A data-driven model for COVID-19 pandemic - Evolution of the attack rate and prognosis for Brazil.

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 vaccinated individual with vaccine failure. The model allows to consider any number of different vaccines with different efficacies and delays between doses. Contacts among age groups are modeled by a contact matrix and the contagion matrix is obtained from a probability of contagion p c per contact. The model uses known epidemiological parameters and the time dependent probability p c is obtained by fitting the model output to the series of deaths in each locality, and reflects non-pharmaceutical interventions. As a benchmark the output of the model is compared to two good quality serological surveys, and applied to study the evolution of the COVID-19 pandemic in the main Brazilian cities with a total population of more than one million. We also discuss with some detail the case of the city of Manaus which raised special attention due to a previous report of We also estimate the attack rate, the total proportion of cases (symptomatic and asymptomatic) with respect to the total population, for all Brazilian states since the beginning of the COVID-19 pandemic. We argue that the model present here is relevant to assessing present policies not only in Brazil but also in any place where good serological surveys are not available.

Interplay of self, epiphany, and positive actions in shaping individual careers.

In this work, we model an individual social career by a finite-size trajectory along a hexagonal lattice moving only forward. At each bifurcation, the individual makes a free-will choice to follow one or the other branch within an uncertain outcome. Considering that those choices are determined by an individual self built from endogenous characteristics, we assume they are random following a binomial distribution. As a result, the individual ascends or descends on the social scale via random progress through the series of bifurcations made at the encountered junctions. The related stochastic process is found to be diffusive. For different selves coming from different points on the social scale, progress does overlap. In addition, we include the possibility of continuous transition across the lattice caused external influences as an epiphany. The occurrence of a quantum leap resulting from an affirmative action opportunity is also included. We also treat the case of a social group being acted by a collective epiphany as with education. The results highlight the key effect of epiphanies and quantum leaps to promote upward mobility across social classes.

The role of stochasticity on compactness of the native state of protein peptide backbone.

A restricted angular random-walk model to build up polypeptide structures, which encompasses properties of the dihedral-angle Ramachandran map of folded proteins, is proposed to study the role of stochasticity on the compactness of the native state of proteins. Sample structures will be built with lengths ranging from 125 up to 400 amino acids for the different fractions of secondary structure motifs, from which dihedral angles were randomly chosen according to narrow Gaussian probability distributions. Physical properties of these polypeptide protein backbones such as the radius of gyration, the compactness parameter, the number of contacts, and the associated energy were computed and analyzed from an ensemble of thousands of realizations of protein peptide chains built with different rates of alpha-helix or beta-strand motifs. Such geometric and physical parameters are compared to data from several globular proteins extracted from the Protein Data Bank indicating that a certain (small fraction) randomness is an essential ingredient for achieving the folded state of proteins, suggesting that they are neither driven by deterministic nor random-walk processes.

Non-Arrhenius behavior and fragile-to-strong transition of glass-forming liquids.

Characterization of the non-Arrhenius behavior of glass-forming liquids is a broad avenue for research toward the understanding of the formation mechanisms of noncrystalline materials. In this context, this paper explores the main properties of the viscosity of glass-forming systems, considering super-Arrhenius diffusive processes. We establish the viscous activation energy as a function of the temperature, measure the degree of fragility of the system, and characterize the fragile-to-strong transition through the standard Angell's plot. Our results show that the non-Arrhenius behavior observed in fragile liquids can be understood through the non-Markovian dynamics that characterize the diffusive processes of these systems. Moreover, the fragile-to-strong transition corresponds to a change in the spatiotemporal range of correlations during the glass transition process.

Characterization of the non-Arrhenius behavior of supercooled liquids by modeling nonadditive stochastic systems.

The characterization of the formation mechanisms of amorphous solids is a large avenue for research, since understanding its non-Arrhenius behavior is challenging to overcome. In this context, we present one path toward modeling the diffusive processes in supercooled liquids near glass transition through a class of nonhomogeneous continuity equations, providing a consistent theoretical basis for the physical interpretation of its non-Arrhenius behavior. More precisely, we obtain the generalized drag and diffusion coefficients that allow us to model a wide range of non-Arrhenius processes. This provides a reliable measurement of the degree of fragility of the system and an estimation of the fragile-to-strong transition in glass-forming liquids, as well as a generalized Stokes-Einstein equation, leading to a better understanding of the classical and quantum effects on the dynamics of nonadditive stochastic systems.

Amino acid hydrophobicity and accessible surface area.

It is well known that the hydrophobic effect is the major factor that drives a protein toward collapse and folding. We analyze the variation of the solvent-accessible surface area of amino acids in small fragments of protein (3N45) . In this way, we look into 5526 protein chains deposited in the Brookhaven Protein Data Bank. The accessible surface area behaves as a power law for N9 . The comparison between the loss of accessible area and the self-similar behavior gives us a measure of the possibility of an amino acid to have apolar or polar side chain. It is therefore possible to infer about amino acid hydrophobicity, i.e., if one amino acid has a hydrophobic side chain or if it has a hydrophilic one. Furthermore, the present findings indicate that the variation of the accessible surface area describes an alternative hydrophobicity scale.

Self-similarity and protein chains.

Fractal properties of 5526 different protein chains are investigated. Characteristic fractal behavior for different molecular systems is obtained from the fractal dimension analysis, which shows that the dimension is delta=2.47 . This dimension gives a measure of the protein compactness. The present finding indicates that the fractal analysis describes some structural properties of proteins and corroborates the explanation about multifractality in the energy hypersurface.

Multifractality, Levinthal paradox, and energy hypersurface.

Multifractal properties in the potential energy hypersurface of polypeptides and proteins are investigated. Characteristic multifractal behavior for different molecular systems is obtained from the f(alpha) spectra. The analysis shows that the dimension of the phase space of the problem influences the accessibility to different parts of the potential energy hypersurface. Also, we show that it is necessary to take into account the H-bond formation between amino acids in the conformational-folding search. The present findings indicate that the f(alpha) function describes some structural properties of a protein. The behavior of the f(alpha) spectra gives an alternative explanation about the Levinthal paradox. Furthermore, the anomalous temperature dependence of the Raman spin-lattice relaxation rates can be related to the perturbations in the secondary structures.

Fluctuation analysis of stellar x-ray binary systems.

We study time series of x-ray sources of 129 stellar binary systems present in the public data collected by the instrument All Sky Monitor on board of the satellite Rossi X-Ray Timing Explorer. The light time series was analyzed by applying detrended fluctuation analysis to estimate the long-range power-law correlation exponents alpha. The scaling exponent was calculated for all systems and its value indicated a signature of each kind of system, i.e., whether flare takes place (with alpha=1.22) or not (with alpha=0.64). As a consequence, our results may identify the stability of the systems from the scaling exponent alpha value, for instance, if alpha approximately 0.5 (white noise) the system is stable and unstable when alpha not equal to 0.5 (long-range power-law correlation).

Nonextensivity and self-affinity in the mammalian neuromuscular junction.

We study time series and the spontaneous miniature end-plate potentials (MEPPs) of mammals recorded at neuromuscular junctions using two different approaches: generalized thermostatistics and detrended fluctuation analysis (DFA). Classical concepts establish that the magnitude of these potentials is characterized by Gaussian statistics and that their intervals are randomly displayed. First we show that MEPP distributions adequately satisfy the q-Gaussian distributions that maximize the Tsallis entropy, indicating their nonextensive and nonequilibrium behavior. We then examine the intervals between the miniature potentials via DFA, where the profile of the intervals between events configures a deviation from the expected random behavior. Some possible physiological substrates for these findings are discussed.

Self-similarity and protein compactness.

The hydrophobic effect is the major factor that drives a protein toward collapse and folding. As a consequence of the folding process a hydrophobic core is shielded by the solvent-accessible surface area of the protein. We analyze the solvent-accessible surface area of 1825 nonhomolog protein chains deposited in the Brookhaven Protein Data Bank. This solvent-accessible surface area presents an intrinsic self-similarity behavior. The comparison between the accessible surface area as function of the number of amino acids and the accessible surface area as function of gyration radius supplies a measure of the scaling exponent close to the one observed by volume as function of radius of gyration or by mass-size exponent. The present finding indicates that the fractal analysis describes the protein compactness as an object packing between random spheres in percolation threshold and crumpled wires.

New stochastic strategy to analyze helix folding.

We propose an alternative stochastic strategy to search secondary structures based on the generalized simulated annealing (GSA) algorithm, by using conformational preferences based on the Ramachandran map. We optimize the search for polypeptide conformational space and apply to peptides considered to be good alpha-helix promoters above a critical number of residues. Our strategy to obtain conformational energies consist in coupling a classical force field (THOR package) with the GSA procedure, biasing the Phi x Psi backbone angles to the allowed regions in the Ramachandran map. For polyalanines we obtained stable alpha-helix structures when the number of residues were equal or exceeded 13 amino acids residues. We also observed that the energy gap between the global minimum and the first local minimum tends to increase with the polypeptide size. These conformations were generated by performing 2880 stochastic molecular optimizations with a continuum medium approach. When compared with molecular dynamics or Monte Carlo methods, GSA can be considered the fastest.