Related papers: Competitive random sequential adsorption of point …
In the classical parking problem, unit intervals ("car lengths") are placed uniformly at random without overlapping. The process terminates at saturation, i.e. until no more unit intervals can be stowed. In this paper, we present a…
We extend Random Access, a fundamental operation that enables efficient search and exploration algorithms, to the modern interactive data systems based on Ranked Retrieval and Similarity Search, where orderings are dynamically defined over…
Stochastic Approximation (SA) is a widely used algorithmic approach in various fields, including optimization and reinforcement learning (RL). Among RL algorithms, Q-learning is particularly popular due to its empirical success. In this…
The problem of reservation in a large distributed system is analyzed via a new mathematical model. A typical application is a station-based car-sharing system which can be described as a closed stochastic network where the nodes are the…
In this paper we develop an encounter-based model of a run-and-tumble particle (RTP) confined to a finite interval $[0,L]$ with partially absorbing, sticky boundaries at both ends. We assume that the particle switches between two constant…
We consider a family of distributions on spatial random partitions that provide a coupling between different models of interest: the ideal Bose gas; the zero-range process; particle clustering; and spatial permutations. These distributions…
Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global coupling among spatial points induced by the underlying…
Random packing of unoriented regular polygons and star polygons on a two-dimensional flat, continuous surface is studied numerically using random sequential adsorption algorithm. Obtained results are analyzed to determine saturated random…
The properties of the number of iterations in random sequential adsorption protocol needed to generate finite saturated random packing of spherically symmetric shapes were studied. Numerical results obtained for one, two, and three…
We apply the replica analysis established by Gardner to the multi-constraint continuous knapsack problem,which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large…
Saturated random packing of particles built of two identical, relatively shifted spheres in two and three dimensional flat and homogeneous space was studied numerically using random sequential adsorption algorithm. The shift between centers…
In this paper we study asymptotic behaviour of a growth process generated by a semi-deterministic variant of cooperative sequential adsorption model (CSA). This model can also be viewed as a particular queueing system with local…
We consider several variants of a car-sharing problem. Given are a number of requests each consisting of a pick-up location and a drop-off location, a number of cars, and nonnegative, symmetric travel times that satisfy the triangle…
Can a transformer learn which attention entries matter during training? In principle, yes: attention distributions are highly concentrated, and a small gate network can identify the important entries post-hoc with near-perfect accuracy. In…
Random sequential adsorption is an irreversible surface deposition of extended objects. In systems with continuous degrees of freedom coverage follows a power law, theta(t) = theta_J - c t^{-alpha}, where the exponent alpha depends on the…
Online contention resolution schemes (OCRSs) are effective rounding techniques for online stochastic combinatorial optimization problems. These schemes randomly and sequentially round a fractional solution to a relaxed problem that can be…
When gas molecules bind to a surface they may do so in such a way that the adsorption of one molecule inhibits the arrival of others. We consider random sequential adsorption in which the empty sites of a graph are irreversibly occupied in…
Consider an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. In a companion article, we introduced the notion of multiscale (first-order) functional inequalities, which extend standard functional inequalities like…
In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a…
Recently, random feature attentions (RFAs) are proposed to approximate the softmax attention in linear time and space complexity by linearizing the exponential kernel. In this paper, we first propose a novel perspective to understand the…