arXiv subjects

Alex Arenas

Publications and source records attributed to Alex Arenas.

At least 73 records · Page 4Linked to original sources

arXiv2018

Fragility and anomalous susceptibility of weakly interacting networks

Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less interlinks than the connections within each layer. For these kinds of structures, both continuous and abrupt phase transition are observed in the size of the giant component. The continuous (second-order) transition corresponds to the formation of a giant cluster inside one layer, and has a well defined percolation threshold. The abrupt transition instead corresponds to the merger of coexisting giant clusters among different layers, and is characterised by a remarkable uncertainty in the percolation threshold, which in turns causes an anomalous trend in the observed susceptibility. We develop a simple mathematical model able to describe this phenomenon and to estimate the critical threshold for which the abrupt transition is more likely to occur. Remarkably, finite-size scaling analysis in the abrupt region supports the hypothesis of a genuine first-order phase transition.

physics.soc-ph↗

arXiv2018

Centralized and distributed cognitive task processing in the human connectome

A key question in modern neuroscience is how cognitive changes in a human brain can be quantified and captured by functional connectomes (FC) . A systematic approach to measure pairwise functional distance at different brain states is lacking. This would provide a straight-forward way to quantify differences in cognitive processing across tasks; also, it would help in relating these differences in task-based FCs to the underlying structural network. Here we propose a framework, based on the concept of Jensen-Shannon divergence, to map the task-rest connectivity distance between tasks and resting-state FC. We show how this information theoretical measure allows for quantifying connectivity changes in distributed and centralized processing in functional networks. We study resting-state and seven tasks from the Human Connectome Project dataset to obtain the most distant links across tasks. We investigate how these changes are associated to different functional brain networks, and use the proposed measure to infer changes in the information processing regimes. Furthermore, we show how the FC distance from resting state is shaped by structural connectivity, and to what extent this relationship depends on the task. This framework provides a well grounded mathematical quantification of connectivity changes associated to cognitive processing in large-scale brain networks.

q-bio.NC↗

arXiv2018

Synchronization Invariance Under Network Structural Transformations

Synchronization processes are ubiquitous despite the many connectivity patterns that complex systems can show. Usually, the emergence of synchrony is a macroscopic observable, however, the microscopic details of the system, as e.g. the underlying network of interactions, is many times partially or totally unknown. We already know that different interaction structures can give rise to a common functionality, understood as a common macroscopic observable. Building upon this fact, here, we propose network transformations that keep the collective behavior of a large system of Kuramoto oscillators functionally invariant. We derive a method based on information theory principles, that allows us to adjust the weights of the structural interactions to map random homogeneous -in degree- networks into random heterogeneous networks and vice-versa, keeping synchronization values invariant. The results of the proposed transformations reveal an interesting principle; heterogeneous networks can be mapped to homogeneous ones with local information, but the reverse process needs to exploit higher-order information. The formalism provides new analytical insight to tackle real complex scenarios when dealing with uncertainty in the measurements of the underlying connectivity structure.

physics.soc-ph↗

arXiv2018

Decongestion of urban areas with hotspot-pricing

The rapid growth of population in urban areas is jeopardizing the mobility and air quality worldwide. One of the most notable problems arising is that of traffic congestion which in turn affects air pollution. With the advent of technologies able to sense real-time data about cities, and its public distribution for analysis, we are in place to forecast scenarios valuable to ameliorate and control congestion. Here, we analyze a local congestion pricing scheme, hotspot pricing, that surcharges vehicles traversing congested junctions. The proposed tax is computed from the estimation of the evolution of congestion at local level, and the expected response of users to the tax (elasticity). Results on cities' road networks, considering real-traffic data, show that the proposed hotspot pricing scheme would be more effective than current mechanisms to decongest urban areas, and paves the way towards sustainable congestion in urban areas.

physics.soc-ph↗

arXiv2018

Interplay between cost and benefits triggers nontrivial vaccination uptake

The containment of epidemic spreading is a major challenge in science. Vaccination, whenever available, is the best way to prevent the spreading, because it eventually immunizes individuals. However, vaccines are not perfect, and total immunization is not guaranteed. Imperfect immunization has driven the emergence of anti-vaccine movements that totally alter the predictions about the epidemic incidence. Here, we propose a mathematically solvable mean-field vaccination model to mimic the spontaneous adoption of vaccines against influenza-like diseases, and the expected epidemic incidence. The results are in agreement with extensive Monte Carlo simulations of the epidemics and vaccination co-evolutionary processes. Interestingly, the results reveal a non-monotonic behavior on the vaccination coverage, that increases with the imperfection of the vaccine and after decreases. This apparent counterintuitive behavior is analyzed and understood from stability principles of the proposed mathematical model.

physics.soc-ph↗

arXiv2018

Multiple structural transitions in interacting networks

Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected networks as inter-network interactions are established. We reveal multiple structural transitions for the algebraic connectivity of such systems, between regimes in which each network layer keeps its independent identity or drives diffusive processes over the whole system, thus generalizing previous results reporting a single transition point. Furthermore we show that, at first order in perturbation theory, the growth of the algebraic connectivity of each layer depends only on the degree configuration of the interaction network (projected on the respective Fiedler vector), and not on the actual interaction topology. Our findings can have important implications in the design of robust interconnected networked system, particularly in the presence of network layers whose integrity is more crucial for the functioning of the entire system. We finally show results of perturbation theory applied to the adjacency matrix of the interconnected network, which can be useful to characterize percolation processes on such systems.

physics.soc-ph↗

arXiv2018

Communication Melting in Graphs and Complex Networks

Complex networks are the representative graphs of interactions in many complex systems. Usually, these interactions are abstractions of the communication/diffusion channels between the units of the system. Real complex networks, e.g. traffic networks, reveal different operation phases governed by the dynamical stress of the system. Here we show how, communicability, a topological descriptor that reveals the efficiency of the network functionality in terms of these diffusive paths, could be used to reveal the transitions mentioned. By considering a vibrational model of nodes and edges in a graph/network at a given temperature (stress), we show that the communicability function plays the role of the thermal Green's function of a network of harmonic oscillators. After, we prove analytically the existence of a universal phase transition in the communicability structure of every simple graph. This transition resembles the melting process occurring in solids. For instance, regular-like graphs resembling crystals, melts at lower temperatures and display a sharper transition between connected to disconnected structures than the random spatial graphs, which resemble amorphous solids. Finally, we study computationally this graph melting process in some real-world networks and observe that the rate of melting of graphs changes either as an exponential or as a power-law with the inverse temperature. At the local level we discover that the main driver for node melting is the eigenvector centrality of the corresponding node, particularly when the critical value of the inverse temperature approaches zero. These universal results sheds light on many dynamical diffusive-like processes on networks that present transitions as traffic jams, communication lost or failure cascades.

physics.soc-ph↗

arXiv2018

A framework for epidemic spreading in multiplex networks of metapopulations

We propose a theoretical framework for the study of epidemics in structured metapopulations, with heterogeneous agents, subjected to recurrent mobility patterns. We propose to represent the heterogeneity in the composition of the metapopulations as layers in a multiplex network, where nodes would correspond to geographical areas and layers account for the mobility patterns of agents of the same class. We analyze both the classical Susceptible-Infected-Susceptible and the Susceptible-Infected-Removed epidemic models within this framework, and compare macroscopic and microscopic indicators of the spreading process with extensive Monte Carlo simulations. Our results are in excellent agreement with the simulations. We also derive an exact expression of the epidemic threshold on this general framework revealing a non-trivial dependence on the mobility parameter. Finally, we use this new formalism to address the spread of diseases in real cities, specifically in the city of Medellin, Colombia, whose population is divided into six socio-economic classes, each one identified with a layer in this multiplex formalism.

physics.soc-ph↗

arXiv2017

Cascading failures in interdependent systems under a flow redistribution model

Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional throughout the cascade. Although suitable for communication networks, this assumption fails to capture the dependencies in systems carrying a flow (e.g., power systems, road transportation networks), where cascading failures are often triggered by redistribution of flows leading to overloading of lines. Here, we consider a model consisting of systems $A$ and $B$ with initial line loads and capacities given by $\{L_{A,i},C_{A,i}\}_{i=1}^{n}$ and $\{L_{B,i},C_{B,i}\}_{i=1}^{n}$, respectively. When a line fails in system $A$, $a$-fraction of its load is redistributed to alive lines in $B$, while remaining $(1-a)$-fraction is redistributed equally among all functional lines in $A$; a line failure in $B$ is treated similarly with $b$ giving the fraction to be redistributed to $A$. We give a thorough analysis of cascading failures of this model initiated by a random attack targeting $p_1$-fraction of lines in $A$ and $p_2$-fraction in $B$. We show that (i) the model captures the real-world phenomenon of unexpected large scale cascades and exhibits interesting transition behavior: the final collapse is always first-order, but it can be preceded by a sequence of first and second-order transitions; (ii) network robustness tightly depends on the coupling coefficients $a$ and $b$, and robustness is maximized at non-trivial $a,b$ values in general; (iii) unlike existing models, interdependence has a multi-faceted impact on system robustness in that interdependency can lead to an improved robustness for each individual network.

physics.soc-ph↗

arXiv2017

The physics of spreading processes in multilayer networks

The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (i.e., "multiplexity") among their constituent components and/or multiple interacting subsystems. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent "multilayer" approach for modeling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. On one hand, it allows one to couple different structural relationships by encoding them in a convenient mathematical object. On the other hand, it also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure.

physics.soc-ph↗

arXiv2017

Centralities of Nodes and Influences of Layers in Large Multiplex Networks

We formulate and propose an algorithm (MultiRank) for the ranking of nodes and layers in large multiplex networks. MultiRank takes into account the full multiplex network structure of the data and exploits the dual nature of the network in terms of nodes and layers. The proposed centrality of the layers (influences) and the centrality of the nodes are determined by a coupled set of equations. The basic idea consists in assigning more centrality to nodes that receive links from highly influential layers and from already central nodes. The layers are more influential if highly central nodes are active in them. The algorithm applies to directed/undirected as well as to weighted/unweighted multiplex networks. We discuss the application of MultiRank to three major examples of multiplex network datasets: the European Air Transportation Multiplex Network, the Pierre Auger Multiplex Collaboration Network and the FAO Multiplex Trade Network.

physics.soc-ph↗

arXiv2017

Collective phenomena emerging from the interactions between dynamical processes in multiplex networks

We introduce a framework to intertwine dynamical processes of different nature, each with its own distinct network topology, using a multilayer network approach. As an example of collective phenomena emerging from the interactions of multiple dynamical processes, we study a model where neural dynamics and nutrient transport are bidirectionally coupled in such a way that the allocation of the transport process at one layer depends on the degree of synchronization at the other layer, and vice versa. We show numerically, and we prove analytically, that the multilayer coupling induces a spontaneous explosive synchronization and a heterogeneous distribution of allocations, otherwise not present in the two systems considered separately. Our framework can find application to other cases where two or more dynamical processes such as synchronization, opinion formation, information diffusion, or disease spreading, are interacting with each other.

nlin.AO↗

arXiv2016

Influence of trust in the spreading of information

The understanding and prediction of information diffusion processes on networks is a major challenge in network theory with many implications in social sciences. Many theoretical advances occurred due to stochastic spreading models. Nevertheless, these stochastic models overlooked the influence of rational decisions on the outcome of the process. For instance, different levels of trust in acquaintances do play a role in information spreading, and actors may change their spreading decisions during the information diffusion process accordingly. Here, we study an information-spreading model in which the decision to transmit or not is based on trust. We explore the interplay between the propagation of information and the trust dynamics happening on a two-layer multiplex network. Actors' trustable or untrustable states are defined as accumulated cooperation or defection behaviors, respectively, in a Prisoner's Dilemma set up, and they are controlled by a memory span. The propagation of information is abstracted as a threshold model on the information-spreading layer, where the threshold depends on the trustability of agents. The analysis of the model is performed using a tree approximation and validated on homogeneous and heterogeneous networks. The results show that the memory of previous actions has a significant effect on the spreading of information. For example, the less memory that is considered, the higher is the diffusion. Information is highly promoted by the emergence of trustable acquaintances. These results provide insight into the effect of plausible biases on spreading dynamics in a multilevel networked system.

physics.soc-ph↗

arXiv2016

Untangling the role of diverse social dimensions in the diffusion of microfinance

Ties between individuals on a social network can represent different dimensions of interactions, and the spreading of information and innovations on these networks could potentially be driven by some dimensions more than by others. In this paper we investigate this issue by studying the diffusion of microfinance within rural India villages and accounting for the whole multilayer structure of the underlying social networks. We define a new measure of node centrality, diffusion versatility, and show that this is a better predictor of microfinance participation rate than previously introduced measures defined on aggregated single-layer social networks. Moreover, we untangle the role played by each social dimension and find that the most prominent role is played by the nodes that are central on layers concerned with trust, shedding new light on the key triggers of the diffusion of microfinance.

physics.soc-ph↗

arXiv2016

Functional Multiplex PageRank

Recently it has been recognized that many complex social, technological and biological networks have a multilayer nature and can be described by multiplex networks. Multiplex networks are formed by a set of nodes connected by links having different connotations forming the different layers of the multiplex. Characterizing the centrality of the nodes in a multiplex network is a challenging task since the centrality of the node naturally depends on the importance associated to links of a certain type. Here we propose to assign to each node of a multiplex network a centrality called Functional Multiplex PageRank that is a function of the weights given to every different pattern of connections (multilinks) existent in the multiplex network between any two nodes. Since multilinks distinguish all the possible ways in which the links in different layers can overlap, the Functional Multiplex PageRank can describe important non-linear effects when large relevance or small relevance is assigned to multilinks with overlap. Here we apply the Functional Page Rank to the multiplex airport networks, to the neuronal network of the nematode c.elegans, and to social collaboration and citation networks between scientists. This analysis reveals important differences existing between the most central nodes of these networks, and the correlations between their so called "pattern to success".

physics.soc-ph↗

arXiv2016

Clustering determines the dynamics of complex contagions in multiplex networks

We present the mathematical analysis of generalized complex contagions in clustered multiplex networks for susceptible-infected-recovered (SIR)-like dynamics. The model is intended to understand diffusion of influence, or any other spreading process implying a threshold dynamics, in setups of interconnected networks with significant clustering. The contagion is assumed to be general enough to account for a content-dependent linear threshold model, where each link type has a different weight (for spreading influence) that may depend on the content (e.g., product, rumor, political view) that is being spread. Using the generating functions formalism, we determine the conditions, probability, and expected size of the emergent global cascades. This analysis provides a generalization of previous approaches and is specially useful in problems related to spreading and percolation. The results present non trivial dependencies between the clustering coefficient of the networks and its average degree. In particular, several phase transitions are shown to occur depending on these descriptors. Generally speaking, our findings reveal that increasing clustering decreases the probability of having global cascades and their size, however this tendency changes with the average degree. There exists a certain average degree from which on clustering favours the probability and size of the contagion. By comparing the dynamics of complex contagions over multiplex networks and their monoplex projections, we demonstrate that ignoring link types and aggregating network layers may lead to inaccurate conclusions about contagion dynamics, particularly when the correlation of degrees between layers is high.

physics.soc-ph↗

arXiv2016

Evaluating the impact of interdisciplinary research: a multilayer network approach

Nowadays, scientific challenges usually require approaches that cross traditional boundaries between academic disciplines, driving many researchers towards interdisciplinarity. Despite its obvious importance, there is a lack of studies on how to quantify the influence of interdisciplinarity on the research impact, posing uncertainty in a proper evaluation for hiring and funding purposes. Here we propose a method based on the analysis of bipartite interconnected multilayer networks of citations and disciplines, to assess scholars, institutions and countries interdisciplinary importance. Using data about physics publications and US patents, we show that our method allows to reward, using a quantitative approach, scholars and institutions that have carried out interdisciplinary work and have had an impact in different scientific areas. The proposed method could be used by funding agencies, universities and scientific policy decision makers for hiring and funding purposes, and to complement existing methods to rank universities and countries.

physics.soc-ph↗

arXiv2016

On controlling networks of limit-cycle oscillators

The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications ranging from the power grid to cardiac excitation. Here we study the control of network-coupled limit cycle oscillators, extending previous work that focused on phase oscillators. Based on stabilizing a target fixed point, our method aims to attain complete frequency synchronization, i.e., consensus, by applying control to as few oscillators as possible. We develop two types of control. The first type directs oscillators towards to larger amplitudes, while the second does not. We present numerical examples of both control types and comment on the potential failures of the method.

nlin.AO↗