On the Effect of Heterogeneity on the Dynamics and Performance of Dynamical Networks

• Main Author: Goudarzi, Alireza
• Format: Others
• Published: PDXScholar 2012
• Subjects: Natural computation; Evolutionary computation; Neural networks (Computer science); Complex systems; Liquid state machine; Random Boolean networks; OS and Networks; Systems Architecture
• Online Access: https://pdxscholar.library.pdx.edu/open_access_etds/369; https://pdxscholar.library.pdx.edu/cgi/viewcontent.cgi?article=1368&context=open_access_etds

The high cost of processor fabrication plants and approaching physical limits have started a new wave research in alternative computing paradigms. As an alternative to the top-down manufactured silicon-based computers, research in computing using natural and physical system directly has recently gained a great deal of interest. A branch of this research promotes the idea that any physical system with sufficiently complex dynamics is able to perform computation. The power of networks in representing complex interactions between many parts make them a suitable choice for modeling physical systems. Many studies used networks with a homogeneous structure to describe the computational circuits. However physical systems are inherently heterogeneous. We aim to study the effect of heterogeneity in the dynamics of physical systems that pertains to information processing. Two particularly well-studied network models that represent information processing in a wide range of physical systems are Random Boolean Networks (RBN), that are used to model gene interactions, and Liquid State Machines (LSM), that are used to model brain-like networks. In this thesis, we study the effects of function heterogeneity, in-degree heterogeneity, and interconnect irregularity on the dynamics and the performance of RBN and LSM. First, we introduce the model parameters to characterize the heterogeneity of components in RBN and LSM networks. We then quantify the effects of heterogeneity on the network dynamics. For the three heterogeneity aspects that we studied, we found that the effect of heterogeneity on RBN and LSM are very different. We find that in LSM the in-degree heterogeneity decreases the chaoticity in the network, whereas it increases chaoticity in RBN. For interconnect irregularity, heterogeneity decreases the chaoticity in LSM while its effects on RBN the dynamics depends on the connectivity. For {K} < 2, heterogeneity in the interconnect will increase the chaoticity in the dynamics and for {K} > 2 it decreases the chaoticity. We find that function heterogeneity has virtually no effect on the LSM dynamics. In RBN however, function heterogeneity actually makes the dynamics predictable as a function of connectivity and heterogeneity in the network structure. We hypothesize that node heterogeneity in RBN may help signal processing because of the variety of signal decomposition by different nodes.