Related papers: A Model for Pairs of Beatty Sequences
World records in athletics provide a measure of physical as well as physiological human performance. Here we analyse running records and show that the mean speed as a function of race time can be described by two scaling laws that have a…
The dynamics is investigated of a free particle on a sphere (rigid rotor or rotator) that is initially in a coherent state. The instability of coherent states with respect to the free evolution leads to nontrivial time-development of…
In this article we address two related issues on the learning of probabilistic sequences of events. First, which features make the sequence of events generated by a stochastic chain more difficult to predict. Second, how to model the…
We introduce a new video analysis problem -- tracking of rigid planar objects in sequences where both their sides are visible. Such coin-like objects often rotate fast with respect to an arbitrary axis producing unique challenges, such as…
Fix irrational numbers $\alpha,\hat\alpha>1$ of finite type and real numbers $\beta,\hat\beta\ge 0$, and let $B$ and $\hat B$ be the Beatty sequences $$ B:=(\lfloor\alpha m+\beta\rfloor)_{m\ge 1}\quad\text{and}\quad\hat…
Human pose detection systems based on state-of-the-art DNNs are on the go to be extended, adapted and re-trained to fit the application domain of specific sports. Therefore, plenty of noisy pose data will soon be available from videos…
We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: * a Becker-D\"{o}ring-type dynamics * a probabilistic cellular automaton model. In both models the group formation is…
Professional sports enhance interaction among athletes through training groups, sponsored events and competitions. Among these, the Olympic Games represent the largest competition with a global impact, providing the participants with a…
A new numerical characterization of symbolic sequences is proposed. The partition of sequence based on Ke and Tong algorithm is a starting point. Algorithm decomposes original sequence into set of distinct subsequences - a patterns. The set…
A common experimental strategy for demonstrating non-classical correlations is to show violation of a Bell inequality by measuring a continuously emitted stream of entangled photon pairs. The measurements involve the detection of photons by…
We show that bodies with two planes of symmetry can display a range of behaviors even without inertia. Any such body supports a conserved quantity in its dynamics, and is either a settler, a drifter or a flutterer, depending only on its…
It is shown that a separated sequence of points in the unit disc of the complex plane is in fact uniformly separated, if there exists a certain intermediate sequence whose separated subsequences are uniformly separated. This property is…
"Oscillations" occur in quite different kinds of many-particle-systems when two groups of particles with different directions of motion meet or intersect at a certain spot. We present a model of pedestrian motion that is able to reproduce…
Sample splitting is widely used in statistical applications, including classically in classification and more recently for inference post model selection. Motivating by problems in the study of diet, physical activity, and health, we…
National Basketball Association (NBA) players are highly motivated and skilled experts that solve complex decision making problems at every time point during a game. As a step towards understanding how players make their decisions, we focus…
In some athletic races, such as cycling and types of speed skating races, athletes have to complete a relatively long distance at a high speed in the presence of direct opponents. To win such a race, athletes are motivated to hide behind…
An existing dialogue between number theory and dynamical systems is advanced. A combinatorial device gives necessary and sufficient conditions for a sequence of non-negative integers to count the periodic points in a dynamical system. This…
Based on the quantum violation of bipartite Bell inequality, it has been demonstrated that the sharing of non-locality can be demonstrated for at most two sequential observers at one end and at most one-pair of observers at both ends. In…
We study the pedestrian escape from an obscure corridor using a lattice gas model with two species of particles. One species, called passive, performs a symmetric random walk on the lattice, whereas the second species, called active, is…
Sports video data is recorded for nearly every major tournament but remains archived and inaccessible to large scale data mining and analytics. It can only be viewed sequentially or manually tagged with higher-level labels which is time…