Related papers: A probabilistic way to discover the rainbow
In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…
The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…
In the bin covering problem, the goal is to fill as many bins as possible up to a certain minimal level with a given set of items of different sizes. Online variants, in which the items arrive one after another and have to be packed…
Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time…
Suppose that your mother gave you n candies. You have to eat at least one candy each day. One possibility is to eat all n of them the first day. The other extreme is to make them last n days, and only eat one candy a day. Altogether, you…
We consider the problem of finding a large rainbow matching in a random graph with randomly colored edges. In particular we analyze the performance of two greedy algorithms for this problem. The algorithms we study are colored versions of…
Take a look around you -- in your family, your school or workplace, in the streets, and you see boys & girls in about equal proportion, and without any easily visible gender patterns in case of siblings. So, to the famous first order of…
To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
Matching markets are of particular interest in computer science and economics literature as they are often used to model real-world phenomena where we aim to equitably distribute a limited amount of resources to multiple agents and…
In this study, potential scatterings are formulated in experimental setups with Gaussian wave packets in accordance with a probability principle and associativity of products. A breaking of an associativity is observed in scalar products…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
A random forest is a popular tool for estimating probabilities in machine learning classification tasks. However, the means by which this is accomplished is unprincipled: one simply counts the fraction of trees in a forest that vote for a…
A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. The study of rainbow subgraphs goes back to the work of Euler on Latin squares and has been the focus of extensive research ever since. Many…
This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise…
Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
In this note we evaluate the expectation and variance of the waiting time to complete $m$ parallel collections of coupons, in the case of coupons which arrives independently, one by one and with equal probabilities.
The key issue in importance sampling is the choice of the alternative sampling distribution, which is often chosen from the exponential tilt family of the underlying distribution. However, when the problem exhibits certain kind of…
Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…