Related papers: And the Winner Is . . . Predicting the Outcome of …
The presence of momentum in sports, where the outcome of a previous event affects a following event, is a belief often held by fans, and has been the subject of statistical study for many sports. This paper investigates the presence and…
The baseball game is often seen as many contests that are performed between individuals. The duel between the pitcher and the batter, for example, is considered the engine that drives the sport. The pitchers use a variety of strategies to…
Tennis is so popular that coaches and players are curious about factors other than skill, such as momentum. This article will try to define and quantify momentum, providing a basis for real-time analysis of tennis matches. Based on the…
An intercomparison of microdosimetric and nanodosimetric quantities simulated Monte Carlo codes is in progress with the goal of assessing the uncertainty contribution to simulated results due to the uncertainties of the electron interaction…
A competitive learning model was introduced in Ref. 1 (A. Mehta and J. M. Luck, Phys. Rev. E 60, 5, 1999), in which the learning is outcome-related. Every individual chooses between a pair of existing strategies or types, guided by a…
This paper presents CourtMotion, a spatiotemporal modeling framework for analyzing and predicting game events and plays as they develop in professional basketball. Anticipating basketball events requires understanding both physical motion…
In this paper, we study the distribution of the boundary points of expansion. As an application, we say something about the lonely runner problem. We show that given $k$ runners $\mathcal{S}_i$ round a unit circular track with the condition…
This paper considers a reach-avoid differential game in three-dimensional space with four equal-speed players. A plane divides the game space into a play subspace and a goal subspace. The evader aims at entering the goal subspace while…
We present a modular framework to benchmark new and existing methods for trajectory planning and control in high-acceleration maneuvers that push autonomous driving to the limits. Our framework includes time-optimal raceline generation,…
The James function, also known as the "log5 method," assigns a probability to the result of a competition between two teams based on their respective winning percentages. This paper, which builds on earlier work of the authors and Steven J.…
An interesting phenomenon that occurs in projectile motion, the "coming and going", is analyzed considering linear air resistance force. By performing both approximate and numerical analysis, it is showed how a determined critical angle and…
The Lonely Runner Conjecture states that if $k+1$ runners start at the same point on a unit-length circular track and run with distinct constant speeds, then each runner is at some time at least $1/(k+1)$-distant from every other runner.…
We study a stochastic process that mimics single-game elimination tournaments. In our model, the outcome of each match is stochastic: the weaker player wins with upset probability q<=1/2, and the stronger player wins with probability 1-q.…
In this paper we analyse local regularity of time-optimal controls and trajectories for an n-dimensional affine control system with a control parameter, taking values in a k-dimensional closed ball. In the case of k equal to n-1, we give…
The quantum bouncer (QB) concept is a known QM textbook example of confined particle, namely, a solution to the 1D Schroedinger equation for a linear potential (the so-called Airy equation). It would be a great methodological challenge to…
In a prediction tournament, contestants "forecast" by asserting a numerical probability for each of (say) 100 future real-world events. The scoring system is designed so that (regardless of the unknown true probabilities) more accurate…
Consider the problem of modeling memory effects in discrete-state random walks using higher-order Markov chains. This paper explores cross validation and information criteria as proxies for a model's predictive accuracy. Our objective is to…
In most professional sports, the structure of the environment is kept neutral so that scoring imbalances may be attributed to differences in team skill. It thus remains unknown what impact structural heterogeneities can have on scoring…
This paper investigates the difference between the circular and elliptical cases in one-on-one pursuit and evasion problems. Using the simultaneous differential equation derived by Barton and Eliezer, we derive a dynamical system based on…
We consider the first, and most well studied, speed scaling problem in the algorithmic literature: where the scheduling quality of service measure is a deadline feasibility constraint, and where the power objective is to minimize the total…