DIGITAL.CSIChttps://digital.csic.esThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 16 Oct 2019 14:52:43 GMT2019-10-16T14:52:43Z50291- An Age Dependent Branching Model for Macroevolutionhttp://hdl.handle.net/10261/45593Title: An Age Dependent Branching Model for Macroevolution
Authors: Keller-Schmidt, Stephanie; Tugrul, Murat; Eguíluz, Víctor M.; Hernández-García, Emilio; Klemm, Konstantin
Abstract: The imbalance of phylogenetic trees exhibits a systematic deviation from the expectation of a purely random tree growth process as in the Yule or ERM models. Here we introduce an age dependent growth model based on the hypothesis that speciation rate is a decreasing function of the waiting time since the last speciation. We find that the imbalance in terms of the mean distance of tips from root (Sackin index) grows as $(log n)^2$ in leading order with tree size $n$. This result is in good agreement with the trend observed by exhaustive analysis of the phylogenetic databases TreeBASE and PANDIT. Exact likelihood computation of the model on the trees up to 20 tips contained in the databases is performed. Higher likelihoods values are found when compared with a previously suggested model (Blum and Francois, 2006).
Tue, 14 Feb 2012 13:49:47 GMThttp://hdl.handle.net/10261/455932012-02-14T13:49:47Z
- Globalization, polarization and cultural drift and social networkshttp://hdl.handle.net/10261/47630Title: Globalization, polarization and cultural drift and social networks
Authors: Klemm, Konstantin; Eguíluz, Víctor M.; Toral, Raúl; San Miguel, Maxi; Centola, Damon
Abstract: •Basics: Interaction of several cultural features based on homophily
and social influence produces a transition between global culture and
polarization.
•Fixed networks: Long range links and degree heterogeneity favor
globalization. High clustering restores polarization in scale free
networks.
•Cultural drift in fixed networks: Essential Qualitative changes.
q-independent, N-dependent noise induced transition between
metastable global culture and noise dominated polarized state.
•Dynamic networks: Stable polarization due to formation of physical
groups. Cultural drift of slow rate becomes inefficient.
Wed, 28 Mar 2012 12:04:30 GMThttp://hdl.handle.net/10261/476302012-03-28T12:04:30Z
- A measure of individual role in collective dynamics: spreading at criticalityhttp://hdl.handle.net/10261/54101Title: A measure of individual role in collective dynamics: spreading at criticality
Authors: Klemm, Konstantin; Serrano, M. Ángeles; Eguíluz, Víctor M.; San Miguel, Maxi
Abstract: Identifying key players in collective dynamics remains a challenge in several research fields, from the
efficient dissemination of ideas to drug target discovery in biomedical problems. The difficulty lies at several
levels: how to single out the role of individual elements in such intermingled systems, or which is the best
way to quantify their importance. Centrality measures describe a node’s importance by its position in a
network. The key issue obviated is that the contribution of a node to the collective behavior is not uniquely
determined by the structure of the system but it is a result of the interplay between dynamics and network
structure. We show that dynamical influence measures explicitly how strongly a node’s dynamical state
affects collective behavior. For critical spreading, dynamical influence targets nodes according to their
spreading capabilities. For diffusive processes it quantifies how efficiently real systems may be controlled by
manipulating a single node.
Fri, 27 Jul 2012 11:49:36 GMThttp://hdl.handle.net/10261/541012012-07-27T11:49:36Z
- Nonequilibrium transitions in complex networks: a model of social interactionhttp://hdl.handle.net/10261/15337Title: Nonequilibrium transitions in complex networks: a model of social interaction
Authors: Klemm, Konstantin; Eguíluz, Víctor M.; Toral, Raúl; San Miguel, Maxi
Abstract: We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The transition point is shifted by the degree of spatial disorder of the underlying network, the network disorder favoring ordered configurations. In random scale-free networks the transition is only observed for finite size systems, showing system size scaling, while in the thermodynamic limit only ordered configurations are always obtained. Thus in the thermodynamic limit the transition disappears. However, in structured scale-free networks, the phase transition between an ordered and a disordered phase is restored.
Description: 6 pages, 9 figures.-- PACS nrs.: 89.75.Fb, 05.50.+q, 87.23.Ge.
Fri, 24 Jul 2009 11:31:30 GMThttp://hdl.handle.net/10261/153372009-07-24T11:31:30Z
- Epidemic threshold in structured scale-free networkshttp://hdl.handle.net/10261/15328Title: Epidemic threshold in structured scale-free networks
Authors: Eguíluz, Víctor M.; Klemm, Konstantin
Abstract: We analyze the spreading of viruses in scale-free networks with high clustering and degree correlations, as found in the Internet graph. For the susceptible-infected-susceptible model of epidemics the prevalence undergoes a phase transition at a finite threshold of the transmission probability. Comparing with the absence of a finite threshold in networks with purely random wiring, our result suggests that high clustering (modularity) and degree correlations protect scale-free networks against the spreading of viruses. We introduce and verify a quantitative description of the epidemic threshold based on the connectivity of the neighborhoods of the hubs.
Description: 4 pages, 4 figures.-- PACS nrs.: 89.75.Hc, 87.19.Xx, 87.23.Ge, 89.20.Hh.-- Printed version published Sep 2, 2002.; ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/0205439
Fri, 24 Jul 2009 11:27:23 GMThttp://hdl.handle.net/10261/153282009-07-24T11:27:23Z
- Global culture: A noise induced transition in finite systemshttp://hdl.handle.net/10261/15315Title: Global culture: A noise induced transition in finite systems
Authors: Klemm, Konstantin; Eguíluz, Víctor M.; Toral, Raúl; San Miguel, Maxi
Abstract: We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the dissemination of culture. The disordered multicultural configurations are found to be metastable. This general result is proven rigorously in d=1, where the dynamics is described in terms of a Lyapunov potential. In d=2, the dynamics is governed by the average relaxation time T of perturbations. Noise at a rate r < 1/T induces monocultural configurations, whereas r > 1/T sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.
Description: 4 pages, 5 figures.-- PACS nrs.: 05.50.+q, 87.23.Ge, 05.40.Ca, 89.65.Ef.-- ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/0205188; Rapid communication.
Fri, 24 Jul 2009 11:22:22 GMThttp://hdl.handle.net/10261/153152009-07-24T11:22:22Z
- Effective dimensions and percolation in hierarchicaly structured scale-free networkshttp://hdl.handle.net/10261/15345Title: Effective dimensions and percolation in hierarchicaly structured scale-free networks
Authors: Eguíluz, Víctor M.; Hernández-García, Emilio; Piro, Oreste; Klemm, Konstantin
Abstract: We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial character of this network that displays scale-free connectivity among other features, it turns out to be approximately one-dimensional. The dimensional characterization is in agreement with the results on statistics of site percolation and other dynamical processes implemented on such a network.
Description: 4 pages, 5 figures.-- PACS nrs.: 89.75.Hc, 05.10.2a.-- ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/0302515
Fri, 24 Jul 2009 11:35:12 GMThttp://hdl.handle.net/10261/153452009-07-24T11:35:12Z
- Growing scale-free networks with small-world behaviorhttp://hdl.handle.net/10261/15314Title: Growing scale-free networks with small-world behavior
Authors: Klemm, Konstantin; Eguíluz, Víctor M.
Abstract: In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small-world effect. While the average shortest path length increases logarithmically as in random networks, the clustering coefficient assumes a large value independent of system size. We derive analytical expressions for the clustering coefficient in two limiting cases: random [C~(ln N)2/N] and highly clustered (C = 5/6) scale-free networks.
Description: 4 pages, 4 figures.-- PACS nrs.: 89.75.Hc, 87.23.Ge, 89.65.-s.-- ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/0107607; More info available at: http://www.nbi.dk/CATS/
Fri, 24 Jul 2009 11:21:55 GMThttp://hdl.handle.net/10261/153142009-07-24T11:21:55Z
- Conservation laws for voter-like models on directed networkshttp://hdl.handle.net/10261/15099Title: Conservation laws for voter-like models on directed networks
Authors: Serrano, M. Ángeles; Klemm, Konstantin; Vázquez, Federico; Eguíluz, Víctor M.; San Miguel, Maxi
Abstract: We study the voter model, under node and link update, and the related invasion process on a single strongly connected component of a directed network. We implement an analytical treatment in the thermodynamic limit using the heterogeneous mean field assumption. From the dynamical rules at the microscopic level, we find the equations for the evolution of the relative densities of nodes in a given state on heterogeneous networks with arbitrary degree distribution and degree-degree correlations. We prove that conserved quantities as weighted linear superpositions of spin states exist for all three processes and, for uncorrelated directed networks, we derive their specific expressions. We also discuss the time evolution of the relative densities that decay exponentially to a homogeneous stationary value given by the conserved quantity. The conservation laws obtained in the thermodynamic limit for a system that does not order in that limit determine the probabilities of reaching the absorbing state for a finite system. The contribution of each degree class to the conserved quantity is determined by a local property. Depending on the dynamics, the highest contribution is associated to influential nodes reaching a large number of outgoing neighbors, not too influenceable ones with a low number of incoming connections, or both at the same time.
Description: 9 pages, 2 figures, 1 table.
Mon, 20 Jul 2009 11:39:19 GMThttp://hdl.handle.net/10261/150992009-07-20T11:39:19Z
- Role of dimensionality in Axelrod's model for the dissemination of culturehttp://hdl.handle.net/10261/14842Title: Role of dimensionality in Axelrod's model for the dissemination of culture
Authors: Klemm, Konstantin; Eguíluz, Víctor M.; Toral, Raúl; San Miguel, Maxi
Abstract: We analyze a model of social interaction in one- and two-dimensional lattices for a moderate number of features. We introduce an order parameter as a function of the overlap between neighboring sites. In a one-dimensional chain, we observe that the dynamics is consistent with a second-order transition, where the order parameter changes continuously and the average domain diverges at the transition point. However, in a two-dimensional lattice the order parameter is discontinuous at the transition point characteristic of a first-order transition between an ordered and a disordered state.
Description: 5 pages, 2 figures.-- PACS nrs.: 89.75.Fb; 05.50.+q; 87.23.Ge.-- Printed version published Sep 1, 2003.-- Issue title: Proceedings of the XIIIth Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics (Colonia del Sacramento, Uruguay, Dec 9-13, 2002).; Full-text paper available Open Access at: http://ifisc.uib-csic.es/~victor/Cult/cult_pa.pdf
Tue, 14 Jul 2009 09:29:32 GMThttp://hdl.handle.net/10261/148422009-07-14T09:29:32Z
- Highly clustered scale-free networkshttp://hdl.handle.net/10261/18030Title: Highly clustered scale-free networks
Authors: Klemm, Konstantin; Eguíluz, Víctor M.
Abstract: We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative correlation between the age of a node and its link attachment rate. Notably, the degree distribution is conserved even though only the most recently grown part of the network is considered. As the network grows, the clustering reaches an asymptotic value larger than for regular lattices of the same average connectivity and similar to the one observed in the networks of movie actors, coauthorship in science, and word synonyms. These high-clustering scale-free networks indicate that memory effects could be crucial for a correct description of the dynamics of growing networks.
Description: 5 pages, 4 figures.-- PACS number(s): 89.75.Hc, 87.23.Ge, 89.65.2s
Mon, 26 Oct 2009 09:05:22 GMThttp://hdl.handle.net/10261/180302009-10-26T09:05:22Z
- Universal Scaling in the Branching of the Tree of Lifehttp://hdl.handle.net/10261/6833Title: Universal Scaling in the Branching of the Tree of Life
Authors: Herrada, E. Alejandro; Tessone, Claudio J.; Klemm, Konstantin; Eguíluz, Víctor M.; Hernández-García, Emilio; Duarte, Carlos M.
Abstract: Understanding the patterns and processes of diversification of life in the planet is a key challenge of science. The Tree of Life represents such diversification processes through the evolutionary relationships among the different taxa, and can be extended down to intra-specific relationships. Here we examine the topological properties of a large set of interspecific and intraspecific phylogenies and show that the branching patterns follow allometric rules conserved across the different levels in the Tree of Life, all significantly departing from those expected from the standard null models. The finding of non-random universal patterns of phylogenetic differentiation suggests that similar evolutionary forces drive diversification across the broad range of scales, from macro-evolutionary to micro-evolutionary processes, shaping the diversity of life on the planet.
Description: 6 pages.-- Supplementary material attached: Text S1. Scaling of branch size and cumulative branch size: TreeBASE vs. manually selected data sets.- Table S1. Break-down of the number of analyzed inter- and intra-species trees with respect to taxa.- Fig. S1. Cumulative complementary distribution functions (CCDFs) for branch size (F(A), panel A) and cumulative branch size (F(C), panel B).- Fig. S2. A: An example of an intraspecific phylogenetic tree, B: The allometric scaling plot showing the relationship of cumulative branch size (C) to branch size (A) from each node of that tree.- Fig. S3: Another example of an interspecific phylogenetic tree.
Thu, 21 Aug 2008 12:21:31 GMThttp://hdl.handle.net/10261/68332008-08-21T12:21:31Z
- Information Feedback and Mass Media Effects in Cultural Dynamicshttp://hdl.handle.net/10261/6088Title: Information Feedback and Mass Media Effects in Cultural Dynamics
Authors: González-Avella, Juan Carlos; Cosenza, Mario G.; Klemm, Konstantin; Eguíluz, Víctor M.; San Miguel, Maxi
Abstract: We study the effects of different forms of information feedback associated with mass media on an agent-agent based model of the dynamics of cultural dissemination. In addition to some processes previously considered, we also examine a model of local mass media influence in cultural dynamics. Two mechanisms of information feedback are investigated: (i) direct mass media influence, where local or global mass media act as an additional element in the network of interactions of each agent, and (ii) indirect mass media influence, where global media acts as a filter of the influence of the existing network of interactions of each agent. Our results generalize previous findings showing that cultural diversity builds up by increasing the strength of the mass media influence. We find that this occurs independently of the mechanisms of action (direct or indirect) of the mass media message. However, through an analysis of the full range of parameters measuring cultural diversity, we establish that the enhancement of cultural diversity produced by interaction with mass media only occurs for strong enough mass media messages. In comparison with previous studies a main different result is that weak mass media messages, in combination with agent-agent interaction, are efficient in producing cultural homogeneity. Moreover, the homogenizing effect of weak mass media messages is more efficient for direct local mass media messages than for global mass media messages or indirect global mass media influences.
Description: ArXiv pre-print: http://arxiv.org/abs/0705.1091.
Tue, 22 Jul 2008 15:06:39 GMThttp://hdl.handle.net/10261/60882008-07-22T15:06:39Z
- Information feedback and mass media effects in cultural dynamicshttp://hdl.handle.net/10261/6046Title: Information feedback and mass media effects in cultural dynamics
Authors: González-Avella, Juan Carlos; Cosenza, Mario G.; Klemm, Konstantin; Eguíluz, Víctor M.; San Miguel, Maxi
Abstract: We study the effects of different forms of information feedback associated with mass media on an agent-agent based model of the dynamics of cultural dissemination. Two mechanisms of information feedback are investigated: (i) direct mass media influence, where local or global mass media act as an additional element in the network of interactions of each agent, and (ii) indirect mass media influence, where global media acts as a filter of the influence of the existing network of interactions of each agent. Our results substantiate previous findings showing that cultural diversity builds-up by increasing the strength of the mass media influence. We find that this occurs independently of the mechanisms of action (direct or indirect) of the mass media message. However, through an analysis of the full range of parameters measuring cultural diversity, we establish that the enhancement of cultural diversity produced by interaction with mass media only occurs for strong enough mass media messages. A main different result is that weak mass media messages, in combination with agent-agent interaction, are efficient in producing cultural homogeneity. Moreover, the homogenizing effect of weak mass media messages are more efficient for direct local mass media
messages than for global mass media messages or indirect global mass media influences.
Description: This article was published in the Journal of Artificial Societies and Social Simulation:
http://jasss.soc.surrey.ac.uk/10/3/9.html.; Published in the Proceedings of the 4th Conference of the European Social Simulation Association (ESSA'07), September 10-14, 2007, Toulouse, France. Editor: Frédéric Amblard.
Tue, 22 Jul 2008 12:50:51 GMThttp://hdl.handle.net/10261/60462008-07-22T12:50:51Z
- Local versus global interactions in nonequilibrium transitions: A model of social dynamicshttp://hdl.handle.net/10261/6107Title: Local versus global interactions in nonequilibrium transitions: A model of social dynamics
Authors: González-Avella, Juan Carlos; Eguíluz, Víctor M.; Cosenza, Mario G.; Klemm, Konstantin; Herrera, José Luis; San Miguel, Maxi
Abstract: A nonequilibrium system of locally interacting elements in a lattice with an absorbing order-disorder phase transition is studied under the effect of additional interacting fields. These fields are shown to produce interesting effects in the collective behavior of this system. Both for autonomous and external fields, disorder grows in the system when the probability of the elements to interact with the field is increased. There exists a threshold value of this probability beyond which the system is always disordered. The domain of parameters of the ordered regime is larger for nonuniform local fields than for spatially uniform fields. However, the zero field limit is discontinous. In the limit of vanishingly small probability of interaction with the field, autonomous or external fields are able to order a system that would fall in a disordered phase under local interactions of the elements alone. We consider different types of fields which are interpreted as forms of mass media acting on a social system in the context of Axelrod's model for cultural dissemination.
Description: 7 pages.-- PACS numbers: 89.75.Fb, 87.23.Ge, 05.50.+q.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevE.73.046119.
Tue, 22 Jul 2008 15:09:56 GMThttp://hdl.handle.net/10261/61072008-07-22T15:09:56Z
- Analysis of attachment models for directory and file treeshttp://hdl.handle.net/10261/6121Title: Analysis of attachment models for directory and file trees
Authors: Klemm, Konstantin; Eguíluz, Víctor M.; San Miguel, Maxi
Abstract: Many networks emerge as the outcome of a collective interaction, like the WWW; others are the consequence of the biological evolution, like the brain. In contrast to these examples, we investigate the topology of trees generated by single individuals. Computer users generate directory structures to store and manage information in files. Analyzing the directory and file-trees generated by different users we have access to different realizations available for statistical analysis. We characterize the architecture of directories and files created by different computer users by means of the degree distributions and number of leaves, degree-degree correlations, average distance to the root, and community size distributions. We compare the different topologies in the search for similar managing patterns, and compare the trees obtained with two simple models of growing networks and with a model that interpolates between them and incorporates the heterogeneity of the computer users.
Description: 7 pages, 6 figures.-- Printed version published Dec 2006.-- Issue title: "Dynamics on Complex Networks and Applications".; Full-text paper available Open Access at: http://ifisc.uib-csic.es/~victor/Filetrees/filetrees_PD.pdf
Tue, 22 Jul 2008 15:12:24 GMThttp://hdl.handle.net/10261/61212008-07-22T15:12:24Z
- Binary and Multivariate Stochastic models of consensus formationhttp://hdl.handle.net/10261/7501Title: Binary and Multivariate Stochastic models of consensus formation
Authors: San Miguel, Maxi; Eguíluz, Víctor M.; Toral, Raúl; Klemm, Konstantin
Abstract: We consider stochastic dynamic models studied via computer simulation. We review some basic results for the voter model which is probably the simplest model of collective behavior. Specifically, we focus on the dynamical effect of who interacts with whom - that is, the consequences of different interaction networks. We also consider R. Axelrod's (1997) model for the dissemination of culture.
Description: 7 pages, 8 figures.-- ArXiv pre-print available: http://arxiv.org/abs/physics/0507201
Fri, 03 Oct 2008 11:33:12 GMThttp://hdl.handle.net/10261/75012008-10-03T11:33:12Z
- Scaling in the structure of directory trees in a computer clusterhttp://hdl.handle.net/10261/7514Title: Scaling in the structure of directory trees in a computer cluster
Authors: Klemm, Konstantin; Eguíluz, Víctor M.; San Miguel, Maxi
Abstract: We describe the topological structure and the underlying organization principles of the directories created by users of a computer cluster when storing his/her own files. We analyze degree distributions, average distance between files, distribution of communities and allometric scaling exponents of the directory trees. We find that users create trees with a broad, scale-free degree distribution. The structure of the directories is well captured by a growth model with a single parameter. The degree distribution of the different trees has a non-universal exponent associated with different values of the parameter of the model. However, the distribution of community sizes has a universal exponent analytically obtained from our model.
Description: 4 pages, 2 figures.-- PACS nrs.: 89.20.Ff, 05.65.+b, 89.75.Da, 89.75.Hc.-- PMID: 16197119 [PubMed].-- ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/0403239
Fri, 03 Oct 2008 11:35:54 GMThttp://hdl.handle.net/10261/75142008-10-03T11:35:54Z
- Conservation laws for voter-like models on random directed networkshttp://hdl.handle.net/10261/25513Title: Conservation laws for voter-like models on random directed networks
Authors: Serrano, M. Ángeles; Klemm, Konstantin; Vázquez, Federico; Eguíluz, Víctor M.; San Miguel, Maxi
Abstract: We study the voter model, under node and link update, and the related invasion process on a single strongly connected component of a directed network. We implement an analytical treatment in the thermodynamic limit using the heterogeneous mean-field assumption. From the dynamical rules at the microscopic level, we find the equations for the evolution of the relative densities of nodes in a given state on heterogeneous networks with arbitrary degree distribution and degree degree correlations. We prove that conserved quantities as weighted linear superpositions of spin states exist for all three processes and, for uncorrelated directed networks, we derive their specific expressions. We also discuss the time evolution of the relative densities that decay exponentially to a homogeneous stationary value given by the conserved quantity. The conservation laws obtained in the thermodynamic limit for a system that does not order in that limit determine the probabilities of reaching the absorbing state for a finite system. The contribution of each degree class to the conserved quantity is determined by a local property. Depending on the dynamics, the highest contribution is associated with influential nodes reaching a large number of outgoing neighbors, not too influenceable ones with a low number of incoming connections, or both at the same time.
Description: 18 pages, 2 figures, 1 table.-- ArXiv pre-print: http://arxiv.org/abs/arXiv:0902.1769
Tue, 22 Jun 2010 10:55:42 GMThttp://hdl.handle.net/10261/255132010-06-22T10:55:42Z
- Temporal networks: Slowing down diffusion by long lasting interactionshttp://hdl.handle.net/10261/116413Title: Temporal networks: Slowing down diffusion by long lasting interactions
Authors: Masuda, Naoki; Klemm, Konstantin; Eguíluz, Víctor M.
Abstract: Interactions among units in complex systems occur in a specific sequential order, thus affecting the flow of information, the propagation of diseases, and general dynamical processes. We investigate the Laplacian spectrum of temporal networks and compare it with that of the corresponding aggregate network. First, we show that the spectrum of the ensemble average of a temporal network has identical eigenmodes but smaller eigenvalues than the aggregate networks. In large networks without edge condensation, the expected temporal dynamics is a time-rescaled version of the aggregate dynamics. Even for single sequential realizations, diffusive dynamics is slower in temporal networks. These discrepancies are due to the noncommutability of interactions. We illustrate our analytical findings using a simple temporal motif, larger network models, and real temporal networks. Published by American Physical Society.
Thu, 11 Jun 2015 09:13:55 GMThttp://hdl.handle.net/10261/1164132015-06-11T09:13:55Z
- Anomalous scaling in an age-dependent branching modelhttp://hdl.handle.net/10261/132850Title: Anomalous scaling in an age-dependent branching model
Authors: Keller-Schmidt, Stephanie; Tugrul, Murat; Eguíluz, Víctor M.; Hernández-García, Emilio; Klemm, Konstantin
Abstract: © 2015 American Physical Society. We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ-α. Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)2. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point.
Wed, 01 Jun 2016 12:04:58 GMThttp://hdl.handle.net/10261/1328502016-06-01T12:04:58Z
- Temporal interactions facilitate endemicity in the susceptible-infected-susceptible epidemic modelhttp://hdl.handle.net/10261/157694Title: Temporal interactions facilitate endemicity in the susceptible-infected-susceptible epidemic model
Authors: Speidel, Leo; Klemm, Konstantin; Eguíluz, Víctor M.; Masuda, Naoki
Abstract: Data of physical contacts and face-to-face communications suggest temporally varying networks as the media on which infections take place among humans and animals. Epidemic processes on temporal networks are complicated by complexity of both network structure and temporal dimensions. Theoretical approaches are much needed for identifying key factors that affect dynamics of epidemics. In particular, what factors make some temporal networks stronger media of infection than other temporal networks is under debate. We develop a theory to understand the susceptible-infected-susceptible epidemic model on arbitrary temporal networks, where each contact is used for a finite duration. We show that temporality of networks lessens the epidemic threshold such that infections persist more easily in temporal networks than in their static counterparts. We further show that the Lie commutator bracket of the adjacency matrices at different times is a key determinant of the epidemic threshold in temporal networks. The effect of temporality on the epidemic threshold, which depends on a data set, is approximately predicted by the magnitude of a commutator norm.
Fri, 24 Nov 2017 09:33:31 GMThttp://hdl.handle.net/10261/1576942017-11-24T09:33:31Z
- Transitions from Trees to Cycles in Adaptive Flow Networkshttp://hdl.handle.net/10261/174127Title: Transitions from Trees to Cycles in Adaptive Flow Networks
Authors: Martens, Erik A.; Klemm, Konstantin
Abstract: Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply. Theoretical and experimental studies have found that real-world transport networks exhibit both tree-like motifs and cycles. When the network is subject to load fluctuations, the presence of cyclic motifs may help to reduce flow fluctuations and, thus, render supply in the network more robust. While previous studies considered network topology via optimization principles, here, we take a dynamical systems approach and study a simple model of a flow network with dynamically adapting weights (conductances). We assume a spatially non-uniform distribution of rapidly fluctuating loads in the sinks and investigate what network configurations are dynamically stable. The network converges to a spatially non-uniform stable configuration composed of both cyclic and tree-like structures. Cyclic structures emerge locally in a transcritical bifurcation as the amplitude of the load fluctuations is increased. The resulting adaptive dynamics thus partitions the network into two distinct regions with cyclic and tree-like structures. The location of the boundary between these two regions is determined by the amplitude of the fluctuations. These findings may explain why natural transport networks display cyclic structures in the micro-vascular regions near terminal nodes, but tree-like features in the regions with larger veins.
Tue, 15 Jan 2019 12:45:48 GMThttp://hdl.handle.net/10261/1741272019-01-15T12:45:48Z
- Slowing down of linear consensus dynamics on temporal networks: some theoretical extensionshttp://hdl.handle.net/10261/134127Title: Slowing down of linear consensus dynamics on temporal networks: some theoretical extensions
Authors: Masuda, Naoki; Klemm, Konstantin; Eguíluz, Víctor M.
Abstract: The conditions for synchronization (equivalently, consensus) in linear and nonlinear switching dynamical systems have been extensively studied. In a previous study, we examined the speed of convergence of linear dynamical systems on switching networks in which each snapshot network defining interaction between dynamical elements is a network Laplacian. We showed that temporal dynamics (i.e., switching) of networks slowed down synchronization processes as compared to the case of aggregate dynamics, i.e., synchronization dynamics occurring on the corresponding static network obtained by the aggregation of the temporal network over time. Here we theoretically extend the results in two ways. First, we derive the conditions imposed on the interaction matrices under which the analytical slowing-down results hold true. The condition turns out to be essentially the same as that for the optimal network, which is known as the condition for the fastest local convergence of nonlinear dynamics on networks. Second, we examine the effect of correlation between different snapshots; in actual temporal networks, the same contact tends to be used consecutively in time. We argue that such temporal correlation further slows down temporal dynamics.
Tue, 28 Jun 2016 07:07:44 GMThttp://hdl.handle.net/10261/1341272016-06-28T07:07:44Z
- Competition in the presence of aging: Dominance, coexistence, and alternation between stateshttp://hdl.handle.net/10261/133274Title: Competition in the presence of aging: Dominance, coexistence, and alternation between states
Authors: Pérez, Toni; Klemm, Konstantin; Eguíluz, Víctor M.
Abstract: We study the stochastic dynamics of coupled states with transition probabilities depending on local persistence, this is, the time since a state has changed. When the system has a preference to adopt older states the system orders quickly due to the dominance of old states. When preference for new states prevails, the system can show coexistence of states or synchronized collective behavior resulting in long ordering times. In this case, the magnetization of the system oscillates around zero. Finally we discuss a potential application in social systems.
Fri, 10 Jun 2016 06:57:29 GMThttp://hdl.handle.net/10261/1332742016-06-10T06:57:29Z
- Epidemic Threshold in Temporally-Switching Networkshttp://hdl.handle.net/10261/173796Title: Epidemic Threshold in Temporally-Switching Networks
Authors: Speidel, Leo; Klemm, Konstantin; Eguíluz, Víctor M.; Masuda, Naoki
Abstract: Infectious diseases have been modelled on networks that summarise physical contacts or close proximity of individuals. These networks are known to be complex in both their structure and how they change over time. We present an overview of recent progress in numerically determining the epidemic threshold in temporally-switching networks, and illustrate that slower switching of snapshots relative to epidemic dynamics lowers the epidemic threshold. Therefore, ignoring the temporally-varying nature of networks may underestimate endemicity. We also identify a predictor for the magnitude of this shift which is based on the commutator norm of snapshot adjacency matrices.
Description: Masuda N., Holme P. (eds).
Tue, 08 Jan 2019 10:47:23 GMThttp://hdl.handle.net/10261/1737962019-01-08T10:47:23Z
- Unveiling noiseless clusters in complex quantum networkshttp://hdl.handle.net/10261/188214Title: Unveiling noiseless clusters in complex quantum networks
Authors: Cabot Martorell, Albert; Galve, Fernando; Eguíluz, Víctor M.; Klemm, Konstantin; Maniscalco, Sabrina; Zambrini, Roberta
Abstract: The transport and storage of quantum information, excitations, and entanglement, within and across complex quantum networks is crucially affected by the presence of noise induced by their surroundings. Generally, the interaction with the environment deteriorates quantum properties initially present, thus limiting the efficiency of any quantum-enhanced protocol or phenomenon. This is of key relevance, for example, in the design of quantum communication networks and for understanding and controlling quantum harvesting on complex systems. Here, we show that complex quantum networks, such as random and small-world ones, can admit noiseless clusters for collective dissipation. We characterize these noiseless structures in connection to their topology addressing their abundance, extension, and configuration, as well as their robustness to noise and experimental imperfections. We show that the network degree variance controls the probability to find noiseless modes and that these are mostly spanning an even number of nodes, like breathers. For imperfections across the network, a family of quasi-noiseless modes is also identified shielded by noise up to times decreasing linearly with frequency inhomogeneities. Large noiseless components are shown to be more resilient to the presence of detuning than to differences in their coupling strengths. Finally, we investigate the emergence of both stationary and transient quantum synchronization showing that this is a rather resilient phenomenon in these networks.
Wed, 14 Aug 2019 07:42:15 GMThttp://hdl.handle.net/10261/1882142019-08-14T07:42:15Z
- Patterning the insect eye: From stochastic to deterministic mechanismshttp://hdl.handle.net/10261/188211Title: Patterning the insect eye: From stochastic to deterministic mechanisms
Authors: Ebadi, Haleh; Perry, Michael; Short, Keith; Klemm, Konstantin; Desplan, Claude; Stadler, Peter F.; Mehta, Anita
Abstract: While most processes in biology are highly deterministic, stochastic mechanisms are sometimes used to increase cellular diversity. In human and Drosophila eyes, photoreceptors sensitive to different wavelengths of light are distributed in stochastic patterns, and one such patterning system has been analyzed in detail in the Drosophila retina. Interestingly, some species in the dipteran family Dolichopodidae (the “long legged” flies, or “Doli”) instead exhibit highly orderly deterministic eye patterns. In these species, alternating columns of ommatidia (unit eyes) produce corneal lenses of different colors. Occasional perturbations in some individuals disrupt the regular columns in a way that suggests that patterning occurs via a posterior-to-anterior signaling relay during development, and that specification follows a local, cellular-automaton-like rule. We hypothesize that the regulatory mechanisms that pattern the eye are largely conserved among flies and that the difference between unordered Drosophila and ordered dolichopodid eyes can be explained in terms of relative strengths of signaling interactions rather than a rewiring of the regulatory network itself. We present a simple stochastic model that is capable of explaining both the stochastic Drosophila eye and the striped pattern of Dolichopodidae eyes and thereby characterize the least number of underlying developmental rules necessary to produce both stochastic and deterministic patterns. We show that only small changes to model parameters are needed to also reproduce intermediate, semi-random patterns observed in another Doli species, and quantification of ommatidial distributions in these eyes suggests that their patterning follows similar rules.; [Author summary] A simple model is able to account for a diversity of photoreceptor patterns in different fly species, ranging from highly deterministic to fully random.
Wed, 14 Aug 2019 07:29:00 GMThttp://hdl.handle.net/10261/1882112019-08-14T07:29:00Z
- Cover-Encodings of Fitness Landscapeshttp://hdl.handle.net/10261/188800Title: Cover-Encodings of Fitness Landscapes
Authors: Klemm, Konstantin; Mehta, Anita; Stadler, Peter F.
Abstract: The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a feature of the typically rugged landscapes encountered arrest the progress of the search process. Another way of tackling optimization problems is by the use of heuristic approximations to estimate a global cost minimum. Here, we present a combination of these two approaches by using cover-encoding maps which map processes from a larger search space to subsets of the original search space. The key idea is to construct cover-encoding maps with the help of suitable heuristics that single out near-optimal solutions and result in landscapes on the larger search space that no longer exhibit trapping local minima. We present cover-encoding maps for the problems of the traveling salesman, number partitioning, maximum matching and maximum clique; the practical feasibility of our method is demonstrated by simulations of adaptive walks on the corresponding encoded landscapes which find the global minima for these problems.
Thu, 22 Aug 2019 07:07:11 GMThttp://hdl.handle.net/10261/1888002019-08-22T07:07:11Z