Related papers: The Camel-Banana Problem
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
We study the capacity of the range of a transient simple random walk on $\mathbb{Z}^d$. Our main result is a central limit theorem for the capacity of the range for $d\ge 6$. We present a few open questions in lower dimensions.
We study the long time behavior of the elephant random walk with stops, introduced by Kumar, Harbola and Lindenberg (2010), and establish the phase transition of the number of visited points up to time $n$, and the correlation between the…
Cost-maps are used by robotic vehicles to plan collision-free paths. The cost associated with each cell in the map represents the sensed environment information which is often determined manually after several trial-and-error efforts. In…
We consider the allocation problem in which $m \leq (1-\epsilon) dn $ items are to be allocated to $n$ bins with capacity $d$. The items $x_1,x_2,\ldots,x_m$ arrive sequentially and when item $x_i$ arrives it is given two possible bin…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
A field deterministic model of the vehicular dynamics in a generic urban street canyon with two neighboring canyons is considered. The assumed hydrodynamical model of vehicular movement is coupled to the gasdynamical model of the air and…
Very recently, a fundamental observable has been introduced and analyzed to quantify the exploration of random walks: the time $\tau_k$ required for a random walk to find a site that it never visited previously, when the walk has already…
We investigate a driven two-channel system where particles on different lanes mutually obstruct each others motion extending an earlier model by Popkov and Peschel [1]. This obstruction may occur in biological contexts due to steric…
In this chapter, we review recent results on the starving random walk (RW) problem, a minimal model for resource-limited exploration. Initially, each lattice site contains a single food unit, which is consumed upon visitation by the RW. The…
The ridesharing problem is that given a set of trips, each trip consists of an individual, a vehicle of the individual and some requirements, select a subset of trips and use the vehicles of selected trips to deliver all individuals to…
Among all kinds of apes, only gibbons have the slim body as human. Gibbons can move in the forest by cross arm swing, what was the locomotion mode of our arboreal ancestor. Since our ancestor had much heavier body but weaker arms than…
We consider a three-level food chain in which an epidemics affects the intermediate population. Two models are presented, respectively either allowing for unlimited food supply for the bottom prey, or instead assuming for it a logistic…
We define a notion of stochastic domination between trees, where one tree dominates another if when the vertices of each are labeled with independent, identically distributed random variables, one tree is always more likely to contain a…
We analyze the movement of a starving forager on a one-dimensional periodic lattice, where each location contains one unit of food. As the forager lands on sites with food, it consumes the food, leaving the sites empty. If the forager lands…
The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and…
Livestock mobility, particularly that of small and large ruminants, is one of the main pillars of production and trade in West Africa: livestock is moved around in search of better grazing or sold in markets for domestic consumption and for…
Elephant random walk is a special type of random walk that incorporates the memory of the past to determine its future steps. The probability of this walk taking a particular step (+1 or -1) at a time point, conditioned on the entire…
The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters they might share the benefit of cooperation while being more protected against non-cooperating individuals, which…
We consider a system of ordered cars moving in $\R$ from right to left. Each car is represented by a point in $\R$; two or more cars can occupy the same point but cannot overpass. Cars have two possible velocities: either 0 or 1. An…