相关论文: Relativistically speaking: Let's walk or run throu…

The classic question of whether one should walk or run in the rain to remain the least wet has inspired a myriad of solutions ranging from physically performing test runs in raining conditions to mathematically modeling human movement…

In this recreational mathematics note, we address a simple, yet instructive question: Justin has to travel a distance of d miles along a bus route. Along this route, there are n bus stops i, each spaced at a distance of d_i from the…

This mathematical recreation extends the analysis of a recent paper, asking when a traveller at a bus stop and not knowing the time of the next bus is best advised to wait or to start walking toward the destination. A detailed analysis and…

We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…

Finding an optimum strategy to reach a certain destination by swimming in a background flow is an interesting question which leads to non-trivial results and swimming paths. Here we consider different strategies for various types of surface…

This contribution investigates situations in pedestrian dynamics, where trying to walk the shortest path leads to largely different results than trying to walk the quickest path. A heuristic one-shot method to model the influence of the…

We carry out a comparative study on the problem for a walker searching on several typical complex networks. The search efficiency is evaluated for various strategies. Having no knowledge of the global properties of the underlying networks…

The run-and-tumble walk, consisting in randomly reoriented ballistic excursions, models phenomena ranging from gas kinetics to bacteria motility. We evaluate the mean time required for this walk to find a fixed target within a 2D or 3D…

We investigate simple strategies that embody the decisions that one faces when trying to park near a popular destination. Should one park far from the target (destination), where finding a spot is easy, but then be faced with a long walk,…

Stability of running on rough terrain depends on the propagation of perturbations due to the ground. We consider stability within the sagittal plane and model the dynamics of running as a two-dimensional body with an alternating aerial and…

The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…

A functional approach for the study of the random walks in random sceneries (RWRS) is proposed. Under fairly general assumptions on the random walk and on the random scenery, functional limit theorems are proved. The method allows to study…

Motion forecasting plays a significant role in various domains (e.g., autonomous driving, human-robot interaction), which aims to predict future motion sequences given a set of historical observations. However, the observed elements may be…

We consider the problem of walking in an unknown street, for a robot that has a minimal sensing capability. The robot is equipped with a sensor that only detects the discontinuities in depth information (gaps) and can locate the target…

We study one-dimensional nearest neighbour random walk in site-random environment. We establish precise (sharp) large deviations in the so-called ballistic regime, when the random walk drifts to the right with linear speed. In the…

Humans experience small fluctuations in their gait when walking on uneven terrain. The fluctuations deviate from the steady, energy-minimizing pattern for level walking, and have no obvious organization. But humans often look ahead when…

We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…

When a large group of pedestrians moves around a corner, most pedestrians do not follow the shortest path, which is to stay as close as possible to the inner wall, but try to minimize the travel time. For this they accept to move on a…

Humans typically walk at low speeds and run at higher speeds. Previous studies of transitions between walking and running were mostly on treadmills, but real-world locomotion allows more flexibility. Here, we study overground locomotion…

In this paper we present a combinatorial optimisation view on the routing problem for connectionless packet networks by using the metaphor of a landscape. We examine the main properties of the routing landscapes as we define them and how…