Related papers: Impartial redistricting: a Markov chain approach t…
In systems of programmable matter, we are given a collection of simple computation elements (or particles) with limited (constant-size) memory. We are interested in when they can self-organize to solve system-wide problems of movement,…
Many people believe that it is disadvantageous for members aligning with a minority party to cluster in cities, as this makes it easier for the majority party to gerrymander district boundaries to diminish the representation of the…
In this work, we study the real-time tracking and reconstruction of an information source with the purpose of actuation. A device monitors the state of the information source and transmits status updates to a receiver over a wireless…
Markov chains are an important tool for modelling and evaluating systems in computer science, economics, biology and numerous other fields. Thus, approximating Markov chains is a useful tool for decreasing the computational effort needed…
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…
This paper studies a large number of homogeneous Markov decision processes where the transition probabilities and costs are coupled in the empirical distribution of states (also called mean-field). The state of each process is not known to…
This paper considers the problem of randomized influence maximization over a Markovian graph process: given a fixed set of nodes whose connectivity graph is evolving as a Markov chain, estimate the probability distribution (over this fixed…
In the context of modern sampling methods for redistricting, we define a natural measurement of the clustering of a political party, and we study how clustering affects the expected election outcome. We first prove general results and then…
Public opinion polling is usually done by random sampling from the entire population, treating individual opinions as independent. In the real world, individuals' opinions are often correlated, e.g., among friends in a social network. In…
The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
We propose a method for redistricting, decomposing a geographical area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are compact and contiguous. Each district is the…
We compare different analytical and numerical methods for studying the partitions of a finite system into fragments. We propose a new numerical method of exploring the partition space by generating the Markov chains of partitions based on…
We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest…
Flexible district heating grids form an important part of future, low-carbon energy systems. We examine probabilistic state estimation in such grids, i.e., we aim to estimate the posterior probability distribution over all grid state…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for…
In this paper, we abstract a kind of stochastic processes from evolving processes of growing networks, this process is called growing network Markov chains. Thus the existence and the formulas of degree distribution are transformed to the…
We model the societal task of redistricting political districts as a partitioning problem: Given a set of $n$ points in the plane, each belonging to one of two parties, and a parameter $k$, our goal is to compute a partition $\Pi$ of the…
We establish a connection between policy evaluation in Markov decision processes and PageRank in network analysis. For a fixed policy, we show that the value function of a discounted Markov decision process can be obtained, up to an…