Related papers: Ripser: efficient computation of Vietoris-Rips per…
We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a…
In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.
We propose a space-efficient algorithm for hidden surface removal that combines one of the fastest previous algorithms for that problem with techniques based on bit manipulation. Such techniques had been successfully used in other settings,…
We study a family of invariants of compact metric spaces that combines the Curvature Sets defined by Gromov in the 1980s with Vietoris-Rips Persistent Homology. For given integers $k\geq 0$ and $n\geq 1$ we consider the dimension $k$…
The correction procedure via reconstruction (CPR, also known as flux reconstruction) is a framework of high order semidiscretisations used for the numerical solution of hyperbolic conservation laws. Using a reformulation of these schemes…
In this paper, we describe a framework to compute expected convergence rates for residuals based on the Calder\'on identities for general second order differential operators for which fundamental solutions are known. The idea is that these…
This paper presents a computationally efficient yet powerful binary framework for robust facial representation based on image gradients. It is termed as structural binary gradient patterns (SBGP). To discover underlying local structures in…
We introduce a theoretical and computational framework to use discrete Morse theory as an efficient preprocessing in order to compute zigzag persistent homology. From a zigzag filtration of complexes $(K_i)$, we introduce a zigzag Morse…
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topological data analysis where matrix reduction is the major…
We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and…
Given a metric space $(X,d)$, the Vietoris-Rips complex of $X$ at a scale of $r >0$ is a simplicial complex whose simplices are all those finite subsets of $X$ with diameter less than $r$. In this paper, we classify, up to simplicial…
A filtration over a simplicial complex $K$ is an ordering of the simplices of $K$ such that all prefixes in the ordering are subcomplexes of $K$. Filtrations are at the core of Persistent Homology, a major tool in Topological Data Analysis.…
Computing the gradients of a rendering process is paramount for diverse applications in computer vision and graphics. However, accurate computation of these gradients is challenging due to discontinuities and rendering approximations,…
Simplex gradients are an essential feature of many derivative free optimization algorithms, and can be employed, for example, as part of the process of defining a direction of search, or as part of a termination criterion. The calculation…
Algorithms for the symbolic computation of conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of…
In this paper, we present a stable and efficient approach for constructing Laguerre pseudospectral differentiation matrices. The proposed method reformulates the off-diagonal entries and computes all required quantities simultaneously using…
This paper presents a novel algorithm, the particle-based, rapid incremental smoother (PaRIS), for efficient online approximation of smoothed expectations of additive state functionals in general hidden Markov models. The algorithm, which…
We present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. Given a system of differential equations possessing conservation laws, our approach is based on…
The Delaunay-Rips filtration is a lighter and faster alternative to the well-known Rips filtration for low-dimensional Euclidean point clouds. Despite these advantages, it has seldom been studied. In this paper, we aim to bridge this gap by…
We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work is an extension of the so-called Sparse Cardinal Sine…