Related papers: A Model for Pairs of Beatty Sequences
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…
Focusing on motion of two interacting players in football games, two velocity vectors for the pair of one player and the nearest opponent player exhibit strong alignment. Especially, we find that there exists a characteristic interpersonal…
Tracking objects in soccer videos is extremely important to gather both player and team statistics, whether it is to estimate the total distance run, the ball possession or the team formation. Video processing can help automating the…
This study proposes a simple method for multi-object tracking (MOT) of players in a badminton court. We leverage two off-the-shelf cameras, one on the top of the court and the other on the side of the court. The one on the top is to track…
We construct an easily described family of partitions of the positive integers into $n$ disjoint sets with essentially the same structure for every $n \geq 2$. In a special case, it interpolates between the Beatty $\frac{1}{\phi} +…
A billiard in the form of a stadium with periodically perturbed boundary is considered. Two types of such billiards are studied: stadium with strong chaotic properties and a near-rectangle billiard. Phase portraits of such billiards are…
We study 2-player impartial games of the form take-away which produce P-positions (second player winning positions) corresponding to complementary Beatty sequences, given by the continued fractions (1;k,1,k,1,...) and (k+1;k,1,k,1,...). Our…
A same-score streak in sports is a sequence of games where the scores are equivalent in all games. The motivating problem arose from college basketball, however due to the difficulty in collecting data, streaks in Major League Baseball…
Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…
Visualizing the trajectory of multiple runners with videos collected at different points in a race could be useful for sports performance analysis. The videos and the trajectories can also aid in athlete health monitoring. While the runners…
Splitting of sequential data, such as videos and time series, is an essential step in various data analysis tasks, including object tracking and anomaly detection. However, splitting sequential data presents a variety of challenges that can…
Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says "Heads" or "Tails". The team wins if all four choices match; otherwise the Devil wins. If all team…
Two observers, who share a pair of particles in an entangled mixed state, can use it to perform some non-bilocal measurement over another bipartite system. In particular, one can construct a specific game played by the observers against a…
Given $0<\alpha<1$, the Beatty sequence of density $\alpha$ is the sequence $B_{\alpha}=(\lfloor n/\alpha\rfloor)_{n\in\mathbb{N}}$. Beatty's theorem states that if $\alpha,\beta$ are irrational numbers with $\alpha+\beta=1$, then the…
Tracking people in a video sequence is a challenging task that has been approached from many perspectives. This task becomes even more complicated when the person to track is a player in a broadcasted sport event, the reasons being the…
Baseball consists of two teams alternating between batting and fielding while competing to score runs through sequential pitching events. Recent advances in tracking technology have enabled all Major League Baseball (MLB) clubs to record…
In the heart of "rhythm games" - games where players must perform actions in sync with a piece of music - are "charts", the directives to be given to players. We newly formulate chart generation as a sequence generation task and train a…
In this paper, a model is presented to extract statistical summaries to characterize the repetition of a cyclic body action, for instance a gym exercise, for the purpose of checking the compliance of the observed action to a template one…
In this paper we find an identity that gives a representation for the logarithm of any two irrational numbers $a, b >1$ in terms of a series whose terms are ratios of elements from the Beatty Sequences generated by these two numbers. We…
Consider the circle $C$ of length 1 and a circular arc $A$ of length $\ell\in (0,1)$. It is shown that there exists $k=k(\ell) \in \mathbb{N}$, and a schedule for $k$ runners along the circle with $k$ constant but distinct positive speeds…