Related papers: A Model for Pairs of Beatty Sequences
We focus in this paper in the estimation of a target trajectory defined by whether a time constant parameter in a simple stochastic process or a random walk with binary observations. The binary observation comes from binary derivative…
Discussions on outstanding---positively and/or negatively---athletes are common practice. The rapidly grown amount of collected sports data now allow to support such discussions with state of the art statistical methodology. Given a…
We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is…
We address the problem of tracking and detecting interactions between the different groups of runners that form during a race. In athletic races control points are set to monitor the progress of athletes over the course. Intuitively, a {\it…
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…
The lonely runner conjecture, now over fifty years old, concerns the following problem. On a unit length circular track, consider $m$ runners starting at the same time and place, each runner having a different constant speed. The conjecture…
We consider sequences counting integer partitions in two colors (red and blue) in which the even parts occur only in blue color. We focus on subsequences defined by constraints on the parity and color of the summands. We establish formulas…
Two processors output correlated sequences using the help of a coordinator with whom they individually share independent randomness. For the case of unlimited shared randomness, we characterize the rate of communication required from the…
In this paper we study the problem of tracking the mean of a piecewise stationary sequence of independent random variables. First we consider the case where the transition times are known and show that a direct running average performs the…
We present here two examples of stochastic modelings of social phenomena. The first topic is pedestrian counter flow. Two groups of model pedestrians move in opposite directions and create congestions. It will be shown that this congestion…
Numerical wave models can output partitioned wave parameters at each grid point using a spectral partitioning technique. Because these wave partitions are usually organized according to the magnitude of their wave energy without considering…
World record setting has long attracted public interest and scientific investigation. Extremal records summarize the limits of the space explored by a process, and the historical progression of a record sheds light on the underlying…
The SportsMOT dataset aims to solve multiple object tracking of athletes in different sports scenes such as basketball or soccer. The dataset is challenging because of the unstable camera view, athletes' complex trajectory, and complicated…
Tracking data is a powerful tool for basketball teams in order to extract advanced semantic information and statistics that might lead to a performance boost. However, multi-person tracking is a challenging task to solve in single-camera…
An interesting example for collective decision making is the so-called Mexican wave during which the spectators in a stadium leap to their feet with their arms up and then sit down again following those to their left (right) with a small…
We study a simple motion differential game of many pursuers and one evader in the plane. We give a nonempty closed convex set in the plane, and the pursuers and evader move on this set. They cannot leave this set during the game. Control…
We consider a bipartite scenario where two parties hold ensembles of $1/2$-spins which can only be measured collectively. We give numerical arguments supporting the conjecture that in this scenario no Bell inequality can be violated for…
Team-based invasion sports such as football, basketball and hockey are similar in the sense that the players are able to move freely around the playing area; and that player and team performance cannot be fully analysed without considering…
Marathons are one of the ultimate challenges of human endeavor. In this paper, we apply recently introduced multifractal techniques which yield a new classification parameter in the processing of physiological data captured on marathon…
Batting average is one of the principle performance measures for an individual baseball player. It is natural to statistically model this as a binomial-variable proportion, with a given (observed) number of qualifying attempts (called…