Related papers: On Rank Driven Dynamical Systems
We consider Schelling's bounded neighbourhood model (BNM) of unorganised segregation of two populations from the perspective of modern dynamical systems theory. We derive a Schelling dynamical system and carry out a complete quantitative…
Following the paradigm set by attraction-repulsion-alignment schemes, a myriad of individual based models have been proposed to calculate the evolution of abstract agents. While the emergent features of many agent systems have been…
Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
We describe the evolution of $E.coli$ populations through a Bak-Sneppen type model which incorporates random mutations. We show that, for a value of the mutation level which coincides with the one estimated from experiments, this model…
We present a detailed numerical analysis of the modified version of a conservative self-organized extremal model introduced by Pianegonda et. al. for the distribution of wealth of the people in a society. Here the trading process has been…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
We demonstrate with a thought experiment that fitness-based population dynamical approaches to evolution are not able to make quantitative, falsifiable predictions about the long-term behavior of evolutionary systems. A key characteristic…
Stochastic multiplicative dynamics characterize many complex natural phenomena such as selection and mutation in evolving populations, and the generation and distribution of wealth within social systems. Population heterogeneity in…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Self-adaptive dynamics occurs in many physical systems such as socio-economics, neuroscience, or biophysics. We formalize a self-adaptive modeling approach, where adaptation takes place within a set of strategies based on the history of the…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
Randomized rankings have been of recent interest to achieve ex-ante fairer exposure and better robustness than deterministic rankings. We propose a set of natural axioms for randomized group-fair rankings and prove that there exists a…
In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the…
The study of adaptive dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former's dynamics is crucial for…
The agent-based model of stock price dynamics on a directed evolving complex network is suggested and studied by direct simulation. The stationary regime is maintained as a result of the balance between the extremal dynamics, adaptivity of…
We apply methods of dynamical systems to study the behaviour of the Randall-Sundrum models. We determine evolutionary paths for all possible initial conditions in a 2-dimensional phase space and we investigate the set of accelerated models.…
The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the Random Energy Model…
We study sequential decision-making when the agent's internal model class is misspecified. Within the infinite-horizon Berk-Nash framework, stable behavior arises as a fixed point: the agent acts optimally relative to a subjective model,…
The dynamics of protection processes has been a fundamental challenge in systemic risk analysis. The conceptual principle and methodological techniques behind the mechanisms involved [in such dynamics] have been harder to grasp than…