537 research outputs found
Coupled Replicator Equations for the Dynamics of Learning in Multiagent Systems
Starting with a group of reinforcement-learning agents we derive coupled
replicator equations that describe the dynamics of collective learning in
multiagent systems. We show that, although agents model their environment in a
self-interested way without sharing knowledge, a game dynamics emerges
naturally through environment-mediated interactions. An application to
rock-scissors-paper game interactions shows that the collective learning
dynamics exhibits a diversity of competitive and cooperative behaviors. These
include quasiperiodicity, stable limit cycles, intermittency, and deterministic
chaos--behaviors that should be expected in heterogeneous multiagent systems
described by the general replicator equations we derive.Comment: 4 pages, 3 figures,
http://www.santafe.edu/projects/CompMech/papers/credlmas.html; updated
references, corrected typos, changed conten
The effects of changes in the order of verbal labels and numerical values on children's scores on attitude and rating scales
Research with adults has shown that variations in verbal labels and numerical scale values on rating scales can affect the responses given. However, few studies have been conducted with children. The study aimed to examine potential differences in childrenâs responses to Likert-type rating scales according to their anchor points and scale direction, and to see whether or not such differences were stable over time. 130 British children, aged 9 to 11, completed six sets of Likert-type rating scales, presented in four different ways varying the position of positive labels and numerical values. The results showed, both initially and 8-12 weeks later, that presenting a positive label or a high score on the left of a scale led to significantly higher mean scores than did the other variations. These findings indicate that different arrangements of rating scales can produce different results which has clear implications for the administration of scales with children
Continuous Strategy Replicator Dynamics for Multi--Agent Learning
The problem of multi-agent learning and adaptation has attracted a great deal
of attention in recent years. It has been suggested that the dynamics of multi
agent learning can be studied using replicator equations from population
biology. Most existing studies so far have been limited to discrete strategy
spaces with a small number of available actions. In many cases, however, the
choices available to agents are better characterized by continuous spectra.
This paper suggests a generalization of the replicator framework that allows to
study the adaptive dynamics of Q-learning agents with continuous strategy
spaces. Instead of probability vectors, agents strategies are now characterized
by probability measures over continuous variables. As a result, the ordinary
differential equations for the discrete case are replaced by a system of
coupled integral--differential replicator equations that describe the mutual
evolution of individual agent strategies. We derive a set of functional
equations describing the steady state of the replicator dynamics, examine their
solutions for several two-player games, and confirm our analytical results
using simulations.Comment: 12 pages, 15 figures, accepted for publication in JAAMA
Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh
Numerous formulations of finite volume schemes for the Euler and
Navier-Stokes equations exist, but in the majority of cases they have been
developed for structured and stationary meshes. In many applications, more
flexible mesh geometries that can dynamically adjust to the problem at hand and
move with the flow in a (quasi) Lagrangian fashion would, however, be highly
desirable, as this can allow a significant reduction of advection errors and an
accurate realization of curved and moving boundary conditions. Here we describe
a novel formulation of viscous continuum hydrodynamics that solves the
equations of motion on a Voronoi mesh created by a set of mesh-generating
points. The points can move in an arbitrary manner, but the most natural motion
is that given by the fluid velocity itself, such that the mesh dynamically
adjusts to the flow. Owing to the mathematical properties of the Voronoi
tessellation, pathological mesh-twisting effects are avoided. Our
implementation considers the full Navier-Stokes equations and has been realized
in the AREPO code both in 2D and 3D. We propose a new approach to compute
accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a
finite volume solver of the Navier-Stokes equations. Through a number of test
problems, including circular Couette flow and flow past a cylindrical obstacle,
we show that our new scheme combines good accuracy with geometric flexibility,
and hence promises to be competitive with other highly refined Eulerian
methods. This will in particular allow astrophysical applications of the AREPO
code where physical viscosity is important, such as in the hot plasma in galaxy
clusters, or for viscous accretion disk models.Comment: 26 pages, 21 figures. Submitted to MNRA
Pedestrian, Crowd, and Evacuation Dynamics
This contribution describes efforts to model the behavior of individual
pedestrians and their interactions in crowds, which generate certain kinds of
self-organized patterns of motion. Moreover, this article focusses on the
dynamics of crowds in panic or evacuation situations, methods to optimize
building designs for egress, and factors potentially causing the breakdown of
orderly motion.Comment: This is a review paper. For related work see http://www.soms.ethz.c
- âŚ