相关论文: And the Winner Is . . . Predicting the Outcome of …
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…
We report an emergence of bifurcation in basketball, a single-particle system governed by Newtonian mechanics. When shooting the basketball, the obvious control parameters are the launch speed and the launch angle. We propose to use the…
The aim of this paper is to bring a mathematical justification to the optimal way of organizing one's effort when running. It is well known from physiologists that all running exercises of duration less than 3mn are run with a strong…
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…
Physicists seeking to understand complex biological systems often find it rewarding to create simple "toy models" that reproduce system behavior. Here a toy model is used to understand a puzzling phenomenon from the sport of track and…
Basketball is often referred to as "a game of runs." We investigate the appropriateness of this claim using data from the full NBA 2016-17 season, comparing actual longest runs of scoring events to what long run theory predicts under the…
This paper is concerned with continuous-time pursuit and evasion games. Typically, we have a lion and a man in a metric space: they have the same speed, and the lion wishes to catch the man while the man tries to evade capture. We are…
The Lonely Runner Conjecture of Wills and Cusick states that if $k+1$ runners start running at distinct constant speeds around a unit-length circular track, then for each runner there is a time when he/she is at least $1/(k+1)$ away from…
Many university texts on Mechanics deal with the problem of the effect of the air drag force, using as example the slowing down of a parachute. Hardly no one discuss what happens when the drag force is proportional to both $u$ and $u^2$. In…
We provide scientific foundations for athletic performance prediction on an individual level, exposing the phenomenology of individual athletic running performance in the form of a low-rank model dominated by an individual power law. We…
Given a monocular video of a soccer match, this paper presents a computational model to estimate the most feasible pass at any given time. The method leverages offensive player's orientation (plus their location) and opponents' spatial…
A quick and fun investigation into the effects of correcting for wind assistance/resistance and drag on 100m sprint performances. Considered are World 100m rankings, as well as Canadian rankings
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 a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…
At the 2008 Summer Olympics in Beijing, Usain Bolt broke the world record for the 100 m sprint. Just one year later, at the 2009 World Championships in Athletics in Berlin he broke it again. A few months after Beijing, Eriksen et al.…
The conflict between Quantum Mechanics (QM) and Local Realism is most noticeable in the correlations observed between distant regions of a spatially spread entangled state. It has been hypothesized that transient deviations (from the values…
Curve matching is a prediction technique that relies on predictive mean matching, which matches donors that are most similar to a target based on the predictive distance. Even though this approach leads to high prediction accuracy, the…
We study the swimming of non-relativistic deformable bodies in (empty) static curved spaces. We focus on the case where the ambient geometry allows for rigid body motions. In this case the swimming equations turn out to be geometric. For a…
In this work, we extend the convex bodies chasing problem (CBC) to an adversarial setting, where an agent (the Player) is tasked with chasing a sequence of convex bodies generated adversarially by another agent (the Opponent). The Player…
Beginning with Witkowski et al. [2022], recent work on forecasting competitions has addressed incentive problems with the common winner-take-all mechanism. Frongillo et al. [2021] propose a competition mechanism based on…