Related papers: On Rank Driven Dynamical Systems
This research considers the ranking and selection with input uncertainty. The objective is to maximize the posterior probability of correctly selecting the best alternative under a fixed simulation budget, where each alternative is measured…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
A punctuated equilibrium model of biological evolution with relative fitness between different species being the fundamental driving force of evolution is introduced. Mutation is modeled as a fitness updating cellular automaton process…
We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal andhuman behavior. Precisely, the system consists of a finite number of particles characterized by their…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Many models of population dynamics are formulated as deterministic iterated maps although real populations are stochastic. This is justifiable in the limit of large population sizes, as the stochastic fluctuations are negligible then.…
Complex systems are high-dimensional nonlinear dynamical systems with intricate interactions among their constituents. To make interpretable predictions about their large-scale behavior, it is typically assumed, without a clear statement,…
We study the existence and uniqueness of rank-based interacting systems of stochastic differential equations. These systems can be seen as modifications with state-dependent coefficients of the Atlas model in mathematical finance. The…
Like distributed systems, biological multicellular processes are subject to dynamic changes and a biological system will not pass the survival-of-the-fittest test unless it exhibits certain features that enable fast recovery from these…
We study the dynamics of the processes in the small-world networks with a power-law degree distribution where every node is considered to be in one of the two available statuses. We present an algorithm for generation of such network and…
We study the statistical properties of trainable agents moving in discrete space. After introducing the mathematical framework, we first analyze the dynamics of two completely random walkers, mutually competing in a chaser-target…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
We consider a certain lattice branching random walk with on-site competition and in an environment which is heterogeneous at a macroscopic scale $1/\varepsilon$ in space and time. This can be seen as a model for the spatial dynamics of a…
In some systems, the behavior of the constituent units can create a `context' that modifies the direct interactions among them. This mechanism of indirect modification inspired us to develop a minimal model of context-dependent spreading.…
We propose a simple model that describes the dynamics of efficiencies of competing agents. Agents communicate leading to increase of efficiencies of underachievers, and an efficiency of each agent can increase or decrease irrespectively of…
Self-organization of a biologically motivated swarm into smaller subgroups of different velocities is found by solving a 1-dimensional adaptive-velocity swarm, in which the velocity of an agent is averaged over a finite local radius of…
Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems. They often take the form of a high-dimensional system of differential equations…
Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function…
In this work we study spin-glass (SG) like behavior in the dynamics of multiple agents in a social or economic context using interactions which are similar to the physical case. The different preferences shown by individual agents are…
We present a non-neutral stochastic model for the dynamics taking place in a meta-community ecosystems in presence of migration. The model provides a framework for describing the emergence of multiple ecological scenarios and behaves in two…