14,289 research outputs found
Symmetry based Structure Entropy of Complex Networks
Precisely quantifying the heterogeneity or disorder of a network system is
very important and desired in studies of behavior and function of the network
system. Although many degree-based entropies have been proposed to measure the
heterogeneity of real networks, heterogeneity implicated in the structure of
networks can not be precisely quantified yet. Hence, we propose a new structure
entropy based on automorphism partition to precisely quantify the structural
heterogeneity of networks. Analysis of extreme cases shows that entropy based
on automorphism partition can quantify the structural heterogeneity of networks
more precisely than degree-based entropy. We also summarized symmetry and
heterogeneity statistics of many real networks, finding that real networks are
indeed more heterogenous in the view of automorphism partition than what have
been depicted under the measurement of degree based entropies; and that
structural heterogeneity is strongly negatively correlated to symmetry of real
networks.Comment: 7 pages, 6 figure
Dynamics-Driven Evolution to Structural Heterogeneity in Complex Networks
The mutual influence of dynamics and structure is a central issue in complex
systems. In this paper we study by simulation slow evolution of network under
the feedback of a local-majority-rule opinion process. If performance-enhancing
local mutations have higher chances of getting integrated into its structure,
the system can evolve into a highly heterogeneous small-world with a global hub
(whose connectivity is proportional to the network size), strong local
connection correlations and power law-like degree distribution. Networks with
better dynamical performance are achieved if structural evolution occurs much
slower than the network dynamics. Structural heterogeneity of many biological
and social dynamical systems may also be driven by various dynamics-structure
coupling mechanisms.Comment: Figure 2 updated. Final version as appear in Physica
Prominent effect of soil network heterogeneity on microbial invasion
Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil
Learning Stability in Economies with Heterogenous Agents
An economy exhibits structural heterogeneity when the forecasts of different agents have different effects on the determination of aggregate variables. Various forms of structural heterogeneity can arise and we study the important case of economies in which agents' behavior depends on forecasts of aggregate variables and show how different forms of heterogeneity in structure, forecasts, and adaptive learning rules affect the conditions for convergence of adaptive learning towards rational expectations equilibrium. Results are applied to the market model with supply lags and a New Keynesian model of interest rate setting.adaptive learning, expectations formation, stability of equilibrium, market model, monetary policy.
Sampling bias in systems with structural heterogeneity and limited internal diffusion
Complex systems research is becomingly increasingly data-driven, particularly
in the social and biological domains. Many of the systems from which sample
data are collected feature structural heterogeneity at the mesoscopic scale
(i.e. communities) and limited inter-community diffusion. Here we show that the
interplay between these two features can yield a significant bias in the global
characteristics inferred from the data. We present a general framework to
quantify this bias, and derive an explicit corrective factor for a wide class
of systems. Applying our analysis to a recent high-profile survey of conflict
mortality in Iraq suggests a significant overestimate of deaths
Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization
Structural heterogeneity constitutes one of the main substrates influencing impulse propagation in living tissues. In cardiac muscle, improved understanding on its role is key to advancing our interpretation of cell-to-cell coupling, and how tissue structure modulates electrical propagation and arrhythmogenesis in the intact and diseased heart. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a mean of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, validated against in-vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies many relevant characteristics of cardiac propagation, including the shortening of action potential duration along the activation pathway, and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media
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