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Distribution of infected mass in disease spreading in scale-free networks

Gallos, Lazaros K.; Argyrakis, Panos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
We use scale-free networks to study properties of the infected mass $M$ of the network during a spreading process as a function of the infection probability $q$ and the structural scaling exponent $\gamma$. We use the standard SIR model and investigate in detail the distribution of $M$, We find that for dense networks this function is bimodal, while for sparse networks it is a smoothly decreasing function, with the distinction between the two being a function of $q$. We thus recover the full crossover transition from one case to the other. This has a result that on the same network a disease may die out immediately or persist for a considerable time, depending on the initial point where it was originated. Thus, we show that the disease evolution is significantly influenced by the structure of the underlying population.; Comment: 7 pages, 3 figures, submitted to Physica A; Improved the discussion and shifted the emphasis on the distributions of figure 2. Because of this we had to change the title of the paper

Reliability of Coupled Oscillators II: Larger Networks

Lin, Kevin K.; Shea-Brown, Eric; Young, Lai-Sang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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We study the reliability of phase oscillator networks in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. In this paper, we extend previous results on two-cell networks to larger systems. The first issue that arises is chaos in the absence of inputs, which we demonstrate and interpret in terms of reliability. We give a mathematical analysis of networks that can be decomposed into modules connected by an acyclic graph. For this class of networks, we show how to localize the source of unreliability, and address questions concerning downstream propagation of unreliability once it is produced.; Comment: Part 2 of 2. Part 1 can be found at 0708.3061

Macroscopic description for networks of spiking neurons

Montbrió, Ernest; Pazó, Diego; Roxin, Alex
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/06/2015 Português
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A major goal of neuroscience, statistical physics and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale numerical simulations. Alternatively, researchers have formulated mean-field theories to gain insight into macroscopic states of large neuronal networks in terms of the collective firing activity of the neurons, or the firing rate. However, these theories have not succeeded in establishing an exact correspondence between the firing rate of the network and the underlying microscopic state of the spiking neurons. This has largely constrained the range of applicability of such macroscopic descriptions, particularly when trying to describe neuronal synchronization. Here we provide the derivation of a set of exact macroscopic equations for a network of spiking neurons. Our results reveal that the spike generation mechanism of individual neurons introduces an effective coupling between two biophysically relevant macroscopic quantities, the firing rate and the mean membrane potential, which together govern the evolution of the neuronal network. The resulting equations exactly describe all possible macroscopic dynamical states of the network...

Average synaptic activity and neural networks topology: a global inverse problem

Burioni, Raffaella; Casartelli, Mario; di Volo, Matteo; Livi, Roberto; Vezzani, Alessandro
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal signals are crucial for brain functioning. They strongly depend on the topology of the network and on the fluctuations of the connectivity. We propose a heterogeneous mean--field approach to neural dynamics on random networks, that explicitly preserves the disorder in the topology at growing network sizes, and leads to a set of self-consistent equations. Within this approach, we provide an effective description of microscopic and large scale temporal signals in a leaky integrate-and-fire model with short term plasticity, where quasi-synchronous events arise. Our equations provide a clear analytical picture of the dynamics, evidencing the contributions of both periodic (locked) and aperiodic (unlocked) neurons to the measurable average signal. In particular, we formulate and solve a global inverse problem of reconstructing the in-degree distribution from the knowledge of the average activity field. Our method is very general and applies to a large class of dynamical models on dense random networks.

Heterogeneous Bond Percolation on Multitype Networks with an Application to Epidemic Dynamics

Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Pourbohloul, Babak
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes -- in which final state can be obtained by studying the underlying network percolation properties -- have raised formidable interest. In this paper, we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability. As previously demonstrated, the multitype approach allows many non-trivial mixing patterns such as assortativity and clustering between nodes. We derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion. We also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism. We further show that the multitype approach, by naturally allowing heterogeneity in the bond occupation probability, overcomes some of the correlation issues encountered by previous models. We illustrate this point in the context of contact network epidemiology.; Comment: 10 pages, 5 figures. Minor modifications were made in figures 3...

Efficient transmission of subthreshold signals in complex networks of spiking neurons

Torres, Joaquin J.; Elices, Irene; Marro, J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances -- that naturally balances the network with excitatory and inhibitory synapses -- and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios...

Stability of Spreading Processes over Time-Varying Large-Scale Networks

Ogura, Masaki; Preciado, Victor M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following limitation: Markovian random graphs can only replicate switching patterns with exponential inter-switching times, while in real applications these times are usually far from exponential. In this paper, we introduce a flexible and tractable extended family of processes able to replicate, with arbitrary accuracy, any distribution of inter-switching times. We then study the stability of spreading processes in this extended family. We first show that a direct analysis based on It\^o's formula provides stability conditions in terms of the eigenvalues of a matrix whose size grows exponentially with the number of edges. To overcome this limitation, we derive alternative stability conditions involving the eigenvalues of a matrix whose size grows linearly with the number of nodes. Based on our results, we also show that heuristics based on aggregated static networks approximate the epidemic threshold more accurately as the number of nodes grows, or the temporal volatility of the random graph process is reduced. Finally...

Robustness of cooperation on scale-free networks under continuous topological change

Ichinose, Genki; Tenguishi, Yuto; Tanizawa, Toshihiro
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
In this paper, we numerically investigate the robustness of cooperation clusters in prisoner's dilemma played on scale-free networks, where the network topologies change by continuous removal and addition of nodes. Each removal and addition can be either random or intentional. We therefore have four different strategies in changing network topology: random removal and random addition (RR), random removal and preferential addition (RP), targeted removal and random addition (TR), and targeted removal and preferential addition (TP). We find that cooperation clusters are most fragile against TR, while they are most robust against RP, even for large values of the temptation coefficient for defection. The effect of the degree mixing pattern of the network is not the primary factor for the robustness of cooperation under continuous change in network topology, which is quite different from the cases observed in static networks. Cooperation clusters become more robust as the number of links of hubs occupied by cooperators increase. Our results might infer the fact that a huge variety of individuals is needed for maintaining global cooperation in social networks in the real world where each node representing an individual is constantly removed and added.; Comment: 6 pages...

Epidemic fronts in complex networks with metapopulation structure

Hindes, Jason; Singh, Sarabjeet; Myers, Christopher R.; Schneider, David J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
Infection dynamics have been studied extensively on complex networks, yielding insight into the effects of heterogeneity in contact patterns on disease spread. Somewhat separately, metapopulations have provided a paradigm for modeling systems with spatially extended and "patchy" organization. In this paper we expand on the use of multitype networks for combining these paradigms, such that simple contagion models can include complexity in the agent interactions and multiscale structure. We first present a generalization of the Volz-Miller mean-field approximation for Susceptible-Infected-Recovered (SIR) dynamics on multitype networks. We then use this technique to study the special case of epidemic fronts propagating on a one-dimensional lattice of interconnected networks - representing a simple chain of coupled population centers - as a necessary first step in understanding how macro-scale disease spread depends on micro-scale topology. Using the formalism of front propagation into unstable states, we derive the effective transport coefficients of the linear spreading: asymptotic speed, characteristic wavelength, and diffusion coefficient for the leading edge of the pulled fronts, and analyze their dependence on the underlying graph structure. We also derive the epidemic threshold for the system and study the front profile for various network configurations. To our knowledge...

Multifractal Characterization of Protein Contact Networks

Maiorino, Enrico; Livi, Lorenzo; Giuliani, Alessandro; Sadeghian, Alireza; Rizzi, Antonello
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
The multifractal detrended fluctuation analysis of time series is able to reveal the presence of long-range correlations and, at the same time, to characterize the self-similarity of the series. The rich information derivable from the characteristic exponents and the multifractal spectrum can be further analyzed to discover important insights about the underlying dynamical process. In this paper, we employ multifractal analysis techniques in the study of protein contact networks. To this end, initially a network is mapped to three different time series, each of which is generated by a stationary unbiased random walk. To capture the peculiarities of the networks at different levels, we accordingly consider three observables at each vertex: the degree, the clustering coefficient, and the closeness centrality. To compare the results with suitable references, we consider also instances of three well-known network models and two typical time series with pure monofractal and multifractal properties. The first result of notable interest is that time series associated to proteins contact networks exhibit long-range correlations (strong persistence), which are consistent with signals in-between the typical monofractal and multifractal behavior. Successively...

Uniqueness, intractability and exact algorithms: reflections on level-k phylogenetic networks

van Iersel, Leo; Kelk, Steven; Mnich, Matthias
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
Phylogenetic networks provide a way to describe and visualize evolutionary histories that have undergone so-called reticulate evolutionary events such as recombination, hybridization or horizontal gene transfer. The level k of a network determines how non-treelike the evolution can be, with level-0 networks being trees. We study the problem of constructing level-k phylogenetic networks from triplets, i.e. phylogenetic trees for three leaves (taxa). We give, for each k, a level-k network that is uniquely defined by its triplets. We demonstrate the applicability of this result by using it to prove that (1) for all k of at least one it is NP-hard to construct a level-k network consistent with all input triplets, and (2) for all k it is NP-hard to construct a level-k network consistent with a maximum number of input triplets, even when the input is dense. As a response to this intractability we give an exact algorithm for constructing level-1 networks consistent with a maximum number of input triplets.

Spike Synchronization Dynamics of Small-World Networks

Harter, Derek
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/09/2013 Português
Relevância na Pesquisa
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In this research report, we examine the effects of small-world network organization on spike synchronization dynamics in networks of Izhikevich spiking units. We interpolate network organizations from regular ring lattices, through the small-world region, to random networks, and measure global spike synchronization dynamics. We examine how average path length and clustering effect the dynamics of global and neighborhood clique spike organization and propagation. We show that the emergence of global synchronization undergoes a phase transition in the small-world region, between the clustering and path length phase transitions that are known to exist. We add additional realistic constraints on the dynamics by introducing propagation delays of spiking signals proportional to wiring length. The addition of delays interferes with the ability of random networks to sustain global synchronization, in relation to the breakdown of clustering in the networks. The addition of delays further enhances the finding that small-world organization is beneficial for balancing neighborhood synchronized waves of organization with global synchronization dynamics.; Comment: 22 pages, 6 figures

Biased imitation in coupled evolutionary games in interdependent networks

Santos, M. D.; Dorogovtsev, S. N.; Mendes, J. F. F.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
We explore the evolutionary dynamics of two games - the Prisoner's Dilemma and the Snowdrift Game - played within distinct networks (layers) of interdependent networks. In these networks imitation and interaction between individuals of opposite layers is established through interlinks. We explore an update rule in which revision of strategies is a biased imitation process: individuals imitate neighbors from the same layer with probability p, and neighbors from the second layer with complementary probability 1 - p. We demonstrate that a small decrease of p from p = 1 (which corresponds to forbidding strategy transfer between layers) is sufficient to promote cooperation in the Prisoner's Dilemma subpopulation. This, on the other hand, is detrimental for cooperation in the Snowdrift Game subpopulation. We provide results of extensive computer simulations for the case in which layers are modelled as regular random networks, and support this study with analytical results for coupled well-mixed populations.; Comment: 20 pages, 8 figures

Rhythmic inhibition allows neural networks to search for maximally consistent states

Mostafa, Hesham; Muller, Lorenz K.; Indiveri, Giacomo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/03/2015 Português
Relevância na Pesquisa
45.57%
Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits yet its computational role still remains elusive. We show that a model of Gamma-band rhythmic inhibition allows networks of coupled cortical circuit motifs to search for network configurations that best reconcile external inputs with an internal consistency model encoded in the network connectivity. We show that Hebbian plasticity allows the networks to learn the consistency model by example. The search dynamics driven by rhythmic inhibition enable the described networks to solve difficult constraint satisfaction problems without making assumptions about the form of stochastic fluctuations in the network. We show that the search dynamics are well approximated by a stochastic sampling process. We use the described networks to reproduce perceptual multi-stability phenomena with switching times that are a good match to experimental data and show that they provide a general neural framework which can be used to model other 'perceptual inference' phenomena.

The diplomat's dilemma: Maximal power for minimal effort in social networks

Holme, Petter; Ghoshal, Gourab
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/05/2008 Português
Relevância na Pesquisa
45.58%
Closeness is a global measure of centrality in networks, and a proxy for how influential actors are in social networks. In most network models, and many empirical networks, closeness is strongly correlated with degree. However, in social networks there is a cost of maintaining social ties. This leads to a situation (that can occur in the professional social networks of executives, lobbyists, diplomats and so on) where agents have the conflicting objectives of aiming for centrality while simultaneously keeping the degree low. We investigate this situation in an adaptive network-evolution model where agents optimize their positions in the network following individual strategies, and using only local information. The strategies are also optimized, based on the success of the agent and its neighbors. We measure and describe the time evolution of the network and the agents' strategies.; Comment: Submitted to Adaptive Networks: Theory, Models and Applications, to be published from Springer

Griffiths phases and the stretching of criticality in brain networks

Moretti, Paolo; Muñoz, Miguel A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.58%
Hallmarks of criticality, such as power-laws and scale invariance, have been empirically found in cortical networks and it has been conjectured that operating at criticality entails functional advantages, such as optimal computational capabilities, memory, and large dynamical ranges. As critical behavior requires a high degree of fine tuning to emerge, some type of self-tuning mechanism needs to be invoked. Here we show that, taking into account the complex hierarchical-modular architecture of cortical networks, the singular critical point is replaced by an extended critical-like region which corresponds --in the jargon of statistical mechanics-- to a Griffiths phase. Using computational and analytical approaches, we find Griffiths phases in synthetic hierarchical networks and also in empirical brain networks such as the human connectome and the caenorhabditis elegans one. Stretched critical regions, stemming from structural disorder, yield enhanced functionality in a generic way, facilitating the task of self-organizing, adaptive, and evolutionary mechanisms selecting for criticality.; Comment: Final version. A misprint in Equation (2) was corrected. Supplementary Information included

Social insect colony as a biological regulatory system: Information flow in dominance networks

Nandi, Anjan K.; Sumana, Annagiri; Bhattacharya, Kunal
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/03/2014 Português
Relevância na Pesquisa
45.58%
Social insects provide an excellent platform to investigate flow of information in regulatory systems since their successful social organization is essentially achieved by effective information transfer through complex connectivity patterns among the colony members. Network representation of such behavioural interactions offers a powerful tool for structural as well as dynamical analysis of the underlying regulatory systems. In this paper, we focus on the dominance interaction networks in the tropical social wasp \textit{Ropalidia marginata} - a species where behavioural observations indicate that such interactions are principally responsible for the transfer of information between individuals about their colony needs, resulting in a regulation of their own activities. Our research reveals that the dominance networks of \textit{R. marginata} are structurally similar to a class of naturally evolved information processing networks, a fact confirmed also by the predominance of a specific substructure - the `feed-forward loop' - a key functional component in many other information transfer networks. The dynamical analysis through Boolean modeling confirms that the networks are sufficiently stable under small fluctuations and yet capable of more efficient information transfer compared to their randomized counterparts. Our results suggest the involvement of a common structural design principle in different biological regulatory systems and a possible similarity with respect to the effect of selection on the organization levels of such systems. The findings are also consistent with the hypothesis that dominance behaviour has been shaped by natural selection to co-opt the information transfer process in such social insect species...

Climatic seasonality may affect ecological network structure: Food webs and mutualistic networks

Takemoto, Kazuhiro; Kanamaru, Saori; Feng, Wenfeng
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/06/2014 Português
Relevância na Pesquisa
45.58%
Ecological networks exhibit non-random structural patterns, such as modularity and nestedness, which indicate ecosystem stability, species diversity, and connectance. Such structure-stability relationships are well known. However, another important perspective is less well understood: the relationship between the environment and structure. Inspired by theoretical studies that suggest that network structure can change due to environmental variability, we collected data on a number of empirical food webs and mutualistic networks and evaluated the effect of climatic seasonality on ecological network structure. As expected, we found that climatic seasonality affects ecological network structure. In particular, an increase in modularity due to climatic seasonality was observed in food webs; however, it is debatable whether this occurs in mutualistic networks. Interestingly, the type of climatic seasonality that affects network structure differs with ecosystem type. Rainfall and temperature seasonality influence freshwater food webs and mutualistic networks, respectively; food webs are smaller, and more modular, with increasing rainfall seasonality. Mutualistic networks exhibit a higher diversity (particularly of animals) with increasing temperature seasonality. These results confirm the theoretical prediction that stability increases with greater perturbation. Although these results are still debatable because of several limitations in the data analysis...

Special homomorphisms between Probabilistic Gene Regulatory Networks

Avino-Diaz, Maria A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/03/2006 Português
Relevância na Pesquisa
45.58%
In this paper we study finite dynamical systems with $n$ functions acting on the same set $X$, and probabilities assigned to these functions, that it is called Probabilistic Regulatory Gene Networks (PRN. his concept is the same or a natural generalization of the concept Probabilistic Boolean Networks (PBN), introduced by I. Shmulevich, E. Dougherty, and W. Zhang, particularly the model PBN has been using to describe genetic networks and has therapeutic applications. In PRNs the most important question is to describe the steady states of the systems, so in this paper we pay attention to the idea of transforming a network to another without lost all the properties, in particular the probability distribution. Following this objective we develop the concepts of homomorphism and $\epsilon$-homomorphism of probabilistic regulatory networks, since these concepts bring the properties from one networks to another. Projections are special homomorphisms, and they always induce invariant subnetworks that contain all cycles and steady states in the network.

Robust Detection of Dynamic Community Structure in Networks

Bassett, Danielle S.; Porter, Mason A.; Wymbs, Nicholas F.; Grafton, Scott T.; Carlson, Jean M.; Mucha, Peter J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.58%
We describe techniques for the robust detection of community structure in some classes of time-dependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations (`optimization variance') and over randomizations of network structure (`randomization variance'). Because the modularity quality function typically has a large number of nearly-degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data.; Comment: 18 pages...