Network evolution towards optimal dynamical performance

Karalus, Steffen; Porto, Markus

doi:10.1209/0295-5075/99/38002

Cited by 6 publications

(17 citation statements)

References 35 publications

(45 reference statements)

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“…[1][2][3][4][5] To understand how these systems function one needs to determine the structure and rates in these networks. In recent years, significant experimental and theoretical advances in investigating mechanisms of complex chemical and biological systems have been achieved.…”

Section: Introductionmentioning

confidence: 99%

Mechanisms and topology determination of complex chemical and biological network systems from first-passage theoretical approach

Li¹,

Kolomeisky²

2013

The Journal of Chemical Physics

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The majority of chemical and biological processes can be viewed as complex networks of states connected by dynamic transitions. It is fundamentally important to determine the structure of these networks in order to fully understand the mechanisms of underlying processes. A new theoretical method of obtaining topologies and dynamic properties of complex networks, which utilizes a first-passage analysis, is developed. Our approach is based on a hypothesis that full temporal distributions of events between two arbitrary states contain full information on number of intermediate states, pathways, and transitions that lie between initial and final states. Several types of network systems are analyzed analytically and numerically. It is found that the approach is successful in determining structural and dynamic properties, providing a direct way of getting topology and mechanisms of general chemical network systems. The application of the method is illustrated on two examples of experimental studies of motor protein systems. © 2013 AIP Publishing LLC.

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Section: Introductionmentioning

confidence: 99%

Mechanisms and topology determination of complex chemical and biological network systems from first-passage theoretical approach

Li¹,

Kolomeisky²

2013

The Journal of Chemical Physics

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“…It has also been shown that networks can be reconstructed from their Laplacian spectra by evolutionary optimization [24,25]. Recently, network evolution was applied to generate networks which display subdiffusive dynamics [26]. Here, subdiffusion is specified by the average return probability of a random walker that decays more slowly than in normal diffusion.…”

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confidence: 99%

“…To elucidate how the spectral properties are encoded in the structure of the evolved networks, in the present work we apply the method of ref. [26] to regular networks, i.e., networks in which each vertex has the same number of neighbors. Two typical network configurations evolved towards a target spectral dimension of d s = 1.4 p-1 arXiv:1503.02446v2 [physics.soc-ph] 27 Aug 2015 are shown in fig.…”

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confidence: 99%

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Symmetry-based coarse-graining of evolved dynamical networks

Karalus¹,

Krug²

2015

EPL

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-Networks with a prescribed power-law scaling in the spectrum of the graph Laplacian can be generated by evolutionary optimization. The Laplacian spectrum encodes the dynamical behavior of many important processes. Here, the networks are evolved to exhibit subdiffusive dynamics. Under the additional constraint of degree-regularity, the evolved networks display an abundance of symmetric motifs arranged into loops and long linear segments. Exploiting results from algebraic graph theory on symmetric networks, we find the underlying backbone structures and how they contribute to the spectrum. The resulting coarse-grained networks provide an intuitive view of how the anomalous diffusive properties can be realized in the evolved structures.Introduction. -Networks have become a principal tool for the modeling of complex systems in a broad range of scientific fields [1][2][3]. In a dynamical network the topology describes the couplings between individual units of a dynamical process [4]. The general underlying question of research on dynamical networks is how the network structure shapes the global dynamical behavior.An important class of processes on networks are Laplacian dynamics in which the graph Laplacian is the operator of the (linearized) time evolution. The Laplacian spectrum and eigenvectors then describe the overall dynamical behavior. This class comprises many physical processes such as dynamics of Gaussian spring polymers [5], transport processes [6], random walks [7], and synchronization of oscillators [8][9][10].Another dynamical aspect is the evolution of network structure. Many systems change their connectivity structure in the course of time which affects the global dynamical behavior. The time scales of these two processes are often well separated with fast dynamics and slowly responding structural evolution. As an example, think of changes in neuronal activity in a brain on the one hand and the formation of synaptic connections on the other hand. In the opposite case, when dynamics and evolution happen on similar time scales one speaks of coevolutionary or adaptive networks [11]. Since the functionality of a system is often closely associated with dynamical behavior evolutionary forces will drive an evolving dynamical network towards some optimized structure.The method of network evolution adopts this strategy

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“…[1][2][3][4][5] Since the functioning of these complex systems is strongly influenced by their structures, the most important step in theoretical analysis is to determine the topology of underlying networks. Despite recent strong advances in understanding the dynamical and structural properties of complex chemical and biological networks, [6][7][8][9][10][11][12][13][14] revealing the hidden structures of networks and their relations to dynamics remains a challenging task.…”

Section: Introductionmentioning

confidence: 99%

Pathway structure determination in complex stochastic networks with non-exponential dwell times

Kolomeisky

Valleriani

2014

The Journal of Chemical Physics

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Analysis of complex networks has been widely used as a powerful tool for investigating various physical, chemical, and biological processes. To understand the emergent properties of these complex systems, one of the most basic issues is to determine the structure and topology of the underlying networks. Recently, a new theoretical approach based on first-passage analysis has been developed for investigating the relationship between structure and dynamic properties for network systems with exponential dwell time distributions. However, many real phenomena involve transitions with nonexponential waiting times. We extend the first-passage method to uncover the structure of distinct pathways in complex networks with non-exponential dwell time distributions. It is found that the analysis of early time dynamics provides explicit information on the length of the pathways associated to their dynamic properties. It reveals a universal relationship that we have condensed in one general equation, which relates the number of intermediate states on the shortest path to the early time behavior of the first-passage distributions. Our theoretical predictions are confirmed by extensive Monte Carlo simulations.

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Network evolution towards optimal dynamical performance

Cited by 6 publications

References 35 publications

Mechanisms and topology determination of complex chemical and biological network systems from first-passage theoretical approach

Mechanisms and topology determination of complex chemical and biological network systems from first-passage theoretical approach

Symmetry-based coarse-graining of evolved dynamical networks

Pathway structure determination in complex stochastic networks with non-exponential dwell times

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