We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and non-fluctuating (hard cutoff) most connected vertices. Logarithmic and power-law decays in time were found for natural and hard cutoffs, respectively. This happens in extended regions of the control parameter space $\lambda_1<\lambda<\lambda_2$, suggesting Griffiths effects, induced by the topological inhomogeneities. Optimal fluctuation theory considering sample-to-sample fluctuations of the pseudo thresholds is presented to explain the observed slow dynamics. A quasistationary analysis shows that response functions remain bounded at $\lambda_2$. We argue these to be signals of a smeared transition. However, in the thermodynamic limit the Griffiths effects loose their relevancy and have a conventional critical point at $\lambda_c=0$. Since many real networks are composed by heterogeneous and weakly connected modules, the slow dynamics found in our analysis of independent and finite networks can play an important role for the deeper understanding of such systems.
Edmilson Roque
Shared posts
Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks. (arXiv:1512.05274v4 [physics.soc-ph] UPDATED)
Network dismantling. (arXiv:1603.08883v2 [physics.soc-ph] UPDATED)
We study the network dismantling problem, which consists in determining a minimal set of vertices whose removal leaves the network broken into connected components of sub-extensive size. For a large class of random graphs, this problem is tightly connected to the decycling problem (the removal of vertices leaving the graph acyclic). Exploiting this connection and recent works on epidemic spreading we present precise predictions for the minimal size of a dismantling set in a large random graph with a prescribed (light-tailed) degree distribution. Building on the statistical mechanics perspective we propose a three-stage Min-Sum algorithm for efficiently dismantling networks, including heavy-tailed ones for which the dismantling and decycling problems are not equivalent. We also provide further insights into the dismantling problem concluding that it is an intrinsically collective problem and that optimal dismantling sets cannot be viewed as a collection of individually well performing nodes.
Ensemble nonequivalence in random graphs with modular structure. (arXiv:1603.08759v2 [math.PR] UPDATED)
Breaking of equivalence between the microcanonical ensemble and the canonical ensemble, describing a large system subject to hard and soft constraints, respectively, was recently shown to occur in large random graphs. Hard constraints must be met by every graph, soft constraints must be met only on average, subject to maximal entropy. In Squartini et al. (2015) it was shown that ensembles of random graphs are non-equivalent when the degrees of the nodes are constrained, in the sense of a non-zero limiting specific relative entropy as the number of nodes diverges. In that paper, the nodes were placed either on a single layer (uni-partite graphs) or on two layers (bi-partite graphs). In the present paper we consider an arbitrary number of intra-connected and inter-connected layers, thus allowing for modular graphs with a multi-partite, multiplex, block-model or community structure. We give a full classification of ensemble equivalence, proving that breakdown occurs if and only if the number of local constraints (i.e., the number of constrained degrees) is extensive in the number of nodes, irrespective of the layer structure. In addition, we derive a formula for the specific relative entropy and provide an interpretation of this formula in terms of Poissonisation of the degrees.
Dynamics of a population of oscillatory and excitable elements. (arXiv:1603.08803v1 [nlin.CD])
We analyze a variant of a model proposed by Kuramoto, Shinomoto, and Sakaguchi for a large population of coupled oscillatory and excitable elements. Using the Ott-Antonsen ansatz, we reduce the behavior of the population to a two-dimensional dynamical system with three parameters. We present the stability diagram and calculate several of its bifurcation curves analytically, for both excitatory and inhibitory coupling. Our main result is that when the coupling function is broad, the system can display bistability between steady states of constant high and low activity, whereas when the coupling function is narrow and inhibitory, one of the states in the bistable regime can show persistent pulsations in activity.
Network dismantling. (arXiv:1603.08883v1 [physics.soc-ph])
We study the problem of network dismantling, that is of finding a minimal set of vertices whose removal leaves the network broken in connected components of sub-extensive size. For a large class of random graphs this problem is tightly connected to the decycling problem (the removal of vertices leaving the graph acyclic). Exploiting this connection and recent works on epidemic spreading we present precise predictions for the minimal size of a dismantling set in a large random graph with a prescribed (light-tailed) degree distribution. Building on the statistical mechanics perspective we propose a three-stage Min-Sum algorithm for efficiently dismantling networks, including heavy-tailed ones for which the dismantling and decycling problems are not equivalent. We also provide insight into the dismantling problem concluding that it is an intrinsically collective problem and optimal dismantling sets cannot be viewed as a collection of individually well performing nodes.
Reconstruction of evolved dynamic networks from degree correlations. (arXiv:1603.08812v2 [physics.soc-ph] UPDATED)
We study the importance of local structural properties in networks which have been evolved for a power-law scaling in their Laplacian spectrum. To this end, the degree distribution, two-point degree correlations, and degree-dependent clustering are extracted from the evolved networks and used to construct random networks with the prescribed distributions. In the analysis of these reconstructed networks it turns out that the degree distribution alone is not sufficient to generate the spectral scaling and the degree-dependent clustering has only an indirect influence. The two-point correlations are found to be the dominant characteristic for the power-law scaling over a broader eigenvalue range.
A polynomial distribution applied to income and wealth distribution. (arXiv:1410.4866v2 [q-fin.GN] UPDATED)
Income and wealth distribution affect stability of a society to a large extent and high inequality affects it negatively. Moreover, in the case of developed countries, recently has been proven that inequality is closely related to all negative phenomena affecting society. So far, Econophysics papers tried to analyse income and wealth distribution by employing distributions such as Fermi-Dirac, Bose-Einstein, Maxwell-Boltzmann, lognormal (Gibrat), and exponential. Generally, distributions describe mostly income and less wealth distribution for low and middle income segment of population, which accounts about 90% of the population. Our approach is based on a totally new distribution, not used so far in the literature regarding income and wealth distribution. Using cumulative distribution method, we find that polynomial functions, regardless of their degree (first, second, or higher), can describe with very high accuracy both income and wealth distribution. Moreover, we find that polynomial functions describe income and wealth distribution for entire population including upper income segment for which traditionally Pareto distribution is used.
A statistical physics analysis of expenditure in the UK. (arXiv:1410.3865v2 [q-fin.GN] UPDATED)
Most papers which explored so far macroeconomic variables took into account income and wealth. Equally important as the previous macroeconomic variables is the expenditure or consumption, which shows the amount of goods and services that a person or a household purchased. Using statistical distributions from Physics, such as Fermi-Dirac and polynomial distributions, we try to fit the data regarding the expenditure distribution divided in deciles of population according to their income (gross and disposable expenditure are taken into account). Using coefficient of determination as theoretical tool in order to assess the degree of success for these distributions, we find that both distributions are really robust in describing the expenditure distribution, regardless the data set or the methodology used to calculate the expenditure values for the deciles of income. This is the first paper to our knowledge which tackles expenditure, especially using a method to describe expenditure such as lower limit on expenditure. This is also relevant since it allows the approach of macroeconomic systems using more variables characterizing their activity, can help in the investigation of living standards and inequality, and points to more theoretical explorations which can be very useful for the Economics and business practice.
An econophysical approach of polynomial distribution applied to income and expenditure. (arXiv:1410.3860v2 [q-fin.GN] UPDATED)
Polynomial distribution can be applied to dynamical systems in certain situations. Macroeconomic systems characterized by economic variables such as income and wealth can be modelled similarly using polynomials. We extend our previous work to data regarding income from a more diversified pool of countries, which contains developed countries with high income, developed countries with middle income, developing and underdeveloped countries. Also, for the first time we look at the applicability of polynomial distribution to expenditure (consumption). Using cumulative distribution function, we found that polynomials are applicable with a high degree of success to the distribution of income to all countries considered without significant differences. Moreover, expenditure data can be fitted very well by this polynomial distribution. We considered a distribution to be robust if the values for coefficient of determination are higher than 90%. Using this criterion, we decided the degree for the polynomials used in our analysis by trying to minimize the number of coefficients, respectively first or second degree. Lastly, we look at possible correlation between the values from coefficient of determination and Gini coefficient for disposable income.
An Econophysical dynamical approach of expenditure and income distribution in the UK. (arXiv:1410.3851v2 [q-fin.GN] UPDATED)
We extend the exploration regarding dynamical approach of macroeconomic variables by tackling systematically expenditure using Statistical Physics models (for the first time to the best of our knowledge). Also, using polynomial distribution which characterizes the behavior of dynamical systems in certain situations, we extend also our analysis to mean income data from the UK that span for a time interval of 35 years. We find that most of the values for coefficient of determination obtained from fitting the data from consecutive years analysis to be above 80%. We used for our analysis first degree polynomial, but higher degree polynomials and longer time intervals between the years considered can dramatically increase goodness of the fit. As this methodology was applied successfully to income and wealth, we can conclude that macroeconomic systems can be treated similarly to dynamic systems from Physics. Subsequently, the analysis could be extended to other macroeconomic indicators.
Applications of statistical physics distributions to several types of income. (arXiv:1410.3811v2 [physics.soc-ph] UPDATED)
This paper explores several types of income which have not been explored so far by authors who tackled income and wealth distribution using Statistical Physics. The main types of income we plan to analyze are income before redistribution (or gross income), income of retired people (or pensions), and income of active people (mostly wages). The distributions used to analyze income distributions are Fermi-Dirac distribution and polynomial distribution (as this is present in describing the behavior of dynamic systems in certain aspects). The data we utilize for our analysis are from France and the UK. We find that both distributions are robust in describing these varieties of income. The main finding we consider to be the applicability of these distributions to pensions, which are not regulated entirely by market mechanisms.
A study of Methods from Statistical Mechanics applied to income distribution. (arXiv:1410.3128v2 [q-fin.GN] UPDATED)
We applied Dirac distribution, Bose-Einstein distribution, and occasionally Boltzmann-Gibbs distribution in order to determine which is optimal for income distribution on a large pool of countries. The best fit to the data was observed in the case of Fermi-Dirac distribution, for which the coefficient of determination showed the best goodness of fit to the data. Using this distribution for data (spun throughout more years), we obtained the underlying critical parameters of annual income distribution such as chemical potential and temperature. The next step was to explore the evolution of income using economic analogues to chemical potential and temperature. Using as background the analogy made by Yakovenko between temperature from thermodynamic systems and nominal income from Economics, we found other analogies that would allow further analysis and explanation of income.
Collective behavior in the spatial spreading of obesity. (arXiv:1202.6345v2 [physics.soc-ph] UPDATED)
Non-communicable diseases like diabetes, obesity and certain forms of cancer have been increasing in many countries at alarming levels. A difficulty in the conception of policies to reverse these trends is the identification of the drivers behind the global epidemics. Here, we implement a spatial spreading analysis to investigate whether diabetes, obesity and cancer show spatial correlations revealing the effect of collective and global factors acting above individual choices. We adapt a theoretical framework for critical physical systems displaying collective behavior to decipher the laws of spatial spreading of diseases. We find a regularity in the spatial fluctuations of their prevalence revealed by a pattern of scale-free long-range correlations. The fluctuations are anomalous, deviating in a fundamental way from the weaker correlations found in the underlying population distribution. This collective behavior indicates that the spreading dynamics of obesity, diabetes and some forms of cancer like lung cancer are analogous to a critical point of fluctuations, just as a physical system in a second-order phase transition. According to this notion, individual interactions and habits may have negligible influence in shaping the global patterns of spreading. Thus, obesity turns out to be a global problem where local details are of little importance. Interestingly, we find the same critical fluctuations in obesity and diabetes, and in the activities of economic sectors associated with food production such as supermarkets, food and beverage stores--- which cluster in a different universality class than other generic sectors of the economy. These results motivate future interventions to investigate the causality of this relation providing guidance for the implementation of preventive health policies.
Characterization of multiple topological scales in multiplex networks through supra-Laplacian eigengaps. (arXiv:1603.08464v3 [physics.soc-ph] UPDATED)
Multilayer networks have been the subject of intense research during the last few years, as they represent better the interdependent nature of many real world systems. Here, we address the question of describing the three different structural phases in which a multiplex network might exist. We show that each phase can be characterized by the presence of gaps in the spectrum of the supra-Laplacian of the multiplex network. We therefore unveil the existence of different topological scales in the system, whose relation characterizes each phase. Moreover, by capitalizing on the coarse-grained representation that is given in terms of quotient graphs, we explain the mechanisms that produce those gaps as well as their dynamical consequences.
Predictive Modeling of Opinion and Connectivity Dynamics in Social Networks. (arXiv:1603.08252v1 [cs.SI])
Recent years saw an increased interest in modeling and understanding the mechanisms of opinion and innovation spread through human networks. Using analysis of real-world social data, researchers are able to gain a better understanding of the dynamics of social networks and subsequently model the changes in such networks over time. We developed a social network model that both utilizes an agent-based approach with a dynamic update of opinions and connections between agents and reflects opinion propagation and structural changes over time as observed in real-world data. We validate the model using data from the Social Evolution dataset of the MIT Human Dynamics Lab describing changes in friendships and health self-perception in a targeted student population over a nine-month period. We demonstrate the effectiveness of the approach by predicting changes in both opinion spread and connectivity of the network. We also use the model to evaluate how the network parameters, such as the level of `openness' and willingness to incorporate opinions of neighboring agents, affect the outcome. The model not only provides insight into the dynamics of ever changing social networks, but also presents a tool with which one can investigate opinion propagation strategies for networks of various structures and opinion distributions.
Disentangling giant component and finite cluster contributions in sparse matrix spectra
Author(s): Reimer Kühn
We describe a method for disentangling giant component and finite cluster contributions to sparse random matrix spectra, using sparse symmetric random matrices defined on Erdös-Renyi graphs as an example and test-bed. Our methods apply to sparse matrices defined in terms of arbitrary graphs in …[Phys. Rev. E] Published Mon Mar 28, 2016
Contact process with temporal disorder. (arXiv:1603.08075v2 [cond-mat.stat-mech] UPDATED)
We investigate the influence of time-varying environmental noise, i.e., temporal disorder, on the nonequilibrium phase transition of the contact process. Combining a real-time renormalization group, scaling theory, and large scale Monte-Carlo simulations in one and two dimensions, we show that the temporal disorder gives rise to an exotic critical point. At criticality, the effective noise amplitude diverges with increasing time scale, and the probability distribution of the density becomes infinitely broad, even on a logarithmic scale. Moreover, the average density and survival probability decay only logarithmically with time. This infinite-noise critical behavior can be understood as the temporal counterpart of infinite-randomness critical behavior in spatially disordered systems, but with exchanged roles of space and time. We also analyze the generality of our results, and we discuss potential experiments.
Characterization of multiple topological scales in multiplex networks through supra-Laplacian eigengaps. (arXiv:1603.08464v3 [physics.soc-ph] UPDATED)
Multilayer networks have been the subject of intense research during the last few years, as they represent better the interdependent nature of many real world systems. Here, we address the question of describing the three different structural phases in which a multiplex network might exist. We show that each phase can be characterized by the presence of gaps in the spectrum of the supra-Laplacian of the multiplex network. We therefore unveil the existence of different topological scales in the system, whose relation characterizes each phase. Moreover, by capitalizing on the coarse-grained representation that is given in terms of quotient graphs, we explain the mechanisms that produce those gaps as well as their dynamical consequences.
Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks
Author(s): Wesley Cota, Silvio C. Ferreira, and Géza Ódor
We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects…
[Phys. Rev. E 93, 032322] Published Mon Mar 28, 2016
Constructing networks from a dynamical system perspective for multivariate nonlinear time series
Author(s): Tomomichi Nakamura, Toshihiro Tanizawa, and Michael Small
We describe a method for constructing networks for multivariate nonlinear time series. We approach the interaction between the various scalar time series from a deterministic dynamical system perspective and provide a generic and algorithmic test for whether the interaction between two measured time…
[Phys. Rev. E 93, 032323] Published Mon Mar 28, 2016
Identical phase oscillator networks: bifurcations, symmetry and reversibility for generalized coupling. (arXiv:1603.07937v2 [math.DS] UPDATED)
For a system of coupled identical phase oscillators with full permutation symmetry, any broken symmetries in dynamical behaviour must come from spontaneous symmetry breaking, i.e. from the nonlinear dynamics of the system. The dynamics of phase differences for such a system depends only on the coupling (phase interaction) function $g(\varphi)$ and the number of oscillators $N$. This paper briefly reviews some results for such systems in the case of general coupling $g$ before exploring two cases in detail: (a) general two harmonic form: $g(\varphi)=q\sin(\varphi-\alpha)+r\sin(2\varphi-\beta)$ and $N$ small (b) the coupling $g$ is odd or even. We extend previously published bifurcation analyses to the general two harmonic case, and show for even $g$ that the dynamics of phase differences has a number of time-reversal symmetries. For the case of even $g$ with one harmonic it is known the system has $N-2$ constants of the motion. This is true for $N=4$ and any $g$, while for $N=4$ and more than two harmonics in $g$, we show the system must have fewer independent constants of the motion.
Interconnectivity structure of a general interdependent network
Author(s): P. Van Mieghem
A general two-layer network (and similar for a general m-layer network) consists of two networks G1 and G2, whose interconnection pattern is specified by the interconnectivity matrix B. We deduce desirable properties of B from a dynamic process point of view. Many dynamic processes are described by …[Phys. Rev. E] Published Mon Mar 21, 2016
Constrained basin stability for studying transient phenomena in dynamical systems
Author(s): Adrian van Kan, Jannes Jegminat, Jonathan F. Donges, and Jürgen Kurths
Transient dynamics are of large interest in many areas of science. Here, a generalization of basin stability (BS) is presented: constrained basin stability (CBS) that is sensitive to various different types of transients arising from finite size perturbations. CBS is applied to the paradigmatic Lore…[Phys. Rev. E] Published Tue Mar 22, 2016
Inhomogeneity induces relay synchronization in complex networks
Author(s): Lucia Valentina Gambuzza, Mattia Frasca, Luigi Fortuna, and Stefano Boccaletti
Relay synchronization is a collective state, originally found in chains of interacting oscillators, in which uncoupled dynamical units synchronize through the action of mismatched inner nodes that relay the information but do not synchronize with them. It is here demonstrated that relay synchronizat…[Phys. Rev. E] Published Tue Mar 22, 2016
Percolation of networks with directed dependency links
Author(s): Dunbiao Niu, Xin Yuan, Minhui Du, H. Eugene Stanley, and Yanqing Hu
The self-consistent probabilistic approach has proven itself powerful in studying the percolation behavior of interdependent or multiplex networks without tracking the percolation process through each cascading step. In order to understand how directed dependency links impact criticality, we employ …[Phys. Rev. E] Published Thu Mar 24, 2016
Grid based partitioning for comparing attractors
Author(s): T. L. Carroll and J. M. Byers
Stationary dynamical systems have invariant measures (or densities) that are characteristic of the particular dynamical system. We develop a method to characterize this density by partitioning the attractor into the smallest regions in phase space that contain information about the structure of the …[Phys. Rev. E] Published Fri Mar 25, 2016
Tweaking Synchronisation by Link Addition. (arXiv:1603.07157v2 [nlin.CD] UPDATED)
Natural and man-made networks often possess locally tree-like sub-structures. Taking such tree networks as our starting point, we show how the addition of links changes the synchronization properties of the network. We focus on two different methods of link addition. The first method adds single links that create cycles of a well-defined length. Following a topological approach we introduce cycles of varying length and analyze how this feature, as well as the position in the network, alters the synchronous behaviour. We show that in particular short cycles can lead to a maximum change of the Laplacian's eigenvalue spectrum, dictating the synchronization properties of such networks. The second method connects a certain proportion of the initially unconnected nodes. We simulate dynamical systems on these network topologies, with the nodes' local dynamics being either a discrete or continuous. Here our main result is that a certain amount of additional links, with the relative position in the network being crucial, can be beneficial to ensure stable synchronization.
Linking Individual and Collective Behavior in Adaptive Social Networks
Author(s): Flávio L. Pinheiro, Francisco C. Santos, and Jorge M. Pacheco
The local interactions of individuals in a network is connected to the global network dynamics using the Prisoner’s Dilemma game theory model.
[Phys. Rev. Lett. 116, 128702] Published Thu Mar 24, 2016
Perturbative calculation of quasi-potential in non-equilibrium diffusions: a mean-field example. (arXiv:1509.03273v2 [cond-mat.stat-mech] UPDATED)
In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational problem, lies at the core of the Freidlin-Wentzell large deviations theory%.~\cite{freidlin1984}.In many interacting particle systems, the particle density is described by fluctuating hydrodynamics governed by Macroscopic Fluctuation Theory%, ~\cite{bertini2014},which formally fits within Freidlin-Wentzell's framework with a weak noise proportional to $1/\sqrt{N}$, where $N$ is the number of particles. The quasi-potential then appears as a natural generalization of the equilibrium free energy to non-equilibrium particle systems. A key physical and practical issue is to actually compute quasi-potentials from their variational characterization for non-equilibrium systems for which detailed balance does not hold. We discuss how to perform such a computation perturbatively in an external parameter $\lambda$, starting from a known quasi-potential for $\lambda=0$. In a general setup, explicit iterative formulae for all terms of the power-series expansion of the quasi-potential are given for the first time. The key point is a proof of solvability conditions that assure the existence of the perturbation expansion to all orders. We apply the perturbative approach to diffusive particles interacting through a mean-field potential. For such systems, the variational characterization of the quasi-potential was proven by Dawson and Gartner%. ~\cite{dawson1987,dawson1987b}. Our perturbative analysis provides new explicit results about the quasi-potential and about fluctuations of one-particle observables in a simple example of mean field diffusions: the Shinomoto-Kuramoto model of coupled rotators%. ~\cite{shinomoto1986}. This is one of few systems for which non-equilibrium free energies can be computed and analyzed in an effective way, at least perturbatively.
Coherent population transfer between uncoupled or weakly coupled states in ladder-type superconducting qutrits
Article
Quantum state engineering necessitates transfer between quantum states. Here the authors demonstrate coherent population transfer between un- or weakly-coupled states of solid state systems, superconducting Xmon and phase qutrits, using stimulated Raman adiabatic passage and microwave driving.
Nature Communications doi: 10.1038/ncomms11018
Authors: H. K. Xu, C. Song, W. Y. Liu, G. M. Xue, F. F. Su, H. Deng, Ye Tian, D. N. Zheng, Siyuan Han, Y. P. Zhong, H. Wang, Yu-xi Liu, S. P. Zhao