Related papers: Walk versus Wait: The Lazy Mathematician Wins
We study two-player reachability games on finite graphs. At each state the interaction between the players is concurrent and there is a stochastic Nature. Players also play stochastically. The literature tells us that 1) Player B, who wants…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
The communication technology revolution in this era has increased the use of smartphones in the world of transportation. In this paper, we propose to leverage IoT device data, capturing passengers' smartphones' Wi-Fi data in conjunction…
A natural extension of a right-continuous integer-valued random walk is one which can jump to the right by one or two units. First passage times above a given fixed level then admit a tractable Laplace transform (probability generating…
We consider stopping problems in which a decision maker (DM) faces an unknown state of nature and decides sequentially whether to stop and take an irreversible action; pay a fee and obtain additional information; or wait without acquiring…
The statistics of persistent events, recently introduced in the context of phase ordering dynamics, is investigated in the case of the 1D lattice random walk in discrete time. We determine the survival probability of the random walker in…
We study the problem of planning routes in road networks when certain streets or areas are closed at certain times. For heavy vehicles, such areas may be very large since many European countries impose temporary driving bans during the…
This paper serves as a user's guide to sampling strategies for sliced optimal transport. We provide reminders and additional regularity results on the Sliced Wasserstein distance. We detail the construction methods, generation time…
We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost. These generalizations are useful when connecting…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
We study a continuous time random walk on the $d$-dimensional lattice, subject to a drift and an attraction to large clusters of a subcritical Bernoulli site percolation. We find two distinct regimes: a ballistic one, and a subballistic one…
This contribution provides microscopic experimental study of pedestrian motion in front of the bottleneck, explains the high variance of individual travel time by the statistical analysis of trajectories. The analysis shows that this…
We present a new oblivious walking strategy for convex subdivisions. Our walk is faster than the straight walk and more generally applicable than the visibility walk. To prove termination of our walk we use a novel monotonically decreasing…
We study a one-dimensional random walk with memory. The behavior of the walker is modified with respect to the simple symmetric random walk (SSRW) only when he is at the maximum distance ever reached from his starting point (home). In this…
We consider two or more simple symmetric walks on some graphs, e.g. the real line, the plane or the two dimensional comb lattice, and investigate the properties of the distance among the walkers.
Suppose that a set of mobile agents, each with a predefined maximum speed, want to patrol a fence together so as to minimize the longest time interval during which a point on the fence is left unvisited. In 2011, Czyzowicz, G\k{a}sieniec,…
Path-finding is one of the most popular subjects in the field of computer science. Pathfinding strategies determine a path from a given coordinate to another. The focus of this paper is on finding the optimal path for the bus transportation…
I study the optimal provision of information in a long-term relationship between a sender and a receiver. The sender observes a persistent, evolving state and commits to send signals over time to the receiver, who sequentially chooses…
In this paper, we present a microscopic agent-based pedestrian behavior model Intend-Wait-Cross. The model is comprised of rules representing behaviors of pedestrians as a series of decisions that depend on their individual characteristics…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…