Related papers: Possible probability and irreducibility of balance…
Tournament solutions provide methods for selecting the "best" alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out…
A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random…
In the gambling foundation of probability theory, rationality requires that a subject should always (never) find desirable all nonnegative (negative) gambles, because no matter the result of the experiment the subject never (always)…
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…
The seminal Bradley-Terry model exhibits transitivity, i.e., the property that the probabilities of player A beating B and B beating C give the probability of A beating C, with these probabilities determined by a skill parameter for each…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in $\mathbb{R}^n$ obtained from the partitions of the fixed positive integer $n$. These distributions arise naturally when…
While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several…
We present two methods for bounding the probabilities of benefit and harm under unmeasured confounding. The first method computes the (upper or lower) bound of either probability as a function of the observed data distribution and two…
The twin prime conjecture asserts that there are infinitely many pairs of primes that differ by two. While recent advances have improved our understanding of bounded prime gaps, the conjecture remains unresolved. This paper refines the…
Given a (possibly infinite) subset $A$ of the natural numbers, we ask how many times a fair six-sided die must be rolled until the rolled numbers add up to an element of $A$. Using a one-dimensional dynamic programming recursion together…
We study the probability that a random polynomial with integer coefficients is reducible when factored over the rational numbers. Using computer-generated data, we investigate a number of different models, including both monic and non-monic…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
Two simple and attractive mechanisms for the fair division of indivisible goods in an online setting are LIKE and BALANCED LIKE. We study some fundamental computational problems concerning the outcomes of these mechanisms. In particular, we…
We consider a simple dice game, which leads to an intriguing study of multinomial walks, with surprising and seemingly paradoxical properties. The winning and losing probabilities of a general version of the game are investigated via…
Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…
It is known that any open necklace with beads of $t$ types in which the number of beads of each type is divisible by $k$, can be partitioned by at most $(k-1)t$ cuts into intervals that can be distributed into $k$ collections, each…
In this paper we propose algorithms for allocating $n$ sequential balls into $n$ bins that are interconnected as a $d$-regular $n$-vertex graph $G$, where $d\ge3$ can be any integer.Let $l$ be a given positive integer. In each round $t$,…
The paper establishes the property of splittability of billiard boundary sequences in n dimensional cube into subsequences of fractional parts. This reveals a new property of integrable and weak perturbated Hamilton systems: under a simple…
Suppose that you have $n$ colours and $m$ mutually independent dice, each of which has $r$ sides. Each dice lands on any of its sides with equal probability. You may colour the sides of each die in any way you wish, but there is one…