Related papers: Trajectory stability in the traveling salesman pro…
In [1], the authors have studied stability of certain causal properties of space-times in general relativity. As a continuation of this work, in the present paper, we review and discuss, some more aspects of stability which occur in various…
We consider the time evolution of a lattice branching random walk with local perturbations. Under certain conditions, we prove the Carleman type estimation for the moments of a particle subpopulation number and show the existence of a…
Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…
The five libration points of a sun-planet system are stable or unstable fixed positions at which satellites or asteroids can remain fixed relative to the two orbiting bodies. A moon orbiting around the planet causes a time-dependent…
We study a dynamic allocation problem that arises in various scenarios where mobile clients joining and leaving the system have to communicate with static stations via radio transmissions. Restrictions are a maximum delay, or laxity,…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc., they normally make decisions based on…
We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable…
Human travelling behaviours are markedly regular, to a large extent, predictable, and mostly driven by biological necessities (\eg sleeping, eating) and social constructs (\eg school schedules, synchronisation of labour). Not surprisingly,…
In the persuasion model, apart from a few special cases, comparative statics has been an open question. We answer it, delineating which shifts of the sender's interim payoff lead her optimally to choose a more informative signal. Our first…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
In this paper we propose some novel path planning strategies for a double integrator with bounded velocity and bounded control inputs. First, we study the following version of the Traveling Salesperson Problem (TSP): given a set of points…
In this paper, we consider a mobility system of travelers and providers, and propose a "mobility game" to study when a traveler is matched to a provider. Each traveler seeks to travel using the services of only one provider, who manages one…
In this paper, we study a variant of the dynamic ridesharing problem with a specific focus on peak hours: Given a set of drivers and rider requests, we aim to match drivers to each rider request by achieving two objectives: maximizing the…
The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly…
An instance of Hamiltonian cycle problem can be solved by converting it to an instance of Travelling salesman problem, assigning any choice of weights to edges of the underlying graph. In this note we demonstrate that, for difficult…
The satisfiability problem is one of the most famous problems in computer science. Its NP-completeness has been used to argue that SAT is intractable. However, there have been tremendous advances that allow SAT solvers to solve instances…
A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…
We study a deterministic dynamics with two time scales in a continuous state attractor network. To the usual (fast) relaxation dynamics towards point attractors (``patterns'') we add a slow coupling dynamics that makes the visited patterns…
This paper studies the stability of tensor ranks under field extensions. Our main contributions are fourfold: (1) We prove that the analytic rank is stable under field extensions. (2) We establish the equivalence between the partition rank…