Related papers: Coverage Problem Revisited
In this paper we study the asymptotic properties of point configurations that achieve optimal covering of sets lacking smoothness. Our results include the proofs of the existence of asymptotics of best covering and maximal polarization for…
The crossing of a continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM). We characterize the spatial distribution of point-like topological defects in the…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
In this paper we provide asymptotic upper bounds on the complexity in two (closely related) situations. We confirm for the total doubling coverings and not only for the chains the expected bounds of the form $$ \kappa({\mathcal U}) \le…
This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These…
Many spherical viruses encapsulate their genome in protein shells with icosahedral symmetry. This process is spontaneous and driven by electrostatic interactions between positive domains on the virus coat proteins and the negative genome.…
The Random Sequential Adsorption (RSA) problem holds crucial theoretical and practical significance, serving as a pivotal framework for understanding and optimizing particle packing in various scientific and technological applications. Here…
Generating data from discrete distributions is important for a number of application domains including text, tabular data, and genomic data. Several groups have recently used random $k$-satisfiability ($k$-SAT) as a synthetic benchmark for…
The Consecutive-Ones Property (C1P) is a classical concept in discrete mathematics that has been used in several genomics applications, from physical mapping of contemporary genomes to the assembly of ancient genomes. A common issue in…
For a probability distribution $P$ on an at most countable alphabet $\mathcal A$, this article gives finite sample bounds for the expected occupancy counts $\mathbb E K_{n,r}$ and probabilities $\mathbb E M_{n,r}$. Both upper and lower…
We discuss the asymptotic behaviour of models of lattice polygons, mainly on the square lattice. In particular, we focus on limiting area laws in the uniform perimeter ensemble where, for fixed perimeter, each polygon of a given area occurs…
We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…
The repeat content and heterozygosity rate of a target genome are important factors in determining the feasibility of achieving a complete telomere-to-telomere assembly. The mathematical relationship between the required coverage and read…
This paper studies two problems that are motivated by the novel recent approach of composite DNA that takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm,…
In this paper, we investigate the combinatorial structure and asymptotic distribution of the solution set of the equation $\sigma(n+1) = k\sigma(n)$ for a given integer $k>1$. From a combinatorial perspective, the solutions to this equation…
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…
Irreversible random sequential deposition of interacting particles is widely used to model aggregation phenomena in physical, chemical, and biophysical systems. We show that in one dimension the exact time dependent solution of such…
We study conditions under which integer sequences with independent, identically distributed gaps are asymptotically $k$-complete, meaning that every sufficiently large integer can be represented as the sum of exactly $k$ distinct elements…
Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This…
In segmentation problems, inference on change-point position and model selection are two difficult issues due to the discrete nature of change-points. In a Bayesian context, we derive exact, non-asymptotic, explicit and tractable formulae…