40 research outputs found
Random walks on complex trees
We study the properties of random walks on complex trees. We observe that the absence of loops is reflected in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and the mean topological displacement from the origin present a considerable slowing down in the tree case. Second, the mean first passage time (MFPT) displays a logarithmic degree dependence, in contrast to the inverse degree shape exhibited in looped networks. This deviation can be ascribed to the dominance of source-target topological distance in trees. To show this, we study the distance dependence of a symmetrized MFPT and derive its logarithmic profile, obtaining good agreement with simulation results. These unique properties shed light on the recently reported anomalies observed in diffusive dynamical systems on trees
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Model reproduces individual, group and collective dynamics of human contact networks
Empirical data on the dynamics of human face-to-face interactions across a variety of social venues have recently revealed a number of context-independent structural and temporal properties of human contact networks. This universality suggests that some basic mechanisms may be responsible for the unfolding of human interactions in the physical space. Here we discuss a simple model that reproduces the empirical distributions for the individual, group and collective dynamics of face-to-face contact networks. The model describes agents that move randomly in a two-dimensional space and tend to stop when meeting "attractive" peers, and reproduces accurately the empirical distributions
Mean-field diffusive dynamics on weighted networks
Diffusion is a key element of a large set of phenomena occurring on natural
and social systems modeled in terms of complex weighted networks. Here, we
introduce a general formalism that allows to easily write down mean-field
equations for any diffusive dynamics on weighted networks. We also propose the
concept of annealed weighted networks, in which such equations become exact. We
show the validity of our approach addressing the problem of the random walk
process, pointing out a strong departure of the behavior observed in quenched
real scale-free networks from the mean-field predictions. Additionally, we show
how to employ our formalism for more complex dynamics. Our work sheds light on
mean-field theory on weighted networks and on its range of validity, and warns
about the reliability of mean-field results for complex dynamics.Comment: 8 pages, 3 figure
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Evolution in a Changing Environment
We propose a simple model for genetic adaptation to a changing environment, describing a fitness landscape characterized by two maxima. One is associated with “specialist” individuals that are adapted to the environment; this maximum moves over time as the environment changes. The other maximum is static, and represents “generalist” individuals not affected by environmental changes. The rest of the landscape is occupied by “maladapted” individuals. Our analysis considers the evolution of these three subpopulations. Our main result is that, in presence of a sufficiently stable environmental feature, as in the case of an unchanging aspect of a physical habitat, specialists can dominate the population. By contrast, rapidly changing environmental features, such as language or cultural habits, are a moving target for the genes; here, generalists dominate, because the best evolutionary strategy is to adopt neutral alleles not specialized for any specific environment. The model we propose is based on simple assumptions about evolutionary dynamics and describes all possible scenarios in a non-trivial phase diagram. The approach provides a general framework to address such fundamental issues as the Baldwin effect, the biological basis for language, or the ecological consequences of a rapid climate change
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Robust modeling of human contact networks across different scales and proximity-sensing techniques
The problem of mapping human close-range proximity networks has been tackled using a variety of technical approaches. Wearable electronic devices, in particular, have proven to be particularly successful in a variety of settings relevant for research in social science, complex networks and infectious diseases dynamics. Each device and technology used for proximity sensing (e.g., RFIDs, Bluetooth, low-power radio or infrared communication, etc.) comes with specific biases on the close-range relations it records. Hence it is important to assess which statistical features of the empirical proximity networks are robust across different measurement techniques, and which modeling frameworks generalize well across empirical data. Here we compare time-resolved proximity networks recorded in different experimental settings and show that some important statistical features are robust across all settings considered. The observed universality calls for a simplified modeling approach. We show that one such simple model is indeed able to reproduce the main statistical distributions characterizing the empirical temporal networks
Heterogeneous pair approximation for voter models on networks
For models whose evolution takes place on a network it is often necessary to
augment the mean-field approach by considering explicitly the degree dependence
of average quantities (heterogeneous mean-field). Here we introduce the degree
dependence in the pair approximation (heterogeneous pair approximation) for
analyzing voter models on uncorrelated networks. This approach gives an
essentially exact description of the dynamics, correcting some inaccurate
results of previous approaches. The heterogeneous pair approximation introduced
here can be applied in full generality to many other processes on complex
networks.Comment: 6 pages, 6 figures, published versio
Effects of mobility on ordering dynamics
Models of ordering dynamics allow us to understand natural systems in which an initially disordered population homogenizes some traits via local interactions. The simplest of these models, with wide applications ranging from evolutionary to social dynamics, are the Voter and Moran processes, usually defined in terms of static or randomly mixed individuals that interact with a neighbor to copy or modify a discrete trait. Here we study the effects of diffusion in Voter/Moran processes by proposing a generalization of ordering dynamics in a metapopulation framework, in which individuals are endowed with mobility and diffuse through a spatial structure represented as a graph of patches upon which interactions take place. We show that diffusion dramatically affects the time to reach the homogeneous state, independently of the underlying network's topology, while the final consensus emerges through different local/global mechanisms, depending on the mobility strength. Our results highlight the crucial role played by mobility in ordering processes and set up a general framework that allows its effect to be studied on a large class of models, with implications in the understanding of evolutionary and social phenomena
Microscopic activity patterns in the Naming Game
The models of statistical physics used to study collective phenomena in some
interdisciplinary contexts, such as social dynamics and opinion spreading, do
not consider the effects of the memory on individual decision processes. On the
contrary, in the Naming Game, a recently proposed model of Language formation,
each agent chooses a particular state, or opinion, by means of a memory-based
negotiation process, during which a variable number of states is collected and
kept in memory. In this perspective, the statistical features of the number of
states collected by the agents becomes a relevant quantity to understand the
dynamics of the model, and the influence of topological properties on
memory-based models. By means of a master equation approach, we analyze the
internal agent dynamics of Naming Game in populations embedded on networks,
finding that it strongly depends on very general topological properties of the
system (e.g. average and fluctuations of the degree). However, the influence of
topological properties on the microscopic individual dynamics is a general
phenomenon that should characterize all those social interactions that can be
modeled by memory-based negotiation processes.Comment: submitted to J. Phys.
Random walks and search in time-varying networks
The random walk process underlies the description of a large number of real
world phenomena. Here we provide the study of random walk processes in time
varying networks in the regime of time-scale mixing; i.e. when the network
connectivity pattern and the random walk process dynamics are unfolding on the
same time scale. We consider a model for time varying networks created from the
activity potential of the nodes, and derive solutions of the asymptotic
behavior of random walks and the mean first passage time in undirected and
directed networks. Our findings show striking differences with respect to the
well known results obtained in quenched and annealed networks, emphasizing the
effects of dynamical connectivity patterns in the definition of proper
strategies for search, retrieval and diffusion processes in time-varying
network
Agreement dynamics on small-world networks
In this paper we analyze the effect of a non-trivial topology on the dynamics of the so-called Naming Game, a recently introduced model which addresses the issue of how shared conventions emerge spontaneously in a population of agents. We consider in particular the small-world topology and study the convergence towards the global agreement as a function of the population size N as well as of the parameter p which sets the rate of rewiring leading to the small-world network. As long as p > > 1/N, there exists a crossover time scaling as N/p2 which separates an early one-dimensional–like dynamics from a late-stage mean-field–like behavior. At the beginning of the process, the local quasi–one-dimensional topology induces a coarsening dynamics which allows for a minimization of the cognitive effort (memory) required to the agents. In the late stages, on the other hand, the mean-field–like topology leads to a speed-up of the convergence process with respect to the one-dimensional case