Related papers: An algebraic theory of Lojasiewicz exponents

In recent papers it has been noted that the local potential approximation of the Legendre and Wilson-Polchinski flow equations give, within numerical error, identical results for a range of exponents and Wilson-Fisher fixed points in three…

We prove that the multiplicity of a filtration of a local ring satisfies various convexity properties. In particular, we show the multiplicity is convex along geodesics. As a consequence, we prove that the volume of a valuation is log…

Different variants of approximate inverse iteration like the locally optimal block preconditioned conjugate gradient method became in recent years increasingly popular for the solution of the large matrix eigenvalue problems arising from…

This work extends the iterative framework proposed by Attouch et al. (in Math. Program. 137: 91-129, 2013) for minimizing a nonconvex and nonsmooth function $\Phi$ so that the generated sequence possesses a Q-superlinear convergence rate.…

We study different maximum principles for non-local non-linear operators with non-standard growth that arise naturally in the context of fractional Orlicz-Sobolev spaces and whose most notable representative is the fractional $g-$Laplacian:…

The Lojasiewicz inequalities for real analytic functions on Euclidean space were first proved by Stanislaw Lojasiewicz (1965) using methods of semianalytic and subanalytic sets, arguments later simplified by Bierstone and Milman (1988). In…

We present a stabilized, structure-preserving finite element framework for solving the Vlasov-Maxwell equations. The method uses a tensor product of continuous polynomial spaces for the spatial and velocity domains, respectively, to…

This paper concerns the geometric structure of optimizers for frame potentials. We consider finite, real or complex frames and rotation or unitarily invariant potentials, and mostly specialize to Parseval frames, meaning the frame potential…

We develop a theory of multiplicities and mixed multiplicities of filtrations, extending the theory for filtrations of $m$-primary ideals to arbitrary (not necessarily Noetherian) filtrations. The mixed multiplicities of $r$ filtrations on…

We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…

The stochastic inverse eigenvalue problem aims to reconstruct a stochastic matrix from its spectrum. While there exists a large literature on the existence of solutions for special settings, there are only few numerical solution methods…

We define for families of finite metric spaces quantitative assembly map estimates that take into account propagation phenomena for pseudo-differential calculus. We relate these estimates to the Novikov conjecture and we show that they fit…

In this paper, we first introduce a preconditioned primal-dual gradient algorithm based on conjugate duality theory. This algorithm is designed to solve composite optimization problem whose objective function consists of two summands: a…

The main aim of the paper is to give a formula for computing the separation \L ojasiewicz exponents for two real analytic set germs via the Newton--Puiseux expansions of their defining functions. Moreover, we present an effective exponent…

Building on work of Maltsev on locally free algebras in finite purely functional languages, we revisit the model theory of (absolutely free) term algebras and their completions. Maltsev's analysis yields a natural axiomatization together…

We introduce a new functional inspired by Perelman's $\lambda$-functional adapted to the asymptotically locally Euclidean (ALE) setting and denoted $\lambda_{\operatorname{ALE}}$. Its expression includes a boundary term which turns out to…

We develop and analyse finite volume methods for the Poisson problem with boundary conditions involving oblique derivatives. We design a generic framework, for finite volume discretisations of such models, in which internal fluxes are not…

We prove non-asymptotic error bounds for particle gradient descent (PGD, Kuntz et al., 2023), a recently introduced algorithm for maximum likelihood estimation of large latent variable models obtained by discretizing a gradient flow of the…

We prove that normal projective stable families of maximal variation, of fixed dimension, and with bounded adjoint volume are birationally bounded. This is a consequence of a substantially stronger statement, formulated a priori…

We develop infinite-dimensional Ramsey theory for Fra\"iss\'e limits of finitely constrained free amalgamation classes in finite binary languages. We show that our approach is optimal and in particular, recovers the exact big Ramsey degrees…