Quantitative analysis of social influence and digital piracy contagion with differential equations on networks.

Illegal file sharing of copyrighted contents through popular file sharing networks poses an enormous threat to providers of digital contents, such as, games, softwares, music and movies. Though empirical studies of network effects on piracy is a well-studied domain, the dynamics of peer effect in the context of evolving social contagion has not been enough explored using dynamical models. In this research, we methodically study the trends of online piracy with a continuous ODE approach and differential equations on graphs to have a clear comparative view. We first formulate a compartmental model to study bifurcations and thresholds mathematically. We later move on with a network-based analysis to illustrate the proliferation of online piracy dynamics with an epidemiological approach over a social network. We figure out a solution for this online piracy problem by developing awareness among individuals and introducing media campaigns, which could be a valuable factor in eradicating and controlling online piracy. Next, using degree-block approximation, network analysis has been performed to investigate the phenomena from a heterogeneous approach and to derive the threshold condition for the persistence of piracy in the population in a steady state. Considering the dual control of positive peer influence and media-driven awareness, we examine the system through realistic parameter selection to better understand the complexity of the dynamics and suggest policy implications.

Promote to protect: data-driven computational model of peer influence for vaccine perception.

Vaccine hesitancy and acceptance, driven by social influence, is usually explored by most researchers using exhaustive survey-based studies, which investigate public preferences, fundamental values, beliefs, barriers, and drivers through closed or open-ended questionnaires. Commonly used simple statistical tools do not do justice to the richness of this data. Considering the gradual development of vaccine acceptance in a society driven by multiple local/global factors as a compartmental contagion process, we propose a novel methodology where drivers and barriers of these dynamics are detected from survey participants' responses, instead of heuristic arguments. Applying rigorous natural language processing analysis to the survey responses of participants from India, who are from various socio-demographics, education, and perceptions, we identify and categorize the most important factors as well as interactions among people of different perspectives on COVID-19 vaccines. With a goal to achieve improvement in vaccine perception, we also analyze the resultant behavioral transitions through platforms of unsupervised machine learning and natural language processing to derive a compartmental contagion model from the data. Analysis of the model shows that positive peer influence plays a very important role and causes a bifurcation in the system that reflects threshold-sensitive dynamics.

How surface and fomite infection affect contagion dynamics: a study with self-propelled particles.

Self-propelled particles have been a tool of choice for many studies for understanding spatial interaction of people and propagation of infectious diseases. Other than the direct contagion process through face-to-face contacts with an infected agent, in some diseases, like COVID-19, the disease can spread by indirect ways, through contaminated object surfaces and puff-clouds created by the infected individual. However, this dual spreading process and the impact of these indirect infections in the entire dynamics are not properly explored. In this work, we consider epidemic spreading in an artificial society, with realistic parameters and movements of people, along with the possibilities of indirect exposure through contaminated surfaces and puff-clouds. This particular simulation based infectious disease dynamics is associated with the movements of some self-propelled free agents executing random motion which is investigated in conjunction with the rules of a realistic contagion process. With mathematical formulation and extensive computational studies, we have accommodated the indirect infection possibilities into the dynamics by incorporating an infectious 'tail' with the infected individuals. Analytical expressions of survival distance and infection probability of individuals have been explicitly calculated and reported. Results of precise and comparative simulation study have revealed the seriousness of indirect infections in connection with several dynamical parameters. Using this framework, interpretation of multiple waves in local as well as global scenarios have been established for COVID-19 infection statistics. Furthermore, the importance of indirect infections are also pointed out through data fitting, showing that ignoring this component might cause a misinterpretation of the dynamical parameters, like, imposed restrictions.

Emergent correlations in gene expression dynamics as footprints of resource competition.

Genetic circuits need a cellular environment to operate in, which naturally couples the circuit function with the overall functionality of gene regulatory network. To execute their functions, all gene circuits draw resources in the form of RNA polymerases, ribosomes, and tRNAs. Recent experiments pointed out that the role of resource competition on synthetic circuit outputs could be immense. However, the effect of complexity of the circuit architecture on resource sharing dynamics is yet unexplored. In this paper, we employ mathematical modelling and in-silico experiments to identify the sources of resource trade-off and to quantify its impact on the function of a genetic circuit, keeping our focus on regulation of immediate downstream proteins, which are often used as protein read-outs. We show that estimating gene expression dynamics from readings of downstream protein data might be unreliable when the resource is limited and ribosome affinities are asymmetric. We focus on the impact of mRNA copy number and ribosome binding site (RBS) strength on the nonlinear isocline that emerges with two regimes, prominently separated by a tipping point, and study how correlation and competition dominate each other depending on various circuit parameters. Focusing further on genetic toggle circuit, we have identified major effects of resource competition in this model motif and quantified the observations. The observations are testable in wet-lab experiments, as all the parameters chosen are experimentally relevant.

Computational Model on COVID-19 Pandemic Using Probabilistic Cellular Automata.

Since March, 2020, Coronavirus disease (COVID-19) has been designated as a pandemic by World Health Organization. This disease is highly infectious and potentially fatal, causing a global public health concern. To contain the spread of COVID-19, governments are adopting nationwide interventions, like lockdown, containment and quarantine, restrictions on travel, cancelling social events and extensive testing. To understand the effects of these measures on the control of the epidemic in a data-driven manner, we propose a probabilistic cellular automata (PCA) based epidemiological model. The transitions associated with the model is driven by data available on chronology, symptoms, pathogenesis and transmissivity of the virus. By arguing that the lattice-based model captures the features of the dynamics along with the existing fluctuations, we perform rigorous computational analyses of the model to take into account of the spatial dynamics of social distancing measures imposed on the people. Considering the probabilistic behavioral aspects associated with mitigation strategies, we study the model considering factors like population density and testing efficiency. Using the model, we focus on the variability of epidemic dynamics data for different countries, and point out the reasons behind these contrasting observations. To the best of our knowledge, this is the first attempt to model COVID-19 spread using PCA that gives us both spatial and temporal variations of the infection spread with the insight about the contributions of different infection parameters.

A data-driven understanding of COVID-19 dynamics using sequential genetic algorithm based probabilistic cellular automata.

COVID-19 pandemic is severely impacting the lives of billions across the globe. Even after taking massive protective measures like nation-wide lockdowns, discontinuation of international flight services, rigorous testing etc., the infection spreading is still growing steadily, causing thousands of deaths and serious socio-economic crisis. Thus, the identification of the major factors of this infection spreading dynamics is becoming crucial to minimize impact and lifetime of COVID-19 and any future pandemic. In this work, a probabilistic cellular automata based method has been employed to model the infection dynamics for a significant number of different countries. This study proposes that for an accurate data-driven modelling of this infection spread, cellular automata provides an excellent platform, with a sequential genetic algorithm for efficiently estimating the parameters of the dynamics. To the best of our knowledge, this is the first attempt to understand and interpret COVID-19 data using optimized cellular automata, through genetic algorithm. It has been demonstrated that the proposed methodology can be flexible and robust at the same time, and can be used to model the daily active cases, total number of infected people and total death cases through systematic parameter estimation. Elaborate analyses for COVID-19 statistics of forty countries from different continents have been performed, with markedly divergent time evolution of the infection spreading because of demographic and socioeconomic factors. The substantial predictive power of this model has been established with conclusions on the key players in this pandemic dynamics.

Ensuring the spread of referral marketing campaigns: a quantitative treatment.

In marketing world, social media is playing a crucial role nowadays. One of the most recent strategies that exploit social contacts for the purpose of marketing, is referral marketing, where a person shares information related to a particular product among his/her social contacts. When this spreading of marketing information goes viral, the diffusion process looks like an epidemic spread. In this work, we perform a systematic study with a goal to device a methodology for using the huge amount of survey data available to understand customer behaviour from a more mathematical and quantitative perspective. We perform an unsupervised natural language processing and hierarchical clustering based analysis of the responses of a recent survey focused on referral marketing to correlate the customers' psychology with transitional dynamics, and investigate some major determinants that regulate the diffusion of a campaign. In addition to natural language processing for topic modeling, detailed differential equation based analysis and graph theoretical treatment have been carried out to explore the conditions of success for the campaign in terms of realistic parameters both for homogeneous and heterogeneous population structure. Finally, experiments have been performed for generation of a recommendation network to understand the diffusion dynamics in realistic scenario. A complete mathematical treatment with analysis over real social networks helped us to determine key customer motivations and their impacts on a marketing strategy, which are important to ensure an effective spread of a designed marketing campaign. Because of its systematic generalized formulation, the prescribed quantitative framework may be useful in all areas of social dynamics, beyond the field of marketing.

Non-genetic heterogeneity, criticality and cell differentiation.

The different cell types in a living organism acquire their identity through the process of cell differentiation in which multipotent progenitor cells differentiate into distinct cell types. Experimental evidence and analysis of large-scale microarray data establish the key role played by a two-gene motif in cell differentiation in a number of cell systems. The two genes express transcription factors which repress each other's expression and autoactivate their own production. A number of theoretical models have recently been proposed based on the two-gene motif to provide a physical understanding of how cell differentiation occurs. In this paper, we study a simple model of cell differentiation which assumes no cooperativity in the regulation of gene expression by the transcription factors. The latter repress each other's activity directly through DNA binding and indirectly through the formation of heterodimers. We specifically investigate how deterministic processes combined with stochasticity contribute in bringing about cell differentiation. The deterministic dynamics of our model give rise to a supercritical pitchfork bifurcation from an undifferentiated stable steady state to two differentiated stable steady states. The stochastic dynamics of our model are studied using the approaches based on the Langevin equations and the linear noise approximation. The simulation results provide a new physical understanding of recent experimental observations. We further propose experimental measurements of quantities like the variance and the lag-1 autocorrelation function in protein fluctuations as the early signatures of an approaching bifurcation point in the cell differentiation process.

Noise-induced regime shifts: A quantitative characterization.

Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise-driven regime shifts even if the system is away from the bifurcation points. In this paper, we propose a new quantitative measure, namely, the propensity transition point as an indicator of stochastic regime shifts. The concepts and the methodology are illustrated for the one-variable May model, a well-known model in ecology and the genetic toggle, a two-variable model of a simple genetic circuit. The general applicability and usefulness of the method for the analysis of regime shifts is further demonstrated in the case of the mycobacterial switch to persistence for which experimental data are available.

Early signatures of regime shifts in gene expression dynamics.

Recently, a large number of studies have been carried out on the early signatures of sudden regime shifts in systems as diverse as ecosystems, financial markets, population biology and complex diseases. The signatures of regime shifts in gene expression dynamics are less systematically investigated. In this paper, we consider sudden regime shifts in the gene expression dynamics described by a fold-bifurcation model involving bistability and hysteresis. We consider two alternative models, models 1 and 2, of competence development in the bacterial population B. subtilis and determine some early signatures of the regime shifts between competence and noncompetence. We use both deterministic and stochastic formalisms for the purpose of our study. The early signatures studied include the critical slowing down as a transition point is approached, rising variance and the lag-1 autocorrelation function, skewness and a ratio of two mean first passage times. Some of the signatures could provide the experimental basis for distinguishing between bistability and excitability as the correct mechanism for the development of competence.

Phenotypic heterogeneity in mycobacterial stringent response.

BACKGROUND: A common survival strategy of microorganisms subjected to stress involves the generation of phenotypic heterogeneity in the isogenic microbial population enabling a subset of the population to survive under stress. In a recent study, a mycobacterial population of M. smegmatis was shown to develop phenotypic heterogeneity under nutrient depletion. The observed heterogeneity is in the form of a bimodal distribution of the expression levels of the Green Fluorescent Protein (GFP) as reporter with the gfp fused to the promoter of the rel gene. The stringent response pathway is initiated in the subpopulation with high rel activity. RESULTS: In the present study, we characterise quantitatively the single cell promoter activity of the three key genes, namely, mprA, sigE and rel, in the stringent response pathway with gfp as the reporter. The origin of bimodality in the GFP distribution lies in two stable expression states, i.e., bistability. We develop a theoretical model to study the dynamics of the stringent response pathway. The model incorporates a recently proposed mechanism of bistability based on positive feedback and cell growth retardation due to protein synthesis. Based on flow cytometry data, we establish that the distribution of GFP levels in the mycobacterial population at any point of time is a linear superposition of two invariant distributions, one Gaussian and the other lognormal, with only the coefficients in the linear combination depending on time. This allows us to use a binning algorithm and determine the time variation of the mean protein level, the fraction of cells in a subpopulation and also the coefficient of variation, a measure of gene expression noise. CONCLUSIONS: The results of the theoretical model along with a comprehensive analysis of the flow cytometry data provide definitive evidence for the coexistence of two subpopulations with overlapping protein distributions.