Related papers: A Model for Pairs of Beatty Sequences
Data analytics in sports is crucial to evaluate the performance of single players and the whole team. The literature proposes a number of tools for both offence and defence scenarios. Data coming from tracking location of players, in this…
Quantum steering is the phenomenon whereby one party (Alice) proves entanglement by "steering'' the system of another party (Bob) into distinct ensembles of states, by performing different measurements on her subsystem. Here, we investigate…
The authors propose a parametric model called the arena model for prediction in paired competitions, i.e. paired comparisons with eliminations and bifurcations. The arena model has a number of appealing advantages. First, it predicts the…
Global Positioning Systems (GPS) are nowadays intensively used in Sport Science as they permit to capture the space-time trajectories of players, with the aim to infer useful information to coaches in addition to traditional statistics. In…
In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved
The objective of the present study is to present a computational model of the motion of a single athlete in a team and to compare the resulting trajectory with experimental data obtained in the field during competitions by match analysis…
With recent advances in sensing and tracking technology, trajectory data is becoming increasingly pervasive and analysis of trajectory data is becoming exceedingly important. A fundamental problem in analyzing trajectory data is that of…
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…
A new approach in team sports analysis consists in studying positioning and movements of players during the game in relation to team performance. State of the art tracking systems produce spatio-temporal traces of players that have…
In competitive sports it is often very hard to quantify the performance. A player to score or overtake may depend on only millesimal of seconds or millimeters. In racquet sports like tennis, table tennis and squash many events will occur in…
We introduce CUT, the class of 2-player partition games. These are NIM type games, played on a finite number of heaps of beans. The rules are given by a set of positive integers, which specifies the number of allowed splits a player can…
Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large…
The sequence counting the number of unique tournaments with n people is the same as the sequence counting non-tracking binary strings corresponding to n-2 radar observations with the tracking rule "3 out of 5 with loss 2." This fact allows…
In the game of cricket, the result of coin toss is assumed to be one of the determinants of match outcome. The decision to bat first after winning the toss is often taken to make the best use of superior pitch conditions and set a big…
Suppose that $k$ runners having different constant speeds run laps on a circular track of unit length. The Lonely Runner Conjecture states that, sooner or later, any given runner will be at distance at least $1/k$ from all the other…
We study the problem of representing integers as sums of prime numbers from a fixed Beatty sequence $B_{\alpha,\beta}$, where $\alpha>1$ is irrational and of finite type.
The score of a vertex $x$ in an oriented graph is defined to be its outdegree, \emph{i.e.}, the number of arcs with initial vertex $x$. The score sequence of an oriented graph is the sequence of all scores arranged in nondecreasing order.…
Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…
Divisor methods are well known to satisfy house monotonicity, which allows representative seats to be allocated sequentially. We focus on stationary divisor methods defined by a rounding cutpoint $c \in [0,1]$. For such methods with…
In order to determine the optimal strategy to run a race on a curved track according to the lane number, we introduce a model based on differential equations for the velocity, the propulsive force and the anaerobic energy which takes into…