Related papers: Minimal cut-generating functions are nearly extrem…
We introduce an interesting method of proving separable reduction theorems - the method of elementary submodels. We are studying whether it is true that a set (function) has given property if and only if it has this property with respect to…
In this paper, we study a class of functions defined recursively on the set of natural numbers in terms of the greatest common divisor algorithm of two numbers and requiring a minimality condition. These functions are permutations, products…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
Our object of study is extremal functions which are defined by distance functions of convex bodies. These functions take values in the moduli spaces of algebraic and geometric objects associated with these ${\mathbb Z}$-modules (geometric…
We construct uncountably generated algebras inside the following sets of special functions: Sierpi\'nski-Zygmund functions, perfectly everywhere surjective functions and nowhere continuous Darboux functions. All conclusions obtained in this…
We consider maps with tight boundaries, i.e. maps whose boundaries have minimal length in their homotopy class, and discuss the properties of their generating functions $T^{(g)}_{\ell_1,\ldots,\ell_n}$ for fixed genus $g$ and prescribed…
We present software for investigations with cut-generating functions in the Gomory--Johnson model and extensions, implemented in the computer algebra system SageMath.
We define and study multi-colored dimer models on a segment and on a circle. The multivariate generating functions for the dimer models satisfy the recurrence relations similar to the one for Fibonacci numbers. We give closed formulae for…
We introduce a notion of locally approximable continuous CR functions on locally closed subsets of reduced complex spaces, generalizing both holomorphic functions and CR functions on CR submanifolds. Under additional assumptions of…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
We consider stationary configurations of points in Euclidean space which are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness.…
We prove three strong approximation theorems for the `supermarket' or `join the shortest queue' model -- a law of large numbers, a jump process approximation and a central limit theorem. The estimates are carried through rather explicitly.…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
Let G be a group generated by $r$ elements $g_1,g_2,..., g_r.$ Among the reduced words in $g_1,g_2,..., g_r$ of length $n$ some, say $\gamma_n,$ represent the identity element of the group $G.$ It has been shown in a combinatorial way that…
Suppose that ${\mathcal M}$ is a model of PA and ${\mathcal N}$ is a countably generated elementary end extension of ${\mathcal M}$. Let ${\mathfrak X}$ be the set of subsets of M that are coded by ${\mathcal N}$. Then ${\mathcal M}$ has a…
We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…
We consider the problem of reconstructing a function given its values on a set of points with finite density. We prove that with probability one, the values of an almost periodic function on a random array of points (with finite density)…
We consider certain finite sets of circle-valued functions defined on intervals of real numbers and estimate how large the intervals must be for the values of these functions to be uniformly distributed in an approximate way. This is used…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…