arXiv subjects

Imre Derenyi

Publications and source records attributed to Imre Derenyi.

At least 19 recordsLinked to original sources

arXiv2008

Fundamental statistical features and self-similar properties of tagged networks

We investigate the fundamental statistical features of tagged (or annotated) networks having a rich variety of attributes associated with their nodes. Tags (attributes, annotations, properties, features, etc.) provide essential information about the entity represented by a given node, thus, taking them into account represents a significant step towards a more complete description of the structure of large complex systems. Our main goal here is to uncover the relations between the statistical properties of the node tags and those of the graph topology. In order to better characterise the networks with tagged nodes, we introduce a number of new notions, including tag-assortativity (relating link probability to node similarity), and new quantities, such as node uniqueness (measuring how rarely the tags of a node occur in the network) and tag-assortativity exponent. We apply our approach to three large networks representing very different domains of complex systems. A number of the tag related quantities display analogous behaviour (e.g., the networks we studied are tag-assortative, indicating possible universal aspects of tags versus topology), while some other features, such as the distribution of the node uniqueness, show variability from network to network allowing for pin-pointing large scale specific features of real-world complex networks. We also find that for each network the topology and the tag distribution are scale invariant, and this self-similar property of the networks can be well characterised by the tag-assortativity exponent, which is specific to each system.

physics.soc-ph↗

arXiv2008

Evolutionary games on minimally structured populations

Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects have, however, proved to be sensitive to the details of the underlying topology and dynamics. Here we introduce a minimal population structure that is described by two distinct hierarchical levels of interaction. We believe this model is able to identify effects of spatial structure that do not depend on the details of the topology. We derive the dynamics governing the evolution of a system starting from fundamental individual level stochastic processes through two successive meanfield approximations. In our model of population structure the topology of interactions is described by only two parameters: the effective population size at the local scale and the relative strength of local dynamics to global mixing. We demonstrate, for example, the existence of a continuous transition leading to the dominance of cooperation in populations with hierarchical levels of unstructured mixing as the benefit to cost ratio becomes smaller then the local population size. Applying our model of spatial structure to the repeated prisoner's dilemma we uncover a novel and counterintuitive mechanism by which the constant influx of defectors sustains cooperation. Further exploring the phase space of the repeated prisoner's dilemma and also of the "rock-paper-scissor" game we find indications of rich structure and are able to reproduce several effects observed in other models with explicit spatial embedding, such as the maintenance of biodiversity and the emergence of global oscillations.

q-bio.PE↗

arXiv2008

Centrality properties of directed module members in social networks

Several recent studies of complex networks have suggested algorithms for locating network communities, also called modules or clusters, which are mostly defined as groups of nodes with dense internal connections. Along with the rapid development of these clustering techniques, the ability of revealing overlaps between communities has become very important as well. An efficient search technique for locating overlapping modules is provided by the Clique Percolation Method (CPM) and its extension to directed graphs, the CPMd algorithm. Here we investigate the centrality properties of directed module members in social networks obtained from e-mail exchanges and from sociometric questionnaires. Our results indicate that nodes in the overlaps between modules play a central role in the studied systems. Furthermore, the two different types of networks show interesting differences in the relation between the centrality measures and the role of the nodes in the directed modules.

physics.soc-ph↗

arXiv2008

The relevance of neck linker docking in the motility of kinesin

Conventional kinesin is a motor protein, which is able to walk along a microtubule processively. The exact mechanism of the stepping motion and force generation of kinesin is still far from clear. In this paper we argue that neck linker docking is a crucial element of this mechanism, without which the experimentally observed dwell times of the steps could not be explained under a wide range of loading forces. We also show that the experimental data impose very strict constraints on the lengths of both the neck linker and its docking section, which are compatible with the known structure of kinesin.

physics.bio-ph↗

arXiv2008

The Effect of Recombination on the Neutral Evolution of Genetic Robustness

Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable, however, it has become apparent that the context dependent effect of mutations and the many-to-one nature inherent in these genotype-phenotype maps can have fundamental evolutionary consequences. It has previously been demonstrated that populations of genotypes evolving on the neutral networks corresponding to all genotypes with the same secondary structure only through neutral mutations can evolve mutational robustness [Nimwegen {\it et al.} Neutral evolution of mutational robustness, 1999 PNAS], by concentrating the population on regions of high neutrality. Introducing recombination we demonstrate, through numerically calculating the stationary distribution of an infinite population on ensembles of random neutral networks that mutational robustness is significantly enhanced and further that the magnitude of this enhancement is sensitive to details of the neutral network topology. Through the simulation of finite populations of genotypes evolving on random neutral networks and a scaled down microRNA neutral network, we show that even in finite populations recombination will still act to focus the population on regions of locally high neutrality.

q-bio.PE↗

arXiv2007

Directed network modules

A search technique locating network modules, i.e., internally densely connected groups of nodes in directed networks is introduced by extending the Clique Percolation Method originally proposed for undirected networks. After giving a suitable definition for directed modules we investigate their percolation transition in the Erdos-Renyi graph both analytically and numerically. We also analyse four real-world directed networks, including Google's own webpages, an email network, a word association graph and the transcriptional regulatory network of the yeast Saccharomyces cerevisiae. The obtained directed modules are validated by additional information available for the nodes. We find that directed modules of real-world graphs inherently overlap and the investigated networks can be classified into two major groups in terms of the overlaps between the modules. Accordingly, in the word-association network and among Google's webpages the overlaps are likely to contain in-hubs, whereas the modules in the email and transcriptional regulatory networks tend to overlap via out-hubs.

physics.soc-ph↗

arXiv2006

Reversible mesoscopic model of protein adsorption: From equilibrium to dynamics

We present a thermodynamically consistent mesoscopic model of protein adsorption at liquid-solid interfaces. First describing the equilibrium state under varying protein concentration of the solution and binding conditions, we predict a non-trivial (non- monotonic) dependence of the experimentally observable properties of the adsorbed layer (such as the surface density and surface coverage) on these parameters. We subsequently proceed to develop a dynamical model consistent with the equilibrium description, which qualitatively reproduces known experimental phenomena and offers a promising way of studying the exchange of the adsorbed proteins by the proteins of the solution.

cond-mat.soft↗

arXiv2006

The maintenance of sex in bacteria is ensured by its potential to reload genes

Why sex is maintained in nature is a fundamental question in biology. Natural genetic transformation (NGT) is a sexual process by which bacteria actively take up exogenous DNA and use it to replace homologous chromosomal sequences. As it has been demonstrated, the role of NGT in repairing deleterious mutations under constant selection is insufficient for its survival, and the lack of other viable explanations have left no alternative except that DNA uptake provides nucleotides for food. Here we develop a novel simulation approach for the long-term dynamics of genome organization (involving the loss and acquisition of genes) in a bacterial species consisting of a large number of spatially distinct populations subject to independently fluctuating ecological conditions. Our results show that in the presence of weak inter-population migration NGT is able to subsist as a mechanism to reload locally lost, intermittently selected genes from the collective gene pool of the species through DNA uptake from migrants. Reloading genes and combining them with those in locally adapted genomes allow individual cells to re-adapt faster to environmental changes. The machinery of transformation survives under a wide range of model parameters readily encompassing real-world biological conditions. These findings imply that the primary role of NGT is not to serve the cell with food, but to provide homologous sequences for restoring genes that have disappeared from or become degraded in the local population.

q-bio.PE↗

arXiv2006

The critical point of k-clique percolation in the Erdos-Renyi graph

Motivated by the success of a k-clique percolation method for the identification of overlapping communities in large real networks, here we study the k-clique percolation problem in the Erdos-Renyi graph. When the probability p of two nodes being connected is above a certain threshold p_c(k), the complete subgraphs of size k (the k-cliques) are organized into a giant cluster. By making some assumptions that are expected to be valid below the threshold, we determine the average size of the k-clique percolation clusters, using a generating function formalism. From the divergence of this average size we then derive an analytic expression for the critical linking probability p_c(k).

cond-mat.dis-nn↗

arXiv2006

CFinder: Locating cliques and overlapping modules in biological networks

Summary: Most cellular tasks are performed not by individual proteins, but by groups of functionally associated proteins, often referred to as modules. In a protein assocation network modules appear as groups of densely interconnected nodes, also called communities or clusters. These modules often overlap with each other and form a network of their own, in which nodes (links) represent the modules (overlaps). We introduce CFinder, a fast program locating and visualizing overlapping, densely interconnected groups of nodes in undirected graphs, and allowing the user to easily navigate between the original graph and the web of these groups. We show that in gene (protein) association networks CFinder can be used to predict the function(s) of a single protein and to discover novel modules. CFinder is also very efficient for locating the cliques of large sparse graphs. Availability: CFinder (for Windows, Linux, and Macintosh) and its manual can be downloaded from http://angel.elte.hu/clustering. Contact: cfinder@angel.elte.hu

q-bio.MN↗

arXiv2005

Uncovering the overlapping community structure of complex networks in nature and society

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins, industrial sectors and groups of people) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.

physics.soc-ph↗

arXiv2005

Clique percolation in random networks

The notion of k-clique percolation in random graphs is introduced, where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated. For the Erdos-Renyi graph of N vertices we obtain that the percolation transition of k-cliques takes place when the probability of two vertices being connected by an edge reaches the threshold pc(k)=[(k-1)N]^{-1/(k-1)}. At the transition point the scaling of the giant component with N is highly non-trivial and depends on k. We discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks.

cond-mat.dis-nn↗

arXiv2004

Reverse engineering of linking preferences from network restructuring

We provide a method to deduce the preferences governing the restructuring dynamics of a network from the observed rewiring of the edges. Our approach is applicable for systems in which the preferences can be formulated in terms of a single-vertex energy function with f(k) being the contribution of a node of degree k to the total energy, and the dynamics obeys the detailed balance. The method is first tested by Monte-Carlo simulations of restructuring graphs with known energies, then it is used to study variations of real network systems ranging from the co-authorship network of scientific publications to the asset graphs of the New York Stock Exchange. The empirical energies obtained from the restructuring can be described by a universal function f(k) -k ln(k), which is consistent with and justifies the validity of the preferential attachment rule proposed for growing networks.

cond-mat.stat-mech↗

arXiv2004

Statistical mechanics of topological phase transitions in networks

We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to the level of noise during the rewiring of the edges. The associated microscopic dynamics satisfies the detailed balance condition and is equivalent to a lattice gas model on the edge-dual graph of a fully connected network. In our studies -- based on an exact enumeration method, Monte-Carlo simulations, and theoretical considerations -- we find a rich variety of topological phase transitions when the temperature is varied. These transitions signal singular changes in the essential features of the global structure of the network. Depending on the energy function chosen, the observed transitions can be best monitored using the order parameters Phi_s=s_{max}/M, i.e., the size of the largest connected component divided by the number of edges, or Phi_k=k_{max}/M, the largest degree in the network divided by the number of edges. If, for example the energy is chosen to be E=-s_{max}, the observed transition is analogous to the percolation phase transition of random graphs. For this choice of the energy, the phase-diagram in the [ ,T] plane is constructed. Single vertex energies of the form E=sum_i f(k_i), where k_i is the degree of vertex i, are also studied. Depending on the form of f(k_i), first order and continuous phase transitions can be observed. In case of f(k_i)=-(k_i+c)ln(k_i), the transition is continuous, and at the critical temperature scale-free graphs can be recovered.

cond-mat.stat-mech↗

arXiv2003

Effects of intermediate bound states in dynamic force spectroscopy

We revisit here some aspects of the interpretation of dynamic force spectroscopy experiments. The standard theory predicts a typical unbinding force $f^*$ linearly proportional to the logarithm of the loading rate $r$ when a single energetical barrier controls the unbinding process; for a more complex situation of $N$ barriers, it predicts at most $N$ linear segments for the $f^*$ vs. $\log(r)$ curve, each segment characterizing a different barrier. We here extend this existing picture using a refined approximation, we provide a more general analytical formula, and show that in principle up to $N(N+1)/2$ segments can show up experimentally. As a consequence the interpretation of data can be ambiguous, for the characteristics and even the number of barriers. A further possible outcome of a multiple-barrier landscape is a bimodal or multimodal distribution of the unbinding force at a given loading rate, a feature recently observed experimentally.

cond-mat.stat-mech↗

arXiv2003

Topological phase transitions of random networks

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables us to establish an equivalence between the equilibrium rewiring problem we consider and the dynamics of a lattice gas on the edge-dual graph of a fully connected network. By assigning energies to the different network topologies and defining the appropriate order parameters, we find a rich variety of topological phase transitions, defined as singular changes in the essential feature(s) of the global connectivity as a function of a parameter playing the role of the temperature. In the ``critical point'' scale-free networks can be recovered.

cond-mat.stat-mech↗

arXiv2002

DNA uptake into nuclei: Numerical and analytical results

The dynamics of polymer translocation through a pore has been the subject of recent theoretical and experimental works. We have considered theoretical estimates and performed computer simulations to understand the mechanism of DNA uptake into the cell nucleus, a phenomenon experimentally investigated by attaching a small bead to the free end of the double helix and pulling this bead with the help of an optical trap. The experiments show that the uptake is monotonous and slows down when the remaining DNA segment becomes very short. Numerical and analytical studies of the entropic repulsion between the DNA filament and the membrane wall suggest a new interpretation of the experimental observations. Our results indicate that the repulsion monotonically decreases as the uptake progresses. Thus, the DNA is pulled in (i) either by a small force of unknown origin, and then the slowing down can be interpreted only statistically; (ii) or by a strong but slow ratchet mechanism, which would naturally explain the observed monotonicity, but then the slowing down requires additional explanations. Only further experiments can unambiguously distinguish between these two mechanisms.

cond-mat.soft↗

arXiv2002

Formation and Interaction of Membrane Tubes

We show that the formation of membrane tubes (or membrane tethers), which is a crucial step in many biological processes, is highly non-trivial and involves first order shape transitions. The force exerted by an emerging tube is a non-monotonic function of its length. We point out that tubes attract each other, which eventually leads to their coalescence. We also show that detached tubes behave like semiflexible filaments with a rather short persistence length. We suggest that these properties play an important role in the formation and structure of tubular organelles.

cond-mat.soft↗