391,225 research outputs found
Size reduction of complex networks preserving modularity
The ubiquity of modular structure in real-world complex networks is being the
focus of attention in many trials to understand the interplay between network
topology and functionality. The best approaches to the identification of
modular structure are based on the optimization of a quality function known as
modularity. However this optimization is a hard task provided that the
computational complexity of the problem is in the NP-hard class. Here we
propose an exact method for reducing the size of weighted (directed and
undirected) complex networks while maintaining invariant its modularity. This
size reduction allows the heuristic algorithms that optimize modularity for a
better exploration of the modularity landscape. We compare the modularity
obtained in several real complex-networks by using the Extremal Optimization
algorithm, before and after the size reduction, showing the improvement
obtained. We speculate that the proposed analytical size reduction could be
extended to an exact coarse graining of the network in the scope of real-space
renormalization.Comment: 14 pages, 2 figure
Critical properties of complex fitness landscapes
Evolutionary adaptation is the process that increases the fit of a population
to the fitness landscape it inhabits. As a consequence, evolutionary dynamics
is shaped, constrained, and channeled, by that fitness landscape. Much work has
been expended to understand the evolutionary dynamics of adapting populations,
but much less is known about the structure of the landscapes. Here, we study
the global and local structure of complex fitness landscapes of interacting
loci that describe protein folds or sets of interacting genes forming pathways
or modules. We find that in these landscapes, high peaks are more likely to be
found near other high peaks, corroborating Kauffman's "Massif Central"
hypothesis. We study the clusters of peaks as a function of the ruggedness of
the landscape and find that this clustering allows peaks to form interconnected
networks. These networks undergo a percolation phase transition as a function
of minimum peak height, which indicates that evolutionary trajectories that
take no more than two mutations to shift from peak to peak can span the entire
genetic space. These networks have implications for evolution in rugged
landscapes, allowing adaptation to proceed after a local fitness peak has been
ascended.Comment: 7 pages, 6 figures, requires alifex11.sty. To appear in Proceedings
of 12th International Conference on Artificial Lif
A Comparison of Machine-Learning Methods to Select Socioeconomic Indicators in Cultural Landscapes
Cultural landscapes are regarded to be complex socioecological systems that originated as a result of the interaction between humanity and nature across time. Cultural landscapes present complex-system properties, including nonlinear dynamics among their components. There is a close relationship between socioeconomy and landscape in cultural landscapes, so that changes in the socioeconomic dynamic have an effect on the structure and functionality of the landscape. Several numerical analyses have been carried out to study this relationship, with linear regression models being widely used. However, cultural landscapes comprise a considerable amount of elements and processes, whose interactions might not be properly captured by a linear model. In recent years, machine-learning techniques have increasingly been applied to the field of ecology to solve regression tasks. These techniques provide sound methods and algorithms for dealing with complex systems under uncertainty. The term ‘machine learning’ includes a wide variety of methods to learn models from data. In this paper, we study the relationship between socioeconomy and cultural landscape (in Andalusia, Spain) at two different spatial scales aiming at comparing different regression models from a predictive-accuracy point of view, including model trees and neural or Bayesian networks
Relative Stability of Network States in Boolean Network Models of Gene Regulation in Development
Progress in cell type reprogramming has revived the interest in Waddington's
concept of the epigenetic landscape. Recently researchers developed the
quasi-potential theory to represent the Waddington's landscape. The
Quasi-potential U(x), derived from interactions in the gene regulatory network
(GRN) of a cell, quantifies the relative stability of network states, which
determine the effort required for state transitions in a multi-stable dynamical
system. However, quasi-potential landscapes, originally developed for
continuous systems, are not suitable for discrete-valued networks which are
important tools to study complex systems. In this paper, we provide a framework
to quantify the landscape for discrete Boolean networks (BNs). We apply our
framework to study pancreas cell differentiation where an ensemble of BN models
is considered based on the structure of a minimal GRN for pancreas development.
We impose biologically motivated structural constraints (corresponding to
specific type of Boolean functions) and dynamical constraints (corresponding to
stable attractor states) to limit the space of BN models for pancreas
development. In addition, we enforce a novel functional constraint
corresponding to the relative ordering of attractor states in BN models to
restrict the space of BN models to the biological relevant class. We find that
BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics
of pancreas cell differentiation. This framework can also determine the genes'
influence on cell state transitions, and thus can facilitate the rational
design of cell reprogramming protocols.Comment: 24 pages, 6 figures, 1 tabl
Markovian Dynamics on Complex Reaction Networks
Complex networks, comprised of individual elements that interact with each
other through reaction channels, are ubiquitous across many scientific and
engineering disciplines. Examples include biochemical, pharmacokinetic,
epidemiological, ecological, social, neural, and multi-agent networks. A common
approach to modeling such networks is by a master equation that governs the
dynamic evolution of the joint probability mass function of the underling
population process and naturally leads to Markovian dynamics for such process.
Due however to the nonlinear nature of most reactions, the computation and
analysis of the resulting stochastic population dynamics is a difficult task.
This review article provides a coherent and comprehensive coverage of recently
developed approaches and methods to tackle this problem. After reviewing a
general framework for modeling Markovian reaction networks and giving specific
examples, the authors present numerical and computational techniques capable of
evaluating or approximating the solution of the master equation, discuss a
recently developed approach for studying the stationary behavior of Markovian
reaction networks using a potential energy landscape perspective, and provide
an introduction to the emerging theory of thermodynamic analysis of such
networks. Three representative problems of opinion formation, transcription
regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see
http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm
- …