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In the domain of Sport Analytics, Global Positioning Systems devices are intensively used as they permit to retrieve players' movements. Team sports' managers and coaches are interested on the relation between players' patterns of movements…
We study the optimal way to estimate the quantum expectation value of a physical observable when a finite number of copies of a quantum pure state are presented. The optimal estimation is determined by minimizing the squared error averaged…
Standard measures of batting performance such as a batting average and an on-base percentage can be decomposed into component rates such as strikeout rates and home run rates. The likelihood of hitting data for a group of players can be…
This paper reports the simulation of an electron gun. The effects of some parameters on the beam quality were studied and optimal choices were identified. It gives numerical beam qualities in common electrostatic triode gun, and the…
In this paper, we develop a logistic regression model to estimate the probability that a particular shot in an NHL game will result in a goal, and use the results to evaluate the performance of NHL skaters, goalies, and teams. We weight…
The speed-accuracy tradeoffs are prevalent in a wide range of physical systems. In this paper, we demonstrate speed-accuracy tradeoffs in the game of cricket, where 'batters' score runs on the balls bowled by the 'bowlers'. It is shown that…
Adjusting ocean wind observations to a standard height, usually 10 m, requires the use of a boundary layer model, and knowledge of the thermodynamical variables. Height adjustment is complicated by the fact that a necessary parameter, the…
The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the…
Pose estimation refers to tracking a human's full body posture, including their head, torso, arms, and legs. The problem is challenging in practical settings where the number of body sensors are limited. Past work has shown promising…
We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance…
We compute the minimal angle spread with respect to the uniform distribution in the probability simplex. The resulting optimization problem is analytically solved. The formula provided shows that the minimal angle spread approaches zero as…
Predicting the outcome of sports events is a hard task. We quantify this difficulty with a coefficient that measures the distance between the observed final results of sports leagues and idealized perfectly balanced competitions in terms of…
The standard mathematical approach to fourth-down decision making in American football is to make the decision that maximizes estimated win probability. Win probability estimates arise from machine learning models fit from historical data.…
We introduce and give examples of applications of an optimality criterion which can be used for the design and comparison of multiple beam profile emittance and Twiss parameters measurement sections and which is independent from the…
In Petanque, each player aims to throw the boule closer to the jack. The closest boule to the jack among players will score the point. Currently, the distance of the boule to the jack is still measured using manual measurement tools such as…
In this study, a novel eye tracking system using a visual camera is developed to extract human's gaze, and it can be used in modern game machines to bring new and innovative interactive experience to players. Central to the components of…
An average pedestrian flow through an exit is one of the most important index in evaluating pedestrian dynamics. In order to study the flow in detail, the floor field model, which is a crowd model by using cellular automaton, is extended by…
It is a well known fact that non-trivial boundary conditions affect the interaction between atoms and the always present quantized electromagnetic field. In this paper, we focus on how the spontaneous emission rate of a given excited atom…
Every shot in basketball has an opportunity cost; one player's shot eliminates all potential opportunities from their teammates for that play. For this reason, player-shot efficiency should ultimately be considered relative to the lineup.…
A single target is hidden at a location chosen from a predetermined probability distribution. Then, a searcher must find a second probability distribution from which random search points are sampled such that the target is found in the…