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Infections diseases are marked by recovering time distributions which can be far from the exponential one associated with Markovian/Poisson processes, broadly applied in epidemic compartmental models. In the present work, we tackled this problem by investigating a susceptible-infected-recovered-susceptible model on networks with $\eta$ independent infectious compartments (SI$_{\eta}$RS), each one with a Markovian dynamics, that leads to a Gamma-distributed recovering times. We analytically develop a theory for the epidemic lifespan on star graphs with a center and $K$ leaves showing that the epidemic lifespan scales with a non-universal power-law $\tau_{K}\sim K^{\alpha/\mu\eta}$ plus logarithm corrections, where $\alpha^{-1}$ and $\mu^{-1}$ are the mean waning immunity and recovering times, respectively. Compared with standard SIRS dynamics with $\eta=1$ and the same mean recovering time, the epidemic lifespan on star graphs is severely reduced as the number of stages increases. In particular, the case $\eta\rightarrow\infty$ leads to a finite lifespan. Numerical simulations support the approximated analytical calculations. For the SIS dynamics, numerical simulations show that the lifespan increases exponentially with the number of leaves, with a nonuniversal rate that decays with the number of infectious compartments. We investigated the SI$_{\eta}$RS dynamics on power-law networks with degree distribution $P(K)\sim k^{-\gamma}$. When $\gamma<5/2$, the epidemic spreading is ruled by a maximum $k$-core activation, the alteration of the hub activity time does not alter either the epidemic threshold or the localization pattern. For $\gamma>3$, where hub mutual activation is at work, the localization is reduced but not sufficiently to alter the threshold scaling with the network size. Therefore, the activation mechanisms remain the same as in the case of Markovian healing., Comment: 12 pages, 8 figures

Soccer attracts the attention of many researchers and professionals in the sports industry. Therefore, the incorporation of science into the sport is constantly growing, with increasing investments in performance analysis and sports prediction industries. This study aims to (i) highlight the use of complex networks as an alternative tool for predicting soccer match outcomes, and (ii) show how the combination of structural analysis of passing networks with match statistical data can provide deeper insights into the game patterns and strategies used by teams. In order to do so, complex network metrics and match statistics were used to build machine learning models that predict the wins and losses of soccer teams in different leagues. The results showed that models based on passing networks were as effective as ``traditional'' models, which use general match statistics. Another finding was that by combining both approaches, more accurate models were obtained than when they were used separately, demonstrating that the fusion of such approaches can offer a deeper understanding of game patterns, allowing the comprehension of tactics employed by teams relationships between players, their positions, and interactions during matches. It is worth mentioning that both network metrics and match statistics were important and impactful for the mixed model. Furthermore, the use of networks with a lower granularity of temporal evolution (such as creating a network for each half of the match) performed better than a single network for the entire game., Comment: To appear in Journal of Complex Networks

This paper presents an approach to enhancing Augmentative and Alternative Communication (AAC) systems by integrating Colourful Semantics (CS) with transformer-based language models specifically tailored for Brazilian Portuguese. We introduce an adapted BERT model, BERTptCS, which incorporates the CS framework for improved prediction of communication cards. The primary aim is to enhance the accuracy and contextual relevance of communication card predictions, which are essential in AAC systems for individuals with complex communication needs (CCN). We compared BERTptCS with a baseline model, BERTptAAC, which lacks CS integration. Our results demonstrate that BERTptCS significantly outperforms BERTptAAC in various metrics, including top-k accuracy, Mean Reciprocal Rank (MRR), and Entropy@K. Integrating CS into the language model improves prediction accuracy and offers a more intuitive and contextual understanding of user inputs, facilitating more effective communication.

Supervised machine learning models and public surveillance data has been employed for infectious disease forecasting in many settings. These models leverage various data sources capturing drivers of disease spread, such as climate conditions or human behavior. However, few models have incorporated the organizational structure of different geographic locations for forecasting. Traveling waves of seasonal outbreaks have been reported for dengue, influenza, and other infectious diseases, and many of the drivers of infectious disease dynamics may be shared across different cities, either due to their geographic or socioeconomic proximity. In this study, we developed a machine learning model to predict case counts of four infectious diseases across Brazilian cities one week ahead by incorporating information from related cities. We compared selecting related cities using both geographic distance and GDP per capita. Incorporating information from geographically proximate cities improved predictive performance for two of the four diseases, specifically COVID-19 and Zika. We also discuss the impact on forecasts in the presence of anomalous contagion patterns and the limitations of the proposed methodology.

Discrete- and continuous-time approaches are frequently used to model the role of heterogeneity on dynamical interacting agents on the top of complex networks. While, on the one hand, one does not expect drastic differences between these approaches, and the choice is usually based on one's expertise or methodological convenience, on the other hand, a detailed analysis of the differences is necessary to guide the proper choice of one or another approach. We tackle this problem, by comparing both discrete- and continuous-time mean-field theories for the susceptible-infected-susceptible (SIS) epidemic model on random networks with power-law degree distributions. We compare the discrete epidemic link equations (ELE) and continuous pair quenched mean-field (PQMF) theories with the corresponding stochastic simulations, both theories that reckon pairwise interactions explicitly. We show that ELE converges to PQMF theory when the time step goes to zero. The epidemic localization analysis performed reckoning the inverse participation ratio (IPR) indicates that both theories present the same localization depence on the network degree exponent $\gamma$: for $\gamma<5/2$ the epidemic is localized on the maximum k-core of network with a vanishing in the infinite-size limit while for $\gamma>5/2$, the localization happens on hubs what leads to a finite value of IPR. However, the IPR and epidemic threshold of ELE depend on the time-step discretization such that a larger time-step leads to more localized epidemics. A remarkable difference between discrete and continuous time approaches is revealed in the epidemic prevalence near the epidemic threshold, in which the discrete-time stochastic simulations indicate a mean-field critical exponent $\theta=1$ instead of the value $\theta=1/(3-\gamma)$ obtained rigorously and verified numerically for the continuous-time SIS on the same networks., Comment: 9 pages, 4 figures

The power-law distribution plays a crucial role in complex networks as well as various applied sciences. Investigating whether the degree distribution of a network follows a power-law distribution is an important concern. The commonly used inferential methods for estimating the model parameters often yield biased estimates, which can lead to the rejection of the hypothesis that a model conforms to a power-law. In this paper, we discuss improved methods that utilize Bayesian inference to obtain accurate estimates and precise credibility intervals. The inferential methods are derived for both continuous and discrete distributions. These methods reveal that objective Bayesian approaches return nearly unbiased estimates for the parameters of both models. Notably, in the continuous case, we identify an explicit posterior distribution. This work enhances the power of goodness-of-fit tests, enabling us to accurately discern whether a network or any other dataset adheres to a power-law distribution. We apply the proposed approach to fit degree distributions for more than 5,000 synthetic networks and over 3,000 real networks. The results indicate that our method is more suitable in practice, as it yields a frequency of acceptance close to the specified nominal level., Comment: 28 pages, 9 figures

Machine learning is a rapidly growing field with the potential to revolutionize many areas of science, including physics. This review provides a brief overview of machine learning in physics, covering the main concepts of supervised, unsupervised, and reinforcement learning, as well as more specialized topics such as causal inference, symbolic regression, and deep learning. We present some of the principal applications of machine learning in physics and discuss the associated challenges and perspectives., Comment: 8 pages, 1 figure. Europhysics Letters (EPL), 2023

In this article, we consider machine learning algorithms to accurately predict two variables associated with the $Q$-voter model in complex networks, i.e., (i) the consensus time and (ii) the frequency of opinion changes. Leveraging nine topological measures of the underlying networks, we verify that the clustering coefficient (C) and information centrality (IC) emerge as the most important predictors for these outcomes. Notably, the machine learning algorithms demonstrate accuracy across three distinct initialization methods of the $Q$-voter model, including random selection and the involvement of high- and low-degree agents with positive opinions. By unraveling the intricate interplay between network structure and dynamics, this research sheds light on the underlying mechanisms responsible for polarization effects and other dynamic patterns in social systems. Adopting a holistic approach that comprehends the complexity of network systems, this study offers insights into the intricate dynamics associated with polarization effects and paves the way for investigating the structure and dynamics of complex systems through modern machine learning methods., Comment: 32 pages, 10 figures

Rogers' diffusion of innovations theory asserts that cultural similarity among individuals plays a crucial role in the acceptance of an innovation in a community. However, most studies on the diffusion of innovations have relied on epidemic-like models where the individuals have no preference on whom they interact with. Here, we use an agent-based model to study the diffusion of innovations in a community of synthetic heterogeneous agents whose interaction preferences depend on their cultural similarity. The community heterogeneity and the agents' interaction preferences are described by Axelrod's model, whereas the diffusion of innovations is described by a variant of the Daley and Kendall model of rumour propagation. The interplay between the social dynamics and the spreading of the innovation is controlled by the parameter $p \in [0,1]$, which yields the probability that the agent engages in social interaction or attempts to spread the innovation. Our findings support Roger's empirical observations that cultural heterogeneity curbs the diffusion of innovations., Comment: 7 pages, 4 figures

Synthetic Aperture Radar (SAR) image understanding is crucial in remote sensing applications, but it is hindered by its intrinsic noise contamination, called speckle. Sophisticated statistical models, such as the $\mathcal{G}^0$ family of distributions, have been employed to SAR data and many of the current advancements in processing this imagery have been accomplished through extracting information from these models. In this paper, we propose improvements to parameter estimation in $\mathcal{G}^0$ distributions using the Method of Log-Cumulants. First, using Bayesian modeling, we construct that regularly produce reliable roughness estimates under both $\mathcal{G}^0_A$ and $\mathcal{G}^0_I$ models. Second, we make use of an approximation of the Trigamma function to compute the estimated roughness in constant time, making it considerably faster than the existing method for this task. Finally, we show how we can use this method to achieve fast and reliable SAR image understanding based on roughness information.

We investigate the use of transfer entropy (TE) as a proxy to detect the contact patterns of the population in epidemic processes. We first apply the measure to a classical age-stratified SIR model and observe that the recovered patterns are consistent with the age-mixing matrix that encodes the interaction of the population. We then apply the TE analysis to real data from the COVID-19 pandemic in Spain and show that it can provide information on how the behavior of individuals changed through time. We also demonstrate how the underlying dynamics of the process allow us to build a coarse-grained representation of the time series that provides more information than raw time series. The macro-level representation is a more effective scale for analysis, which is an interesting result within the context of causal analysis across different scales. These results open the path for more research on the potential use of informational approaches to extract retrospective information on how individuals change and adapt their behavior during a pandemic, which is essential for devising adequate strategies for an efficient control of the spreading.

In this work, we investigate the evolution of polarization, influence, and domination in online interaction networks. Twitter data collected before and during the 2022 Brazilian elections is used as a case study. From a theoretical perspective, we develop a methodology called d-modularity that allows discovering the contribution of specific groups to network polarization using the well-known modularity measure. While the overall network modularity (somewhat unexpectedly) decreased, the proposed group-oriented approach allows concluding that the contribution of the right-leaning community to this modularity increased, remaining very high during the analyzed period. Our methodology is general enough to be used in any situation when the contribution of specific groups to overall network modularity and polarization is needed to investigate. Moreover, using the concept of partial domination, we are able to compare the reach of sets of influential profiles from different groups and their ability to accomplish coordinated communication inside their groups and across segments of the entire network during some specific time window. We show that in the whole network, the left-leaning high-influential information spreaders dominated, reaching a substantial fraction of users with fewer spreaders. However, when comparing domination inside the groups, the results are inverse. Right-leaning spreaders dominate their communities using few nodes, showing as the most capable of accomplishing coordinated communication. The results bring evidence of extreme isolation and the ease of accomplishing coordinated communication that characterized right-leaning communities during the 2022 Brazilian elections.

The inference of outcomes in dynamic processes from structural features of systems is a crucial endeavor in network science. Recent research has suggested a machine learning-based approach for the interpretation of dynamic patterns emerging in complex network systems. The hypothesis is applied in this study towards showing opinions can be classified in the voter model with the use of topological features from complex networks. An analysis was first performed with 2 (0 or 1) opinions from a voter model and extended for 3 and then 4 opinions from the same model. A breakdown of the key network topological features for the estimation is provided and network metrics are ranked in the order of importance with high accuracy. Our generalized approach is applicable to dynamical processes running on complex networks. This study is a step towards the application of machine learning methods to studies of dynamical patterns from complex network systems., Comment: Proc. of the Interdisciplinary Conference on Mechanics, Computers and Electrics (ICMECE 2022) 6-7 October 2022, Barcelona, Spain

In this work we propose a completely new way to obtain statistics distributions from fluctuations balance. By dimensionless fluctuation analysis we obtain Boltzmann, Planck, Fermi-Dirac, Bose-Einstein and Schr\"odinger Distributions using the same fundamental principle. Our result point to a general foundation that was successful verified to principal Physics Distributions. We name it as Dimensionless Fluctuation Balance Principle. This is a great achievement which enable us to discuss exchange between different physical quantities, like we do when treat energy conservation when some type of energy is converted to another, but with more generality, because we can exchange one physical quantity to any other. All physics model which needs distribution can take advantage of methodology presented in this paper including: Statistical Physics, Schr\"odinger's Quantum Mechanics, Nanomaterials, Thin Films and New Materials Modeling. Keywords: Fluctuations, PDEs, Boltzmann, Planck, Entropy, Fermi-Dirac, Bose-Einstein, Schr\"odinger, Distributions.

Game theory is fundamental to understanding cooperation between agents. Mainly, the Prisoner's Dilemma is a well-known model that has been extensively studied in complex networks. However, although the emergence of cooperation has been investigated before, the influence of memory in its evolution is not well understood. This paper presents a detailed study of cooperation dynamics in which agents have memory. We simulate the evolutionary Prisoner's dilemma game on random, scale-free and networks presenting degree-degree correlation. Through extensive simulations, we show that assortativity can improve cooperation when the temptation to defect increases. Moreover, we show that the inclusion of memory decreases the network structure influence. Our results contribute to understanding the role of the network structure and the player's memory of cooperation.

The role of waning immunity in basic epidemic models on networks has been undervalued while being noticeable fundamental for real epidemic outbreaks. One central question is which mean-field approach is more accurate in describing the epidemic dynamics. We tackled this problem considering the susceptible-infected-recovered-susceptible (SIRS) epidemic model on networks. Two pairwise mean-field theories, one based on recurrent dynamical message-passing (rDMP) and the other on the pair quenched mean-field theory (PQMF), are compared with extensive stochastic simulations on large networks of different levels of heterogeneity. For waning immunity times longer than or comparable with the recovering time, rDMP outperforms PQMF theory on power-law networks with degree distribution $P(k) \sim k^{-\gamma}$. In particular, for $\gamma > 3$, the epidemic threshold observed in simulations is finite, in qualitative agreement with rDMP, while PQMF leads to an asymptotically null threshold. The critical epidemic prevalence for $\gamma > 3$ is localized in a finite set of vertices in the case of the PQMF theory. In contrast, the localization happens in a subextensive fraction of the network in rDMP theory. Simulations, however, indicate that localization patterns of the actual epidemic lay between the two mean-field theories, and improved theoretical approaches are necessary to understanding the SIRS dynamics., Comment: 10 pages, 4 figures

Recent infectious disease outbreaks, such as the COVID-19 pandemic and the Zika epidemic in Brazil, have demonstrated both the importance and difficulty of accurately forecasting novel infectious diseases. When new diseases first emerge, we have little knowledge of the transmission process, the level and duration of immunity to reinfection, or other parameters required to build realistic epidemiological models. Time series forecasts and machine learning, while less reliant on assumptions about the disease, require large amounts of data that are also not available in early stages of an outbreak. In this study, we examine how knowledge of related diseases can help make predictions of new diseases in data-scarce environments using transfer learning. We implement both an empirical and a theoretical approach. Using empirical data from Brazil, we compare how well different machine learning models transfer knowledge between two different disease pairs: (i) dengue and Zika, and (ii) influenza and COVID-19. In the theoretical analysis, we generate data using different transmission and recovery rates with an SIR compartmental model, and then compare the effectiveness of different transfer learning methods. We find that transfer learning offers the potential to improve predictions, even beyond a model based on data from the target disease, though the appropriate source disease must be chosen carefully. While imperfect, these models offer an additional input for decision makers during pandemic response.

Built upon the concept of causal faithfulness, the so-called causal discovery algorithms propose the breakdown of mutual information (MI) and conditional mutual information (CMI) into sets of variables to reveal causal influences. These algorithms suffer from the lack of accounting emergent causes when connecting links, resulting in a spuriously embellished view of the organization of complex systems. Here, we show that causal emergent information is necessarily contained in CMIs. We also connect this result with the intrinsic violation of faithfulness and elucidate the importance of the concept of causal minimality. Finally, we show how faithfulness can be wrongly assumed only because of the appearance of spurious correlations by providing an example of a non-pairwise systems which should violate faithfulness, in principle, but it does not. The net result proposes an update to causal discovery algorithms, which can, in principle, detect and isolate emergent causal influences in the network reconstruction problems undetected so far.

Despite the advanced stage of epidemic modeling, there is a major demand for methods to incorporate behavioral responses to the spread of a disease such as social distancing and adoption of prevention methods. Mobility plays an important role in epidemic dynamics and is also affected by behavioral changes, but there are many situations in which real mobility data is incomplete or inaccessible. We present a model for epidemic spreading in temporal networks of mobile agents that incorporates local behavioral responses. Susceptible agents are allowed to move towards the opposite direction of infected agents in their neighborhood. We show that this mechanism considerably decreases the stationary prevalence when the spatial density of agents is low. However, for higher densities, the mechanism causes an abrupt phase transition, where a new bistable phase appears. We develop a semi-analytic approach for the case when the mobility is fast compared to the disease dynamics, and use it to argue that the bistability is caused by the emergence of spatial clusters of susceptible agents. Finally, we characterize the temporal networks formed in the fast mobility regime, showing how the degree distributions and other metrics are affected by the behavioral mechanism. Our work incorporates results previously known from adaptive networks into the population of mobile agents, which can be further developed to be used in mobility-driven models., Comment: 10 pages and 12 figures

Countries participate in global value chains by engaging in backward and forward transactions connecting multiple geographically dispersed production stages. Inspired by network theory, we model global trade as a multilayer network and study its power structure by investigating the tendency of eigenvector centrality to concentrate on a small fraction of countries, a phenomenon called localization transition. We show that the market underwent a significant structural variation in 2007 just before the global financial crisis. That year witnessed an abrupt repositioning of countries in the global value chains, and in particular a remarkable reversal of leading role between the two major economies, the US and China. We uncover the hierarchical structure of the multilayer network based on countries' time series of eigenvector centralities, and show that trade tends to concentrate between countries with different power dynamics, yet in geographical proximity. We further investigate the contribution of individual industries to countries' economic dominance, and show that also within industry variations in countries' market positioning took place in 2007. Moreover, we shed light on the crucial role that domestic trade played in the geopolitical landscape leading China to overtake the US and cement its status as leading economy of the global value chains. Our study shows how the 2008 crisis can offer insights to policy makers and governments on how to turn early structural signals of upcoming exogenous shocks into opportunities for redesigning countries' global roles in a changing geopolitical landscape., Comment: 34 pages, including a SM

Mathematical models represent one of the fundamental ways of studying nature. In special, epidemic models have shown to be particularly useful in the understanding of the course of diseases and in the planning effective control policies. A particular type of epidemic model considers the individuals divided into populations. When studied in graphs, it is already known that the graph topology can play an important role in the evolution of the disease. At the same time, one may want to study the effect of the presence of an underlying \emph{attraction landscape} of the vertices, apart from the respectively underlying topology. In this work, we study metapopulations with small number of individuals in the presence of an attraction landscape. Individuals move across populations and get infected according to the SIS compartmental model. By using a Markov chain approach, we provide a numerical approximation to the prediction of the long-term prevalence of the disease. More specifically, an approach that combines two binomial distributions for mobility, with appropriate assumptions, is proposed to approximate the model. The problem setting is simulated through Monte-Carlo experiments and the obtained results are compared to the mathematic-analytical approach. Substantial agreement is observed between both approaches, which corroborates the effectiveness of the reported numerical approach. In addition, we also study the impact of different levels of attraction landscapes, as well as propagation on the local scale of the entire population. All in all, this study proposes a potentially effective approach to a mostly unexplored setting of disease transmission.

Mental disorders are among the leading causes of disability worldwide. The first step in treating these conditions is to obtain an accurate diagnosis, but the absence of established clinical tests makes this task challenging. Machine learning algorithms can provide a possible solution to this problem, as we describe in this work. We present a method for the automatic diagnosis of mental disorders based on the matrix of connections obtained from EEG time series and deep learning. We show that our approach can classify patients with Alzheimer's disease and schizophrenia with a high level of accuracy. The comparison with the traditional cases, that use raw EEG time series, shows that our method provides the highest precision. Therefore, the application of deep neural networks on data from brain connections is a very promising method to the diagnosis of neurological disorders., Comment: 10 pages, 5 figures, 9 tables

We consider random geometric graphs on the plane characterized by a non-uniform density of vertices. In particular, we introduce a graph model where $n$ vertices are independently distributed in the unit disc with positions, in polar coordinates $(l,\theta)$, obeying the probability density functions $\rho(l)$ and $\rho(\theta)$. Here we choose $\rho(l)$ as a normal distribution with zero mean and variance $\sigma\in(0,\infty)$ and $\rho(\theta)$ as an uniform distribution in the interval $\theta\in [0,2\pi)$. Then, two vertices are connected by an edge if their Euclidian distance is less or equal than the connection radius $\ell$. We characterize the topological properties of this random graph model, which depends on the parameter set $(n,\sigma,\ell)$, by the use of the average degree $\left\langle k \right\rangle$ and the number of non-isolated vertices $V_\times$; while we approach their spectral properties with two measures on the graph adjacency matrix: the ratio of consecutive eigenvalue spacings $r$ and the Shannon entropy $S$ of eigenvectors. First we propose a heuristic expression for $\left\langle k(n,\sigma,\ell) \right\rangle$. Then, we look for the scaling properties of the normalized average measure $\left\langle \overline{X} \right\rangle$ (where $X$ stands for $V_\times$, $r$ and $S$) over graph ensembles. We demonstrate that the scaling parameter of $\left\langle \overline{V_\times} \right\rangle=\left\langle V_\times \right\rangle/n$ is indeed $\left\langle k \right\rangle$; with $\left\langle \overline{V_\times} \right\rangle \approx 1-\exp(-\left\langle k \right\rangle)$. Meanwhile, the scaling parameter of both $\left\langle \overline{r} \right\rangle$ and $\left\langle \overline{S} \right\rangle$ is proportional to $n^{-\gamma} \left\langle k \right\rangle$ with $\gamma\approx 0.16$., Comment: 15 pages, 14 figures

Due to a lack of treatments and universal vaccine, early forecasts of Dengue are an important tool for disease control. Neural networks are powerful predictive models that have made contributions to many areas of public health. In this systematic review, we provide an introduction to the neural networks relevant to Dengue forecasting and review their applications in the literature. The objective is to help inform model design for future work. Following the PRISMA guidelines, we conduct a systematic search of studies that use neural networks to forecast Dengue in human populations. We summarize the relative performance of neural networks and comparator models, model architectures and hyper-parameters, as well as choices of input features. Nineteen papers were included. Most studies implement shallow neural networks using historical Dengue incidence and meteorological input features. Prediction horizons tend to be short. Building on the strengths of neural networks, most studies use granular observations at the city or sub-national level. Performance of neural networks relative to comparators such as Support Vector Machines varies across study contexts. The studies suggest that neural networks can provide good predictions of Dengue and should be included in the set of candidate models. The use of convolutional, recurrent, or deep networks is relatively unexplored but offers promising avenues for further research, as does the use of a broader set of input features such as social media or mobile phone data., Comment: 16 pages, 6 figures, 1 table

To contain the propagation of emerging diseases that are transmissible from human to human, non-pharmaceutical interventions (NPIs) aimed at reducing the interactions between humans are usually implemented. One example of the latter kind of measures is social distancing, which can be either policy-driven or can arise endogenously in the population as a consequence of the fear of infection. However, if NPIs are lifted before the population reaches herd immunity, further re-introductions of the pathogen would lead to secondary infections. Here we study the effects of different social distancing schemes on the large scale spreading of diseases. Specifically, we generalize metapopulation models to include social distancing mechanisms at the subpopulation level and model short- and long-term strategies that are fed with local or global information about the epidemics. We show that different model ingredients might lead to very diverse outcomes in different subpopulations. Our results suggest that there is not a unique answer to the question of whether contention measures are more efficient if implemented and managed locally or globally and that model outcomes depends on how the full complexity of human interactions is taken into account., Comment: 14 pages, 11 figures

The purpose of this paper is to calculate the risk-dependent centrality (RDC) of the Brazilian stock market. We computed the RDC for assets traded on the Brazilian stock market between January 2008 to June 2020 at different levels of external risk. We observed that the ranking of assets based on the RDC depends on the external risk. Rankings' volatility is related to crisis events, capturing the recent Brazilian economic-political crisis. Moreover, we have found a negative correlation between the average volatility of assets' ranking based on the RDC and the average daily returns on the stock market. It goes in hand with the hypothesis that the rankings' volatility is higher in periods of crisis., Comment: 12 pages, 7 figures, 2 tables

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.

The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios, particularly within embedded systems technology, where numerical methods are impractical. This study introduces a generalized form of the MLE that yields closed-form estimators under certain conditions. We derive the asymptotic properties of the proposed estimator and demonstrate that our approach retains key properties such as invariance under one-to-one transformations, strong consistency, and an asymptotic normal distribution. The effectiveness of the generalized MLE is exemplified through its application to the Gamma, Nakagami, and Beta distributions, showcasing improvements over the traditional MLE. Additionally, we extend this methodology to a bivariate gamma distribution, successfully deriving closed-form estimators. This advancement presents significant implications for real-time statistical analysis across various applications.

The present paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and biology. We reparametrize the model in terms of entropy, and different objective priors are derived, such as Jeffreys prior, reference prior, and matching priors. Since the obtained priors are improper, we prove that the obtained posterior distributions are proper and that their respective posterior means are finite. An intensive simulation study is conducted to select the prior that returns better results regarding bias, mean square error, and coverage probabilities. The proposed approach is illustrated in two datasets: the first relates to the Achaemenid dynasty reign period, and the second describes the time to failure of an electronic component in a sugarcane harvest machine.

In this review, we present a simple guide for researchers to obtain pseudo-random samples with censored data. We focus our attention on the most common types of censored data, such as type I, type II, and random censoring. We discussed the necessary steps to sample pseudo-random values from long-term survival models where an additional cure fraction is informed. For illustrative purposes, these techniques are applied in the Weibull distribution. The algorithms and codes in R are presented, enabling the reproducibility of our study. Finally, we developed an R package that encapsulates these methodologies, providing researchers with practical tools for implementation.

Drought is a costly natural hazard, many aspects of which remain poorly understood. It has many contributory factors, driving its outset, duration, and severity, including land surface, anthropogenic activities, and, most importantly, meteorological anomalies. Prediction plays a crucial role in drought preparedness and risk mitigation. However, this is a challenging task at socio-economically critical lead times (1-2 years), because meteorological anomalies operate at a wide range of temporal and spatial scales. Among them, past studies have shown a correlation between the Sea Surface Temperature (SST) anomaly and the amount of precipitation in various locations in Africa. In its Eastern part, the cooling phase of El Nino-Southern Oscillation (ENSO) and SST anomaly in the Indian ocean are correlated with the lack of rainfall. Given the intrinsic shortcomings of correlation coefficients, we investigate the association among SST modes of variability and the monthly fraction of grid points in Ethiopia, which are in drought conditions in terms of causality. Using the empirical extreme quantiles of precipitation distribution as a proxy for drought, We show that the level of SST second mode of variability in the prior year influences the occurrence of drought in Ethiopia. The causal link between these two variables has a negative coefficient that verifies the conclusion of past studies that rainfall deficiency in the Horn of Africa is associated with ENSO's cooling phase., Comment: Conference paper, 8 pages, 7 figures, 2 tables