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In a recent breakthrough, Adiprasito, Avvakumov, and Karasev constructed a triangulation of the $n$-dimensional real projective space with a subexponential number of vertices. They reduced the problem to finding a small downward closed…

Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for…

Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…

In {\cal N} = 2 superconformal three-dimensional field theory the R-symmetry is determined by locally maximizing the free energy F on the three-sphere. Using F-maximization, we study the {\cal N} = 2 supersymmetric U(N_c) gauge theory…

Several finite difference methods are proposed for the infinitesimal generator of 1D asymmetric $\alpha$-stable L\'{e}vy motions, based on the fact that the operator becomes a multiplier in the spectral space. These methods take the general…

This paper is devoted to show a discrete adaptive finite element approximation result for the isotropic two-dimensional Griffith energy arising in fracture mechanics. The problem is addressed in the geometric measure theoretic framework of…

For a permutation f of an n-dimensional vector space V over a finite field of order q we let k-affinity(f) denote the number of k-flats X of V such that f(X) is also a k-flat. By k-spectrum(n,q) we mean the set of integers k-affinity(f)…

Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…

Let $G=(V,E)$ be a simple, connected graph. One is often interested in a short path between two vertices $u,v$. We propose a spectral algorithm: construct the function $\phi:V \rightarrow \mathbb{R}_{\geq 0}$ $$ \phi = \arg\min_{f:V…

We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…

We show that Fr\'echet Distance (FD), long considered impractical as a training objective, can in fact be effectively optimized in the representation space. Our idea is simple: decouple the population size for FD estimation (e.g., 50k) from…

Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…

The Special Affine Fourier Transformation(SAFT), which generalizes several well-known unitary transformations, has been demonstrated as a valuable tool in signal processing and optics. In this paper, we explore the multivariate dynamical…

We present an anytime algorithm that generates a collision-free configuration-space path that closely follows a desired path in task space, according to the discrete Frechet distance. By leveraging tools from computational geometry, we…

Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…

New method for construction of gauge-invariant deformed theory from an initial gauge theory proposed in our previous papers [1], [2] for closed/open gauge algebras is extended to the case of reducible gauge algebras. The deformation…

We consider an optimization problem in a convex space $E$ with an affine objective function, subject to $J$ constraints in the forms of inequalities on some other affine functions, where $J$ is a given nonnegative integer. Under suitable…

The problem of jam formation during the discharge by gravity of granular material through a two-dimensional silo has a number of practical applications. In many problems the estimation of the minimum outlet size which guarantees that the…

We explore the space of extremal functionals in the conformal bootstrap. By recasting the bootstrap problem as a set of non-linear equations parameterized by the CFT data, we find an efficient algorithm for converging to the extremal…

We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…