Related papers: Competition between Discrete Random Variables, wit…
We present decidability results for a sub-class of "non-interactive" simulation problems, a well-studied class of problems in information theory. A non-interactive simulation problem is specified by two distributions $P(x,y)$ and $Q(u,v)$:…
In this work we study the problem of user association and resource allocation to maximize the proportional fairness of a wireless network with limited backhaul capacity. The optimal solution of this problem requires solving a mixed integer…
For three natural classes of dynamic decision problems; 1. additively separable problems, 2. discounted problems, and 3. discounted problems for a fixed discount factor; we provide necessary and sufficient conditions for one sequential…
We present a mathematical model for communication subject to both network interference and noise. We introduce a framework where the interferers are scattered according to a spatial Poisson process, and are operating asynchronously in a…
Competition is ubiquitous in many complex biological, social, and technological systems, playing an integral role in the evolutionary dynamics of the systems. It is often useful to determine the dominance hierarchy or the rankings of the…
We extend the study of the occupancy fraction of the hard-core model in two novel directions. One direction gives a tight lower bound in terms of individual vertex degrees, extending work of Sah, Sawhney, Stoner and Zhao which bounds the…
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The…
Occupancy models are frequently used by ecologists to quantify spatial variation in species distributions while accounting for observational biases in the collection of detection-nondetection data. However, the common assumption that a…
Multivariate interaction between two or more classes (or species) has important consequences in many fields and causes multivariate clustering patterns such as segregation or association. The spatial segregation occurs when members of a…
We study the classical rent division problem, where $n$ agents must allocate $n$ indivisible rooms and split a fixed total rent $R$. The goal is to compute an envy-free (EF) allocation, where no agent prefers another agent's room and rent…
A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to…
We present a stylized model of the allocation of resources on a network. By considering as a concrete example the network of sectors of the airspace, where each node is a sector characterized by a maximal number of simultaneously present…
Evolutionary Prisoner's Dilemma games with quenched inhomogeneities in the spatial dynamical rules are considered. The players following one of the two pure strategies (cooperation or defection) are distributed on a two-dimensional lattice.…
It is the intention of this paper to rigorously clarify the role of the occupation numbers in the current practical applications of the density functional formalism. In these calculations one has to decide how to distribute a given, fixed…
Many complex phenomena, from the selection of traits in biological systems to hierarchy formation in social and economic entities, show signs of competition and heterogeneous performance in the temporal evolution of their components, which…
This paper attempts to find out numerically the distribution of the queue-length ratio in the context of a model of preferential attachment. Here we consider two restaurants only and a large number of customers (agents) who come to these…
In the classical cake cutting problem, a resource must be divided among agents with different utilities so that each agent believes they have received a fair share of the resource relative to the other agents. We introduce a variant of the…
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…
For simultaneous independent events with finitely many outcomes, consider the expected-utility problem with nonnegative wagers and an endogenous cash position. We prove a short support theorem for a broad class of strictly increasing…
In this paper we address two basic questions in wireless communication: First, how long does it take to schedule an arbitrary set of communication requests? Second, given a set of communication requests, how many of them can be scheduled…