-symplectic PDEs with cubic invariants. The methods are tested on the one-dimensional Korteweg-de Vries equation and the two-dimensional ... More
mgcpy: A Comprehensive High Dimensional Independence Testing Python PackageJul 03 2019With the increase in the amount of data in many fields, a method to consistently and efficiently decipher relationships within high dimensional data sets is important. Because many modern datasets are high-dimensional, univariate independence tests are ... More
bayes4psy -- an Open Source R Package for Bayesian Statistics in PsychologyJul 03 2019Research in psychology generates interesting data sets and unique statistical modelling tasks. However, these tasks, while important, are often very specific, so appropriate statistical models and methods cannot be found in accessible Bayesian tools. ... More
Spectral zeta functionsJul 03 2019This paper discusses the simplest examples of spectral zeta functions, especially those associated with graphs, a subject which has not been much studied. The analogy and the similar structure of these functions, such as their parallel definition in terms ... More
Multi-dimensional interpolations in C++Jul 03 2019A C++ software design is presented that can be used to interpolate data in any number of dimensions. The design is based on a combination of templates of functional collections of elements and so-called type lists. The design allows for different search ... More
Using binary decision diagrams for constraint handling in combinatorial interaction testingJul 03 2019Constraints among test parameters often have substantial effects on the performance of test case generation for combinatorial interaction testing. This paper investigates the effectiveness of the use of Binary Decision Diagrams (BDDs) for constraint handling. ... More
A fourth-order compact solver for fractional-in-time fourth-order diffusion equationsJul 03 2019A fourth-order compact scheme is proposed for a fourth-order subdiffusion equation with the first Dirichlet boundary conditions. The fourth-order problem is firstly reduced into a couple of spatially second-order system and we use an averaged operator ... More
Simplicial complexity of surface groups and systolic areaJul 02 2019The simplicial complexity is an invariant for finitely presentable groups that was recently introduced by Babenko, Balacheff and Bulteau to study systolic area. The simplicial complexity $\kappa(G)$ was proved to be a good approximation of the systolic ... More
A Column Generation Approach to the Discrete Barycenter ProblemJul 02 2019The minimum-cost mass transport problem for a set of discrete probability measures, called the discrete barycenter problem, can be solved exactly using exponential-sized linear programs. In applications, the support sets of the probability measures have ... More
On strong exceptional collections of line bundles of maximal length on Fano toric Deligne-Mumford stacksJul 02 2019We study strong exceptional collections of line bundles on Fano toric Deligne-Mumford stacks $\mathbb{P}_{\mathbf{\Sigma}}$ with rank of Picard group at most two. We prove that any strong exceptional collection of line bundles generates the derived category ... More
GPU-based Parallel Computation Support for StanJul 01 2019This paper details an extensible OpenCL framework that allows Stan to utilize heterogeneous compute devices. It includes GPU-optimized routines for the Cholesky decomposition, its derivative, other matrix algebra primitives and some commonly used likelihoods, ... More
Algorithms and data structures for matrix-free finite element operators with MPI-parallel sparse multi-vectorsJul 01 2019Traditional solution approaches for problems in quantum mechanics scale as $\mathcal O(M^3)$, where $M$ is the number of electrons. Various methods have been proposed to address this issue and obtain linear scaling $\mathcal O(M)$. One promising formulation ... More
Optimization on flag manifoldsJul 01 2019A flag is a sequence of nested subspace. Flags are ubiquitous in numerical analysis, arising in finite elements, multigrid, spectral, and pseudospectral methods for numerical PDE; they arise as Krylov subspaces in matrix computations, and as multiresolution ... More
Improved hardness for H-colourings of G-colourable graphsJul 01 2019We present new results on approximate colourings of graphs and, more generally, approximate H-colourings and promise constraint satisfaction problems. First, we show NP-hardness of colouring $k$-colourable graphs with $\binom{k}{\lfloor k/2\rfloor}-1$ ... More
Improved hardness for H-colourings of G-colourable graphsJul 01 2019Jul 05 2019We present new results on approximate colourings of graphs and, more generally, approximate H-colourings and promise constraint satisfaction problems. First, we show NP-hardness of colouring $k$-colourable graphs with $\binom{k}{\lfloor k/2\rfloor}-1$ ... More
Lossy Compression for Large Scale PDE ProblemsJul 01 2019Jul 08 2019Solvers for partial differential equations (PDE) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that needs to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth ... More
Lossy Compression for Large Scale PDE ProblemsJul 01 2019Solvers for partial differential equations (PDE) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that needs to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth ... More
Linear Independence of Covariant Derivatives and Space-CurvaturesJul 01 2019It is developed the considerations from (S. M. Min\v{c}i\'c, [14, 15]) about curvature tensors and pseudotensors for a non-symmetric affine connection space in this paper. How many kinds of covariant derivatives are enough to be defined for complete researching ... More
A multiscale reduced basis method for Schrödinger equation with multiscale and random potentialsJun 30 2019The semiclassical Schr\"{o}dinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wavefunction develops high-frequency oscillations in both the physical ... More
Kissing number in hyperbolic spaceJun 29 2019This paper provides upper and lower bounds on the kissing number of congruent radius $r > 0$ spheres in $\mathbb{H}^n$, for $n\geq 2$. For that purpose, the kissing number is replaced by the kissing function $\kappa(n, r)$ which depends on the radius ... More
Solving Polynomial Systems with phcpyJun 28 2019The solutions of a system of polynomials in several variables are often needed, e.g.: in the design of mechanical systems, and in phase-space analyses of nonlinear biological dynamics. Reliable, accurate, and comprehensive numerical solutions are available ... More
An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal EquationJun 28 2019In this paper we propose and analyze an energy stable numerical scheme for the square phase field crystal (SPFC) equation, a gradient flow modeling crystal dynamics at the atomic scale in space but on diffusive scales in time. In particular, a modification ... More
Detection of time-varying heat sources using an analytic forward modelJun 28 2019We present a simple, analytic point source model for both static and time-varying point-like heat sources and the resulting temperature profile that solves the heat equation in dimension three. Simple algorithms to detect the location and spectral content ... More
Adaptive second-order Crank-Nicolson time-stepping schemes for time fractional molecular beam epitaxial growth modelsJun 27 2019Adaptive second-order Crank-Nicolson time-stepping methods using the recent scalar auxiliary variable (SAV) approach are developed for the time-fractional Molecular Beam Epitaxial models with Caputo's derivative. Based on the piecewise linear interpolation, ... More
Simple maximum-principle preserving time-stepping methods for time-fractional Allen-Cahn equationJun 27 2019Two fast L1 time-stepping methods, including the backward Euler and stabilized semi-implicit schemes, are suggested for the time-fractional Allen-Cahn equation with Caputo's derivative. The time mesh is refined near the initial time to resolve the intrinsically ... More
Remark on Algorithm 680: evaluation of the complex error function: Cause and Remedy for the Loss of Accuracy Near the Real AxisJun 27 2019In this remark we identify the cause of the loss of accuracy in the computation of the Faddeyeva function, w(z), near the real axis when using Algorithm 680. We provide a simple correction to this problem which allows us to restore this code as one of ... More
Global manifold structure of a continuous-time heterodimensional cycleJun 27 2019A heterodimensional cycle consists of a pair of heteroclinic connections between two saddle periodic orbits with unstable manifolds of different dimensions. Recent theoretical work on chaotic dynamics beyond the uniformly hyperbolic setting has shown ... More
An Explicit Mapped Tent Pitching Scheme for Maxwell EquationsJun 26 2019We present a new numerical method for solving time dependent Maxwell equations, which is also suitable for general linear hyperbolic equations. It is based on an unstructured partitioning of the spacetime domain into tent-shaped regions that respect causality. ... More
A Modular and Extensible Software Architecture for Particle DynamicsJun 26 2019Creating a highly parallel and flexible discrete element software requires an interdisciplinary approach, where expertise from different disciplines is combined. On the one hand domain specialists provide interaction models between particles. On the other ... More
A High-Performance Implementation of a Robust Preconditioner for Heterogeneous ProblemsJun 26 2019We present an efficient implementation of the highly robust and scalable GenEO preconditioner in the high-performance PDE framework DUNE. The GenEO coarse space is constructed by combining low energy solutions of a local generalised eigenproblem using ... More
Investigating the OPS intermediate representation to target GPUs in the Devito DSLJun 26 2019The Devito DSL is a code generation tool for the solution of partial differential equations using the finite difference method specifically aimed at seismic inversion problems. In this work we investigate the integration of OPS, an API to generate highly ... More
A High-Order Lower-Triangular Pseudo-Mass Matrix for Explicit Time Advancement of hp Triangular Finite Element MethodsJun 25 2019Explicit time advancement for continuous finite elements requires the inversion of a global mass matrix. For spectral element simulations on quadrilaterals and hexahedra, there is an accurate approximate mass matrix which is diagonal, making it computationally ... More
Parallel Performance of Algebraic Multigrid Domain Decomposition (AMG-DD)Jun 25 2019Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of communication ... More
Had You Looked Where I'm Looking: Cross-user Similarities in Viewing Behavior for 360$^{\circ}$ Video and Caching ImplicationsJun 24 2019The demand and usage of 360$^{\circ}$ video services are expected to increase. However, despite these services being highly bandwidth intensive, not much is known about the potential value that basic bandwidth saving techniques such as server or edge-network ... More
A hybrid Hermite WENO scheme for hyperbolic conservation lawsJun 22 2019In this paper, we propose a hybrid finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for solving one and two dimensional hyperbolic conservation laws. The zeroth-order and the first-order moments are used in the spatial reconstruction, ... More
Removing numerical dispersion from linear evolution equationsJun 22 2019In this paper we describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. We prove that the method results in a solution with ... More
Low-regularity integrators for nonlinear Dirac equationsJun 22 2019In this work, we consider the numerical integration of the nonlinear Dirac equation and the Dirac-Poisson system (NDEs) under rough initial data. We propose a ultra low-regularity integrator (ULI) for solving the NDEs which enables optimal first-order ... More
Convergence of stochastic structure-preserving schemes for computing effective diffusivity in random flowsJun 21 2019In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by stochastic differential ... More
Minimal resolutions of monomial idealsJun 20 2019An explicit combinatorial minimal free resolution of an arbitrary monomial ideal $I$ in a polynomial ring in $n$ variables over a field of characteristic $0$ is defined canonically, without any choices, using higher-dimensional generalizations of combined ... More
Program Generation for Linear Algebra Using Multiple Layers of DSLsJun 20 2019Numerical software in computational science and engineering often relies on highly-optimized building blocks from libraries such as BLAS and LAPACK, and while such libraries provide portable performance for a wide range of computing architectures, they ... More
Regional based query in graph active learningJun 20 2019Graph convolution networks (GCN) have emerged as the leading method to classify node classes in networks, and have reached the highest accuracy in multiple node classification tasks. In the absence of available tagged samples, active learning methods ... More
Endotactic Networks and Toric Differential InclusionsJun 19 2019An important dynamical property of biological interaction networks is persistence, which intuitively means that "no species goes extinct". It has been conjectured that dynamical system models of weakly reversible networks (i.e., networks for which each ... More
Model selection for high-dimensional linear regression with dependent observationsJun 18 2019We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. ... More
Parallel Random Block-Coordinate Forward-Backward Algorithm: A Unified Convergence AnalysisJun 18 2019Jul 03 2019We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to fully exploit ... More
Parallel Random Block-Coordinate Forward-Backward Algorithm: A Unified Convergence AnalysisJun 18 2019We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to fully exploit ... More
Efficient IMEX Runge-Kutta methods for nonhydrostatic dynamicsJun 17 2019We analyze the stability and accuracy (up to third order) of a new family of implicit-explicit Runge-Kutta (IMEX RK) methods. This analysis expedites development of methods with various balances in the number of explicit stages and implicit solves. We ... More
Gradient Flow Finite Element Discretizations with Energy-Based Adaptivity for the Gross-Pitaevskii EquationJun 17 2019We present an effective adaptive procedure for the numerical approximation of the steady-state Gross-Pitaevskii equation. Our approach is solely based on energy minimization, and consists of a combination of gradient flow iterations and adaptive finite ... More
Infimal Convolution and Duality in Convex Optimal Control Problems with Second Order Evolution Differential InclusionsJun 17 2019The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying infimal convolution ... More
Gröbner bases and the Cohen-Macaulay property of Li's double determinantal varietiesJun 17 2019Jul 08 2019We consider double determinantal varieties, a special case of Nakajima quiver varieties. Li conjectured that double determinantal varieties are normal, irreducible, Cohen-Macaulay varieties whose defining ideals have a Gr\"obner basis given by their natural ... More
Gr{ö}bner bases and the Cohen-Macaulay property of Li's double determinantal varietiesJun 17 2019We consider double determinantal varieties, a special case of Nakajima quiver varities. Li conjectured that double determinantal varieties are normal, irreducible, Cohen-Macaulay varieties whose defining ideals have a Gr{\"o}bner basis given by their ... More
A tunable multiresolution smoother for scattered data with application to particle filteringJun 16 2019A smoothing algorithm is presented that can reduce the small-scale content of data observed at scattered locations in a spatially extended domain. The smoother works by forming a Gaussian interpolant of the input data, and then convolving the interpolant ... More
Finding optimal solutions by stochastic cellular automataJun 16 2019Finding a ground state of a given Hamiltonian is an important but hard problem. One of the potential methods is to use a Markov chain Monte Carlo (MCMC) to sample the Gibbs distribution whose highest peaks correspond to the ground states. In this short ... More
A parametrized Poincare-Hopf Theorem and Clique Cardinalities of graphsJun 15 2019Given a locally injective real function g on the vertex set V of a finite simple graph G=(V,E), we prove the Poincare-Hopf formula f_G(t) = 1+t sum_{x in V} f_{S_g(x)}(t), where S_g(x) = { y in S(x), g(y) less than g(x) } and f_G(t)=1+f_0 t + ... + f_{d} ... More
On the Configuration Space of Steiner Minimal TreesJun 15 2019Among other results, we prove the following theorem about Steiner minimal trees in $d$-dimensional Euclidean space: if two finite sets in $\mathbb{R}^d$ have unique and combinatorially equivalent Steiner minimal trees, then there is a homotopy between ... More
Computing Theta Functions with JuliaJun 15 2019We present a new package Theta.jl for computing with the Riemann theta function. It is implemented in Julia and offers accurate numerical evaluation of theta functions with characteristics and their derivatives of arbitrary order. Our package is optimized ... More
Dimension Reduction and Kernel Principal Component AnalysisJun 15 2019We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space transforms. ... More
A tractable second-order cone certificate for external positivity with application to model order reductionJun 14 2019For linear time-invariant systems, a tractable certificate of external positivity based on second-order cones is presented. Further, we show how balanced truncation can be modified to preserve second-order cone invariance, which together with our certificate ... More
Computational singular perturbation method for nonstandard slow-fast systemsJun 14 2019The computational singular perturbation (CSP) method is an algorithm which iteratively approximates slow manifolds and fast fibers in multiple-timescale dynamical systems. Since its inception due to Lam and Goussis, the convergence of the CSP method has ... More
Bspline solids manipulation with MathematicaJun 14 2019Bspline solids are used for solid objects modeling in R3. Mathematica incorporates a several commands to manipulate symbolic and graphically Bspline basis functions and to graphically manipulate Bsplines curves and surfaces; however, it does not incorporate ... More
Monotone vector fields and generation of nonexpansive semigroups in complete CAT(0) spacesJun 14 2019In this paper, we discuss about monotone vector fields, which is a typical extension to the theory of convex functions, by exploiting the tangent space structure. This new approach to monotonicity in CAT(0) spaces stands in opposed to the monotonicity ... More
A stabilized DG cut cell method for discretizing the linear transport equationJun 13 2019We present new stabilization terms for solving the linear transport equation on a cut cell mesh using the discontinuous Galerkin (DG) method in two dimensions with piecewise linear polynomials. The goal is to allow for explicit time stepping schemes, ... More
Tensor train optimization for mathematical model of social networksJun 12 2019The optimization algorithms for solving multi-parameter inverse problem for the mathematical model of parabolic equations arising in social networks, epidemiology and economy are investigated. The data fitting is formulated as optimization of least squares ... More
Convergence of second-order, entropy stable methods for multi-dimensional conservation lawsJun 12 2019High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space dimensions. ... More
Quantum Random Numbers generated by the Cloud Superconducting Quantum ComputerJun 11 2019A cloud quantum computer is similar to a random number generator in that its physical mechanism is inaccessible to the users. In this respect, a cloud quantum computer is a black box. In both devices, the users decide the device condition from the output. ... More