Related papers: Approximations of Mappings
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…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
We discuss the feasibility of the following learning problem: given unmatched samples from two domains and nothing else, learn a mapping between the two, which preserves semantics. Due to the lack of paired samples and without any…
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…
We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…
We show that badly approximable matrices are exactly those that, for any inhomogeneous parameter, can not be inhomogeneous approximated at every monotone divergent rate, which generalizes Ram\'irez's result (2018). We also establish some…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
By studying $\mathbb{A}^1$-curves on varieties, we propose a geometric approach to strong approximation problem over function fields of complex curves. We prove that strong approximation holds for smooth, low degree affine complete…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
We are studying spatial mappings that satisfy some space analog of a hydrodynamical type of growth in the neighborhood of the infinity. It is proved that homeomorphisms of the specified class form equicontinuous families under some…
We give the theorem of coincidence of a class of functions defined by a generalised modulus of smoothness with a class of functions defined by the order of the best approximation by algebraic polynomials. We also prove the appropriate…
We study the maximum Hamming distance (or rather, the complementary notion of "minimum approximability") of a general function on a finite group $G$ to either of the sets $\operatorname{End}(G)$ and $\operatorname{Aff}(G)$, of group…
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and…
The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler, and 10-1000 times…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of…
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of…
We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…
It was conjectured that if $f\in C^1(\mathbb{R}^n,\mathbb{R}^n)$ satisfies $\operatorname{rank} Df\leq m<n$ everywhere in $\mathbb{R}^n$, then $f$ can be uniformly approximated by $C^\infty$-mappings $g$ satisfying $\operatorname{rank}…