Modelling Biological Networks via Tailored Random Graphs

Coolen, Anthony C. C.; Fraternali, Franca; Annibale, Alessia; Fernandes, Luis P.; Kleinjung, Jens

doi:10.1002/9781119970606.ch15

Cited by 8 publications

(9 citation statements)

References 52 publications

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“…Some further criteria are needed to focus on a particular one. One approach is to use degree-based tailored random graphs as null models for both undirected 19 20 21 and directed 22 23 networks. The criteria that we use to select a particular Y -series in this study are simplicity and the importance of subgraph- and degree-based statistics in networks.…”

Section: Resultsmentioning

confidence: 99%

Quantifying randomness in real networks

et al. 2015

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Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks—the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain—and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs.

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Section: Resultsmentioning

confidence: 99%

Quantifying randomness in real networks

et al. 2015

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“…For derivations of these equilibrium distributions see [34,35]. Although the Glauber dynamics is the one that leads to the usual Ising Hamiltonian, in what follows we focus on the synchronous case for two reasons: (i) the path integral formulation is slightly simpler in terms of notation and (ii) the synchronous case has been the focus of recent work on the dynamics of hard spin models, including our own on the inverse problem of inferring the couplings in the model from the statistics of the spin history [36][37][38].…”

Section: Path Integrals For Hard Spin Modelsmentioning

confidence: 99%

Path integral methods for the dynamics of stochastic and disordered systems

Hertz

Roudi

Sollich

2016

J. Phys. A: Math. Theor.

107

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We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin-Siggia-Rose path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models.

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“…For instance, it makes no sense to use Erdös-Rényi graphs [14] as null models against which to test occurrence frequencies of motifs in biological networks: almost any measurement will come out as significant, simply because our yardstick is not realistic. Tailored random graph ensembles [15][16][17][18] involve measures p(c) that are constructed such that specified topological features of the generated graphs c will systematically resemble those of a given real-world graph c ∈ G. To construct such measures one first defines the set of L observables {ω 1 (c), . .…”

Section: Tailored Random Graph Ensemblesmentioning

confidence: 99%

Random graph ensembles with many short loops

Roberts

Coolen

2014

ESAIM: Proc.

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Networks observed in the real world often have many short loops. This violates the tree-like assumption that underpins the majority of random graph models and most of the methods used for their analysis. In this paper we sketch possible research routes to be explored in order to make progress on networks with many short loops, involving old and new random graph models and ideas for novel mathematical methods. We do not present conclusive solutions of problems, but aim to encourage and stimulate new activity and in what we believe to be an important but under-exposed area of research. We discuss in more detail the Strauss model, which can be seen as the 'harmonic oscillator' of 'loopy' random graphs, and a recent exactly solvable immunological model that involves random graphs with extensively many cliques and short loops.Résumé. Les réseaux observés dans la Nature ont souvent des cycles courts. Ceci contredit le postulat de hiérarchie sur lequel se base la majorité des modèles de réseaux aléatoires et la plupart des méthodes utilisées pour leur analyse. Dans cet article, nous esquissons des directions de recherches possibles, afin de progresser sur les réseaux contenant beaucoup de cycles courts, faisant appel à des modèles de réseaux aléatoires éprouvés ou nouveaux, et des idées pour de nouvelles méthodes mathématiques. Nous ne présentons pas de solutions définitives, mais notre but est d'encourager et de stimuler de nouveaux travaux dans ce que nous croyons être une direction de recherche importante, bien que insuffisamment explorée. Nous discutons en détail le modèle de Strauss, qui peut être interprété comme 'l'oscillateur harmonique' des réseaux aléatoires 'Ãȃ boucles', ainsi qu'un modèle immunologique soluble exactement qui implique des réseaux aléatoires avec de nombreux cliques et cycles courts.

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Modelling Biological Networks via Tailored Random Graphs

Cited by 8 publications

References 52 publications

Quantifying randomness in real networks

Quantifying randomness in real networks

Path integral methods for the dynamics of stochastic and disordered systems

Random graph ensembles with many short loops

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