Dynamic Peer-to-Peer Competition

The dynamic behavior of a multiagent system in which the agent size $s_{i}$ is variable it is studied along a Lotka-Volterra approach. The agent size has hereby for meaning the fraction of a given market that an agent is able to capture (market share). A Lotka-Volterra system of equations for prey-predator problems is considered, the competition factor being related to the difference in size between the agents in a one-on-one competition. This mechanism introduces a natural self-organized dynamic competition among agents. In the competition factor, a parameter $\sigma$ is introduced for scaling the intensity of agent size similarity, which varies in each iteration cycle. The fixed points of this system are analytically found and their stability analyzed for small systems (with $n=5$ agents). We have found that different scenarios are possible, from chaotic to non-chaotic motion with cluster formation as function of the $\sigma$ parameter and depending on the initial conditions imposed to the system. The present contribution aim is to show how a realistic though minimalist nonlinear dynamics model can be used to describe market competition (companies, brokers, decision makers) among other opinion maker communities.Comment: 17 pages, 50 references, 6 figures, 1 tabl

Validity of the independence assumption for the separation of instantaneous and convolutive mixtures of speech and music sources

International audienceIn this paper, we study the validity of the assumption that speech source signals exhibit lower dependency and therefore better separability with Independent Component Analysis algorithms than music sources. In particular, we investigate some dependency measures in the temporal and the time-frequency domains, resp. in the framework of instantaneous and convolutive mixtures. Moreover, we test several ICA methods, based on the above dependency measures, on the same source signals. We experimentally show that speech and music sources tend to have the same mean behaviour for excerpt durations above 20~ms, but music signals provide more spread dependency measures and SIR values. Lastly, we experimentally show that Gaussian nonstationary mutual information is better suited to audio signals than mutual information