Related papers: Holonomic approximation through convex integration
The geometrical structure known as Tulczyjew triple has been used with success in analytical mechanics and first order field theory to describe a wide range of physical systems including Lagrangian/Hamiltonian systems with constraints…
We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of curves with only one place at infinity. In the affirmative case, our algorithm…
This paper is to prove superconvergence of a family of simple conforming mixed finite elements of first orderfor the linear elasticity problem with the Hellinger--Reissner variational formulation. The analysis is based on three main…
The convergence rate of various first-order optimization algorithms is a pivotal concern within the numerical optimization community, as it directly reflects the efficiency of these algorithms across different optimization problems. Our…
Being able to decorrelate a feature space from protected attributes is an area of active research and study in ethics, fairness, and also natural sciences. We introduce a novel decorrelation method using Convex Neural Optimal Transport…
The purpose of this note is to revisit the results of arXiv:1407.4324 from a slightly different perspective, outlining how, if the integral closures of a finite set of prime ideals abide the expected convexity patterns, then the existence…
What has become known as Stahl's Theorem in power-engineering circles has been used to justify a convergence guarantee of the Holomorphic Embedding Method (HEM) as it applies to the power-flow problem. In this, the second part of a two-part…
For convex partitions of a convex body $B$ we prove that we can put a homothetic copy of $B$ into each set of the partition so that the sum of homothety coefficients is $\ge 1$. In the plane the partition may be arbitrary, while in higher…
In the first part of this paper, we consider, in the context of an arbitrary hyperplane arrangement, the map between compactly supported cohomology to the usual cohomology of a local system. A formula (i.e., an explicit algebraic de Rham…
This paper is devoted to a study of mathematical structures arising from choice functions satisfying the path independence property (Plott functions). We broaden the notion of a choice function by allowing of empty choice. This enables us…
We make several new contributions to the study of proper holomorphic mappings between balls. Our results include a degree estimate for rational proper maps, a new gap phenomenon for convex families of arbitrary proper maps, and an…
This paper investigates the relationship between the solvability of first-order differential equations and the topology of the underlying domain through the lens of de\,Rham cohomology. We analyze the conditions under which a closed 1-form…
We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence…
The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…
We study the approximation of holomorphic functions of several complex variables by the ring $\mathcal{P}^S(\mathbb{C}^n)$ of polynomials whose exponents are restricted to a convex cone $\mathbb{R}_+S$ for some compact convex $S\in…
This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
We introduce new global and local inexact oracle concepts for a wide class of convex functions in composite convex minimization. Such inexact oracles naturally come from primal-dual framework, barrier smoothing, inexact computations of…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
From dedicated QCD studies to new physics background estimation, jets will be everywhere at the LHC. In these proceedings, we discuss two important recent series of improvements. In the first one, we introduce new algorithms and new…