Related papers: Lonely runners in function fields
We consider a random walk on $\R^d$ in a polynomially mixing random environment that is refreshed at each time step. We use a martingale approach to give a necessary and sufficient condition for the almost-sure functional central limit…
We study nearest-neighbors branching random walks started from a point at the interior of a hypercube. We show that the probability that the process escapes the hypercube is monotonically decreasing with respect to the distance of its…
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…
Why do moving objects appear rigid when projected retinal images are deformed nonrigidly? We used rotating rigid objects that can appear rigid or non-rigid to test whether shape features contribute to rigidity perception. When two circular…
Cycling is a green transportation mode, and is promoted by many governments to mitigate traffic congestion. However, studies concerning the traffic dynamics of bicycle flow are very limited. This study experimentally investigated bicycle…
A unified metric is given for the evaluation of object tracking systems. The metric is inspired by KL-divergence or relative entropy, which is commonly used to evaluate clustering techniques. Since tracking problems are fundamentally…
The problem of describing isolated rotating bodies in equilibrium in General Relativity has so far been treated under the assumption of the circularity condition in the interior of the body. For a fluid without energy flux, this condition…
The investigation of random walks is central to a variety of stochastic processes in physics, chemistry, and biology. To describe a transport phenomenon, we study a variant of the one-dimensional persistent random walk, which we call a…
The pursuit problem is a historical issue of the application of mathematics in physics, which has been discussed for centuries since the time of Leonardo Da Vinci, and its applications are wide ranging from military and industrial to…
Relativistic rigid motion suggests a new version for the so-called `twin paradox', comparing the ages of two astronauts on a very long spaceship. Although there is always an instantaneous inertial frame in which the whole spaceship, being…
We consider a nearest neighbor random walk on the one-dimensional integer lattice with drift towards the origin determined by an asymptotically vanishing function of the number of visits to zero. We show the existence of distinct regimes…
In recent decades, running has become an increasingly popular pastime activity due to its accessibility, ease of practice, and anticipated health benefits. However, the risk of running-related injuries is substantial for runners of…
The mathematical model of J. Keller for predicting World Record race times, based on a simple differential equation of motion, predicted quite well the records of the day. One of its shortcoming is that it neglects to account for a…
Major League Baseball (MLB) recently limited pitchers to three pickoff attempts, creating a cat-and-mouse game between pitcher and runner. Each failed attempt adds pressure on the pitcher to avoid using another, and the runner can intensify…
Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random…
In recent years, numerous studies have been published dealing with the effect of individual characteristics of pedestrians on the fundamental diagram. These studies compared cumulative data on individuals in a group homogeneous in terms of…
We consider the diffusion-advection problem in two simple cellular flow models (often invoked as examples for subdiffusive tracer's motion) and concentrate on the intermediate time range, in which the tracer's motion indeed may show…
We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including…
The role of the quintessence field as a probable candidate for the repulsive dark energy, the conditions for tracking and the requisites for tracker fields are examined. The concept of `integrated tracking' is introduced and a new criterion…
The problem Orienteering asks whether there exists a walk which visits a number of sites without exceeding some fuel budget. In the variant of the problem we consider, the cost of each edge in the walk is dependent on the time we depart one…