On Universality in Human Correspondence Activity

Identifying and modeling patterns of human activity has important ramifications in applications ranging from predicting disease spread to optimizing resource allocation. Because of its relevance and availability, written correspondence provides a powerful proxy for studying human activity. One school of thought is that human correspondence is driven by responses to received correspondence, a view that requires distinct response mechanism to explain e-mail and letter correspondence observations. Here, we demonstrate that, like e-mail correspondence, the letter correspondence patterns of 16 writers, performers, politicians, and scientists are well-described by the circadian cycle, task repetition and changing communication needs. We confirm the universality of these mechanisms by properly rescaling letter and e-mail correspondence statistics to reveal their underlying similarity.Comment: 17 pages, 3 figures, 1 tabl

Application of Optimal Control of Infectious Diseases in a Model-Free Scenario

Optimal control for infectious diseases has received increasing attention over the past few decades. In general, a combination of cost state variables and control effort have been applied as cost indices. Many important results have been reported. Nevertheless, it seems that the interpretation of the optimal control law for an epidemic system has received less attention. In this paper, we have applied Pontryagin’s maximum principle to develop an optimal control law to minimize the number of infected individuals and the vaccination rate. We have adopted the compartmental model SIR to test our technique. We have shown that the proposed control law can give some insights to develop a control strategy in a model-free scenario. Numerical examples show a reduction of 50% in the number of infected individuals when compared with constant vaccination. There is not always a prior knowledge of the number of susceptible, infected, and recovered individuals required to formulate and solve the optimal control problem. In a model-free scenario, a strategy based on the analytic function is proposed, where prior knowledge of the scenario is not necessary. This insight can also be useful after the development of a vaccine to COVID-19, since it shows that a fast and general cover of vaccine worldwide can minimize the number of infected, and consequently the number of deaths. The considered approach is capable of eradicating the disease faster than a constant vaccination control method

Acoustic-Friction Networks and the Evolution of Precursory Rupture Fronts in Laboratory Earthquakes

We show that the mesoscopic and transport characteristics of networks follow the same trends for the same type of the shear ruptures in terms of rupture speed while also comparing the results of three different friction experiments.The classified fronts obtained from a saw cut Westerly granite fault regarding friction network parameters show a clear separation into two groups indicating two different rupture fronts. With respect to the scaling of local ruptures durations with the networks parameters we show that the gap is related to the possibility of a separation between slow and regular fronts

Impact of network topology on the spread of infectious diseases

The complex network theory constitutes a natural support for the study of a disease propagation. In this work, we present a study of an infectious disease spread with the use of this theory in combination with the Individual Based Model. More specifically, we use several complex network models widely known in the literature to verify their topological effects in the propagation of the disease. In general, complex networks with different properties result in curves of infected individuals with different behaviors, and thus, the growth of a given disease is highly sensitive to the network model used. The disease eradication is observed when the vaccination strategy of 10% of the population is used in combination with the random, small world or modular network models, which opens an important space for control actions that focus on changing the topology of a complex network as a form of reduction or even elimination of an infectious disease

Duality between time series and networks.

Studying the interaction between a system's components and the temporal evolution of the system are two common ways to uncover and characterize its internal workings. Recently, several maps from a time series to a network have been proposed with the intent of using network metrics to characterize time series. Although these maps demonstrate that different time series result in networks with distinct topological properties, it remains unclear how these topological properties relate to the original time series. Here, we propose a map from a time series to a network with an approximate inverse operation, making it possible to use network statistics to characterize time series and time series statistics to characterize networks. As a proof of concept, we generate an ensemble of time series ranging from periodic to random and confirm that application of the proposed map retains much of the information encoded in the original time series (or networks) after application of the map (or its inverse). Our results suggest that network analysis can be used to distinguish different dynamic regimes in time series and, perhaps more importantly, time series analysis can provide a powerful set of tools that augment the traditional network analysis toolkit to quantify networks in new and useful ways

Application of Optimal Control of Infectious Diseases in a Model-Free Scenario

Optimal control for infectious diseases has received increasing attention over the past few decades. In general, a combination of cost state variables and control effort have been applied as cost indices. Many important results have been reported. Nevertheless, it seems that the interpretation of the optimal control law for an epidemic system has received less attention. In this paper, we have applied Pontryagin’s maximum principle to develop an optimal control law to minimize the number of infected individuals and the vaccination rate. We have adopted the compartmental model SIR to test our technique. We have shown that the proposed control law can give some insights to develop a control strategy in a model-free scenario. Numerical examples show a reduction of 50% in the number of infected individuals when compared with constant vaccination. There is not always a prior knowledge of the number of susceptible, infected, and recovered individuals required to formulate and solve the optimal control problem. In a model-free scenario, a strategy based on the analytic function is proposed, where prior knowledge of the scenario is not necessary. This insight can also be useful after the development of a vaccine to COVID-19, since it shows that a fast and general cover of vaccine worldwide can minimize the number of infected, and consequently the number of deaths. The considered approach is capable of eradicating the disease faster than a constant vaccination control method

Application of Optimal Control of Infectious Diseases in a Model-Free Scenario

Optimal control for infectious diseases has received increasing attention over the past few decades. In general, a combination of cost state variables and control effort have been applied as cost indices. Many important results have been reported. Nevertheless, it seems that the interpretation of the optimal control law for an epidemic system has received less attention. In this paper, we have applied Pontryagin’s maximum principle to develop an optimal control law to minimize the number of infected individuals and the vaccination rate. We have adopted the compartmental model SIR to test our technique. We have shown that the proposed control law can give some insights to develop a control strategy in a model-free scenario. Numerical examples show a reduction of 50% in the number of infected individuals when compared with constant vaccination. There is not always a prior knowledge of the number of susceptible, infected, and recovered individuals required to formulate and solve the optimal control problem. In a model-free scenario, a strategy based on the analytic function is proposed, where prior knowledge of the scenario is not necessary. This insight can also be useful after the development of a vaccine to COVID-19, since it shows that a fast and general cover of vaccine worldwide can minimize the number of infected, and consequently the number of deaths. The considered approach is capable of eradicating the disease faster than a constant vaccination control method

Illustration of the forward map to chaotic time series from Lorenz and Rossler systems.

<p>We use 10,000 time points of the variable of the chaotic Lorenz and Rossler equations and construct networks using quantiles by applying the forward map. Each node is colored according to the module to which it belongs. The resulting networks display clear differences in topologies. The network of Lorenz's system is bulky with two large modules. It has a modularity value of , that is much larger than the mean (standard error) modularity value obtained from networks built from the randomizations of the original time series. Furthermore, the two lobes of the Lorenz attractor are mapped into the two largest connected modules in the network. On the other hand, the network of Rossler's system presents an elongated, chain-like pattern due the strong periodicity present in its corresponding time series. The network of Rossler's system is also modular, with five small modules and it has a modularity value of . This value is much larger than the mean (standard error) modularity value obtained from networks built from the randomizations of the original time series.</p

Statistical properties of the time series presented in <b>Figure 9</b>, generated from the <i>Arabidopsis thaliana</i> network and the USA Internet 1997.

<p>Note that the long-range correlations present in the metabolic network are well captured by the autocorrelation function and the corresponding power density spectrum, which displays a clear power-law scaling. On the other hand, the results in the USA Internet 1997 bear the footprint of the short-correlated signal generated by the Internet network. Note a power-law scaling with a less steep slope.</p

Illustration of the proposed forward map to the problem of detecting differences in the data structures of patients in different health conditions.

<p>We use 100-minute normalized heart rate time series from a healthy subject (upper panel) and a subject with severe congestive heart failure (lower panel) sampled every seconds ( = 10,000 points) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0023378#pone.0023378-Physionet1" target="_blank">[36]</a>. We construct the networks using quantiles by applying from the corresponding time series. The resulting networks display clear differences in topology, which are especially apparent on the relatively separated cluster in the network associated with the unhealthy subject. These differences in topology are confirmed by generating networks with different number of nodes (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0023378#pone-0023378-g007" target="_blank">Fig. 7</a>) and using time series from different healthy and unhealthy subjects (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0023378#pone-0023378-g008" target="_blank">Fig. 8</a>).</p