Related papers: Daniel Litt's Probability Puzzle
The interest in the combination of probability with logics for modeling the world has rapidly increased in the last few years. One of the most effective approaches is the Distribution Semantics which was adopted by many logic programming…
A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.
Given a probability distribution $\mu$ a set $\Lambda (\mu)$ of positive real numbers is introduced, so that $\Lambda (\mu)$ measures the "divisibility" of $\mu$. The basic properties of $\Lambda (\mu)$ are described and examples of…
Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
The exponent puzzle of the Anderson-Mott transition is discussed on the basis of a duality model for strongly correlated electrons.
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…
The union-closed sets conjecture, also known as Frankl's conjecture, is a well-studied problem with various formulations. In terms of lattices, the conjecture states that every finite lattice $L$ with more than one element contains a…
I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but…
In this expository note, we present an approach to the generalization of Serre of the Sato-Tate Conjecture. Most of its content is taken from Serre's original references. However, we provide a few new examples and supply references to…
We establish fun parallels between coin-weighing puzzles and knights-and-knaves puzzles.
We study a system of interacting reinforced random walks defined on polygons. At each stage, each particle chooses an edge to traverse which is incident to its position. We allow the probability of choosing a given edge to depend on the sum…
Notes on the Spinpossible puzzle game. We give a mathematical description of the game, prove some elementary bounds on the length of optimal solutions, and consider variations of the game which place restrictions on the set of permitted…
One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largely an open problem. In this paper, we present a series of…
We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities…
Distributional data tells us that a man can swallow candy, but not that a man can swallow a paintball, since this is never attested. However both are physically plausible events. This paper introduces the task of semantic plausibility:…
We give a brief description of the Birch and Swinnerton-Dyer Conjecture which is one of the seven Clay problems.
We collect, survey and develop methods of (one-dimensional) stochastic approximation in a framework that seems suitable to handle fairly broad generalizations of Polya urns. To show the applicability of the results we determine the limiting…
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
A popular variant of the collector's problem is the following: Assume there are $N$ different types of coupons with equal occurring probabilities. There is one main collector who collects coupons. When she gets a "double," she gives it to…