相关论文: The football player and the infinite series
We provide a self-contained introduction to finite extensive games with perfect information. In these games players proceed in turns having, at each stage, finitely many moves to their disposal, each play always ends, and in each play the…
In recent years excessive monetization of football and professionalism among the players has been argued to have affected the quality of the match in different ways. On the one hand, playing football has become a high-income profession and…
Change of direction is a key element of player movement in American football, yet there remains a lack of objective approaches for in-game performance evaluation of this athletic trait. Using tracking data, we propose a Bayesian…
The main result establishes the existence of a solution in a generalized sense for a nonlinear Dirichlet problem driven by a competing operator and exhibiting a convection term composed with an intrinsic operator. A finite dimensional…
Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…
Mertens [In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) (1987) 1528-1577 Amer. Math. Soc.] proposed two general conjectures about repeated games: the first one is that, in any two-person zero-sum…
Although the data-driven analysis of football players' performance has been developed for years, most research only focuses on the on-ball event including shots and passes, while the off-ball movement remains a little-explored area in this…
Sports broadcasters inject drama into play-by-play commentary by building team and player narratives through subjective analyses and anecdotes. Prior studies based on small datasets and manual coding show that such theatrics evince…
This book is devoted to the problem of sequential probability forecasting, that is, predicting the probabilities of the next outcome of a growing sequence of observations given the past. This problem is considered in a very general setting…
In a function that takes its inputs from various players, the effect of a player measures the variation he can cause in the expectation of that function. In this paper we prove a tight upper bound on the number of players with large effect,…
We study a pursuit-evasion differential game with finite number of pursuers and one evader in Hilbert space with geometric constraints on the control functions of players. We solve the game by presenting explicit strategies for pursuers…
This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is natural to search for bodies that are, in a sense, close to invisible. We…
Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an…
In this paper, we study collective interaction dynamics emerging in the game of football-soccer. To do so, we surveyed a database containing body-sensors traces measured during three professional football matches, where we observed…
This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…
As artificial intelligence spreads out to numerous fields, the application of AI to sports analytics is also in the spotlight. However, one of the major challenges is the difficulty of automated acquisition of continuous movement data…
In this paper, we study interaction dynamics in the game of football-soccer in the context of ball possession intervals. To do so, we analyze a database comprising one season of the five major football leagues of Europe. Using this input,…
The aim of this work is to expose some asymptotic series associated to some expressions involving the volume of the n-dimensional unit ball. All proofs and the methods used for improving the classical inequalities announced in the final…
Let $\mathcal{D}=(d_n)_{n=1}^\infty$ be a bounded sequence of integers with $d_n\ge 2$ and let $(i, j)$ be a pair of strictly positive numbers with $i+j=1$. We prove that the set of $x \in \RR$ for which there exists some constant $c(x) >…
Analogous to G\"odel's incompleteness theorems is a theorem in physics to the effect that the set of explanations of given evidence is uncountably infinite. An implication of this theorem is that contact between theory and experiment…