Related papers: The Camel-Banana Problem
We propose a minimal model of predator-swarm interactions which captures many of the essential dynamics observed in nature. Different outcomes are observed depending on the predator strength. For a "weak" predator, the swarm is able to…
We study the dynamics of a starving random walk in general spatial dimension $d$. This model represents an idealized description for the fate of an unaware forager whose motion is not affected by the presence or absence of resources. The…
The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Lambda, is classically estimated using the capacity of Lambda with respect to the Green kernel G(x,y). We show that replacing the Green kernel by…
Individuals traversing challenging obstacles are faced with a decision: they can adopt traversal strategies that minimally disrupt their normal locomotion patterns or they can adopt strategies that substantially alter their gait, conferring…
A quantum central limit theorem for a continuous-time quantum walk on a homogeneous tree is derived from quantum probability theory. As a consequence, a new type of limit theorems for another continuous-time walk introduced by the walk is…
Nuclear pore complexes are constantly confronted by large fluxes of macromolecules and macromolecular complexes that need to get into and out of the nucleus. Such bi-directional traffic occurring in a narrow channel can easily lead to…
Piecewise affine maps (PAMs) are frequently used as a reference model to show the openness of the reachability questions in other systems. The reachability problem for one-dimentional PAM is still open even if we define it with only two…
We study a greedy forager who consumes food throughout a region. If the forager does not eat any food for $S$ time steps it dies. We assume that the forager moves preferentially in the direction of greatest smell of food. Each food item in…
We investigate methods for modelling metabolism within populations of cells. Typically one represents the interaction of a cloned population of cells with their environment as though it were one large cell. The question is as to whether any…
Machine Learning~(ML) has provided promising results in recent years across different applications and domains. However, in many cases, qualities such as reliability or even safety need to be ensured. To this end, one important aspect is to…
We study coupled transport in the nonequilibrium stationary state of a model consisting of independent random walkers, moving along a one-dimensional channel, which carry a conserved energy-like quantity, with density and temperature…
Molecular motors perform active movements along cytoskeletal filaments and drive the traffic of organelles and other cargo particles in cells. In contrast to the macroscopic traffic of cars, however, the traffic of molecular motors is…
We analyze a scaling law for the consumption of agricultural soil by cities. The nonlinear dependence of the size of the city on the number of inhabitants gives rise to an equation for population dynamics. We found the asymptotic limit of…
Given a set of integers $S = \{k_1,\ k_2,...,\ k_n\}$, the Cookie Monster Problem is the problem of making all elements of the set equal 0 in the minimum number of moves. Consider the analogy of cookie jars with distinct numbers of cookies,…
Thanks to recent technological advances, it is now possible to track with an unprecedented precision and for long periods of time the movement patterns of many living organisms in their habitat. The increasing amount of data available on…
Given a plane oval, is it possible to go around it so that, at all times, the two tangent segments to the oval from the moving point have unequal lengths? In this note we construct an example of such an oval.
We analyze a model for a walker moving on a ratchet potential. This model is motivated by the properties of transport of motor proteins, like kinesin and myosin. The walker consists of two feet represented as two particles coupled…
Different populations of vehicles travel along a network. Each population has its origin, destination and travel costs - which may well be unbounded. Under the only requirement of the continuity of the travel costs, we prove the existence…
Recently, a new model of quantum walk, utilizing recycled coins, was introduced; however little is yet known about its properties. In this paper, we study its behavior on the cycle graph. In particular, we will consider its time averaged…
Growth economies continue to be more reliant on roadways than ever before. Over 30,000 miles of road are added yearly to the already enormous road system that exists in the United States. As roads segment habitats, animals have no option…