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Implicit-Explicit multistep methods for hyperbolic systems with multiscale relaxationApr 08 2019We consider the development of high order space and time numerical methods based on Implicit-Explicit (IMEX) multistep time integrators for hyperbolic systems with relaxation. More specifically, we consider hyperbolic balance laws in which the convection ... More
State and Parameter Estimation from Observed Signal IncrementsMar 26 2019The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classic state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated ... More
Parametric finite element approximations of curvature driven interface evolutionsMar 22 2019Parametric finite elements lead to very efficient numerical methods for surface evolution equations. We introduce several computational techniques for curvature driven evolution equations based on a weak formulation for the mean curvature. The approaches ... More
Transfer operators, atomic decomposition and the BestiaryMar 16 2019Arbieto and S. recently used atomic decomposition to study transfer operators. We give a long list of old and new expanding dynamical systems for which those results can be applied, obtaining the quasi-compactness of transfer operator acting on Besov ... More
Transfer operators and atomic decompositionMar 16 2019Apr 16 2019We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, ... More
Transfer operators and atomic decompositionMar 16 2019We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, ... More
A discontinuous Galerkin fast spectral method for multi-species full Boltzmann on streaming multi-processorsMar 12 2019When the molecules of a gaseous system are far apart, say in microscale gas flows where the surface to volume ratio is high and hence the surface forces dominant, the molecule-surface interactions lead to the formation of a local thermodynamically non-equilibrium ... More
A discontinuous Galerkin fast spectral method for the multi-species Boltzmann equationMar 07 2019We introduce a fast Fourier spectral method for the multi-species Boltzmann collision operator. The method retains the riveting properties of the single-species fast spectral method (Gamba et al. SIAM J. Sci. Comput., 39 pp. B658--B674 2017) including: ... More
t-wise Berge and t-heavy hypergraphsFeb 08 2019In many proofs concerning extremal parameters of Berge hypergraphs one starts with analyzing that part of that shadow graph which is contained in many hyperedges. Capturing this phenomenon we introduce two new types of hypergraphs. A hypergraph $\mathcal{H}$ ... More
Jones representations of Thompson's group $F$ arising from Temperley-Lieb-Jones algebrasJan 29 2019Following a procedure due to V. Jones, using suitably normalized elements in a Temperley-Lieb-Jones (planar) algebra we introduce a 3-parametric family of unitary representations of the Thompson's group $F$ equipped with canonical (vacuum) vectors and ... More
Polynomial to exponential transition in Ramsey theoryJan 17 2019Given $s \ge k\ge 3$, let $h^{(k)}(s)$ be the minimum $t$ such that there exist arbitrarily large $k$-uniform hypergraphs $H$ whose independence number is at most polylogarithmic in the number of vertices and in which every $s$ vertices span at most $t$ ... More
Algorithms for $\ell_p$-based semi-supervised learning on graphsJan 15 2019We develop fast algorithms for solving the variational and game-theoretic $p$-Laplace equations on weighted graphs for $p>2$. The graph $p$-Laplacian for $p>2$ has been proposed recently as a replacement for the standard ($p=2$) graph Laplacian in semi-supervised ... More
Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learningDec 31 2018Jan 29 2019The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context. The framework builds on a synergy between persistent homology and the theory of group actions. We define group-equivariant non-expansive ... More
Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learningDec 31 2018Mar 03 2019The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context. The framework builds on a synergy between persistent homology and the theory of group actions. We define group-equivariant non-expansive ... More
Isogeometric Mortar Coupling for Electromagnetic ProblemsDec 27 2018This paper discusses and analyses two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretised by either N\'ed\'elec-type polynomial finite elements or spline-based isogeometric analysis. The first ... More
On ultrafilter extensions of first-order models and ultrafilter interpretationsDec 15 2018There exist two known canonical concepts of ultrafilter extensions of first-order models; one comes from modal logic and universal algebra, another one from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as its main ... More
Sensitivity-driven adaptive sparse stochastic approximations in plasma microinstability analysisNov 30 2018Quantifying uncertainty in predictive simulations for real-world problems is of paramount importance - and far from trivial, mainly due to the large number of stochastic parameters and significant computational requirements. Adaptive sparse grid approximations ... More
Traces and Extensions of Bounded Divergence-Measure Fields on Rough Open SetsOct 30 2018We prove that an open set $\Omega \subset \mathbb{R}^n$ can be approximated by smooth sets with uniformly bounded perimeters from the interior if and only if the open set $\Omega$ satisfies \begin{align*} &\qquad \qquad\qquad\qquad\qquad\qquad\qquad \mathscr{H}^{n-1}(\partial ... More
Maximal $L^p$-regularity for perturbed evolution equations in Banach spacesOct 21 2018The main purpose of this paper is to investigate the concept of maximal $L^p$-regularity for perturbed evolution equations in Banach spaces. We mainly consider three classes of perturbations: Miyadera-Voigt perturbations, Desch-Schappacher perturbations, ... More
A Discontinuous Galerkin Fast Spectral Method for the Full Boltzmann Equation with General Collision KernelsSep 26 2018Nov 02 2018The Boltzmann equation, an integro-differential equation for the molecular distribution function in the physical and velocity phase space, governs the fluid flow behavior at a wide range of physical conditions, including compressible, turbulent, as well ... More
A Physical Perspective on Control Points and Polar Forms: Bézier Curves, Angular Momentum and Harmonic OscillatorsSep 19 2018Bernstein polynomials and B\'ezier curves play an important role in computer-aided geometric design and numerical analysis, and their study relates to mathematical fields such as abstract algebra, algebraic geometry and probability theory. We describe ... More
SNS: A Solution-based Nonlinear Subspace method for time-dependent model order reductionSep 11 2018Feb 05 2019Several reduced order models have been successfully developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction techniques ... More
Cauchy Fluxes and Gauss-Green Formulas for Divergence-Measure Fields over General Open SetsSep 04 2018Jan 18 2019We establish the interior and exterior Gauss-Green formulas for divergence-measure fields in $L^p$ over general open sets, motivated by the rigorous mathematical formulation of the physical principle of balance law via the Cauchy flux in the axiomatic ... More
Data Assimilation: The Schrödinger PerspectiveJul 22 2018Dec 02 2018Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based ... More
Data Assimilation: The Schrödinger PerspectiveJul 22 2018Apr 10 2019Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based ... More
Geometric Shape Features Extraction Using a Steady State Partial Differential Equation SystemJun 13 2018Jan 25 2019A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to extract the ... More
Geometric Shape Features Extraction Using a Steady State Partial Differential Equation SystemJun 13 2018Apr 13 2019A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to extract the ... More
Selections and Higher Separation AxiomsMay 19 2018Oct 15 2018This survey presents some historical background and recent developments in the area of selections for set-valued mappings along with several open questions. It was written with the hope that the presented material may pique an interest in the selection ... More
Quaternionic Fundamental Cardinal Splines: Interpolation and SamplingApr 18 2018B-splines $B_{q}$, $\Sc q > 1$, of quaternionic order $q$, for short quaternionic B-splines, are quaternion-valued piecewise M\"{u}ntz polynomials whose scalar parts interpolate the classical Schoenberg splines $B_{n}$, $n\in\N$, with respect to degree ... More
New recursive approximations for variable-order fractional operators with applicationsApr 04 2018To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation. In this paper, we develop Laguerre spectral collocation methods for solving variable-order fractional ... More
A note on two-colorability of nonuniform hypergraphsMar 08 2018For a hypergraph $H$, let $q(H)$ denote the expected number of monochromatic edges when the color of each vertex in $H$ is sampled uniformly at random from the set of size 2. Let $s_{\min}(H)$ denote the minimum size of an edge in $H$. Erd\H{o}s asked ... More
PDE-constrained optimization in medical image analysisFeb 28 2018PDE-constrained optimization problems find many applications in medical image analysis, for example, neuroimaging, cardiovascular imaging, and oncological imaging. We review related literature and give examples on the formulation, discretization, and ... More
Function approximation using gradient information with application to parametric and stochastic differential equationsFeb 05 2018In the paper we consider the problem of multivariate function approximation in polynomial basis. In order to solve this problem, we adjust the least squares method (LSM) by adding information about derivatives of the function. This modification allows ... More
A Probabilistic Subspace Bound with Application to Active SubspacesJan 02 2018Given a real symmetric positive semi-definite matrix E, and an approximation S that is a sum of n independent matrix-valued random variables, we present bounds on the relative error in S due to randomization. The bounds do not depend on the matrix dimensions ... More
Hypergraphs not containing a tight tree with a bounded trunkDec 12 2017An $r$-uniform hypergraph is a tight $r$-tree if its edges can be ordered so that every edge $e$ contains a vertex $v$ that does not belong to any preceding edge and the set $e-v$ lies in some preceding edge. A conjecture of Kalai [Kalai], generalizing ... More
On Mubayi's Conjecture and conditionally intersecting setsNov 15 2017Oct 31 2018Mubayi's Conjecture states that if $\mathcal{F}$ is a family of $k$-sized subsets of $[n] = \{1,\ldots,n\}$ which, for $k \geq d \geq 2$, satisfies $A_1 \cap\cdots\cap A_d \neq \emptyset$ whenever $|A_1 \cup\cdots\cup A_d| \leq 2k$ for all distinct sets ... More
Rigorous numerics of finite-time singularities in dynamical systems - methodology and applicationsNov 06 2017This paper aims at providing rigorous numerical computation procedure for finite-time singularities in dynamical systems. Combination of time-scale desingularization as well as Lyapunov functions validation on stable manifolds of invariant sets for desingularized ... More
Circulant embedding with QMC -- analysis for elliptic PDE with lognormal coefficientsOct 25 2017Apr 02 2018In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random coefficients. ... More
Efficient Statistically Accurate Algorithms for the Fokker-Planck Equation in Large DimensionsSep 16 2017Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing the fat tailed ... More
Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified SettingsSep 01 2017Oct 30 2018This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than ... More
A Koksma-Hlawka-Potential Identity on the $d$ Dimensional Sphere and its Applications to DiscrepancyJul 27 2017Let $d\geq 2$ be an integer, $S^d\subset {\mathbb R}^{d+1}$ the unit sphere and $\sigma$ a finite signed measure whose positive and negative parts are supported on $S^d$ with finite energy. In this paper, we derive an error estimate for the quantity $\left|\int_{S^d}fd\sigma\right|$, ... More
Asymptotic expansion for solutions of the Navier-Stokes equations with non-potential body forcesJul 25 2017Nov 21 2017We study the long-time behavior of spatially periodic solutions of the Navier-Stokes equations in the three-dimensional space. The body force is assumed to possess an asymptotic expansion or, resp., finite asymptotic approximation, in either Sobolev or ... More
Paths in hypergraphs: a rescaling phenomenonJun 26 2017Let $P^k_\ell$ denote the loose $k$-path of length $\ell$ and let define $f^k_\ell(n,m)$ as the minimum value of $\Delta(H)$ over all $P^k_\ell$-free $k$-graphs $H$ with $n$ vertices and $m$ edges. In the paper we study the behavior of $f^4_2(n,m)$ and ... More
Warps and grids for double and triple vector bundlesMay 02 2017May 22 2017A triple vector bundle is a cube of vector bundle structures which commute in the (strict) categorical sense. A grid in a triple vector bundle is a collection of sections of each bundle structure with certain linearity properties. A grid provides two ... More
A hybridizable discontinuous Galerkin method for the Navier--Stokes equations with pointwise divergence-free velocity fieldApr 25 2017Jan 31 2018We introduce a hybridizable discontinuous Galerkin method for the incompressible Navier--Stokes equations for which the approximate velocity field is pointwise divergence-free. The method builds on the method presented by Labeur and Wells [SIAM J. Sci. ... More
A Numerical Algorithm for C2-splines on Symmetric SpacesMar 28 2017Mar 07 2018Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing need for spline ... More
Automatic Data Deformation Analysis on Evolving Folksonomy Driven EnvironmentDec 30 2016The Folksodriven framework makes it possible for data scientists to define an ontology environment where searching for buried patterns that have some kind of predictive power to build predictive models more effectively. It accomplishes this through an ... More
FolksoDrivenCloud: an annotation and process application for social collaborative networkingDec 30 2016In this paper we present the FolksoDriven Cloud (FDC) built on Cloud and on Semantic technologies. Cloud computing has emerged in these recent years as the new paradigm for the provision of on-demand distributed computing resources. Semantic Web can be ... More
Fluids, Geometry, and the Onset of Navier-Stokes Turbulence in Three Space DimensionsDec 27 2016Oct 03 2017A theory for the evolution of a metric $g$ driven by the equations of three-dimensional continuum mechanics is developed. This metric in turn allows for the local existence of an evolving three-dimensional Riemannian manifold immersed in the six-dimensional ... More
On the homogenization of the Helmholtz problem with thin perforated walls of finite lengthNov 18 2016Jun 22 2017In this work, we present a new solution representation for the Helmholtz transmission problem in a bounded domain in $\mathbb{R}^2$ with a thin and periodic layer of finite length. The layer may consists of a periodic pertubation of the material coefficients ... More
On the homogenization of the Helmholtz problem with thin perforated walls of finite lengthNov 18 2016In this work, we present a new solution representation for the Helmholtz transmission problem in a bounded domain in $\mathbb{R}^2$ with a thin and periodic layer of finite length. The layer may consists of a periodic pertubation of the material coefficients ... More
High codegree subgraphs in weakly quasirandom 3-graphsOct 20 2016We show that we can extract large subgraphs with high minimum codegree from sequences of weakly quasirandom $3$-graphs, for a particular notion of weakly quasirandom studied by Reiher, R\"odl and Schacht. In particular for any family of nonempty $3$-graphs ... More
Besov Regularity for the Stationary Navier-Stokes Equation on Bounded Lipschitz DomainsAug 02 2016We use the scale $B^s_{\tau}(L_\tau(\Omega))$, $1/\tau=s/d+1/2$, $s>0$, to study the regularity of the stationary Stokes equation on bounded Lipschitz domains $\Omega\subset\mathbb{R}^d$, $d\geq 3$, with connected boundary. The regularity in these Besov ... More
Dimensions of multi-fan algebrasJul 13 2016Given an arbitrary non-zero simplicial cycle and a generic vector coloring of its vertices, there is a way to produce a graded Poincare duality algebra associated with these data. The procedure relies on the theory of volume polynomials and multi-fans. ... More
Dimensions of multi-fan algebrasJul 13 2016Dec 01 2016Given an arbitrary non-zero simplicial cycle and a generic vector coloring of its vertices, there is a way to produce a graded Poincare duality algebra associated with these data. The procedure relies on the theory of volume polynomials and multi-fans. ... More
Fluids, Elasticity, Geometry, and the Existence of Wrinkled SolutionsMay 10 2016Sep 24 2016We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the interconnected nonlinear partial differential equations. In this paper, we develop such ... More
Fluids, Elasticity, Geometry, and the Existence of Wrinkled SolutionsMay 10 2016Aug 26 2017We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we develop such connections ... More
A Monte Carlo method for integration of multivariate smooth functions I: Sobolev spacesApr 20 2016We study a Monte Carlo algorithm that is based on a specific (randomly shifted and dilated) lattice point set. The main result of this paper is that the mean squared error for a given compactly supported, square-integrable function is bounded by $n^{-1/2}$ ... More
A Monte Carlo method for integration of multivariate smooth functionsApr 20 2016Jun 21 2017We study a Monte Carlo algorithm that is based on a specific (randomly shifted and dilated) lattice point set. The main result of this paper is that the mean squared error for a given compactly supported, square-integrable function is bounded by $n^{-1/2}$ ... More
Scaling invariant Harnack inequalities in a general settingApr 06 2016Jul 13 2016In a setting, where only "exit measures" are given, as they are associated with an arbitrary right continuous strong Markov process on a separable metric space, we provide simple criteria for the validity of Harnack inequalities for positive harmonic ... More
On a generalized uniform zero-two law for positive contractions of non-commutative $L_1$-spaces and its vector-valued extensionMar 25 2016First, Ornstein and Sucheston proved that for a given positive contraction $T:L_1\to L_1$ there exists $m\in N$ such that $\big\|T^{m+1}-T^m\|<2$ then $$ \lim_{n\to\infty}\|T^{n+1}-T^n\|=0. $$ Such a result was labeled as "zero-two" law. In the present ... More
The coherent matching distance in 2D persistent homologyMar 12 2016Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by considering a suitable family of filtering functions associated with lines ... More
Position paper: Towards an observer-oriented theory of shape comparisonMar 07 2016In this position paper we suggest a possible metric approach to shape comparison that is based on a mathematical formalization of the concept of observer, seen as a collection of suitable operators acting on a metric space of functions. These functions ... More
A sharp interface immersed boundary method for solving flow with arbitrarily irregular and changing geometryFeb 22 2016In this paper, a sharp interface immersed boundary method is developed for efficiently and robustly solving flow with arbitrarily irregular and changing geometries. The proposed method employs a three-step prediction-correction flow reconstruction scheme ... More
An immersed boundary method for solving compressible flow with arbitrarily irregular and moving geometryFeb 22 2016Apr 18 2018In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy boundary conditions ... More
Mathematical Modeling of Myosin Induced Bistability of Lamellipodial FragmentsNov 27 2015For various cell types and for lamellipodial fragments on flat surfaces, externally induced and spontaneous transitions between symmetric nonmoving states and polarized migration have been observed. This behavior is indicative of bistability of the cytoskeleton ... More
Stability and Turán numbers of a class of hypergraphs via LagrangiansOct 12 2015Given a family of $r$-uniform hypergraphs ${\cal F}$ (or $r$-graphs for brevity), the Tur\'an number $ex(n,{\cal F})$ of ${\cal F}$ is the maximum number of edges in an $r$-graph on $n$ vertices that does not contain any member of ${\cal F}$. A pair $\{u,v\}$ ... More
A green perspective on capacitated time-dependent vehicle routing problem with time windowsSep 29 2015Sep 17 2017This study presents a novel approach to the vehicle routing problem by focusing on greenhouse gas emissions and fuel consumption aiming to mitigate adverse environmental effects of transportation. A time-dependent model with time windows is developed ... More
A green perspective on capacitated time-dependent vehicle routing problem with time windowsSep 29 2015This study presents a novel approach to the vehicle routing problem by focusing on greenhouse gas emissions and fuel consumption aiming to mitigate adverse environmental effects of transportation. A time-dependent model with time windows is developed ... More
Exact simulation of the Wright-Fisher diffusionJun 23 2015Jul 22 2016The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article we demonstrate that it is in fact ... More
Turán numbers of hypergraph treesMay 13 2015An $r$-graph is an $r$-uniform hypergraph tree (or $r$-tree) if its edges can be ordered as $E_1,\ldots, E_m$ such that $\forall i>1 \, \exists \alpha(i)<i$ such that $E_i\cap (\bigcup_{j=1}^{i-1} E_j)\subseteq E_{\alpha(i)}$. The Tur\'an number $ex(n,{\cal ... More
Asymptotics of parabolic Green's functions on latticesApr 10 2015Jun 29 2016For parabolic spatially discrete equations, we consider Green's functions, also known as heat kernels on lattices. We obtain their asymptotic expansions with respect to powers of time variable $t$ up to an arbitrary order and estimate the remainders uniformly ... More
Existence results in dislocation based rate-independent isotropic gradient plasticity with kinematical hardening and plastic spin: The case with symmetric local backstressApr 08 2015In this paper we use convex analysis and variational inequality methods to establish an existence result for a model of infinitesimal rate-independent gradient plasticity with kinematic hardening and plastic spin, in which the local backstress tensor ... More
A Survey of Manoeuvring Target Tracking MethodsMar 06 2015A comprehensive review of the literature on manoeuvring target tracking for both uncluttered and cluttered measurements is presented. Various discrete-time dynamical models including non-random input, random-input and switching or hybrid system manoeuvre ... More
On "stability" in the Erdős-Ko-Rado theoremFeb 19 2015Denote by $K_p(n,k)$ the random subgraph of the usual Kneser graph $K(n,k)$ in which edges appear independently, each with probability $p$. Answering a question of Bollob\'as, Narayanan, and Raigorodskii,we show that there is a fixed $p<1$ such that a.s. ... More
Function of Forgetfulness for the Tedium of Oblivion on Liquidity of Ontology MatchingJan 02 2015The shallow and fragile knowledge on the Web does not examine in depth the things: it behaves lightly. The conditions created by the Web makes our attention labile and especially fickle, it's unable to concentrate for long as we are trained to "surf" ... More
Liquidity on Web Dynamic NetworkDec 31 2014Nowadays, the exponentially growing of the Web renders the problem of correlation among different topics of paramount importance. The proposed model can be used to study the evolution of network depicted by different topics on the web correlated by a ... More
On 3-uniform hypergraphs without a cycle of a given lengthDec 27 2014Dec 30 2014We study the maximum number of hyperedges in a 3-uniform hypergraph on $n$ vertices that does not contain a Berge cycle of a given length $\ell$. In particular we prove that the upper bound for $C_{2k+1}$-free hypergraphs is of the order $O(k^2n^{1+1/k})$, ... More
Efficient XVA Management: Pricing, Hedging, and Attribution using Trade-Level Regression and Global ConditioningDec 17 2014Dec 22 2014Banks must manage their trading books, not just value them. Pricing includes valuation adjustments collectively known as XVA (at least credit, funding, capital and tax), so management must also include XVA. In trading book management we focus on pricing, ... More
Infinite loop spaces and positive scalar curvatureNov 26 2014Mar 02 2016We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a secondary ... More
Infinite loop spaces and positive scalar curvatureNov 26 2014Jan 23 2017We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a secondary ... More
Computing minimal interpolants in $C^{1,1}(\mathbb{R}^d)$Nov 20 2014Oct 26 2016We consider the following interpolation problem. Suppose one is given a finite set $E \subset \mathbb{R}^d$, a function $f: E \rightarrow \mathbb{R}$, and possibly the gradients of $f$ at the points of $E$. We want to interpolate the given information ... More
Computing minimal interpolants in $C^{1,1}(\mathbb{R}^d)$Nov 20 2014Jun 17 2016We consider the following interpolation problem. Suppose one is given a finite set $E \subset \mathbb{R}^d$, a function $f: E \rightarrow \mathbb{R}$, and possibly the gradients of $f$ at the points of $E$. We want to interpolate the given information ... More
Representation of group isomorphisms. The compact caseNov 06 2014Dec 18 2014Let $G$ be a discrete group and let $\mathcal A$ and $\mathcal B$ be two subgroups of $G$-valued continuous functions defined on two $0$-dimensional compact spaces $X$ and $Y$. A group isomorphism $H$ defined between $\mathcal A$ and $\mathcal B$ is called ... More
Well-posedness for dislocation based gradient visco-plasticity with isotropic hardeningNov 05 2014In this work we establish the well-posedness for infinitesimal dislocation based gradient viscoplasticity with isotropic hardening for general gradient monotone plastic flows. We assume an additive split of the displacement gradient into non-symmetric ... More
Partition of unity systems and B-splinesOct 20 2014This paper presents the basic principles of partition of unity systems and B-splines. Analysis of these systems is performed using Fourier analysis, multi-resolution analysis, and wavelet analysis.
Fluctuation Analysis of Adaptive Multilevel SplittingAug 27 2014Sep 18 2015Multilevel Splitting is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel Splitting techniques. ... More
Entropy dissipation estimates for the Landau equation in the Coulomb case and applicationsAug 26 2014Oct 28 2014We present in this paper an estimate which bounds from below the entropy dissipation D(f) of the Landau operator with Coulomb interaction by a weighted H^1 norm of the square root of f. As a consequence, we get a weighted L^1_t(L^3_v) estimate for the ... More
A stochastic Gauss-Bonnet-Chern formulaAug 25 2014Apr 28 2015We prove that a Gaussian ensemble of smooth random sections of a real vector bundle over compact manifold canonically defines a metric on the bundle together with a connection compatible with it. Additionally, we prove a refined Gauss-Bonnet-Chern theorem ... More
Min-max representations of viscosity solutions of Hamilton-Jacobi equations and applications in rare-event simulationJun 13 2014In this paper a duality relation between the Ma\~{n}\'e potential and Mather's action functional is derived in the context of convex and state-dependent Hamiltonians. The duality relation is used to obtain min-max representations of viscosity solutions ... More
VAR and ES/CVAR Dependence on data cleaning and Data Models: Analysis and ResolutionMay 29 2014Historical (Stressed-) Value-at-Risk ((S)VAR), and Expected Shortfall (ES), are widely used risk measures in regulatory capital and Initial Margin, i.e. funding, computations. However, whilst the definitions of VAR and ES are unambiguous, they depend ... More
On hypergraph LagrangiansApr 30 2014It is conjectured by Frankl and F\"uredi that the $r$-uniform hypergraph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${\mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-uniform hypergraphs with $m$ edges in \cite{FF}. ... More
On particle Gibbs Markov chain Monte Carlo modelsApr 23 2014Oct 25 2014This article analyses a new class of advanced particle Markov chain Monte Carlo algorithms recently introduced by Andrieu, Doucet, and Holenstein (2010). We present a natural interpretation of these methods in terms of well known unbiasedness properties ... More
The Gauss-Bonnet-Chern theorem: a probabilistic perspectiveApr 21 2014Jan 18 2016We prove that the Euler form of a metric connection on real oriented vector bundle $E$ over a compact oriented manifold $M$ can be identified, as a current, with the expectation of the random current defined by the zero-locus of a certain random section ... More
Measurable bundles of Banach algebrasApr 13 2014In the present paper we investigate Banach--Kantorovich algebras over faithful solid subalgebras of algebras measurable functions. We prove that any Banach--Kantorovich algebra over faithful solid subalgebras of algebra measurable functions represented ... More
Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic Keller-Segel system in the planeMar 11 2014In the present article we consider several issues concerning the doubly parabolic Keller-Segel system in the plane, when the initial data belong to critical scaling-invariant Lebesgue spaces. More specifically, we analyze the global existence of integral ... More
A family of energy stable, skew-symmetric finite difference schemes on collocated gridsFeb 05 2014A simple scheme for incompressible, constant density flows is presented, which avoids odd-even decoupling for the Laplacian on a collocated grids. Energy stability is implied by maintaining strict energy conservation. Momentum is conserved. Arbitrary ... More
Combining persistent homology and invariance groups for shape comparisonDec 27 2013Jan 28 2016In many applications concerning the comparison of data expressed by $\mathbb{R}^m$-valued functions defined on a topological space $X$, the invariance with respect to a given group $G$ of self-homeomorphisms of $X$ is required. While persistent homology ... More