Related papers: Maximal Counts in the Stopped Occupancy Problem

We study the classical occupancy problem from the viewpoint of its embedding Markov chain. We derive new expressions for the probability mass function and (complementary) distribution function in generalized form. Furthermore, we derive a…

Brownian diffusion subject to stochastic resetting to a fixed position has been widely studied for applications to random search processes. In an unbounded domain, the mean first-passage time at a target site can be minimized for a…

Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…

We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…

We examine the problem of allocating a given total storage budget in a distributed storage system for maximum reliability. A source has a single data object that is to be coded and stored over a set of storage nodes; it is allowed to store…

The authors present empirical distributions for the halting time (measured by the number of iterations to reach a given accuracy) of optimization algorithms applied to two random systems: spin glasses and deep learning. Given an algorithm,…

We study the factorised steady state of a general class of mass transport models in which mass, a conserved quantity, is transferred stochastically between sites. Condensation in such models is exhibited when above a critical mass density…

In proving large deviation estimates, the lower bound for open sets and upper bound for compact sets are essentially local estimates. On the other hand, the upper bound for closed sets is global and compactness of space or an exponential…

In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive…

We define the notion of infimum of a set of points with respect to the second order cone. This problem can be showed to be equivalent to the minimum ball containing a set of balls problem and to the maximum intersecting ball problem, as…

We take an existing implementation of an algorithm for the maximum clique problem and modify it so that we can distribute it over an ad-hoc cluster of machines. Our goal was to achieve a significant speedup in performance with minimal…

We study a stochastic network that consists of a set of servers processing multiple classes of jobs. Each class of jobs requires a concurrent occupancy of several servers while being processed, and each server is shared among the job…

An innovative numerical technique is presented to adjust the inflow to a supply chain in order to achieve a desired outflow, reducing the costs of inventory, or the goods timing in warehouses. The supply chain is modelled by a conservation…

This paper studies explicitly solvable multidimensional optimal stopping problems of sum- and product-type in discrete and continuous time using the monotone case approach. It gives a review on monotone case stopping using the Doob…

We describe an approach that allows us to deduce the limiting return times distribution for arbitrary sets to be compound Poisson distributed. We establish a relation between the limiting return times distribution and the probability of the…

We consider an infinite balls-into-bins process with deletions where in each discrete step $t$ a coin is tossed as to whether, with probability $\beta(t) \in (0,1)$, a new ball is allocated using the Greedy[2] strategy (which places the…

In this paper, we propose three generic models of capacitated coverage and, more generally, submodular maximization to study task-worker assignment problems that arise in a wide range of gig economy platforms. Our models incorporate the…

Divisor methods are well known to satisfy house monotonicity, which allows representative seats to be allocated sequentially. We focus on stationary divisor methods defined by a rounding cutpoint $c \in [0,1]$. For such methods with…

The article explores the asymptotic behavior of the expected number of drawings in the Coupon Collector's Problem with group-drawing under the uniform distribution. In this variant, each draw consists of a package of $s$ distinct coupons…

We study several stochastic combinatorial problems, including the expected utility maximization problem, the stochastic knapsack problem and the stochastic bin packing problem. A common technical challenge in these problems is to optimize…