Related papers: Simplicial approximation and complexity growth

It is known that any two triangulations of a compact 3-manifold are related by finite sequences of certain local transformations. We prove here an upper bound for the length of a shortest transformation sequence relating any two…

Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step…

This paper introduces some inverse sequences of different polyhedra all based on finite approximations of a compact metric space so they can be used to capture the shape type of the original space. It is shown that they are HPol-expansions,…

We consider a subclass of tilings, the tilings obtained by cut and projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent \alpha in terms of the ranks of…

This note establishes smooth approximation from above for J-plurisubharmonic functions on an almost complex manifold (X,J). The following theorem is proved. Suppose X is J-pseudoconvex, i.e., X admits a smooth strictly J-plurisubharmonic…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

Small, finite entities are easier and simpler to manipulate than gigantic, infinite ones. Consequently huge chunks of mathematics are devoted to methods reducing the study of big, cumbersome objects to an analysis of their finite building…

We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…

The notions Golodness and tightness for simplicial complexes come from algebra and geometry, respectively. We prove these two notions are equivalent for 3-manifold triangulations, through a topological characterization of a polyhedral…

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued…

This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the…

We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…

The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The…

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…

We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…

We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…

We consider two categories related to symplectic manifolds: 1. Objects are symplectic manifolds and morphisms are symplectic embeddings. 2. Objects are symplectic manifolds endowed with compatible almost complex structure and morphisms are…

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…

Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…