Related papers: Stabilization Time in Minority Processes
In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
Frei et al. [6] showed that the problem to decide whether a graph is stable with respect to some graph parameter under adding or removing either edges or vertices is $\Theta_2^{\text{P}}$-complete. They studied the common graph parameters…
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
We investigate further several properties of the minority game we have recently introduced. We explain the origin of the phase transition and give an analytical expression of $\sigma^2/N$ in the $N\ll2^M$ region. The ability of the players…
Based on a non-rigorous formalism called the "cavity method", physicists have put forward intriguing predictions on phase transitions in discrete structures. One of the most remarkable ones is that in problems such as random $k$-SAT or…
Majority dynamics is a process on a simple, undirected graph $G$ with an initial Red/Blue color for every vertex of $G$. Each day, each vertex updates its color following the majority among its neighbors, using its previous color for…
In this article, we study feature attributions of Machine Learning (ML) models originating from linear game values and coalitional values defined as operators on appropriate functional spaces. The main focus is on random games based on the…
Bounded-size rules are dynamic random graph processes which incorporate limited choice along with randomness in the evolution of the system. One starts with the empty graph and at each stage two edges are chosen uniformly at random. One of…
A streaming algorithm is considered to be adversarially robust if it provides correct outputs with high probability even when the stream updates are chosen by an adversary who may observe and react to the past outputs of the algorithm. We…
In the standard minority game, every agent switches to his best strategy in hand at each time step. If only a small number of agents are allowed to switch their strategies at each time step, the population variance of the system plunges.…
The Minority Game framework was recently generalized to account for the possibility that agents adapt not only through strategy selection but also by diversifying their response according to the kind of dynamical regime, or the risk, they…
We investigate space-time trade-offs for population protocols in sparse interaction graphs. In complete interaction graphs, optimal space-time trade-offs are known for the leader election and exact majority problems. However, it has…
A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…
We study diffusion processes that are stopped or reflected on the boundary of a domain. The generator of the process is assumed to contain two parts: the main part that degenerates on the boundary in a direction orthogonal to the boundary…
We prove that any Markov chain that performs local, reversible updates on randomly chosen vertices of a bounded-degree graph necessarily has mixing time at least $\Omega(n\log n)$, where $n$ is the number of vertices. Our bound applies to…
In this paper we consider convergence of moments in the small-time limit theorems for L\'evy processes. We provide precise asymptotics for all the absolute moments of positive order. The convergence of moments in limit theorems holds…
Consider a graph $G=(V,E)$ and an initial random coloring where each vertex $v \in V$ is blue with probability $P_b$ and red otherwise, independently from all other vertices. In each round, all vertices simultaneously switch their color to…
This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially,…
The operation of creating edges has been widely applied to optimize relevant quantities of opinion dynamics. In this paper, we consider a problem of polarization optimization for the leader-follower opinion dynamics in a noisy social…