José Fernando Mendes

University of Aveiro | UA · Department of Physics

The nonbacktracking matrix and the related nonbacktracking centrality (NBC) play a crucial role in models of percolation-type processes on networks, such as nonrecurrent epidemics. Here we study the localization of NBC in infinite sparse networks that contain an arbitrary finite subgraph. Assuming the local tree likeness of the enclosing network, a...

We study a model of nonidentical swarmalators, generalizations of phase oscillators that both sync in time and swarm in space. The model produces four collective states: asynchrony, sync clusters, vortexlike phase waves, and a mixed state. These states occur in many real-world swarmalator systems such as biological microswimmers, chemical nanomotor...

We solve the weak percolation problem for multiplex networks with overlapping edges. In weak percolation, a vertex belongs to a connected component if at least one of its neighbors in each of the layers is in this component. This is a weaker condition than for a mutually connected component in interdependent networks, in which any two vertices must...

We study how available data on COVID-19 cases and deaths in different countries are reliable. Our analysis is based on a modification of the law of anomalous numbers, the Newcomb-Benford law, applied to the daily number of deaths and new cases in each country. We first revisit the Newcomb-Benford law and show how to avoid false negative compliance...

The nonbacktracking matrix, and the related nonbacktracking centrality (NBC) play a crucial role in models of percolation-type processes on networks, such as non-recurrent epidemics. Here we study the localization of NBC in infinite sparse networks that contain an arbitrary finite subgraph. Assuming the local tree-likeness of the enclosing network,...

We solve the weak percolation problem for multiplex networks with overlapping edges. In weak percolation, a vertex belongs to a connected component if at least one of its neighbors in each of the layers is in this component. This is a weaker condition than for a mutually connected component in interdependent networks, in which any two vertices must...

We study a one-dimensional (1D) model of non-identical swarmalators, generalizations of phase oscillators that both sync in time and swarm in space. The model produces three collective states: asynchrony, sync clusters, and vortex-like phase-waves. These states occur in many real-world swarmalator systems such as biological microswimmers, chemical...

Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem. This anomalous transition occurs in networks of three or more layers without unconnected nodes, $$P(0)\,=\,0$$ P...

We report strong evidence of the importance of contact hubs (or superspreaders) in mitigating the current COVID-19 pandemic. Contact hubs have a much larger number of contacts than the average in the population, and play a key role on the effectiveness of vaccination strategies. By using an age-structures compartmental SEIAHRV (Susceptible, Exposed...

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially generalised to multiple layers. This Element describes a generalisation of percolation to multilayer networks: weak mult...

Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem. This anomalous transition occurs in networks of three or more layers without unconnected nodes, $P(0)=0$. Above a...

We present an analysis of the relationship between SARS-CoV-2 infection rates and a social distancing metric from data for all the states and most populous cities in the United States and Brazil, all the 22 European Economic Community countries and the United Kingdom. We discuss why the infection rate, instead of the effective reproduction number o...

Message-passing theories have proved to be invaluable tools in studying percolation, nonrecurrent epidemics, and similar dynamical processes on real-world networks. At the heart of the message-passing method is the nonbacktracking matrix, whose largest eigenvalue, the corresponding eigenvector, and the closely related nonbacktracking centrality pla...

Quantifying dissimilarities between networks is a fundamental and challenging problem in network science. Current metrics for network comparison either assume the homogeneous distribution of nodal degrees or ignore the community structure of the network. Here we propose an efficient measure for comparing heterogeneous networks with communities from...

The function and performance of neural networks are largely determined by the evolution of their weights and biases in the process of training, starting from the initial configuration of these parameters to one of the local minima of the loss function. We perform the quantitative statistical characterization of the deviation of the weights of two-h...

We present a detailed analysis of the relationship between the infection rate by SARS-CoV-2 and a distancing index based on COVID-19 Community Mobility Report by Google, for all states in the United States and Brazil, its most populous counties and municipalities, respectively, and all the 22 European Economic Community countries and the United Kin...

We studied the impact of field heterogeneity on entrainment in a system of uniformly interacting phase oscillators. Field heterogeneity is shown to induce dynamical heterogeneity in the system. In effect, the heterogeneous field partitions the system into interacting groups of oscillators that feel the same local field strength and phase. Based on...

We introduce a compartmental model SEIAHRV (Susceptible, Exposed, Infected, Asymptomatic, Hospitalized, Recovered, Vaccinated) with age structure for the spread of the SARAS-CoV virus. In order to model current different vaccines we use compartments for individuals vaccinated with one and two doses without vaccine failure and a compartment for vacc...

We introduce a compartmental model with age structure to study the dynamics of the SARS-COV−2 pandemic. The contagion matrix in the model is given by the product of a probability per contact with a contact matrix explicitly taking into account the contact structure among different age groups. The probability of contagion per contact is considered a...

We introduce a compartmental model with age structure to study the dynamics of the SARS-COV-2 pandemic. The contagion matrix in the model is given by the product of a probability per contact with a contact matrix explicitly taking into account the contact structure among different age groups. The probability of contagion per contact is considered a...

Example of the script [used in Physica A 360, 548 (2006)] to get the number frequency from 1980 to 2019, making use of the lynx text-based web browser.

Frequency of Occurrence of Numbers in the World Wide Web -- Poster presented in Sigmaphi'05 (Kolymbari, Greece) conference (http://www.sigmaphi.polito.it/2005/Abstract1PDF/Abstract_Oliveira.pdf).

Identifying communities in networks is a fundamental and challenging problem of practical importance in many fields of science. Current methods either ignore the heterogeneous distribution of nodal degrees or assume prior knowledge of the number of communities. Here we propose an efficient hypothesis test for community detection based on quantifyin...

We studied the impact of field heterogeneity on entrainment in a system of uniformly interacting phase oscillators. Field heterogeneity is shown to induce dynamical heterogeneity in the system. In effect, the heterogeneous field partitions the system into interacting groups of oscillators that feel the same local field strength and phase. Based on...

A complete bifurcation analysis of explicit dynamical equations for the periodically forced Kuramoto model was performed in [L. M. Childs and S. H. Strogatz. Chaos 18, 043128 (2008)], identifying all bifurcations within the model. We show that the phase diagram predicted by this analysis is incomplete. Our numerical analysis of the equations reveal...

Message-passing theories have proved to be invaluable tools in studying percolation, non-recurrent epidemics and similar dynamical processes on real-world networks. At the heart of the message-passing method is the nonbacktracking matrix whose largest eigenvalue, the corresponding eigenvector and the closely related nonbacktracking centrality play...

Dependency links in single-layer networks offer a convenient way of modeling nonlocal percolation effects in networked systems where certain pairs of nodes are only able to function together. We study the percolation properties of the weak variant of this model: Nodes with dependency neighbors may continue to function if at least one of their depen...

Coronavirus disease 2019 (COVID-19) pandemic, a virus infection caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus, has impacted all countries of the world, and the main 2021’s challenge is clearly vaccinating the greater number of persons, in the shortest time span, for a maximal reduction in the number of deaths and...

A complete bifurcation analysis of explicit dynamical equations for the periodically forced Kuramoto model was performed in [L. M. Childs and S. H. Strogatz. Chaos 18, 043128 (2008)], identifying all bifurcations within the model. However, our numerical analysis of the equations reveals that the model can undergo an abrupt phase transition from osc...

The function and performance of neural networks is largely determined by the evolution of their weights and biases in the process of training, starting from the initial configuration of these parameters to one of the local minima of the loss function. We perform the quantitative statistical characterization of the deviation of the weights of two-hi...

Dependency links in single-layer networks offer a convenient way of modeling nonlocal percolation effects in networked systems where certain pairs of nodes are only able to function together. We study the percolation properties of the weak variant of this model: nodes with dependency neighbours may continue to function if at least one of their depe...

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially generalised to multiple layers. We describe a generalisation of percolation to multilayer networks: weak multiplex perco...

Compression, filtering, and cryptography, as well as the sampling of complex systems, can be seen as processing information. A large initial configuration or input space is nontrivially mapped to a smaller set of output or final states. We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tr...

The structure of an evolving network contains information about its past. Extracting this information efficiently, however, is, in general, a difficult challenge. We formulate a fast and efficient method to estimate the most likely history of growing trees, based on exact results on root finding. We show that our linear-time algorithm produces the...

We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is not the case for the more commonly studied generalization of percolation to multiplex networks, the mutually con...

We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter...

We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is not the case for the more commonly studied generalization of percolation to multiplex networks, the mutually con...

In filtering, each output is produced by a certain number of different inputs. We explore the statistics of this degeneracy in an explicitly treatable filtering problem in which filtering performs the maximal compression of relevant information contained in inputs (arrays of zeros and ones). This problem serves as a reference model for the statisti...

The structure of an evolving network contains information about its past. Extracting this information efficiently, however, is, in general, a difficult challenge. We formulate a fast and efficient method to estimate the most likely history of growing trees, based on exact results on root finding. We show that our algorithm produces the exact stepwi...

Many social, technological, and biological systems with asymmetric interactions display a variety of collective phenomena, such as opinion formation and synchronization. This has motivated much research on the dynamical impact of local and mesoscopic structure in directed networks. However, the unique constraints imposed by the global organization...

In filtering, each output is produced by a certain number of different inputs. We explore the statistics of this degeneracy in an explicitly treatable filtering problem in which filtering performs the maximal compression of relevant information contained in inputs. The filter patterns in this problem conveniently allow a microscopic, combinatorial...

The giant mutually connected component (GMCC) of an interdependent or multiplex network collapses with a discontinuous hybrid transition under random damage to the network. If the nodes to be damaged are selected in a targeted way, the collapse of the GMCC may occur significantly sooner. Finding the minimal damage set which destroys the largest mut...

We explore structural stability of weighted and unweighted networks of positively interacting agents against a negative external field. We study how the agents support the activity of each other to confront the negative field, which suppresses the activity of agents and can lead to a collapse of the whole network. The competition between the intera...

The spermatozoon is a specialized cell virtually incapable of genetic expression. Any functional alteration in these cells depends on processes such as protein post-translational modifications (e.g. phosphorylation) and mechanisms based on the disruption/formation of protein complexes. Phosphoprotein phosphatase 1 catalytic subunit gamma 2 (PPP1CC2...

Three-dimensional shells can be synthesized from the spontaneous self-folding of two-dimensional templates of interconnected panels, called nets. The yield is maximized following sequentially two design rules: (i) maximum number of vertices with a single-edge cut and (ii) minimum radius of gyration of the net. Previous methods to identify the optim...

We study complex networks formed by triangulations and higher-dimensional simplicial complexes of closed evolving manifolds. In particular, for triangulations, the set of possible transformations of these networks is restricted by the condition that at each step, all the faces must be triangles. We show that each of these transformations can be per...

We study the sensitivity of directed complex networks to the addition and pruning of edges and vertices and introduce the susceptibility, which quantifies this sensitivity. We show that topologically different parts of a directed network have different sensitivity to the addition and pruning of edges and vertices and, therefore, they are characteri...

Message passing equations yield a sharp percolation transition in finite graphs, as an artefact of the locally treelike approximation. For an arbitrary finite, connected, undirected graph we construct an infinite tree having the same local structural properties as this finite graph, when observed by a non-backtracking walker. Formally excluding the...

Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each layer having its own kind of edges, represented by different colors. An important fundamental structural feature o...

In multiplex networks, cycles cannot be characterized only by their length, as edges may occur in different layers in different combinations. We define a classification of cycles by the number of edges in each layer and the number of switches between layers. We calculate the expected number of cycles of each type in the configuration model of a lar...

A majority of studied models for scale-free networks have degree distributions with exponents greater than two. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free equilibrium networks that have the degree distribution exponent γ=1, P(q)∼q-γ. Such degree distributions can b...

We reveal a hierarchical organization of finite directed components---tendrils---around the giant components represented by the celebrated "bow-tie" diagram for directed networks. We develop an efficient algorithm to find tendril layers. It is used together with the message passing technique, generalized to directed graphs, to find the structure an...

We describe the phenomenon of localization in the epidemic SIS model on highly heterogeneous networks in which strongly connected nodes (hubs) play the role of centers of localization. We find that in this model the localized states below the epidemic threshold are metastable. The longevity and scale of the metastable outbreaks do not show a sharp...

We study the impact of random pinning fields on the emergence of synchrony in the Kuramoto model on complete graphs and uncorrelated random complex networks. We consider random fields with uniformly distributed directions and homogeneous and heterogeneous (Gaussian) field magnitude distribution. In our analysis we apply the Ott-Antonsen method and...

A majority of studied models for scale-free networks have degree distributions with exponents greater than $2$. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free equilibrium networks that have the degree distribution exponent $\gamma = 1$, $P(q) \sim q^{-\gamma}$. Such "s...

Studying abroad has become very popular among students. The ERASMUS mobility program is one of the largest international student exchange programs in the world, which has supported already more than three million participants since 1987. We analyzed the mobility pattern within this program in 2011-12 and found a gender gap across countries and subj...

ERASMUS data. Data set of ERASMUS participants. (ZIP)

We develop the theory of sparse multiplex networks with partially overlapping links based on their local tree-likeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary correlations between connections of different types. We find that correlations between the overlapping and non-o...

Currently the ranking of scientists is based on the $h$-index, which is widely perceived as an imprecise and simplistic though still useful metric. We find that the $h$-index actually favours modestly performing researchers and propose a simple criterion for proper ranking.

We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure, and solve them numerically and, in the critical regime of the process, analytically. We show that the pruning proces...

In the usual Achlioptas processes the smallest clusters of a few randomly chosen are selected for merging together at each step. The resulting aggregation process leads to the delayed birth of a giant cluster and the so-called explosive percolation transition showing a set anomalous features. We explore a process with the opposite selection rule, i...

Background Amyloid precursor protein (APP) is widely recognized for playing a central role in Alzheimer's disease pathogenesis. Although APP is expressed in several tissues outside the human central nervous system, the functions of APP and its family members in other tissues are still poorly understood. APP is involved in several biological functio...

We describe the emergence of the giant mutually connected component in networks of networks in which each node has a single replica node in any layer and can be interdependent only on its replica nodes in the interdependent layers. We prove that if in these networks, all the nodes of one network (layer) are interdependent on the nodes of the same o...

We describe the effect of power-law initial distributions of clusters on ordinary percolation and its generalizations, specifically, models of explosive percolation processes based on local optimization. These aggregation processes were shown to exhibit continuous phase transitions if the evolution starts from a set of disconnected nodes. Since the...