arXiv subjects

Angélica S. Mata

Publications and source records attributed to Angélica S. Mata.

13 recordsLinked to original sources

arXiv2021

From subcritical behavior to elusive transitions in rumor models

Rumor and information spreading are natural processes that emerge from human-to-human interaction. Mathematically, this was explored in the popular Maki-Thompson model, where a phase transition was thought to be absent. Here, we show that a second-order phase transition is present in this model which is not captured by first-order mean-field approximations. Moreover, we propose and explore a modified version of the Maki-Thompson model that includes a forgetting mechanism. This modification changes the Markov chain's nature from infinitely many absorbing states in the classical setup to a single absorbing state. In practice, this allows us to use a plethora of analytic and numeric methods that permit the models' characterization. In particular, we find a counter-intuitive behavior in the subcritical regime of these models, where the lifespan of a rumor increases as the spreading rate drops, following a power-law relationship. This means that, even below the critical threshold, rumors can survive for a long time. Together, our findings suggest that the dynamic behavior of rumor models can be much richer than previously thought. Thus, we hope that our results motivate further research both analytically and numerically.

physics.soc-ph↗

arXiv2020

An overview of epidemic models with phase transitions to absorbing states running on top of complex networks

Dynamical systems running on the top of complex networks has been extensively investigated for decades. But this topic still remains among the most relevant issues in complex network theory due to its range of applicability. The contact process (CP) and the susceptible-infected-susceptible (SIS) model are used quite often to describe epidemic dynamics. Despite their simplicity, these models are robust to predict the kernel of real situations. In this work, we review concisely both processes that are well-known and very applied examples of models that exhibit absorbing-state phase transitions. In the epidemic scenario, individuals can be infected or susceptible. A phase transition between a disease-free (absorbing) state and an active stationary phase (where a fraction of the population is infected) are separated by an epidemic threshold. For the SIS model, the central issue is to determine this epidemic threshold on heterogeneous networks. For the CP model, the main interest is to relate critical exponents with statistical properties of the network.

physics.soc-ph↗

arXiv2019

On the onset of synchronization of Kuramoto oscillators in scale-free networks

Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent $2 < γ\leq 3$, in line with what has been observed for other dynamical processes in such networks. For $γ> 3$, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators.

cond-mat.stat-mech↗

arXiv2018

Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks

We analyze two alterations of the standard susceptible-infected-susceptible (SIS) dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree. All models have the same epidemic thresholds in mean-field theories but depending on the network properties, simulations yield a dual scenario, in which the epidemic thresholds of the modified SIS models can be either dramatically altered or remain unchanged in comparison with the standard dynamics. For uncorrelated synthetic networks having a power-law degree distribution with exponent $γ<5/2$, the SIS dynamics are robust exhibiting essentially the same outcomes for all investigated models. A threshold in better agreement with the heterogeneous rather than quenched mean-field theory is observed in the modified dynamics for exponent $γ>5/2$. Differences are more remarkable for $γ>3$ where a finite threshold is found in the modified models in contrast with the vanishing threshold of the original one. This duality is elucidated in terms of epidemic lifespan on star graphs. We verify that the activation of the modified SIS models is triggered in the innermost component of the network given by a $k$-core decomposition for $γ<3$ while it happens only for $γ<5/2$ in the standard model. For $γ>3$, the activation in the modified dynamics is collective involving essentially the whole network while it is triggered by hubs in the standard SIS. The duality also appears in the finite-size scaling of the critical quantities where mean-field behaviors are observed for the modified, but not for the original dynamics. Our results feed the discussions about the most proper conceptions of epidemic models to describe real systems and the choices of the most suitable theoretical approaches to deal with these models.

physics.soc-ph↗

arXiv2016

Fractal Dimension and Universality in Avascular Tumor Growth

The comprehension of tumor growth is a intriguing subject for scientists. New researches has been constantly required to better understand the complexity of this phenomenon. In this paper, we pursue a physical description that account for some experimental facts involving avascular tumor growth. We have proposed an explanation of some phenomenological (macroscopic) aspects of tumor, as the spatial form and the way it growths, from a individual-level (microscopic) formulation. The model proposed here is based on a simple principle: competitive interaction between the cells dependent on their mutual distances. As a result, we reproduce many empirical evidences observed in real tumors, as exponential growth in their early stages followed by a power law growth. The model also reproduces the fractal space distribution of tumor cells and the universal behavior presented in animals and tumor growth, conform reported by West, Guiot {\it et. al.}\cite{West2001,Guiot2003}. The results suggest that the universal similarity between tumor and animal growth comes from the fact that both are described by the same growth equation - the Bertalanffy-Richards model - even they does not necessarily share the same biophysical properties.

physics.bio-ph↗

arXiv2015

The lifespan method as a tool to study criticality in absorbing-state phase transitions

In a recent work, a new numerical method (the lifespan method) has been introduced to study the critical properties of epidemic processes on complex networks [Phys. Rev. Lett. \textbf{111}, 068701 (2013)]. Here, we present a detailed analysis of the viability of this method for the study of the critical properties of generic absorbing-state phase transitions in lattices. Focusing on the well understood case of the contact process, we develop a finite-size scaling theory to measure the critical point and its associated critical exponents. We show the validity of the method by studying numerically the contact process on a one-dimensional lattice and comparing the findings of the lifespan method with the standard quasi-stationary method. We find that the lifespan method gives results that are perfectly compatible with those of quasi-stationary simulations and with analytical results. Our observations confirm that the lifespan method is a fully legitimate tool for the study of the critical properties of absorbing phase transitions in regular lattices.

cond-mat.stat-mech↗

arXiv2015

Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks

The epidemic threshold of the susceptible-infected-susceptible (SIS) dynamics on random networks having a power law degree distribution with exponent $γ>3$ has been investigated using different mean-field approaches, which predict different outcomes. We performed extensive simulations in the quasistationary state for a comparison with these mean-field theories. We observed concomitant multiple transitions in individual networks presenting large gaps in the degree distribution and the obtained multiple epidemic thresholds are well described by different mean-field theories. We observed that the transitions involving thresholds which vanishes at the thermodynamic limit involve localized states, in which a vanishing fraction of the network effectively contribute to epidemic activity, whereas an endemic state, with a finite density of infected vertices, occurs at a finite threshold. The multiple transitions are related to the activations of distinct sub-domains of the network, which are not directly connected.

physics.soc-ph↗

arXiv2014

Slow relaxation dynamics and aging in random walks on activity driven temporal networks

We investigate the dynamic relaxation of random walks on temporal networks by focusing in the recently proposed activity driven model [Perra \textit{et al.} Sci. Rep. srep00469 (2012)]. For realistic activity distributions with a power-law form, we observe the presence of a very slow relaxation dynamics compatible with aging effects. A theoretical description of this processes in achieved by means of a mapping to Bouchaud's trap model. The mapping highlights the profound difference in the dynamics of the random walks according to the value of the exponent $γ$ in the activity distribution.

cond-mat.stat-mech↗

arXiv2014

Heterogeneous pair-approximation for the contact process on complex networks

Recent works have shown that the contact process running on the top of highly heterogeneous random networks is described by the heterogeneous mean-field theory. However, some important aspects as the transition point and strong corrections to the finite-size scaling observed in simulations are not quantitatively reproduced in this theory. We develop a heterogeneous pair approximation, the simplest mean-field approach that takes into account dynamical correlations, for the contact process. The transition points obtained in this theory are in very good agreement with simulations. The proximity with a simple homogeneous pair-approximation is elicited showing that the transition point in successive homogeneous cluster approximations moves away from the simulation results. We show that the critical exponents of the heterogeneous pair-approximation in the infinite-size limit are the same as those of the one-vertex theory. However, excellent matches with simulations, for a wide range of network sizes, is obtained when sub-leading finite-size corrections given by the new theory are explicitly taken into account. The present approach can be suited to dynamical processes on networks in general providing a profitable strategy to analytically assess fine-tuning theoretical corrections.

cond-mat.stat-mech↗

arXiv2013

Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks

We investigate the effects of local population structure in reaction-diffusion processes representing a contact process (CP) on metapopulations represented as complex networks. Considering a model in which the nodes of a large scale network represent local populations defined in terms of a homogeneous graph, we show by means of extensive numerical simulations that the critical properties of the reaction-diffusion system are independent of the local population structure, even when this one is given by a ordered linear chain. This independence is confirmed by the perfect matching between numerical critical exponents and the results from a heterogeneous mean field theory suited, in principle, to describe situations of local homogeneous mixing. The analysis of several variations of the reaction-diffusion process allow to conclude the independence from population structure of the critical properties of CP-like models on metapopulations, and thus of the universality of the reaction-diffusion description of this kind of models.

physics.bio-ph↗

arXiv2013

Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks

We present a quenched mean-field (QMF) theory for the dynamics of the susceptible-infected-susceptible (SIS) epidemic model on complex networks where dynamical correlations between connected vertices are taken into account by means of a pair approximation. We present analytical expressions of the epidemic thresholds in the star and wheel graphs and in random regular networks. For random networks with a power law degree distribution, the thresholds are numerically determined via an eigenvalue problem. The pair and one-vertex QMF theories yield the same scaling for the thresholds as functions of the network size. However, comparisons with quasi-stationary simulations of the SIS dynamics on large networks show that the former is quantitatively much more accurate than the latter. Our results demonstrate the central role played by dynamical correlations on the epidemic spreading and introduce an efficient way to theoretically access the thresholds of very large networks that can be extended to dynamical processes in general.

physics.bio-ph↗

arXiv2011

Addendum to "Anomalous scaling and super-roughness in the growth of CdTe polycrystalline films"

The scaling of the growth of CdTe films on glass substrates was investigated by Mata \textit{et al.} [Phys. Rev. B \textbf{78}, 115305 (2008)]. Part of the analysis consisted of the estimation of the correlation length $ξ$ using the decay in the height-height correlation function. Afterwards, the dynamical exponent $z$ was determined using the scaling hypothesis $ξ\sim t^{1/z}$. In this Addendum, we show that the correlation lengths obtained by Mata \textit{et al.} provide a long wavelength coarsening exponent that does not correspond to the dynamical exponent $z$. We also show that the short wavelength coarsening exponent is consistent with the exponent $z$ obtained by Nascimento \textit{et al}. [arXiv:1101.1493] via generic dynamical scaling theory.

cond-mat.mtrl-sci↗

arXiv2011

Anomalous scaling and super-roughness in the growth of CdTe polycrystalline films

CdTe films grown on glass substrates covered by fluorine doped tin oxide by Hot Wall Epitaxy (HWE) were studied through the interface dynamical scaling theory. Direct measures of the dynamical exponent revealed an intrinsically anomalous scaling characterized by a global roughness exponent $α$ distinct from the local one (the Hurst exponent $H$), previously reported [Ferreira \textit{et al}., Appl. Phys. Lett. \textbf{88}, 244103 (2006)]. A variety of scaling behaviors was obtained with varying substrate temperature. In particular, a transition from a intrinsically anomalous scaling regime with $H\neα<1$ at low temperatures to a super-rough regime with $H\neα>1$ at high temperatures was observed. The temperature is a growth parameter that controls both the interface roughness and dynamical scaling exponents. Nonlocal effects are pointed as the factors ruling the anomalous scaling behavior.

cond-mat.stat-mech↗