Physica A: Statistical Mechanics and its Applications

The analysis of computer simulation data requires efficient statistical and computational approaches, based on well-established theoretical frameworks. This study aims to introduce such approaches for topological data analysis within the persistent homology framework and to describe the manifold of the protein structure dynamics within the differential geometry of the directed graphs framework. Furthermore, the asymmetric kernel-directed graphs determined by the transfer entropy will describe the information flow in this manifold. The primary goal is to characterise changes in the topology of the protein structure due to the mutations. Moreover, this study aims to define the embedded manifold of dimension m of the amino acid sequence interaction network using the graphs Laplacian matrix for determining the local embedded vector fields and coordinate vectors in this manifold for each amino acid as the vertices of either a directed or undirected graph. Furthermore, this study strives to show that encoding the amino acid sequence information in an m-dimensional manifold is statistically efficient by decoding that information in a much lower-dimensional space. Then, using the topological data analysis, we can observe protein structure dynamics changes in a multidimensional manifold, for example, due to amino acid mutations. The analysis showed that short equilibrium structure fluctuations at a few nanoseconds enable the construction of such a manifold. As a case study, the influence of the mutation of the two disulphide bridges on the three-dimensional structure of the Bovine Pancreatic Trypsin Inhibitor protein is investigated.

The cumulative records of COVID-19 are rapidly increasing day by day in India. The key question prevailing in minds of all is when will it get over? There have been several attempts in literature to address this question using time series, Machine learning, epidemiological and statistical models. However due to high level of uncertainty in the domain and lack of big historical data, the performance of these models suffer. In this work, we present an intuitive model that uses a combination of epidemiological model (SEIR) and mathematical curve fitting method to forecast spread of COVID-19 in India in future. By using the combination model, we get characteristics benefits of these models under limited knowledge and historical data about the novel Coronavirus. Instead of fixing parameters of the standard SEIR model before simulation, we propose to learn them from the real data set consisting of progression of Corona spread in India. The learning of model is carefully designed by understanding that available data set consist of records of cases under full, partial to zero lockdown phases in India. Hence, we make two separate predictions by our propose model. One under the situation of full lockdown in India and, other with partial to zero restrictions in India. With continued strict lockdown after May 03, 2020, our model predicted May 14, 2020 as the date of peak of Coronavirus in India. However, in current scenario of partial to zero lockdown phase in India, the peak of Coronavirus cases is predicted to be July 31, 2020. These two predictions presented in this work provide awareness among citizens of India on importance of control measures such as full, partial and zero lockdown and the spread of Corona disease infection rate. In addition to this, it is a beneficial study for the government of India to plan the things ahead.

Using a notably large amount of data in investigating physical and chemical phenomena demands new statistical and computational approaches; besides, the cross-validations require well-established theoretical frameworks. This study aims to validate the statistical efficiency of alternative definitions for the information-theoretic measures, such as transfer entropy, using the so-called (, q)-framework. The primary goal is to find measurements of high-order correlations that preserve information-theoretic properties of information transfer between the components of a dynamical system (such as a protein) due to local operations. Besides, this study aims to decode the information contained in the amino acid sequence establishing a three-dimensional protein structure by comparing the amino acids physical-chemical properties with their ranked role in the protein interaction network topology using new graph-theoretic measures based on the constructed digraph models of (, q) information transfer within a heat flow kernel embedding framework. Moreover, this study aims to use the Deep Graph Convolution Neural Networks for classifying the role of each amino acid in a protein trained upon short equilibrium structure fluctuations at sub-nanosecond time scales. In particular, this study examines the influence of disulphide bridges on the three-dimensional structure of the Bovine Pancreatic Trypsin Inhibitor wild type and mutated analogue protein.

It was observed that the multiple peaks of coronavirus disease-19 (COVID-19) appeared in different seasons in different countries. There were countries where the COVID-19 peak occurred during extremely low temperatures, such as Norway, Canada and on the other hand there were countries with high-temperature ranges such as Brazil, India, UAE. Most of the high-latitude countries received their outbreak in winter and most of the countries near the equator mark the outbreak during the summer. Most of the biological organisms have their growth dependant on the temperature, and hence we explored that if there is any relation of temperature versus COVID-19 outbreak in the particular country. It was also seen that people are not behaving differently during the peak of the COVID-19 wave, hence it was important to know whether the COVID-19 virus has evolved or the global temperature variation caused these multiple peaks. This work focuses on finding the effect of temperature variation on the COVID-19 outbreak. We used Levenberg-Marquardt technique to find the correlation between the temperature at which COVID-19 outbreak peaks and the latitude of the particular country. We found that between the temperature range of 14 {degrees}C to 20 {degrees}C spread of the COVID-19 is minimal. Based on our results we can also say that the COVID-19 outbreak is seen in lower temperature (0 {degrees}C to 13 {degrees}C) ranges as well as in the higher temperature ranges (21 {degrees}C to 35 {degrees}C). The current data analysis will help the authorities to manage their resources in advance to prepare for any further outbreaks that might occur in the COVID-19 or even in the next pandemic.

The novel coronal virus has spread across more than 213 countries within the space of six months causing devastating public health hazard and monumental economic loss. In the absence of clinically approved pharmaceutical intervention, attentions are shifted to non-pharmaceutical controls to mitigate the burden of the novel pandemic. In this regard, a ten mutually exclusive compartmental mathematical model is developed to investigate possible effects of both pharmaceutical and non-pharmaceutical controls incorporating both private and governments quarantine and treatments. Several reproduction numbers were calculated and used to determine the impact of both control measures as well as projected benefits of social distancing, treatments and vaccination. We investigate and compare the possible impact of social distancing incorporating different levels of vaccination, with vaccination programme incorporating different levels of treatment. Using the officially published South African COVID-19 data, the numerical simulation shows that the community reproduction threshold will be 30 when there is no social distancing but will drastically reduced to 5 (about 83% reduction) when social distancing is enforced. Furthermore, when there is vaccination with perfect efficacy, the community reproduction threshold will be 4 which increases to 12 (about 67% increment) with-out vaccination. We also established that the implementation of both interventions is enough to curtail the spread of COVID-19 pandemic in South Africa which is in confirmation with the recommendation of the world health organization.

Estimation of COVID-19 dynamics and its evolution is a multidisciplinary effort, which requires the unification of heterogeneous disciplines (scientific, mathematics, epidemiological, biological/bio-chemical, virologists and health disciplines to mention the most relevant) to work together in a better understanding of this pandemic. Time series analysis is of great importance to determine both the similarity in the behavior of COVID-19 in certain countries/states and the establishment of models that can analyze and predict the transmission process of this infectious disease. In this contribution, an analysis of the different states of the United States will be carried out to measure the similarity of COVID-19 time series, using dynamic time warping distance (DTW) as a distance metric. A parametric methodology is proposed to jointly analyze infected and deceased persons. This metric allows to compare time series that have a different time length, making it very appropriate for studying the United States, since the virus did not spread simultaneously in all the states/provinces. After a measure of the similarity between the time series of the states of United States was determined, a hierarchical cluster was created, which makes it possible to analyze the behavioral relationships of the pandemic between different states and to discover interesting patterns and correlations in the underlying data of COVID-19 in the United States. With the proposed methodology, nine different clusters were obtained, showing a different behavior in the eastern zone and western zone of the United States. Finally, to make a prediction of the evolution of COVID-19 in the states, Logistic, Gompertz and SIR model was computed. With these mathematical model it is possible to have a more precise knowledge of the evolution and forecast of the pandemic.

AO_SCPLOWBSTRACTC_SCPLOWIn this paper the concept of Critical Community Size (CCS) for the deterministic SIR model is introduced and its consequences for the disease dynamics are stressed. The disease can fade out after an outburst. Also the principle of competitive exclusion holds no longer true. This is exemplified for the dynamics of two competing virus strains. The virus with higher R0 can be eradicated from the population.

Since its origin in December 2019, Novel Coronavirus or COVID-19 has caused massive panic in the word by infecting millions of people with a varying fatality rate. The main objective of Governments worldwide is to control the extent of the outbreak until a vaccine or cure has been devised. Machine learning has been an efficient mechanism to train, map, analyze, and predict datasets. This paper aims to utilize regression, a supervised machine learning algorithm to assess time-series datasets of COVID-19 pandemic by performing comparative analysis on datasets of India and two Municipal Corporations of Maharashtra, namely, Mira-Bhayander and Akola. Current study is an attempt towards drawing attention to the dynamics and nature of the pandemic in a controlled locality such as Municipal Corporation; which differs from the exponential nature observed nationally. However, for limited area like the one considered the nature of curve is observed to be cubic for total cases and multi-peak Gaussian for active cases. In conclusion, Government should empower district/ corporations/local authorities to adopt their own methodology and decision-making policy to contain the pandemic at regional-level like the case study discussed herein.

The collective intelligence of animal groups is a complex algorithm for computer scientist and a many-body problem for physics of living system. We show how the time evolution of features in such a system, like number of ants in particular state for colonies, can be mapped to many-body problems in non-equilibrium statistical mechanics. There exist role transitions of active and passive ant between distributed functions, including exploration, assessing, recruiting and transportation in the house-hunting process. Theoretically, such a process can be approximately described as birth-death process where large number of particles living in the Fock space and particles of one sub-type transfer to a different sub-type with some probability. Started from the master equation with constrain of the quorum criterion, we express the evolution operator as a functional integral mapping from operators acting on Fock space in number representation to functional space in coherent state representation. We then read out the action from the evolution operator, and we use least action principal equations of motion, which are the number field equations. The equations we get are couple ordinary differential equations, which can faithfully describe the original master equation, and hence fully describe the system. This method provides us differential equation-based algorithm, which allow us explore parameter space with respect to more complicated agent-based algorithm. The algorithm also allows exploring stochastic process with memory in a Markovian way, which provide testable prediction on collective decision making.

1Today we are able to describe genome evolution but, there are still several open questions on this area such as: Which is the probability that a mutation occurs at a nucleotide level? Is it possible to predict the evolution of a particular genome?, or talking about preservation, is there a way to simulate the genetic diversity for endangered species? In this paper it is shown that it is possible to make a mathematical model not only of mutations on the genome of species, but of evolution itself, including factors such as artificial and natural selection. It is also presented the algorithm to obtain the probabilities of mutation for each specific part of the genome and for each specie.\n\nEven more, it is presented a mathematical method to estimate the amount of generations between two related genomes and a function capable of predict the amount of mutations through time a genome will suffer.\n\nThe potential of having this tool is giantic going from genetic engineering applied to medicine to filling up blank spaces in phylogenetic studies or preservation of endangered species due to genetic diversity.

Developing antiviral drugs is an exigent task since viruses mutate to overcome the effect of antiviral drugs. As a result, the efficacy of most antiviral drugs is short-lived. To include this effect, we modify the Neumann and Dahari model. Considering the fact that the efficacy of the antiviral drug varies in time, the differential equations introduced in the previous model systems are rewritten to study the correlation between the viral load and antiviral drug. The effect of antiviral drug that either prevents infection or stops the production of a virus is explored. First, the efficacy of the drug is considered to decreases monotonously as time progresses. In this case, our result depicts that when the efficacy of the drug is low, the viral load decreases and increases back in time revealing the effect of the antiviral drugs is short-lived. On the other hand, for the antiviral drug with high efficacy, the viral load, as well as the number of infected cells, monotonously decreases while the number of uninfected cells increases. The dependence of the critical drug efficacy on time is also explored. Moreover, the correlation between viral load, the antiviral drug, and CTL response is also explored. In this case, not only the dependence for the basic reproduction ratio on the model parameters is explored but also we analyze the critical drug efficacy as a function of time. We show that the term related to the basic reproduction ratio increases when the CTL response step up. A simple analytically solvable mathematical model is also presented to analyze the correlation between viral load and antiviral drugs.

Protein-DNA complexes are involved in vital cellular functions like gene regulation, replication, transcription, packaging, rearrangement, and damage repair. In this work, streamlined geometric formalism for computing the absolute binding free energy was used to obtain chemical accurate in silico estimation of binding free energy of three Protein-DNA complexes. Additionally, molecular interactions between Protein and DNA involved hydrogen bonds, electrostatic, van der Waals, and hydrophobic interactions. Using this formalism, researcher can obtain the absolute binding free energy for a Protein-DNA complex with remarkable accuracy and modest computational cost.

AO_SCPLOWBSTRACTC_SCPLOWIn this paper, we study the absorption and fixation times for evolutionary processes on graphs, under different updating rules. While in Moran process a single neighbour is randomly chosen to be replaced, in proliferation processes other neighbours can be replaced using Bernoulli or binomial draws depending on 0 < p [&le;] 1. There is a critical value pc such that the proliferation is advantageous or disadvantageous in terms of fixation probability depending on whether p > pc or p < pc. We clarify the role of symmetries for computing the fixation time in Moran process. We show that the Maruyama-Kimura symmetry depend on the graph structure induced in each state, implying asymmetry for all graphs except cliques and cycles. There is a fitness value, not necessarily 1, beyond which the fixation time decreases monotonically. We apply Harris graphical method to prove that the fixation time decreases monotonically depending on p. Thus there exists another value pt for which the proliferation is advantageous or disadvantageous in terms of time. However, at the critical level p = pc, the proliferation is highly advantageous when r [-&gt;] +{infty}.

Novel topological methods are introduced to protein research. The aim is to identify hot-spot sites where a bifurcation can change the local topology of the protein backbone. Since the shape of a protein is intimately related to its biological function, a mutation that takes place at such a bifurcation hot-spot has an enhanced capacity to change the proteins biological function. The methodology applies to any protein but it is developed with the SARS-CoV-2 spike protein as a timely example. First, topological criteria are introduced to identify and classify potential mutation hot-spot sites along the protein backbone. Then, the expected outcome of a substitution mutation is estimated for a general class of hot-spots, by a comparative analysis of the backbone segments that surround the hot-spot sites. This analysis employs the statistics of commensurable amino acid fragments in the Protein Data Bank, in combination with general stereochemical considerations. It is observed that the notorious D614G substitution of the spike protein is a good example of such a mutation hot-spot. Several topologically similar examples are then analyzed in detail, some of them are even better candidates for a mutation hot-spot than D614G. The local topology of the recently observed N501Y mutation is also inspected, and it is found that this site is prone to a different kind of local topology changing bifurcation.

We propose an algorithm to simulate Markovian SIS epidemics with homogeneous rates and pairwise interactions on a fixed undirected graph, assuming a distributed memory model of parallel programming and limited bandwidth. We offer an implementation of the algorithm in the form of pseudocode in the Appendix. Also, we analyze its algorithmic complexity and its induced dynamical system. Finally, we design experiments to show its scalability and faithfulness. We believe this algorithm offers a way of scaling out, allowing researchers to run simulation tasks at a scale that was not accessible before. Furthermore, we believe this algorithm lays a solid foundation for extensions to simulating more advanced epidemic processes and graph dynamics in other fields. Author summaryModeling and simulation are two essential components in many decision-making processes. Many real-world phenomena can be modeled by a spreading process on a graph, such as the gossip protocol in distributed computing, the word-of-mouth effect in marketing, and a contagious disease that spreads among a population. It is not always possible to study these problems analytically, making computer-based simulations the only tool to make predictions about the system under study. Depending on the scale of the system, such simulations can be computationally expensive, especially when a large range of parameters are to be tested. We propose in this article an algorithm to leverage parallel or distributed computing hardware for discrete event simulations and use a simple susceptible-infected-susceptible epidemic to illustrate the key idea of the algorithm. This algorithm allows one to make trade-offs between scalability and accuracy of the simulation. We believe that this algorithm will find wide applications in simulating graph dynamics.

The outbreak of COVID-19 has an undeniable global impact, both socially and economically. March 11th, 2020, COVID-19 was declared as a pandemic worldwide. Many governments, worldwide, have imposed strict lockdown measures to minimize the spread of COVID-19. However, these measures cannot last forever; therefore, many countries are already considering relaxing the lockdown measures. This study, quantitatively, investigated the impact of this relaxation in the United States, Germany, the United Kingdom, Italy, Spain, and Canada. A modified version of the SIR model is used to model the reduction in lockdown based on the already available data. The results showed an inevitable second wave of COVID-19 infection following loosening the current measures. The study tries to reveal the predicted number of infected cases for different reopening dates. Additionally, the predicted number of infected cases for different reopening dates is reported.

Forecast of the peak-out and settling timing of COVID-19 at an early stage should help the people how to cope with the situation. Curve-fitting method with an asymmetric log-normal function has been applied to daily confirmed cases data in various countries. Most of the curve-fitting could show good forecasts, while the reason has not been clearly shown. The K value has recently been proposed which can provide good reasoning of curve-fitting mechanism by corresponding a long and steep slope on the K curve with fitting stability. Since K can be expressed by a time differential of logarithmic total cases, the physical background of the above correspondence was discussed in terms of the growth rate in epidemic entropy.

The computation model for evaluation of conformational entropy changes upon binding ligands to receptors is described. Then, changes of conformational entropy component and of binding free energy are compared. Interest to conformational entropy arises from developing new drugs as it might be changed purposefully. It is shown that conformational entropy may be used for prediction of affinity to a certain receptor. Examples of directed affinity change under the modification of substances conformational flexibility are given. The specific role of the conformational entropy in the receptors protection from the irreversible inactivation is identified.

The catastrophic outbreak of Severe Acute Respiratory Syndrome - Coronavirus (SARS-CoV-2) also known as COVID-2019 has brought the worldwide threat to the living society. The whole world is putting incredible efforts to fight against the spread of this deadly disease in terms of infrastructure, finance, data sources, protective gears, life-risk treatments and several other resources. The artificial intelligence researchers are focusing their expertise knowledge to develop mathematical models for analyzing this epidemic situation using nationwide shared data. To contribute towards the well-being of living society, this article proposes to utilize the machine learning and deep learning models with the aim for understanding its everyday exponential behaviour along with the prediction of future reachability of the COVID-2019 across the nations by utilizing the real-time information from the Johns Hopkins dashboard.

There is no consensus about when a potential viral infection event presents greater risk of a successful transmission. Some authors suggest that late infection stages present higher risk of transmission. Others suggest that the early infection stages play a most relevant role in transmission events. However, studies considering the fitness or mutational effects on the viral particles over transmission events are lacking. We propose to approach this question through a two-level mathematical model based on RNA viral population dynamics. The first level of the model represents the intra-host viral population dynamics and the second level of the model represents the host-to-host dynamics of transmission events. The intra-host dynamics model uses the fitness of viral particles as means to track the presence of highly infective particles during transmission bottlenecks. More specifically, the intra-host dynamics is described by a stochastic quasispecies, based on a multivariate branching process. The host-to-host dynamics of transmission events is emulated by a putative transmission tree with host zero at the root and a fixed number of branches emanating from each internal node. A Monte Carlo strategy was adopted to explore the tree by sampling random walks along transmission chains along the tree. Viral infections of a single host and several transmission events among hosts were simulated in early and late infection stages scenarios. The results show that the early infection stages may represent a key factor in the viral pandemic. Over the evolution of the viral population within each host the mean fitness decreases due to occurrence of mutations (most of them causing deleterious effects). Despite the small opportunity interval, transmissions that occur in early stages could probably infect new hosts at a higher rate than in late stages. It was observed that a very early transmission scenario could reach a transmission chain 20 times longer than a very late transmission scenario. This indicates that the quality of the viral particles is a relevant factor for transmission events.