相关论文: Pass the Buck on a Complete Binary Tree

We consider numerical schemes for root finding of noisy responses through generalizing the Probabilistic Bisection Algorithm (PBA) to the more practical context where the sampling distribution is unknown and location-dependent. As in…

We show how to derive the Black-Scholes model and its generalisation to the `exchange-option' (to exchange one asset for another) via the continuum limit of the Binomial tree. No knowledge of stochastic calculus or partial differential…

Chip-firing is a combinatorial game played on a graph in which we place and disperse chips on vertices until a stable state is reached. We study a chip-firing variant played on an infinite rooted directed $k$-ary tree, where we place…

Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…

In this paper, we present a new method for determining the optimal pebbling number of a complete binary tree. This method reveals a curious connection between the optimal pebbling numbers of complete binary trees and the Conolly-Fox…

We present some exact expressions for the number of paths of a given length in a perfect $m$-ary tree. We first count the paths in perfect rooted $m$-ary trees and then use the results to determine the number of paths in perfect unrooted…

Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for…

Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of…

We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…

We present a Spades bidding algorithm that is superior to recreational human players and to publicly available bots. Like in Bridge, the game of Spades is composed of two independent phases, \textit{bidding} and \textit{playing}. This paper…

We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…

In an all-pay auction, only one bidder wins but all bidders must pay the auctioneer. All-pay bidding games arise from attaching a similar bidding structure to traditional combinatorial games to determine which player moves next. In contrast…

Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…

A particular case of a causal set is considered that is a directed dyadic acyclic graph. This is a model of a discrete pregeometry on a microscopic scale. The dynamics is a stochastic sequential growth of the graph. New vertexes of the…

We study two-player games with alternating moves played on infinite trees. Our main focus is on the case where the trees are full (regular) and the winning set is open (with respect to the product topology on the tree). Gale and Stewart…

One of the main objective of this paper is to relate Beck's conjecture for k-in-a-row games. The conjecture states that playing on the same board Picker is better off in a Chooser-Picker game than the second player in the Maker-Breaker…

We investigate the benefit of treating all the parameters in a Bayesian neural network stochastically and find compelling theoretical and empirical evidence that this standard construction may be unnecessary. To this end, we prove that…

A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…

This paper considers a problem of planning an attack in robotic football (RoboCup). The problem is reduced to finding a trajectory of the ball from its current position to the opponents goals. Heuristic search algorithm, i.e. A*, is used to…

Motivated by the question of computing the probability of successful power domination by placing k monitors uniformly at random, in this paper we give a recursive formula to count the number of power domination sets of size k in a labeled…