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The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…
We continue the investigations of lattice walks in the three dimensional lattice restricted to the positive octant. We separate models which clearly have a D-finite generating function from models for which there is no reason to expect that…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…
Algebraic Combinatorics originated in Algebra and Representation Theory, studying their discrete objects and integral quantities via combinatorial methods which have since developed independent and self-contained lives and brought us some…
Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a…
Let $F(x)= \sum_{\nu\in\NN^d} F_\nu x^\nu$ be a multivariate power series with complex coefficients that converges in a neighborhood of the origin. Assume $F=G/H$ for some functions $G$ and $H$ holomorphic in a neighborhood of the origin.…
The classical approach to analyzing extreme value data is the generalized Pareto distribution (GPD). When the GPD is used to explain a target variable with the large dimension of covariates, the shape and scale function of covariates…
Let $G$ be a directed graph on finitely many vertices and edges, and assign a positive weight to each edge on $G$. Fix vertices $u$ and $v$ and consider the set of paths that start at $u$ and end at $v$, self-intersecting in any number of…
In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical…
We define the asymptotic behavior "almost everywhere" of additive and multiplicative arithmetic functions in the paper. Classes of additive and multiplicative arithmetic functions are singled out for which the asymptotics coincides "almost…
Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively…
Persistent homology has undergone significant development in recent years. However, one outstanding challenge is to build a coherent statistical inference procedure on persistent diagrams. In this paper, we first present a new lattice path…
We propose new ensemble models for multivariate functional data classification as combinations of semi-metric-based weak learners. Our models extend current semi-metric-type methods from the univariate to the multivariate case, propose new…
In stochastic optimization, a common tool to deal sequentially with large sample is to consider the well-known stochastic gradient algorithm. Nevertheless, since the stepsequence is the same for each direction, this can lead to bad results…
The process by which one may take a discrete model of a biophysical process and construct a continuous model based on it is of mathematical interest as well as being of practical use. In this paper, we first study the singular limit of a…
For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…
Many processes of scientific and technological interest are characterized by time scales that render their simulation impossible if one uses present day simulation capabilities. To overcome this challenge a variety of enhanced simulation…
Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on…
In this article we combine the study of solutions of PDEs with the study of asymptotic properties of the solutions via compactification of the domain. We define new spaces of functions on which study the equations, prove a version of…