arXiv research

The paper studies stability of nilpotent structures on collapsed manifolds.

We present a fully nonparametric method to estimate the value function, via simulation, in the context of expected infinite-horizon discounted rewards for Markov chains. Estimating such value functions plays an important role in approximate dynamic programming and applied probability in general. We incorporate "soft in…

This paper determines the flexible exponent for non-geometric 3-manifolds.

A lot of effort has been invested into characterizing the convergence rates of gradient based algorithms for non-linear convex optimization. Recently, motivated by large datasets and problems in machine learning, the interest has shifted towards distributed optimization. In this work we present a distributed algorithm …

Study shows how to control jump-diffusion processes with stable feedback controls in reinforcement learning.

New bounds on mapping degrees for geometric 3-manifolds.

This work analyzes how deep neural networks' expressiveness increases with depth and width.

Study examines equivalence relations on the pair of pants, proving k-equivalence implies 1-equivalence and 2-equivalence.

Study geometric equivalence of smooth map germs.

Paper solves equivalence problems for fifth-order differential operators using Cartan's method.

Paper extends Stanford's equivalence to virtual knots and proves equivalence to Goussarov-Polyak-Viro's n-equivalence.

Geodesically equivalent metrics on homogeneous spaces are shown to be affinely equivalent.

In this paper we discuss four problems regarding Markov equivalences for subclasses of loopless mixed graphs. We classify these four problems as finding conditions for internal Markov equivalence, which is Markov equivalence within a subclass, for external Markov equivalence, which is Markov equivalence between subclas…

This paper shows that certain knots are equivalent under a specific relation.

This article is dedicated to solve the equivalence problem for two third order differential operators on the line under general fiber--preserving transformation using the Cartan method of equivalence. We will do three versions of the equivalence problems: first via the direct equivalence problem, second equivalence pro…

Polynomials with similar modulus levels are bilipschitz equivalent.

Equivalent bicategories constructed from action Lie groupoids.

Paper discusses when virtual links are equivalent as twisted links.

Develops $L_\infty$ spaces over dg manifolds and establishes an equivalence with $L_\infty$ algebroids.

Two Riemannian manifolds are called eigenvalue equivalent when their sets of eigenvalues of the Laplace-Beltrami operator are equal (ignoring multiplicities). They are (primitive) length equivalent when the sets of lengths of their (primitive) closed geodesics are equal. We give a general construction of eigenvalue equ…

Develops a new method for solving equivalence problems in pseudo-groups.

Unified notion of equivalence for causal graphs, cyclic or acyclic.

Paper refines braidoid equivalence for spherical knotoids.

In this paper, two sufficient conditions are provided for given two K-equivalent map-germs to be bi-Lipschitz A-equivalent. These are Lipschitz analogues of the known results on C^r-A-equivalence $(0 \leq r \leq \infty)$ for given two K-equivalent map-germs. As a corollary of one of our results, a Lipschitz version of …

New Upsilon invariants rule out stable equivalence of knot complexes.

Paper explores state-action equivalence in RL, improving regret bounds.

New R-equivalence classes found for torus knot diagrams.

In present paper, the equivalence problem for fourth order differential operators with one variable under general fiber-preserving transformation using the Cartan method of equivalence is applied. Two versions of equivalence problems are considered. First, the direct equivalence problem and second equivalence problem i…

Link-homotopy and self Delta-equivalence are equivalence relations on links. It was shown by J. Milnor (resp. the last author) that Milnor invariants determine whether or not a link is link-homotopic (resp. self Delta-equivalent) to a trivial link. We study link-homotopy and self Delta-equivalence on a certain componen…

Paper defines curvature equivalence for Legendre curves in a plane.

The equivalence (or weak equivalence) classes of orientation-preserving free actions of a finite group G on an orientable 3-dimensional handlebody of genus g can be enumerated in terms of sets of generators of G. They correspond to the equivalence classes of generating n-vectors of elements of G, where n=1+(g-1)/|G|, u…

Let $M$ and $N$ be Nash manifolds, and $f$ and $g$ Nash maps from $M$ to $N$. If $M$ and $N$ are compact and if $f$ and $g$ are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, $C^infty$ R-L equivalence of two Nash map germs implies Nash R-L equivalence. This shows a difference of Nash…

Study stable equivalence relations on 4-manifolds, proving homotopy equivalent manifolds with abelian fundamental group are stably diffeomorphic.

Study shows equivalence in foliations and pre-symplectic forms aligns with gauge equivalence.

The paper studies Lipschitz equivalence of Cantor sets via polynomial irreducibility.

Establishes equivalence between models of derived stacks.

Handlebody groups are rigid under measure equivalence.

Complex equivalence classes found in graph homotopy.

If the fundamental group of the complement of a smooth embedding f: S^2 \subset R^4 is a cyclic group, the map can be deformed to the standard embedding by a generic one-parameter family with at most cusp singularities. If two smooth embeddings are connected by such a deformation, they will be called cusp equivalent. W…

Characterizes Bayesian networks up to unconditional equivalence.

We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent in…

System uses neural networks to prove program equivalence via rewrite rules.

Homotopy equivalence of cotangent bundles' function algebras is shown.

New equivalence for singular foliations preserves transverse geometry.

Equivalence proven between different Ricci curvature definitions.

Smooth orbit equivalence proves metric equivalence for geodesic flows.

Dynamic systems linked to infinite permutation matrices.

This paper classifies superintegrable systems on 2D geometries with projective symmetries.