arXiv subjects

R. F. S. Andrade

Publications and source records attributed to R. F. S. Andrade.

14 recordsLinked to original sources

arXiv2021

Estimating the effective reproduction number for heterogeneous models using incidence data

The effective reproduction number, R(t), is a central point in the study of infectious diseases. It establishes in an explicit way the extent of an epidemic spread process in a population. The current estimation methods for the time evolution of R(t), using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or already known distributions from the literature. However, there are systems, especially highly heterogeneous ones, in which there is a lack of data and an adequate methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining an explicit expression of the reproduction numbers and the generation interval distributions provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of Covid-19 in municipalities of the state of Rio de janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others. Our results point out the importance of mathematical modelling to provide epidemiological meaning of the available data.

q-bio.PE↗

arXiv2018

Discrete-time quantum walks generated by aperiodic fractal sequence of space coin operators

Properties of one dimensional discrete-time quantum walks are sensitive to the presence of inhomogeneities in the substrate, which can be generated by defining position dependent coin operators. Deterministic aperiodic sequences of two or more symbols provide ideal environments where these properties can be explored in a controlled way. This work discusses a two-coin model resulting from the construction rules that lead to the usual fractal Cantor set. Although the fraction of the less frequent coin $\rightarrow 0$ as the size of the chain is increased, it leaves peculiar properties in the walker dynamics. They are characterized by the wave function, from which results for the probability distribution and its variance, as well as the entanglement entropy were obtained. A number of results for different choices of the two coins are presented. The entanglement entropy has shown to be very sensitive to uncover subtle quantum effects present in the model.

quant-ph↗

arXiv2017

Exact evaluation of the causal spectrum and localization properties of electronic states on a scale-free network

A nearest-neighbor tight-binding model on a tree structure is investigated. The full energy spectrum of the normalized Hamiltonian can be expressed in terms of successively increasing number of contributions at any finite step of construction of the tree, resulting in a causal chain. The degree of quantum localization of any eigenstate, measured by the inverse participation ratio (IPR), is also analytically expressed by means of terms in corresponding eigenvalue chain. The resulting IPR scaling behavior is expressed by the tails of eigenvalue chains as well.

cond-mat.stat-mech↗

arXiv2017

The influence of statistical properties of Fourier coefficients on random surfaces

Many examples of natural systems can be described by random Gaussian surfaces. Much can be learned by analyzing the Fourier expansion of the surfaces, from which it is possible to determine the corresponding Hurst exponent and consequently establish the presence of scale invariance. We show that this symmetry is not affected by the distribution of the modulus of the Fourier coefficients. Furthermore, we investigate the role of the Fourier phases of random surfaces. In particular, we show how the surface is affected by a non-uniform distribution of phases.

cond-mat.stat-mech↗

arXiv2016

How the site degree influences quantum probability on inhomogeneous substrates

We investigate the effect of the node degree and energy $E$ on the electronic wave function for regular and irregular structures, namely, regular lattices, disordered percolation clusters, and complex networks. We evaluate the dependence of the quantum probability for each site on its degree. For bi-regular structures, we prove analytically that the probability $P_k(E)$ of finding the particle on any site with $k$ neighbors is independent of $E$. For more general structures, the dependency of $P_k(E)$ on $E$ is discussed by taking into account exact results on a one-dimensional semi-regular chain: $P_k(E)$ is large for small values of $E$ when $k$ is also small, and its maximum values shift towards large values of $|E|$ with increasing $k$. Numerical evaluations of $P_k(E)$ for two different types of percolation clusters and the Apollonian network suggest that this feature might be generally valid

cond-mat.stat-mech↗

arXiv2014

Height distribution of equipotential lines in a region confined by a rough conducting boundary

This work considers the behavior of the height distributions of the equipotential lines in a region confined by two interfaces: a cathode with an irregular interface and a distant flat anode. Both boundaries, which are maintained at distinct and constant potential values, are assumed to be conductors. The morphology of the cathode interface results from the deposit of $2 \times 10^{4}$ monolayers that are produced using a single competitive growth model based on the rules of the Restricted Solid on Solid and Ballistic Deposition models, both of which belong to the Kadar-Parisi-Zhang (KPZ) universality class. At each time step, these rules are selected with probability $p$ and $q = 1 - p$. For several irregular profiles that depend on $p$, a family of equipotential lines is evaluated. The lines are characterized by the skewness and kurtosis of the height distribution. The results indicate that the skewness of the equipotential line increases when they approach the flat anode, and this increase has a non-trivial convergence to a delta distribution that characterizes the equipotential line in a uniform electric field. The morphology of the equipotential lines is discussed; the discussion emphasizes their features for different ranges of $p$ that correspond to positive, null and negative values of the coefficient of the non-linear term in the KPZ equation.

physics.comp-ph↗

arXiv2014

Mandala Networks: ultra-robust, ultra-small-world and highly sparse graphs

The increasing demands in security and reliability of infrastructures call for the optimal design of their embedded complex networks topologies. The following question then arises: what is the optimal layout to fulfill best all the demands? Here we present a general solution for this problem with scale-free networks, like the Internet and airline networks. Precisely, we disclose a way to systematically construct networks which are 100$\%$ robust against random failures as well as to malicious attacks. Furthermore, as the sizes of these networks increase, their shortest paths become asymptotically invariant and densities of links go to zero, making them ultra-small worlds and highly sparse, respectively. The first property is ideal for communication and navigation purposes, while the second is interesting economically.

physics.soc-ph↗

arXiv2013

Exact evaluation of the cutting path length in a percolation model on a hierarchical network

This work presents an approach to evaluate the exact value of the fractal dimension of the cutting path $d^{CP}_f$ on hierarchical structures with finite order of ramification. This represents the first renormalization group treatment of the universality class of watersheds. By making use of the self-similar property, we show that $d^{CP}_f$ depends only on the average cutting path (CP) of the first generation of the structure. For the simplest Wheastone hierarchical lattice (WHL), we present a mathematical proof. For a larger WHL structure, the exact value of $d^{CP}_f$ is derived based on an computer algorithm that identifies the length of all possible CP's of the first generation.

cond-mat.stat-mech↗

arXiv2008

Ising model on the Apollonian network with node dependent interactions

This work considers an Ising model on the Apollonian network, where the exchange constant $J_{i,j}\sim1/(k_ik_j)^μ$ between two neighboring spins $(i,j)$ is a function of the degree $k$ of both spins. Using the exact geometrical construction rule for the network, the thermodynamical and magnetic properties are evaluated by iterating a system of discrete maps that allows for very precise results in the thermodynamic limit. The results can be compared to the predictions of a general framework for spins models on scale-free networks, where the node distribution $P(k)\sim k^{-γ}$, with node dependent interacting constants. We observe that, by increasing $μ$, the critical behavior of the model changes, from a phase transition at $T=\infty$ for a uniform system $(μ=0)$, to a T=0 phase transition when $μ=1$: in the thermodynamic limit, the system shows no exactly critical behavior at a finite temperature. The magnetization and magnetic susceptibility are found to present non-critical scaling properties.

cond-mat.stat-mech↗

arXiv2008

Periodic forcing in a three level cellular automata model for a vector transmitted disease

The transmission of vector infectious diseases, which produces complex spatiotemporal patterns, is analyzed by a periodically forced two-dimensional cellular automata model. The system, which comprises three population levels, is introduced to describe complex features of the dynamics of the vector transmitted dengue epidemics, known to be very sensitive to seasonal variables. The three coupled levels represent the human, the adult and immature vector populations. The dynamics includes external seasonality forcing (rainfall intensity data), human and mosquito mobility, and vector control effects. The model parameters, even if bounded to well defined intervals obtained from reported data, can be selected to reproduce specific epidemic outbursts. In the current study, explicit results are obtained by comparison with actual data retrieved from the time-series of dengue epidemics in two cities in Brazil. The results show fluctuations that are not captured by mean-field models. It also reveals the qualitative behavior of the spatiotemporal patterns of the epidemics. In the extreme situation of absence of external periodic drive, the model predicts completely distinct long time evolution. The model is robust in the sense that it is able to reproduce the time series of dengue epidemics of different cities, provided the forcing term takes into account the local rainfall modulation. Finally, the dependence between epidemics threshold and vector control undergoes a transition from power law to stretched exponential behavior due to human mobility effect.

nlin.CG↗

arXiv2005

Neighborhood properties of complex networks

A concept of neighborhood in complex networks is addressed based on the criterion of the minimal number os steps to reach other vertices. This amounts to, starting from a given network $R_1$, generating a family of networks $R_\ell, \ell=2,3,...$ such that, the vertices that are $\ell$ steps apart in the original $R_1$, are only 1 step apart in $R_\ell$. The higher order networks are generated using Boolean operations among the adjacency matrices $M_\ell$ that represent $R_\ell$. The families originated by the well known linear and the Erdös-Renyi networks are found to be invariant, in the sense that the spectra of $M_\ell$ are the same, up to finite size effects. A further family originated from small world network is identified.

physics.data-an↗

arXiv2005

The network of concepts in written texts

Complex network theory is used to investigate the structure of meaningful concepts in written texts of individual authors. Networks have been constructed after a two phase filtering, where words with less meaning contents are eliminated, and all remaining words are set to their canonical form, without any number, gender or time flexion. Each sentence in the text is added to the network as a clique. A large number of written texts have been scrutinized, and its found that texts have small-world as well as scale-free structures. The growth process of these networks has also been investigated, and a universal evolution of network quantifiers have been found among the set of texts written by distinct authors. Further analyzes, based on shufling procedures taken either on the texts or on the constructed networks, provide hints on the role played by the word frequency and sentence length distributions to the network structure. Since the meaningful words are related to concepts in the author's mind, results for text networks may uncover patterns in communication and language processes that occur in the mind.

physics.data-an↗

arXiv2003

Critical properties of an aperiodic model for interacting polymers

We investigate the effects of aperiodic interactions on the critical behavior of an interacting two-polymer model on hierarchical lattices (equivalent to the Migadal-Kadanoff approximation for the model on Bravais lattices), via renormalization-group and tranfer-matrix calculations. The exact renormalization-group recursion relations always present a symmetric fixed point, associated with the critical behavior of the underlying uniform model. If the aperiodic interactions, defined by s ubstitution rules, lead to relevant geometric fluctuations, this fixed point becomes fully unstable, giving rise to novel attractors of different nature. We present an explicit example in which this new attractor is a two-cycle, with critical indices different from the uniform model. In case of the four-letter Rudin-Shapiro substitution rule, we find a surprising closed curve whose points are attractors of period two, associated with a marginal operator. Nevertheless, a scaling analysis indicates that this attractor may lead to a new critical universality class. In order to provide an independent confirmation of the scaling results, we turn to a direct thermodynamic calculation of the specific-heat exponent. The thermodynamic free energy is obtained from a transfer matrix formalism, which had been previously introduced for spin systems, and is now extended to the two-polymer model with aperiodic interactions.

cond-mat.stat-mech↗

arXiv2000

Multifractal Properties of Aperiodic Ising Model: role of geometric fluctuations

The role of the geometric fluctuations on the multifractal properties of the local magnetization of aperiodic ferromagnetic Ising models on hierachical lattices is investigated. The geometric fluctuations are introduced by generalized Fibonacci sequences. The local magnetization is evaluated via an exact recurrent procedure encompassing a real space renormalization group decimation. The symmetries of the local magnetization patterns induced by the aperiodic couplings is found to be strongly (weakly) different, with respect to the ones of the corresponding homogeneous systems, when the geometric fluctuations are relevant (irrelevant) to change the critical properties of the system. At the criticality, the measure defined by the local magnetization is found to exhibit a non-trivial F(alpha) spectra being shifted to higher values of alpha when relevant geometric fluctuations are considered. The critical exponents are found to be related with some special points of the F(alpha) function and agree with previous results obtained by the quite distinct transfer matrix approach.

cond-mat.dis-nn↗