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Researcher profile

Alex Arenas

Alex Arenas contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
physics.soc-phnlin.AOSocial and Information Networkscond-mat.stat-mechPopulations and EvolutionComputer Science and Game Theorycond-mat.dis-nnecon.GNMachine Learningmath.DSMethodologynlin.PSphysics.data-anq-fin.EC

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Published work

18 published item(s)

preprint2026arXiv

Decentralization can hinder frequency synchronization in power grids through multiple phase transitions

Decarbonization is rapidly increasing the penetration of inverter-based renewables and other low-capacity generators, intensifying concerns about frequency synchronization in increasingly decentralized power grids. A common heuristic from Kuramoto onset theory and homogeneous parameter swing-equation models is that distributing generation across many smaller units reduces the effective heterogeneity of nodal injections (natural frequencies) and lowers the coupling required for synchronization. Here, using a second-order Kuramoto model, we investigate how decentralization affects frequency synchronization when inertia and damping scale with power generation and consumption. We find that decentralization does not always lower the critical frequency synchronization threshold. Instead, increasing decentralization can induce a non-monotonic dependence of the critical coupling strength and lead to a double phase transition in frequency synchronization. These behaviors remain robust under asymmetric inertia between consumers and generators. Even when empirical power-generation and power-consumption distributions are considered, a region in which the critical threshold remains nearly constant is observed as decentralization increases. Our results demonstrate that decentralization can give rise to complex collective dynamics and caution against assuming that decentralization alone ensures improved frequency synchronization.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Emergent Self-Attention from Astrocyte-Gated Associative Memory Dynamics

We introduce a Hopfield-type associative memory in which effective connectivity is multiplicatively modulated by astrocytic gains evolving under an entropy-regularized replicator equation. The coupled neuron-astrocyte dynamics admit a Lyapunov function, ensuring global convergence. At fixed points, astrocytic gains implement a softmax-normalized allocation over pattern similarity scores, yielding a mechanistic realization of self-attention as emergent routing on the gain simplex. In regimes of high memory load and interference, the model significantly improves retrieval accuracy relative to classical Hopfield dynamics and recent neuron-astrocyte baselines. These results establish a dynamical systems framework linking glial modulation, competitive resource allocation, and attention-like computation.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Characterization of interactions' persistence in time-varying networks

Many complex networked systems exhibit volatile dynamic interactions among their vertices, whose order and persistence reverberate on the outcome of dynamical processes taking place on them. To quantify and characterize the similarity of the snapshots of a time-varying network -- a proxy for the persistence,-- we present a study on the persistence of the interactions based on a descriptor named \emph{temporality}. We use the average value of the temporality, $\overline{\mathcal{T}}$, to assess how ``\emph{special}'' is a given time-varying network within the configuration space of ordered sequences of snapshots. We analyze the temporality of several empirical networks and find that empirical sequences are much more similar than their randomized counterparts. We study also the effects on $\overline{\mathcal{T}}$ induced by the (time) resolution at which interactions take place.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks

The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence of infected individuals to an endemic state. Here, we study this transition, from the perspective of dynamical systems, for a discrete-time compartmental epidemic model known as Microscopic Markov Chain Approach, whose applicability for forecasting future scenarios of epidemic spreading has been proved very useful during the COVID-19 pandemic. We show that there is an endemic state which is stable and a global attractor and that its existence is a consequence of a transcritical bifurcation. This mathematical analysis grounds the results of the model in practical applications.

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preprint2022arXiv

Contagion-diffusion processes with recurrent mobility patterns of distinguishable agents

The analysis of contagion-diffusion processes in metapopulations is a powerful theoretical tool to study how mobility influences the spread of communicable diseases. Nevertheless, many metapopulation approaches use indistinguishable agents to alleviate analytical difficulties. Here, we address the impact that recurrent mobility patterns, and the spatial distribution of distinguishable agents, have on the unfolding of epidemics in large urban areas. We incorporate the distinguishable nature of agents regarding both, their residence, and their usual destination. The proposed model allows both a fast computation of the spatio-temporal pattern of the epidemic trajectory and. the analytical calculation of the epidemic threshold. This threshold is found as the spectral radius of a mixing matrix encapsulating the residential distribution, and the specific commuting patterns of agents. We prove that the simplification of indistinguishable individuals overestimates the value of the epidemic threshold.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Diffusion and synchronization dynamics reveal the multi-scale patterns of spatial segregation

Urban systems are characterized by populations with heterogeneous characteristics, and whose spatial distribution is crucial to understand inequalities in life expectancy or education level. Traditional studies on spatial segregation indicators focus often on first-neighbour correlations but fail to capture complex multi-scale patterns. In this work, we aim at characterizing the spatial distribution heterogeneity of socioeconomic features through diffusion and synchronization dynamics. In particular, we use the time needed to reach the synchronization as a proxy for the spatial heterogeneity of a socioeconomic feature, as for example, the income. Our analysis for 16~income categories in cities from the United States reveals that the spatial distribution of the most deprived and affluent citizens leads to higher diffusion and synchronization times. By measuring the time needed for a neighborhood to reach the global phase we are able to detect those that suffer from a steeper segregation. Overall, the present manuscript exemplifies how diffusion and synchronization dynamics can be used to assess the heterogeneity in the presence of node information.

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preprint2022arXiv

The resilience of the multirelational structure of geopolitical treaties is critically linked to past colonial world order and offshore fiscal havens

The governance of the political and economic world order builds on a complex architecture of international treaties at various geographical scales. In a historical phase of high institutional turbulence, assessing the stability of such architecture with respect to the unilateral defection of single countries and to the breakdown of single treaties is important. We carry out this analysis on the whole global architecture and find that the countries with the highest disruption potential are not major world powers (with the exception of Germany and France) but mostly medium-small and micro-countries. Political stability is highly dependent on many former colonial overseas territories that are today part of the global network of fiscal havens, as well as on emerging economies, mostly from South-East Asia. Economic stability depends on medium sized European and African countries. However, single global treaties have surprisingly less disruptive potential, with the major exception of the WTO. These apparently counter-intuitive results highlight the importance to a nonlinear approach to international relations where the complex multilayered architecture of global governance is analyzed using advanced network science techniques. Our results suggest that the potential fragility of the world order seem to be much more directly related to global inequality and fiscal injustice than it is commonly believed, and that the legacy of the colonial world order is still very strong in the current international relations scenario. In particular, vested interests related to tax avoidance seem to have a structural role in the political architecture of global governance

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

A message-passing approach to epidemic tracing and mitigation with apps

With the hit of new pandemic threats, scientific frameworks are needed to understand the unfolding of the epidemic. The use of mobile apps that are able to trace contacts is of utmost importance in order to control new infected cases and contain further propagation. Here we present a theoretical approach using both percolation and message--passing techniques, to the role of contact tracing, in mitigating an epidemic wave. We show how the increase of the app adoption level raises the value of the epidemic threshold, which is eventually maximized when high-degree nodes are preferentially targeted. Analytical results are compared with extensive Monte Carlo simulations showing good agreement for both homogeneous and heterogeneous networks. These results are important to quantify the level of adoption needed for contact-tracing apps to be effective in mitigating an epidemic.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Higher-order interactions improve optimal collective dynamics on networks

Collective behavior plays a key role in the function of a wide range of physical, biological, and neurological systems where empirical evidence has recently uncovered the prevalence of higher-order interactions, i.e., structures that represent interactions between more than just two individual units, in complex network structures. Here, we study the optimization of collective behavior in networks with higher-order interactions encoded in clique complexes. Our approach involves adapting the Synchrony Alignment Function framework to a new composite Laplacian matrix that encodes multi-order interactions including, e.g., both dyadic and triadic couplings. We show that as higher-order coupling interactions are equitably strengthened, so that overall coupling is conserved, the optimal collective behavior improves. We find that this phenomenon stems from the broadening of a composite Laplacian's eigenvalue spectrum, which improves the optimal collective behavior and widens the range of possible behaviors. Moreover, we find in constrained optimization scenarios that a nontrivial, ideal balance between the relative strengths of pair-wise and higher-order interactions leads to the strongest collective behavior supported by a network. This work provides insight into how systems balance interactions of different types to optimize or broaden their dynamical range of behavior, especially for self-regulating systems like the brain.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Interplay between intra-urban population density and mobility in determining the spread of epidemics

In this work, we address the connection between population density centers in urban areas, and the nature of human flows between such centers, in shaping the vulnerability to the onset of contagious diseases. A study of 163 cities, chosen from four different continents reveals a universal trend, whereby the risk induced by human mobility increases in those cities where mobility flows are predominantly between high population density centers. We apply our formalism to the spread of SARS-COV-2 in the United States, providing a plausible explanation for the observed heterogeneity in the spreading process across cities. Armed with this insight, we propose realistic mitigation strategies (less severe than lockdowns), based on modifying the mobility in cities. Our results suggest that an optimal control strategy involves an asymmetric policy that restricts flows entering the most vulnerable areas but allowing residents to continue their usual mobility patterns.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Symmetry-breaking mechanism for the formation of cluster chimera patterns

The emergence of order in collective dynamics is a fascinating phenomenon that characterizes many natural systems consisting of coupled entities. Synchronization is such an example where individuals, usually represented by either linear or nonlinear oscillators, can spontaneously act coherently with each other when the interactions' configuration fulfills certain conditions. However, synchronization is not always perfect, and the coexistence of coherent and incoherent oscillators, broadly known in the literature as chimera states, is also possible. Although several attempts have been made to explain how chimera states are created, their emergence, stability, and robustness remain a long-debated question. We propose an approach that aims to establish a robust mechanism through which chimeras originate. We first introduce a stability-breaking method where clusters of synchronized oscillators can emerge. Similarly, one or more clusters of oscillators may remain incoherent within yielding a particular class of patterns that we here name cluster chimera states.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Virus spread versus contact tracing: two competing contagion processes

After the blockade that many nations suffered to stop the growth of the incidence curve of COVID-19 during the first half of 2020, they face the challenge of resuming their social and economic activity. The rapid airborne transmissibility of SARS-CoV-2, and the absence of a vaccine, calls for active containment measures to avoid the propagation of transmission chains. The best strategy up to date, popularly known as Test-Track-Treat (TTT), consist in testing the population for diagnosis, track the contacts of those infected, and treat by quarantine all these cases. The dynamical process that better describes the combined action of the former mechanisms is that of a contagion process that competes with the spread of the pathogen, cutting off potential contagion pathways. Here we propose a compartmental model that couples the dynamics of the infection with the contact tracing and isolation of cases. We develop an analytical expression for the effective case reproduction number $R_c(t)$ that reveals the role of contact tracing in the mitigation and suppression of the epidemics. We show that there is a trade off between the infection propagation and the isolation of cases. If the isolation is limited to symptomatic individuals only, the incidence curve can be flattened but not bended. However, if contact tracing is applied to asymptomatic individuals too, the strategy can bend the curve and suppress the epidemics. Quantitative results are dependent on the network topology. We quantify, the most important indicator of the effectiveness of contact tracing, namely its capacity to reverse the increasing tendency of the epidemic curve, causing its bending.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Abrupt phase transition of epidemic spreading in simplicial complexes

Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading, using the Susceptible-Infected-Susceptible (SIS) model, in simplicial complexes. In particular, we analyze the dynamics of SIS in complex networks characterized by pairwise interactions (links), and three-body interactions (filled triangles, also known as 2-simplices). This higher-order description of the epidemic spreading is analytically formulated using a microscopic Markov chain approximation. The analysis of the fixed point solutions of the model, reveal an interesting phase transition that becomes abrupt with the infectivity parameter of the 2-simplices. Our results pave the way for network theorists to advance in our physical understanding of epidemic spreading in real scenarios where diseases are transmitted among groups as well as among pairs, and to better understand the behaviour of dynamical processes in simplicial complexes.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Evolution of Cooperation in the Presence of Higher-Order Interactions: from Networks to Hypergraphs

Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions going beyond pairwise models, such as graphs, in which all the interactions are considered as involving only two individuals at a time. Hypergraphs respond to this need, providing a mathematical representation of a system allowing from pairs to larger groups. In this work, through the use of different hypergraphs, we study how group interactions influence the evolution of cooperation in a structured population, by analyzing the evolutionary dynamics of the public goods game. Here we show that, likewise network reciprocity, group interactions also promote cooperation. More importantly, by means of an invasion analysis in which the conditions for a strategy to survive are studied, we show how, in heterogeneously-structured populations, reciprocity among players is expected to grow with the increasing of the order of the interactions. This is due to the heterogeneity of connections and, particularly, to the presence of individuals standing out as hubs in the population. Our analysis represents a first step towards the study of evolutionary dynamics through higher-order interactions, and gives insights into why cooperation in heterogeneous higher-order structures is enhanced. Lastly, it also gives clues about the co-existence of cooperative and non-cooperative behaviors related to the structural properties of the interaction patterns.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Pulsating-campaigns of human prophylaxis driven by risk perception palliate oscillations of direct contact transmitted diseases

Human behavioral responses play an important role in the impact of disease outbreaks and yet they are often overlooked in epidemiological models. Understanding to what extent behavioral changes determine the outcome of spreading epidemics is essential to design effective intervention policies. Here we explore, analytically, the interplay between the personal decision to protect oneself from infection and the spreading of an epidemic. We do so by coupling a decision game based on the perceived risk of infection with a Susceptible-Infected-Susceptible model. Interestingly, we find that the simple decision on whether to protect oneself is enough to modify the course of the epidemics, by generating sustained steady oscillations in the prevalence. We deem these oscillations detrimental, and propose two intervention policies aimed at modifying behavioral patterns to help alleviate them. Surprisingly, we find that pulsating campaigns, compared to continuous ones, are more effective in diminishing such oscillations.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

A Framework for the Construction of Generative Models for Mesoscale Structure in Multilayer Networks

Multilayer networks allow one to represent diverse and coupled connectivity patterns --- e.g., time-dependence, multiple subsystems, or both --- that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as dense sets of nodes known as communities, to discover network features that are not apparent at the microscale or the macroscale. The ill-defined nature of mesoscale structure and its ubiquity in empirical networks make it crucial to develop generative models that can produce the features that one encounters in empirical networks. Key purposes of such generative models include generating synthetic networks with empirical properties of interest, benchmarking mesoscale-detection methods and algorithms, and inferring structure in empirical multilayer networks. In this paper, we introduce a framework for the construction of generative models for mesoscale structures in multilayer networks. Our framework provides a standardized set of generative models, together with an associated set of principles from which they are derived, for studies of mesoscale structures in multilayer networks. It unifies and generalizes many existing models for mesoscale structures in fully-ordered (e.g., temporal) and unordered (e.g., multiplex) multilayer networks. One can also use it to construct generative models for mesoscale structures in partially-ordered multilayer networks (e.g., networks that are both temporal and multiplex). Our framework has the ability to produce many features of empirical multilayer networks, and it explicitly incorporates a user-specified dependency structure between layers.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Effect of shortest path multiplicity on congestion of multiplex networks

Shortest paths are representative of discrete geodesic distances in graphs, and many descriptors of networks depend on their counting. In multiplex networks, this counting is radically important to quantify the switch between layers and it has crucial implications in the transportation efficiency and congestion processes. Here we present a mathematical approach to the computation of the joint distribution of distance and multiplicity (degeneration) of shortest paths in multiplex networks, and exploit its relation to congestion processes. The results allow to approximate semi-analytically the onset of congestion in multiplex networks as a function of the congestion of its layers.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Impact of temporal scales and recurrent mobility patterns on the unfolding of epidemics

Human mobility plays a key role on the transformation of local disease outbreaks into global pandemics. Thus, the inclusion of human movements into epidemic models has become mandatory for understanding current epidemic episodes and to design efficient prevention policies. Following this challenge, here we develop a Markovian framework which enables to address the impact of recurrent mobility patterns on the epidemic onset at different temporal scales. This formalism is validated by comparing their predictions with results from mechanistic simulations. The fair agreement between both theory and simulations enables to get an analytical expression for the epidemic threshold which captures the critical conditions triggering epidemic outbreaks. Finally, by performing an exhaustive analysis of this epidemic threshold, we reveal that the impact of tuning human mobility on the emergence of diseases is strongly affected by the temporal scales associated to both epidemiological and mobility processes.

0 citations0 reviewsNo code linkedOpen access