Networks, Dynamics, and Modularity

Variano, Evan; McCoy, Jonathan H.; Lipson, Hod

doi:10.1103/physrevlett.92.188701

Cited by 112 publications

(86 citation statements)

References 21 publications

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“…Within brains, modular and hierarchical organization reflects constraints on the genetic encoding of brain development (43) as well as anatomical constraints such as the optimization of axonal lengths (44). Hierarchical organization may also serve functional roles, for example, in the adaptive distribution of reentrant signals (45) and in providing robustness of responses to perturbations (46). Hierarchical and compositional structures may also relate to recursive relations at the phenomenal level.…”

Section: Dimensions Of Relevant Complexitymentioning

confidence: 99%

Theories and measures of consciousness: An extended framework

Seth

Izhikevich

Reeke

et al. 2006

Proc. Natl. Acad. Sci. U.S.A.

257

214

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A recent theoretical emphasis on complex interactions within neural systems underlying consciousness has been accompanied by proposals for the quantitative characterization of these interactions. In this article, we distinguish key aspects of consciousness that are amenable to quantitative measurement from those that are not. We carry out a formal analysis of the strengths and limitations of three quantitative measures of dynamical complexity in the neural systems underlying consciousness: neural complexity, information integration, and causal density. We find that no single measure fully captures the multidimensional complexity of these systems, and all of these measures have practical limitations. Our analysis suggests guidelines for the specification of alternative measures which, in combination, may improve the quantitative characterization of conscious neural systems. Given that some aspects of consciousness are likely to resist quantification altogether, we conclude that a satisfactory theory is likely to be one that combines both qualitative and quantitative elements.complexity ͉ differentiation ͉ dynamic core ͉ integration

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Section: Dimensions Of Relevant Complexitymentioning

confidence: 99%

Theories and measures of consciousness: An extended framework

Seth

Izhikevich

Reeke

et al. 2006

Proc. Natl. Acad. Sci. U.S.A.

257

214

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“…This suggestion is based on the expectation that designs with higher modularity have higher adaptability and therefore higher survival rates in changing environments. However, computer evolution simulations under randomly changing environments do not seem to be sufficient to produce modularity (25,27).Here, we build on the suggestion of Lipson et al (25,27, †). The key feature in our study is evolution under an environment (evolutionary goal) that changes with time in a modular fashion.…”

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confidence: 99%

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confidence: 99%

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Spontaneous evolution of modularity and network motifs

Kashtan

Alon²

2005

Proc. Natl. Acad. Sci. U.S.A.

779

803

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Biological networks have an inherent simplicity: they are modular with a design that can be separated into units that perform almost independently. Furthermore, they show reuse of recurring patterns termed network motifs. Little is known about the evolutionary origin of these properties. Current models of biological evolution typically produce networks that are highly nonmodular and lack understandable motifs. Here, we suggest a possible explanation for the origin of modularity and network motifs in biology. We use standard evolutionary algorithms to evolve networks. A key feature in this study is evolution under an environment (evolutionary goal) that changes in a modular fashion. That is, we repeatedly switch between several goals, each made of a different combination of subgoals. We find that such ''modularly varying goals'' lead to the spontaneous evolution of modular network structure and network motifs. The resulting networks rapidly evolve to satisfy each of the different goals. Such switching between related goals may represent biological evolution in a changing environment that requires different combinations of a set of basic biological functions. The present study may shed light on the evolutionary forces that promote structural simplicity in biological networks and offers ways to improve the evolutionary design of engineered systems. B iological and engineered systems share general design features: they display modularity, defined as the separability of the design into units that perform independently, at least to a first approximation (1-3, 5). † Furthermore, they show reuse of certain circuit patterns, termed network motifs (6-11), in many different parts of the system. These features allow construction of extremely complex systems by using simple building blocks (12).These features of biological networks are not captured by most current models of biological evolution. For example, many models of biological evolution use computers to evolve networks to attain a defined goal. In these simulations, networks in a population are varied by means of mutations, crossover, and duplication (13-15). Networks that perform better are selected in the next generation. A well known feature of these computational models of biological evolution is that the evolved systems are usually intricately wired and nonmodular. The nonmodular solutions are often more highly optimized than their human-engineered counterparts (16,17,20).The fundamental reason for the lack of modularity in these evolved networks is that modular structures are usually less optimal than nonmodular ones. Typically, there are many possible connections that break modularity and increase fitness. Thus, even an initially modular solution rapidly evolves into one of many possible nonmodular solutions.Lack of modularity is one of the reasons that computational evolution can currently generate designs for simple tasks, but has difficulty in scaling up to higher complexity. In the field of evolutionary design of engineered systems, approaches have been dev...

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“…To drive networks' evolution, we use a standard evolutionary algorithm consisting of successive cycles of random mutations and selection. Similar algorithms have been applied to boolean networks to study the emergence of homeostasis and noise imprinting 9 , evolutionary plasticity of biological systems 16 , modularity 21 , and more recently the emergence of motifs 8 in engineered systems. In this study, we wish to compare the evolutionary paths of networks with either scale-free or homogeneous random topologies.…”

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confidence: 99%

Effects of topology on network evolution

Oikonomou

Cluzel

2006

Nature Phys

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T he ubiquity of scale-free topology in nature raises the question of whether this particular network design confers an evolutionary advantage 1 . A series of studies has identified key principles controlling the growth and the dynamics of scale-free networks 2-4 . Here, we use neuron-based networks of boolean components as a framework for modelling a large class of dynamical behaviours in both natural and artificial systems [5][6][7] . Applying a training algorithm, we characterize how networks with distinct topologies evolve towards a preestablished target function through a process of random mutations and selection [8][9][10] . We find that homogeneous random networks and scale-free networks exhibit drastically different evolutionary paths. Whereas homogeneous random networks accumulate neutral mutations and evolve by sparse punctuated steps 11,12 , scale-free networks evolve rapidly and continuously. Remarkably, this latter property is robust to variations of the degree exponent. In contrast, homogeneous random networks require a specific tuning of their connectivity to optimize their ability to evolve. These results highlight an organizing principle that governs the evolution of complex networks and that can improve the design of engineered systems.In recent years, studies of the architecture of large complex networks have unveiled a topology, known as scale-free, in which the connectivity between elements is power-law distributed 3 . In biology, the intricate interactions of genes and proteins can be viewed as neuron-based networks that control biological signals 13 . It is also common to model large technological and social systems using similar neuronal networks. For example, electronic devices that carry out computational tasks are built using large networks of interconnected logic gates, whereas collective social behaviours emerge from a complex structure of social relations and the dynamics of personal influences 14,15 . In such real-world networks, the topology is important because it mediates the effect of modifications in local interaction that can sometimes affect the networks dynamical behaviour. Topology could thus be a determining factor to modify or evolve the function of networks 16 . In this picture, new dynamical behaviours emerge from 'tinkering' the local interactions from old systems. In living organisms, genetic and protein networks have evolved through a process of mutations and selection to carry out specific functions under specific environmental conditions. This process has inspired physical scientists to apply a similar evolutionary approach to explore solutions to difficult optimization problems and to search for novel designs of artificial systems 17 . For example, evolutionary algorithms have been used to train software and even reconfigurable electronic chips to carry out pre-determined tasks 18 . Also known as 'evolvable hardware' , these electronic devices are composed of large numbers of neuron-like elements whose interactions are programmable 19 . To exploit the power of th...

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Networks, Dynamics, and Modularity

Cited by 112 publications

References 21 publications

Theories and measures of consciousness: An extended framework

Theories and measures of consciousness: An extended framework

Spontaneous evolution of modularity and network motifs

Effects of topology on network evolution

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