Thomas

The properties of the cerium metal have intrigued physicists and chemists for many decades. In particular a lot of attention has been directed towards its high pressure behavior, where an isostructural volume collapse (γ phase → α phase) has been observed. Two main models of the electronic aspect of this transformation have been proposed; one where the 4f electron undergoes a change from being localized into an itinerant metallic state, and one where the focus is on the interaction between the 4f electron and the conduction electrons, often referred to as the Kondo volume collapse model. However, over the years it has been repeatedly questioned whether the cerium collapse really is isostructural. Most recently, detailed experiments have been able to remove this worrisome uncertainty. Therefore the isostructural aspect of the α-γ transition has now to be seriously addressed in the theoretical modeling, something which has been very much neglected. A study of this fundamental characteristic of the cerium volume collapse is made in present paper and we show that the localized delocalized 4f electron picture provides an adequate description of this unique behavior. This agreement makes it possible to suggest that an appropriate crossroad position for cerium in The Periodic Table.

Scientific Reports 4 doi: 10.1038/srep06398

A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from given limit-cycle oscillator models. Moreover, using the phase coupling function, the stability of phase clusters can be analyzed. We demonstrate our theory with the Brusselator model. Experiments are carried out to confirm the presence of phase clusters close to Hopf bifurcations with electrochemical oscillators.

The effort to understand network systems in increasing detail has resulted in a diversity of methods designed to extract their large-scale structure from data. Unfortunately, many of these methods yield diverging descriptions of the same network, making both the comparison and understanding of their results a difficult challenge. A possible solution to this outstanding issue is to shift the focus away from ad hoc methods and move towards more principled approaches based on statistical inference of generative models. As a result, we face instead the more well-defined task of selecting between competing generative processes, which can be done under a unified probabilistic framework. Here, we consider the comparison between a variety of generative models including features such as degree correction, where nodes with arbitrary degrees can belong to the same group, and community overlap, where nodes are allowed to belong to more than one group. Because such model variants possess an increasing number of parameters, they become prone to overfitting. In this work, we present a method of model selection based on the minimum description length criterion and posterior odds ratios that is capable of fully accounting for the increased degrees of freedom of the larger models, and selects the best one according to the statistical evidence available in the data. In applying this method to many empirical unweighted networks from different fields, we observe that community overlap is very often not supported by statistical evidence and is selected as a better model only for a minority of them. On the other hand, we find that degree correction tends to be almost universally favored by the available data, implying that intrinsic node proprieties (as opposed to group properties) are often an essential ingredient of network formation.

In this short paper, following the most recent advances in complex network theory, a new approach to number theory with potential applications to other fields is proposed. The model by Garcia-Perez, Serrano and Boguna, introduces an algorithm which allows to create a bipartite graph of integers (with primes and composites) statistically very close to the real one. Since the algorithm is defined a priori, we can have a description of the simulated prime number distribution in terms of a known differential equation, which in general can be treated more easily. The so determined properties of the simulated distribution can give useful hints about the behavior of the real prime number distribution. In principle it could be also possible to demonstrate open questions in number theory, proven the total equivalence of the simulated and real distributions.

Author(s): Kaj-Kolja Kleineberg and Marián Boguñá

Online social networks offer a data-driven way to study patterns of human behavior on small and large scales. Researchers show that individuals are significantly more likely to enroll in social networks based on the influence of one active friend than the influence of mass-media campaigns.

[Phys. Rev. X 4, 031046] Published Tue Sep 09, 2014

Author(s): Maxim S. Shkarayev and R. K. P. Zia

Motivated by fundamental issues in nonequilibrium statistical mechanics, we study the venerable susceptible-infected-susceptible (SIS) model of disease spreading in an idealized, simple setting. Using Monte Carlo and analytic techniques, we consider a fully connected, unidirectional network of odd n...

[Phys. Rev. E 90, 032107] Published Mon Sep 08, 2014

Difficulties encountered by teachers in giving a definition of the term ‘energy’, and by students in grasping its actual meaning, reflect the lengthy process through which the concept eventually came to maturity around 1850. Tracing the history of this process illuminates the different aspects covered by the term and shows the important role played by advancements in animal physiology in the concept’s elaboration. A unique example of cross-fertilization between historically separate fields, the history of the studies on animal heat, is recounted here. The recount starts from the early experiments by Boyle and Hooke on the effect of void on living beings and from Lavoisier’s revolutionary interpretation of respiration as a ‘slow combustion’ process, touching on the contributions by Spallanzani, von Humboldt and Liebig. It ends with the first enunciation of an energy conservation law by two German physicians, Meyer and Helmholtz, in advance of the elaboration of a coherent thermody...

Interdependent networks are characterized by two kinds of interactions: The usual connectivity links within each network and the dependency links coupling nodes of different networks. Due to the latter links such networks are known to suffer from cascading failures and catastrophic breakdowns. When modeling these phenomena, usually one assumes that a fraction of nodes gets damaged in one of the networks, which is followed possibly by a cascade of failures. In real life the initiating failures do not occur at once and effort is made replace the ties eliminated due to the failing nodes. Here we study a dynamic extension of the model of interdependent networks and introduce the possibility of link formation with a probability w, called healing, to bridge non-functioning nodes and enhance network resilience. A single random node is removed, which may initiate an avalanche. After each removal step healing sets in resulting in a new topology. Then a new node fails and the process continues until the giant component disappears either in a catastrophic breakdown or in a smooth transition. Simulation results are presented for square lattices as starting networks under random attacks of constant intensity. We find that the shift in the position of the breakdown has a power-law scaling as a function of the healing probability with an exponent close to 1. Below a critical healing probability, catastrophic cascades form and the average degree of surviving nodes decreases monotonically, while above this value there are no macroscopic cascades and the average degree has first an increasing character and decreases only at the very late stage of the process. These findings facilitate to plan intervention in case of crisis situation by describing the efficiency of healing efforts needed to suppress cascading failures.

Empirical temporal networks display strong heterogeneities in their dynamics, which profoundly affect processes taking place on these networks, such as rumor and epidemic spreading. Despite the recent wealth of data on temporal networks, little work has been devoted to the understanding of how such heterogeneities can emerge from microscopic mechanisms at the level of nodes and links. Here we show that long-term memory effects are present in the creation and disappearance of links in empirical networks. We thus consider a simple generative modeling framework for temporal networks able to incorporate these memory mechanisms. This allows us to study separately the role of each of these mechanisms in the emergence of heterogeneous network dynamics. In particular, we show analytically and numerically how heterogeneous distributions of contact durations, of inter-contact durations and of numbers of contacts per link emerge. We also study the individual effect of heterogeneities on dynamical processes, such as the paradigmatic Susceptible-Infected epidemic spreading model. Our results confirm in particular the crucial role of the distributions of inter-contact durations and of the numbers of contacts per link.

We analyze the data about works (papers, books) from the time period 1990-2010 that are collected in Zentralblatt MATH database. The data were converted into four 2-mode networks (works $\times$ authors, works $\times$ journals, works $\times$ keywords and works $\times$ MSCs) and into a partition of works by publication year. The networks were analyzed using Pajek -- a program for analysis and visualization of large networks. We explore the distributions of some properties of works and the collaborations among mathematicians. We also take a closer look at the characteristics of the field of graph theory as were realized with the publications.

The non-backtracking operator was recently shown to provide a significant improvement when used for spectral clustering of sparse networks. In this paper we analyze its spectral density on large random sparse graphs using a mapping to the correlation functions of a certain interacting quantum disordered system on the graph. On sparse, tree-like graphs, this can be solved efficiently by the cavity method and a belief propagation algorithm. We show that there exists a paramagnetic phase, leading to zero spectral density, that is stable outside a circle of radius ##IMG## [http://ej.iop.org/images/0295-5075/107/5/50005/epl16510ieqn1.gif] {$\sqrt{\rho}$} , where ρ is the leading eigenvalue of the non-backtracking operator. We observe a second-order phase transition at the edge of this circle, between a zero and a non-zero spectral density. The fact that this phase transition is absent in the spectral density of other matrices commonly used for spectral clu...

In many real-world networks nodes represent agents or objects of different sizes or importance. However, the size of the nodes is rarely taken into account in network analysis, possibly inducing bias in network measures and confusion in their interpretation. Recently, a new axiomatic scheme of node-weighted network measures has been suggested for networks with undirected and unweighted edges. However, many real-world systems are best represented by complex networks which have directed and/or weighted edges. Here, we extend this approach and suggest new versions of the degree and the clustering coefficient associated to network motifs for networks with directed and/or weighted edges and weighted nodes. We apply these measures to a spatially embedded network model and a real-world moisture recycling network. We show that these measures improve the representation of the underlying systems' structure and are of general use for studying any type of complex network.

Sicily has played an important role in the development of the new research area named "Econophysics". In fact some key ideas supporting this new hybrid discipline were originally formulated in a pioneering work of the Sicilian born physicist Ettore Majorana. The article he wrote was entitled "The value of statistical laws in physics and social sciences". I will discuss its origin and history that has been recently discovered in the study of Stefano Roncoroni. This recent study documents the true reasons and motivations that triggered the pioneering work of Majorana. It also shows that the description of this work provided by Edoardo Amaldi was shallow and misleading. In the second part of the talk I will recollect the first years of development of econophysics and in particular the role of the "International Workshop on Econophysics and Statistical Finance" held in Palermo on 28-30 September 1998 and the setting in 1999 of the "Observatory of Complex Systems" the research group on Econophysics of Palermo University and Istituto Nazionale di Fisica della Materia.

We investigate synchronization in networks of Kuramoto oscillators with inertia. More specifically, we introduce a rewiring algorithm consisting basically in a {\em hill climb} scheme in which the edges of the network are swapped in order to enhance its synchronization capacity. We show that the the synchrony-optimized networks generated by our algorithm have some interesting topological and dynamical properties. In particular, they typically exhibit an anticipation of the synchronization onset and are more robust against certain types of perturbations. We consider synthetic random networks and also a network with a topology based in an approximated model of the (high voltage) power grid of Spain, since networks of Kuramoto oscillators with inertia have been used recently as simplified models for power grids, for which synchronization is obviously a crucial issue. Despite the extreme simplifications adopted in these models, our results, among others recently obtained in the literature, may provide interesting principles to guide the future growth and development of real-world grids, specially in the case of a change of the current paradigm of centralized towards distributed generation power grids.

The phenomenon of spontaneous synchronization, particularly within the framework of the Kuramoto model, has been a subject of intense research over the years. The model comprises oscillators with distributed natural frequencies interacting through a mean-field coupling, and serves as a paradigm to study synchronization. In this review, we put forward a general framework in which we discuss in a unified way known results with more recent developments obtained for a generalized Kuramoto model that includes inertial effects and noise. We describe the model from a different perspective, highlighting the long-range nature of the interaction between the oscillators, and emphasizing the equilibrium and out-of-equilibrium aspects of its dynamics from a statistical physics point of view. In this review, we first introduce the model and discuss both for the noiseless and noisy dynamics and for unimodal frequency distributions the synchronization transition that occurs in the stationary sta...

The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony (phase locking). Here we present a classical Hamiltonian (and thus conservative) system with $2N$ state variables that in its ac...

We considered a clustered network of bursting neurons described by the Huber-Braun model. In the upper level of the network we used the connectivity matrix of the cat cerebral cortex network, and in the lower level each cortex area (or cluster) is modelled as a small-world network. There are two dif...

With great theoretical and practical significance, identifying the node spreading influence of complex network is one of the most promising domains. So far, various topology-based centrality measures have been proposed to identify the node spreading influence in a network. However, the node spreading influence is a result of the interplay between the network topology structure and spreading dynamics. In this paper, we build up the systematic method by combining the network structure and spreading dynamics to identify the node spreading influence. By combining the adjacent matrix $A$ and spreading parameter $\beta$, we theoretical give the node spreading influence with the eigenvector of the largest eigenvalue. Comparing with the Susceptible-Infected-Recovered (SIR) model epidemic results for four real networks, our method could identify the node spreading influence more accurately than the ones generated by the degree, K-shell and eigenvector centrality. This work may provide a systematic method for identifying node spreading influence.

Author(s): M. V. Tamm, A. B. Shkarin, V. A. Avetisov, O. V. Valba, and S. K. Nechaev

We consider random nondirected networks subject to dynamics conserving vertex degrees and study, analytically and numerically, equilibrium three-vertex motif distributions in the presence of an external field h coupled to one of the motifs. For small h, the numerics is well described by the “chemica...

[Phys. Rev. Lett. 113, 095701] Published Tue Aug 26, 2014

One of the better studied topology metrics of complex networks is the second smallest eigenvalue of the Laplacian matrix of a network's graph, referred to as algebraic connectivity $\mu _{N-1}$. This spectral metric plays a decisive role in synchronization of coupled oscillators, network robustness, consensus problems, belief propagation, graph partitioning and distributed filtering in sensor networks. However, computing the graph spectra is computationally slow and its convergence greatly depends on the topology; thus a number of lower bounds have been proposed over the years in order to find good approximations. To date, the closest bound is the one proposed by Rad et al. (2011. Linear Algebra Appl., 435, 186–192) in 2009. The current paper proposes new approximations for the algebraic connectivity based on three variations of the betweenness centrality, a popular centrality score often used in social studies to characterize the importance of a node or link within a network. Based on numerical and a partly analytic analysis, we show that our approximations provide accurate lower bounds for the algebraic connectivity for a wide range of graphs, including random, power-law, small-world and lattice graphs. In particular, we numerically show that the average weighted Brandes betweenness can be treated as a lower bound for large enough networks, which greatly improves state-of-the-art bounds.

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such ‘multilayer’ features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize ‘traditional’ network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other and provide a thorough discussion that compares, contrasts and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.

Author(s): Azadeh Nematzadeh, Emilio Ferrara, Alessandro Flammini, and Yong-Yeol Ahn

Clustering can enhance the spread of information in networks, via intra-community interactions.

[Phys. Rev. Lett. 113, 088701] Published Mon Aug 18, 2014

Author(s): Maurizio Serva

In a recent paper we proposed a non-Markovian random walk model with memory of the maximum distance ever reached from the starting point (home). The behavior of the walker is different from the simple symmetric random walk only when she is at this maximum distance, where, having the choice to move e...

[Phys. Rev. E 90, 022121] Published Tue Aug 19, 2014

What can we learn from the collective dynamics of a complex network about its interaction topology? Taking the perspective from nonlinear dynamics, we briefly review recent progress on how to infer structural connectivity (direct interactions) from accessing the dynamics of the units. Potential applications range from interaction networks in physics, to chemical and metabolic reactions, protein and gene regulatory networks as well as neural circuits in biology and electric power grids or wireless sensor networks in engineering. Moreover, we briefly mention some standard ways of inferring effective or functional connectivity.

Author(s): Giulia Menichetti, Luca Dall’Asta, and Ginestra Bianconi

The problem of controllability of the dynamical state of a network is central in network theory and has wide applications ranging from network medicine to financial markets. The driver nodes of the network are the nodes that can bring the network to the desired dynamical state if an external signal ...

[Phys. Rev. Lett. 113, 078701] Published Wed Aug 13, 2014

Author(s): G. Harder, D. Mogilevtsev, N. Korolkova, and Ch. Silberhorn

A new method for measuring the photon number distribution of an optical field is demonstrated; the unknown photon signal is mixed with incoherent noise and then measured with a simple on/off detector.

[Phys. Rev. Lett. 113, 070403] Published Wed Aug 13, 2014

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.

Human languages are rule governed, but almost invariably these rules have exceptions in the form of irregularities. Since rules in language are efficient and productive, the persistence of irregularity is an anomaly. How does irregularity linger in the face of internal (endogenous) and external (exogenous) pressures to conform to a rule? Here we address this problem by taking a detailed look at simple past tense verbs in the Corpus of Historical American English. The data show that the language is open, with many new verbs entering. At the same time, existing verbs might tend to regularize or irregularize as a consequence of internal dynamics, but overall, the amount of irregularity sustained by the language stays roughly constant over time. Despite continuous vocabulary growth, and presumably, an attendant increase in expressive power, there is no corresponding growth in irregularity. We analyze the set of irregulars, showing they may adhere to a set of minority rules, allowing for increased stability of irregularity over time. These findings contribute to the debate on how language systems become rule governed, and how and why they sustain exceptions to rules, providing insight into the interplay between the emergence and maintenance of rules and exceptions in language.

We study the stability of the synchronized state in time varying complex networks using the concept of basin stability which is a nonlocal and nonlinear measure of stability that can be easily applied to high$-$dimensional systems{ \it [P. J. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nature Physi...

Author(s): Guillermo García-Pérez, M. Ángeles Serrano, and Marián Boguñá

Prime numbers, and their distribution in the sequence of natural numbers, are of interest for fundamental as well as practical reasons. The authors introduce a stochastic model based on a network representation that closely matches some statistical properties of the prime numbers, and that can be useful as a tool in the study of the distribution of primes.

[Phys. Rev. E 90, 022806] Published Tue Aug 12, 2014