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We undertake extensive analysis of English Premier League data over the period 2009/10 to 2017/18 to identify and rank key factors affecting the economic and footballing performances of the teams. Alternative end-of-season league tables are generated by re-ranking the teams based on five different descriptors - total expenditure, total funds spent on players, total funds spent on foreign players, the ratio of foreign to British players and the overall profit. The unequal distribution of resources and expenditure between the clubs is analyzed through Lorenz curves. A comparative analysis of the differences between the alternative tables and the conventional end-of-season league table establishes the most likely factors to influence the performances of the teams that we also rank using Principal Component Analysis. We find that the top teams in the league are also those that tend to have the highest expenditure overall, for all players, including foreign players; they also have the highest ratios of foreign to British players. Our statistical and machine learning study also indicates that successful performance on the field may not guarantee healthy profits at the end of the season., Comment: Graphical Abstract & 8 figures in the main text, 3 Appendices with additional figures and tables

The study explores Artificial Intelligence (AI) powered modeling to predict the evolution of cancer tumor cells in mice under different forms of treatment. The AI models are analyzed against varying ambient and systemic parameters, e.g. drug dosage, volume of the cancer cell mass, and time taken to destroy the cancer cell mass. The data required for the analysis have been synthetically extracted from plots available in both published and unpublished literature (primarily using a Matlab architecture called "Grabit"), that are then statistically standardized around the same baseline for comparison. Three forms of treatment are considered - saline (multiple concentrations used), magnetic nanoparticles (mNPs) and fluorodeoxyglycose iron oxide magnetic nanoparticles (mNP-FDGs) - analyzed using three Machine Learning (ML) algorithms, Decision Tree (DT), Random Forest (RF), Multilinear Regression (MLR), and a Deep Learning (DL) module, the Adaptive Neural Network (ANN). The AI models are trained on 60-80% data, the rest used for validation. Assessed over all three forms of treatment, ANN consistently outperforms other predictive models. Our models predict mNP-FDG as the most potent treatment regime that kills the cancerous tumor completely in ca 13 days from the start of treatment. The models can be generalized to other forms of cancer treatment regimens., Comment: 7 figures, 24 pages

Resilient supply chains are often inherently dependent on the nature of their complex interconnected networks that are simultaneously multi-dimensional and multi-layered. This article presents a Supply Chain Network (SCN) model that can be used to regulate downstream relationships towards a sustainable SME using a 4-component cost function structure - Environmental (E), Demand (D), Economic (E), and Social (S). As a major generalization to the existing practice of using phenomenological interrelationships between the EDES cost kernels, we propose a complementary time varying model of a cost function, based on Lagrangian mechanics (incorporating SCN constraints through Lagrange multipliers), to analyze the time evolution of the SCN variables to interpret the competition between economic inertia and market potential. Multicriteria decision making, based on an Analytic Hierarchy Process (AHP), ranks performance quality, identifying key business decision makers. The model is first solved numerically and then validated against real data pertaining to two Small and Medium Enterprises (SMEs) from diverse domains, establishing the domain-independent nature of the model. The results quantify how increases in a production line without appropriate consideration of market volatility can lead to bankruptcy, and how high transportation cost together with increased production may lead to a break-even state. The model also predicts the time it takes a policy change to reinvigorate sales, thereby forecasting best practice operational procedure that ensures holistic sustainability on all four sustainability fronts., Comment: 8 figures, 1 table, 2 appendices. arXiv admin note: text overlap with arXiv:2003.00884

We analyze conflict between a citizenry and an insurgent group over a fixed resource such as land. The citizenry has an elected leader who proposes a division such that, the lower the land ceded to the insurgents, the higher the cost of conflict. Leaders differ in ability and ideology such that the higher the leader's ability, the lower the cost of conflict, and the more hawkish the leader, the higher his utility from retaining land. We show that the conflict arises from the political process with re-election motives causing leaders to choose to cede too little land to signal their ability. We also show that when the rents of office are high, the political equilibrium and the second best diverge; in particular, the policy under the political equilibrium is more hawkish compared to the second best. When both ideology and ability are unknown, we provide a plausible condition under which the probability of re-election increases in the leader's hawkishness, thereby providing an explanation for why hawkish politicians may have a natural advantage under the electoral process., Comment: 2 figures, 1 table, accepted in PLOS One

Model analogies and exchange of ideas between physics or chemistry with biology or epidemiology have often involved inter-sectoral mapping of techniques. Material mechanics has benefitted hugely from such interpolations from mathematical physics where dislocation patterning of platstically deformed metals [1,2,3] and mass transport in nanocomposite materials with high diffusivity paths such as dislocation and grain boundaries, have been traditionally analyzed using the paradigmatic Walgraef-Aifantis (W-A) double-diffusivity (D-D) model [4,5,6,7,8,9]. A long standing challenge in these studies has been the inherent nonlinear correlation between the diffusivity paths, making it extremely difficult to analyze their interdependence. Here, we present a novel method of approximating a closed form solution of the ensemble averaged density profiles and correlation statistics of coupled dynamical systems, drawing from a technique used in mathematical biology to calculate a quantity called the {\it basic reproduction number} $R_0$, which is the average number of secondary infections generated from every infected. We show that the $R_0$ formulation can be used to calculate the correlation between diffusivity paths, agreeing closely with the exact numerical solution of the D-D model. The method can be generically implemented to analyze other reaction-diffusion models., Comment: 5 two-pannelled figures, 13 pages

Clinicians make routine diagnosis by scrutinizing patients' medical signs and symptoms, a skill popularly referred to as "Clinical Eye". This skill evolves through trial-and-error and improves with time. The success of the therapeutic regime relies largely on the accuracy of interpretation of such sign-symptoms, analyzing which a clinician assesses the severity of the illness. The present study is an attempt to propose a complementary medical front by mathematically modeling the "Clinical Eye" of a VIRtual DOCtor, using Statistical and Machine Intelligence tools (SMI), to analyze Dengue epidemic infected patients (100 case studies with 11 weighted sign-symptoms). The SMI in VIRDOCD reads medical data and translates these into a vector comprising Multiple Linear Regression (MLR) coefficients to predict infection severity grades of dengue patients that clone the clinician's experience-based assessment. Risk managed through ANOVA, the dengue severity grade prediction accuracy from VIRDOCD is found higher (ca 75%) than conventional clinical practice (ca 71.4%, mean accuracy profile assessed by a team of 10 senior consultants). Free of human errors and capable of deciphering even minute differences from almost identical symptoms (to the Clinical Eye), VIRDOCD is uniquely individualized in its decision-making ability. The algorithm has been validated against Random Forest classification (RF, ca 63%), another regression-based classifier similar to MLR that can be trained through supervised learning. We find that MLR-based VIRDOCD is superior to RF in predicting the grade of Dengue morbidity. VIRDOCD can be further extended to analyze other epidemic infections, such as COVID-19., Comment: 17 pages, 5 figures, 8 tables

Covid-19 is raging a devastating trail with the highest mortality-to-infected ratio ever for a pandemic. Lack of vaccine and therapeutic has rendered social exclusion through lockdown as the singular mode of containment. Harnessing the predictive powers of Machine Learning within a 6 dimensional infection kinetic model, depicting interactive evolution of 6 infection stages - healthy susceptible ($H$), predisposed comorbid susceptible ($P$), infected ($I$), recovered ($R$), herd immunized ($V$) and mortality ($D$) - the model, PHIRVD, provides the first accurate mortality prediction of 18 countries at varying stages of strategic lockdown, up to 30 days beyond last data training. PHIRVD establishes mortality-to-infection ratio as the correct pandemic descriptor, substituting reproduction number, and highlights the importance of early and prolonged but strategic lockdown to contain secondary relapse. Significance Statement: 1. Accurate prediction of the day-by-day mortality profiles of 18 countries, 30 days beyond the last data of data training. 2. Precise quantification of the impact of early-vs-later lockdown impositions. 3. Accurate prediction of secondary relapse timelines/ 4. Establishment of mortality-to-infected ratio as the correct pandemic descriptor substituting the popular choice of reproduction number, a proven failure in predicting future infection kinetics and secondary surge. The outcomes have potential to redefine healthy policy landscape, particularly in light of secondary relapse and possible future SARS-COV/Ebola group incursion., Comment: 13 pages main text (8figures, 2 tables), 20 pages of appendices (21 figures, 5 tables)

Structured on the paradigmatic Navier-Stokes flow model, we study a stochastically forced Taylor-Couette system in the narrow gap limit, in order to analyze the simultaneous impact of a non-conserved (Gaussian) force and a nonlinear perturbation, in determining linear stability. Our analysis identifies key parametric windows within which the model remarkably retains its linear stability, even against jointly varying stochastic forcing and nonlinear fluctuations. We identify this feature as a {\it latent universality}, that we then utilize to answer the elusive question as to how a recent groundbreaking accretion flow model retains its stability, even in presence of nonlinear perturbations and non-conserved stochastic forcing. Our analytical outline goes beyond the immediate model studied and lays a generic foundation of analyzing stability for nonlinear sheared models acted on by external forces and subjected to boundary layer instability. presence of nonlinear perturbations and non-conserved stochastic forcing. Our analytical outline goes beyond the immediate model studied and lays a generic foundation of analyzing stability for nonlinear sheared models acted on by external forces and subjected to boundary layer instability., Comment: 24 pages, 33 figures

Studies on the influence of a modern lifestyle in abetting Coronary Heart Diseases (CHD) have mostly focused on deterrent health factors, like smoking, alcohol intake, cheese consumption and average systolic blood pressure, largely disregarding the impact of a healthy lifestyle in mitigating CHD risk. In this study, 30+ years' World Health Organization (WHO) data have been analyzed, using a wide array of advanced Machine Learning techniques, to quantify how regulated reliance on positive health indicators, e.g. fruits/vegetables, cereals can offset CHD risk factors over a period of time. Our research ranks the impact of the negative outliers on CHD and then quantifies the impact of the positive health factors in mitigating the negative risk-factors. Our research outcomes, presented through simple mathematical equations, outline the best CHD prevention strategy using lifestyle control only. We show that a 20% increase in the intake of fruit/vegetable leads to 3-6% decrease in SBP; or, a 10% increase in cereal intake lowers SBP by 3%; a simultaneous increase of 10% in fruit-vegetable can further offset the effects of SBP by 6%. Our analysis establishes gender independence of lifestyle on CHD, refuting long held assumptions and unqualified beliefs. We show that CHD risk can be lowered with incremental changes in lifestyle and diet, e.g. fruit-vegetable intake ameliorating effects of alcohol-smoking-fatty food. Our multivariate data model also estimates functional relationships amongst lifestyle factors that can potentially redefine the diagnostics of Framingham score-based CHD-prediction., Comment: 10 pages, 7 tables, 2 figures together with a detailed online supplementary section including another 9 tables and 4 figures

The importance of supply chain management in analyzing and later catalyzing economic expectations while simultaneously prioritizing cleaner production aspects is a vital component of modern finance. Such predictions, though, are often known to be less than accurate due to the ubiquitous uncertainty plaguing most business decisions. Starting from a multi-dimensional cost function defining the sustainability of the supply chain (SC) kernel, this article outlines a 4-component SC module - environmental, demand, economic, and social uncertainties - each ranked according to its individual weight. Our mathematical model then assesses the viability of a sustainable business by first ranking the potentially stochastic variables in order of their subjective importance, and then optimizing the cost kernel, defined from a utility function. The model will then identify conditions (as equations) validating the sustainability of a business venture. The ranking is initially obtained from an Analytical Hierarchical Process; the resultant weighted cost function is then optimized to analyze the impact of market uncertainty based on our supply chain model. Model predictions are then ratified against SME data to emphasize the importance of cleaner production in business strategies., Comment: 18 pages, 9 figures; 3 additional appendices (14 pages)

This is an epidemiological SIRV model based study that is designed to analyze the impact of vaccination in containing infection spread, in a 4-tiered population compartment comprised of susceptible, infected, recovered and vaccinated agents. While many models assume a lifelong protection through vaccination, we focus on the impact of waning immunization due to conversion of vaccinated and recovered agents back to susceptible ones. Two asymptotic states exist, the "disease-free equilibrium" and the "endemic equilibrium"; we express the transitions between these states as function of the vaccination and conversion rates using the basic reproduction number as a descriptor. We find that the vaccination of newborns and adults have different consequences in controlling epidemics. We also find that a decaying disease protection within the recovered sub-population is not sufficient to trigger an epidemic at the linear level. Our simulations focus on parameter sets that could model a disease with waning immunization like pertussis. For a diffusively coupled population, a transition to the endemic state can be initiated via the propagation of a traveling infection wave, described successfully within a Fisher-Kolmogorov framework., Comment: Published version In EPJB has 11 pages (2-columned), 1 Table, 10 figures

A phenomenological mean-field theory is presented to describe the role of external magnetic field, pressure and chemical substitution on the nature of ferromagnetic (FM) to paramagnetic (PM) phase transition in manganites. The application of external field (or pressure) shifts the transition, leading to a field (or pressure) dependent phase boundary along which a tricritical point is shown to exist where a first-order FM-PM transition becomes second-order. We show that the effect of chemical substitution on the FM transition is analogous to that of external perturbations (magnetic field and pressure); this includes the existence of a tricritical point at which the order of transition changes. Our theoretical predictions satisfactorily explain the nature of FM-PM transition, observed in several systems. The modeling hypothesis has been critically verified from our experimental data from a wide range of colossal magnetoresistive manganite single crystals like Sm$_{0.52}$Sr$_{0.48}$MnO$_3$. The theoretical model prediction of a tricritical point has been validated in this experiment which provides a major ramification of the strength of the model proposed., Comment: 17 pages, 5 figures

Linguistic analysis of protein sequences is an underexploited technique. Here, we capitalize on the concept of the lipogram to characterize sequences at the proteome levels. A lipogram is a literary composition which omits one or more letters. A protein lipogram likewise omits one or more types of amino acid. In this article, we establish a usable terminology for the decomposition of a sequence collection in terms of the lipogram. Next, we characterize Uniref50 using a lipogram decomposition. At the global level, protein lipograms exhibit power-law properties. A clear correlation with metabolic cost is seen. Finally, we use the lipogram construction to differentiate proteomes between the four branches of the tree-of-life: archaea, bacteria, eukaryotes and viruses. We conclude from this pilot study that the lipogram demonstrates considerable potential as an additional tool for sequence analysis and proteome classification., Comment: 8 pages, 2 columns, 5 figures

Starting from a Langevin formulation of a thermally perturbed nonlinear elastic model of the ferroelectric smectic-C$^*$ (SmC${*}$) liquid crystals in the presence of an electric field, this article characterizes the hitherto unexplored dynamical phase transition from a thermo-electrically forced ferroelectric SmC${}^{*}$ phase to a chiral nematic liquid crystalline phase and vice versa. The theoretical analysis is based on a combination of dynamic renormalization (DRG) and numerical simulation of the emergent model. While the DRG architecture predicts a generic transition to the Kardar-Parisi-Zhang (KPZ) universality class at dynamic equilibrium, in agreement with recent experiments, the numerical simulations of the model show simultaneous existence of two phases, one a "subdiffusive" (SD) phase characterized by a dynamical exponent value of 1, and the other a KPZ phase, characterized by a dynamical exponent value of 1.5. The SD phase flows over to the KPZ phase with increased external forcing, offering a new universality paradigm, hitherto unexplored in the context of ferroelectric liquid crystals., Comment: 14 pages, 6 figures

Recent experiments on mixed liquid crystals have highlighted the hugely significant role of ferromagnetic nanoparticle impurities in defining the nematic-smectic-A phase transition point. Structured around a Flory-Huggins free energy of isotropic mixing and Landau-de Gennes free energy, this article presents a phenomenological mean-field model that quantifies the role of such impurities in analyzing thermodynamic phases, in a mixture of thermotropic smectic liquid crystal and ferromagnetic nanoparticles. First we discuss the impact of ferromagnetic nanoparticles on the isotropic-ferronematic and ferronematic-ferrosmectic phase transitions and their transition temperatures. This is followed by analysis of various topologies in the phase diagrams. Our model results indicate that there exists a critical concentration of nanoparticle impurities for which the second order N-SmA transition becomes first order at a tricritical point. Calculations based on this model show remarkable agreement with experiment., Comment: 14 pages, 5 figures

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. Technically, the model pans out as a system of coupled {\it Fick type} diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two non-equilibrium local temperature baths e.g. ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, {\it i.e.}, by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified timescale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real life fluctuating environments., Comment: 17 pages, 9 figures; Physical Review E (accepted)

In this article, we discuss a dynamical stochastic model that represents the time evolution of income distribution of a population, where the dynamics develop from an interplay of multiple economic exchanges in the presence of multiplicative noise. The model remit stretches beyond the conventional framework of a Langevin-type kinetic equation in that our model dynamics is self-consistently constrained by dynamical conservation laws emerging from population and wealth conservation. This model is numerically solved and analyzed to interpret the inequality of income as a function of relevant dynamical parameters like the {\it mobility} $M$ and the {\it total income} $\mu$. In our model, inequality is quantified by the {\it Gini index} $G$. In particular, correlations between any two of the mobility index $M$ and/or the total income $\mu$ with the Gini index $G$ are investigated and compared with the analogous correlations resulting from an equivalent additive noise model. Our findings highlight the importance of a multiplicative noise based economic modeling structure in the analysis of inequality. The model also depicts the nature of correlation between mobility and total income of a population from the perspective of inequality measure., Comment: 15 pages, 4 figures

In a recent work (Chattopadhyay, A. K. et al, Europhys. Lett. {\bf 91}, 58003, 2010) based on food consumption statistics, we showed how a stochastic agent based model could represent the time variation of the income distribution statistics in a developing economy, thereby defining an alternative \enquote{poverty index} (PI) that largely agreed with poverty gap index data. This PI used two variables, the probability density function of the income statistics and a consumption deprivation (CD) function, representing the shortfall in the minimum consumption needed for survival. Since the time dependence of the CD function was introduced there through data extrapolation only and not through an endogenous time dependent series, this model left unexplained how the minimum consumption needed for survival varies with time. The present article overcomes these limitations and arrives at a new unified theoretical structure through time varying consumption and income distributions where trade is only allowed when the income exceeds consumption deprivation (CD). Our results reveal that such CD-dynamics reduces the threshold level of consumption of basic necessities, suggesting a possible dietary transition in terms of lower saturation level of food-grain consumption. The new poverty index conforms to recently observed trends more closely than conventional measures of poverty and allows probabilistic prediction of PI for future times., Comment: 10 (2 columned) pages, 8 figures

The dynamical evolution of dislocations in plastically deformed metals is controlled by both deterministic factors arising out of applied loads and stochastic effects appearing due to fluctuations of internal stress. Such type of stochastic dislocation processes and the associated spatially inhomogeneous modes lead to randomness in the observed deformation structure. Previous studies have analyzed the role of randomness in such textural evolution but none of these models have considered the impact of a finite decay time (all previous models assumed instantaneous relaxation which is "unphysical") of the stochastic perturbations in the overall dynamics of the system. The present article bridges this knowledge gap by introducing a colored noise in the form of an Ornstein-Uhlenbeck noise in the analysis of a class of linear and nonlinear Wiener and Ornstein-Uhlenbeck processes that these structural dislocation dynamics could be mapped on to. Based on an analysis of the relevant Fokker-Planck model, our results show that linear Wiener processes remain unaffected by the second time scale in the problem but all nonlinear processes, both Wiener type and Ornstein-Uhlenbeck type, scale as a function of the noise decay time $\tau$. The results are expected to ramify existing experimental observations and inspire new numerical and laboratory tests to gain further insight into the competition between deterministic and random effects in modeling plastically deformed samples., Comment: 8 pages, 7 figures; to appear in Physical Review E

Loss of coherence with increasing excitation amplitudes and spatial size modulation is a fundamental problem in designing Raman fiber lasers. While it is known that ramping up laser pump power increases the amplitude of stochastic excitations, such higher energy inputs can also lead to a transition from a linearly stable coherent laminar regime to a non-desirable disordered turbulent state. This report presents a new statistical methodology, based on first passage statistics, that classifies lasing regimes in Raman fiber lasers, thereby leading to a fast and highly accurate identification of a strong instability leading to a laminar-turbulent phase transition through a self-consistently defined order parameter. The results have been consistent across a wide range of pump power values, heralding a breakthrough in the non-invasive analysis of fiber laser dynamics., Comment: To be published in Nature Scientific Report; 4 figures

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatio-temporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatio-temporal correlations become stronger, such that even small noise can induce standing waves in this parameter regime. With larger noise strengths, standing waves could be induced at finite distances from the (deterministic) phase boundary. The overall dynamics is defined through the interplay of noisy forcing with the inherent reaction-diffusion dynamics., Comment: 8 two-columned pages, 5 figures; Published in PRE; URL: http://link.aps.org/doi/10.1103/PhysRevE.93.05222

The article analyzes the contribution of stochastic thermal fluctuations in the attachment times of the immature T-cell receptor TCR: peptide-major-histocompatibility-complex pMHC immunological synapse bond. The key question addressed here is the following: how does a synapse bond remain stabilized in the presence of high frequency thermal noise that potentially equates to a strong detaching force? Focusing on the average time persistence of an immature synapse, we show that the high frequency nodes accompanying large fluctuations are counterbalanced by low frequency nodes that evolve over longer time periods. Our analysis shows that such a behavior could be easily explained from the fact that the survival probability distribution is governed by two distinct phases, for the two different time regimes. The relatively shorter time scales correspond to the cohesion:adhesion induced immature bond formation whereas the larger time reciprocates the association:dissociation regime leading to TCR:pMHC signaling. From an estimation of the bond survival probability, we show that at shorter time scales, this probability $P_{\Delta}(\tau)$ scales with time $\tau$ as an universal function of a rescaled noise amplitude $\frac{D}{\Delta^2}$, such that $P_{\Delta}(\tau)\sim \tau^{-(\frac{\Delta}{\sqrt{D}}+\frac{1}{2})}$, $\Delta$ being the distance from the mean inter-membrane (T cell:Antigen Presenting Cell) separation distance. The crossover from this shorter to a longer time regime leads to an universality in the dynamics, at which point the survival probability shows a different power-law scaling compared to the one at shorter time scales. In biological terms, such a crossover indicates that the TCR:pMHC bond has a survival probability with a slower decay rate than the longer LFA-1:ICAM-1 bond justifying its stability., Comment: 8 pages, 8 figures; published in Physical Review E, vol. 92, 012706 (2015); DOI:http://dx.doi.org/10.1103/PhysRevE.92.012706

Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic secular variation in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long standing theoretical insufficiency by invoking a compact exact $n$-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third ordered perturbative solution, that leads to a seamless extension to higher order (e.g. fifth order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides., Comment: 4 pages, two columned; to appear in European Physical Journal Plus

Within bioinformatics, the textual alignment of amino acid sequences has long dominated the determination of similarity between proteins, with all that implies for shared structure, function and evolutionary descent. Despite the relative success of modern-day sequence alignment algorithms, so-called alignment-free approaches offer a complementary means of determining and expressing similarity, with potential benefits in certain key applications, such as regression analysis of protein structure-function studies, where alignment-base similarity has performed poorly. Here, we offer a fresh, statistical physics-based perspective focusing on the question of alignment-free comparison, in the process adapting results from 'first passage probability distribution' to summarize statistics of ensemble averaged amino acid propensity values. In this article, we introduce and elaborate this approach., Comment: 6 pages, 3 figures; published in Bioinformatics Journal, vol 31(15), pages 2469-2474; doi: 10.1093/bioinformatics/btv167

Based on dynamic renormalization group techniques, this letter analyzes the effects of external stochastic perturbations on the dynamical properties of cholesteric liquid crystals, studied in presence of a random magnetic field. Our analysis quantifies the nature of the temperature dependence of the dynamics; the results also highlight a hitherto unexplored regime in cholesteric liquid crystal dynamics. We show that stochastic fluctuations drive the system to a second-ordered Kosterlitz-Thouless phase transition point, eventually leading to a Kardar-Parisi-Zhang (KPZ) universality class. The results go beyond quasi-first order mean-field theories, and provides the first theoretical understanding of a KPZ phase in distorted nematic liquid crystal dynamics., Comment: Europhysics Letters, vol. 112, 60002 (2015); DOI: http://dx.doi.org/10.1209/0295-5075/112/60002

Recent epidemiological evidences indicate that arsenic exposure increases risk of atherosclerosis, cardiovascular diseases and microangiopathies in addition to the serious global health concern related to its carcinogenic effects. In experiments on animals, acute and chronic exposure to arsenic directly correlates cardiac tachyarrhythmia, and atherogenesis in a concentration and duration dependent manner. Moreover, the other effects of long-term arsenic exposure include induction of non-insulin dependent diabetes by mechanisms yet to be understood. On the other hand, there are controversial issues, gaps in knowledge, and future research priorities of accelerated incidences of CVD and mortalities in patients with HIV who are under long-term anti-retroviral therapy (ART). Although, both HIV infection itself and various components of ART initiate significant pathological alterations in the myocardium and the vasculature, simultaneous environmental exposure to arsenic which is more convincingly being recognized as a facilitator of HIV viral cycling in the infected immune cells, may contribute an additional layer of adversity in these patients. In this mini-review which have been fortified with our own preliminary data, we will discuss some of the key current understating of chronic arsenic exposure, and its possible impact on the accelerated HIV/ART induced CVD. The review will conclude with notes on recent developments in mathematical modeling in this field that probabilistically forecast incidence prevalence as functions of aging and life style parameters, most of which vary with time themselves; this interdisciplinary approach provides a complementary kernel to conventional biology., Comment: 15 pages, 4 figures; accepted in Bengal Heart Journal

Supply chain optimization schemes have more often than not underplayed the role of inherent stochastic fluctuations in the associated variables. The present article focuses on the associated reengagement and correlated renormalization of supply chain predictions now with the inclusion of stochasticity induced fluctuations in the structure. With a processing production plant in mind that involves stochastically varying production and transportation costs both from the site to the plant as well as from the plant to the customer base, this article proves that the producer may benefit through better outlay in the form of higher sale prices with lowered optimized production costs only through a suitable selective choice of producers whose production cost probability density function abides a Pareto distribution. Lower the Pareto exponent, better is the supply chain prediction for cost optimization. On the other hand, other symmetric (normal) and asymmetric (lognormal) distributions lead to upscaled costs both in terms of inlays and outlays. While this is an averaged out statistics over large time regimes, transient features may still affect such probabilistic predictions and offset results. The predictions are shown to be in good harmony with model results shown., Comment: 25 pages, 7 figures, 1 table

Origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for long. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay, {\it et al} where it was shown that such instabilities, especially for non-magnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a \enquote{cold} accretion flow at 3000K is too \enquote{hot} in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross-correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). In this article we show that nonzero noise cross-correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross-correlation magnifies the strength of the field concerned., Comment: 13 figures in main tex, 8 figures in online supplemental, accepted in Physical Review E

We present a data based statistical study on the effects of seasonal variations in the growth rates of the gastro-intestinal (GI) parasitic infection in livestock. The alluded growth rate is estimated through the variation in the number of eggs per gram (EPG) of faeces in animals. In accordance with earlier studies, our analysis too shows that rainfall is the dominant variable in determining EPG infection rates compared to other macro-parameters like temperature and humidity. Our statistical analysis clearly indicates an oscillatory dependence of EPG levels on rainfall fluctuations. Monsoon recorded the highest infection with a comparative increase of at least 2.5 times compared to the next most infected period (summer). A least square fit of the EPG versus rainfall data indicates an approach towards a super diffusive (i. e. root mean square displacement growing faster than the square root of the elapsed time as obtained for simple diffusion) infection growth pattern regime for low rainfall regimes (technically defined as zeroth level dependence) that gets remarkably augmented for large rainfall zones. Our analysis further indicates that for low fluctuations in temperature (true on the bulk data), EPG level saturates beyond a critical value of the rainfall, a threshold that is expected to indicate the onset of the nonlinear regime. The probability density functions (PDFs) of the EPG data show oscillatory behavior in the large rainfall regime (greater than 500 mm), the frequency of oscillation, once again, being determined by the ambient wetness (rainfall, and humidity). Data recorded over three pilot projects spanning three measures of rainfall and humidity bear testimony to the universality of this statistical argument., Comment: 9 pages, 12 figures

The letter resolves the long standing debate as to the proper time scale ($<\tau>$) of the onset of the immunological synapse (IS) bond, the non-covalent chemical bond defining the immune pathways involving T-cells and antigen presenting cells (APC). Results from our model calculations show $<\tau>$ to be of the order of seconds instead of minutes. Close to the linearly stable regime, we show that in between the two critical spatial thresholds defined by the integrin:ligand pair ($\Delta_2\sim$ 40-45 nm) and the T cell receptor (TCR):pMHC bond ($\Delta_1\sim$ 14-15 nm), $<\tau>$ grows monotonically with increasing co-receptor bond length separation $\delta$ (= $\Delta_2-\Delta_1\sim$ 26-30 nm) while $<\tau>$ decays with $\Delta_1$ for fixed $\Delta_2$. The non-universal $\delta$-dependent power-law structure of the probability density function (PDF) further explains why only the TCR:pMHC bond is a likely candidate to form a stable synapse., Comment: 5 pages, 5 figures

We investigate the evolution of magnetohydrodynamic/hydromagnetic perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable, but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations/experiments. The mismatch seems to have been resolved, atleast in certain regimes, in the presence of weak magnetic field revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial auto-correlations and cross-correlations of perturbation and hence large energy dissipations of perturbation, which generate instability. Interestingly, auto-correlations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work, to the best of our knowledge, is the first attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise., Comment: 14 pages including 18 figures; accepted for publication in Physical Review E. arXiv admin note: text overlap with arXiv:1211.5135

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and then the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations of perturbation, which presumably generate instability. A range of angular velocity (\Omega) profiles of background flow, starting from that of constant specific angular momentum (\lambda = \Omega r^2 ; r being the radial coordinate) to that of constant circular velocity (v_\phi = \Omega r), is explored. However, all the background angular velocities exhibit identical growth and roughness exponents of perturbations, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive noise to the underlying linearized governing equations. This has important implications to resolve the turbulence problem in astrophysical hydrodynamic flows such as accretion disks., Comment: 23 pages including 10 figures; to appear in Journal of Physics A: Mathematical and Theoretical

We study the comparative importance of thermal to non-thermal fluctuations for membrane-based models in the linear regime. Our results, both in 1+1 and 2+1 dimensions, suggest that non-thermal fluctuations dominate thermal ones only when the relaxation time $\tau$ is large. For moderate to small values of $\tau$, the dynamics is defined by a competition between these two forces. The results are expected to act as a quantitative benchmark for biological modelling in systems involving cytoskeletal and other non-thermal fluctuations., Comment: 4 pages, 1 figure

Cilia and flagella are hair-like extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consists of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally., Comment: 19 pages, 5 figures

We present a stochastic agent-based model for the distribution of personal incomes in a developing economy. We start with the assumption that incomes are determined both by individual labour and by stochastic effects of trading and investment. The income from personal effort alone is distributed about a mean, while the income from trade, which may be positive or negative, is proportional to the trader's income. These assumptions lead to a Langevin model with multiplicative noise, from which we derive a Fokker-Planck (FP) equation for the income probability density function (IPDF) and its variation in time. We find that high earners have a power-law income distribution while the low income groups have a Levy IPDF. Comparing our analysis with the Indian survey data (obtained from the world bank website) taken over many years we obtain a near-perfect data collapse onto our model's equilibrium IPDF. The theory quantifies the economic notion of "given other things". Using survey data to relate the IPDF to actual food consumption we define a poverty index, which is consistent with traditional indices, but independent of an arbitrarily chosen "poverty line" and therefore less susceptible to manipulation.

In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement., Comment: revised version, content reorganized, 15 pages including figures, references added

We analyse the size and density of thermally induced regions of close contact in cell:cell contact interfaces within a harmonic potential approximation, estimating these regions to be below one-tenth of a micron across. Our calculations indicate that as the distance between the close contact threshold depth and the mean membrane-membrane separation increases, the density of close contact patches decreases exponentially while there is only a minimal variation in their mean size. The technique developed can be used to calculate the probability of first crossing in reflection symmetry violating systems., Comment: To be published in Europhysics Letters

We show that the energy levels predicted by a 1/N-expansion method for an N-dimensional Hydrogen atom in a spherical potential are always lower than the exact energy levels but monotonically converge towards their exact eigenstates for higher ordered corrections. The technique allows a systematic approach for quantum many body problems in a confined potential and explains the remarkable agreement of such approximate theories when compared to the exact numerical spectrum., Comment: 8 pages, 1 figure

With a new deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the `global' mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reduction in poverty while an increase in the variance of the income distribution increases poverty. This altruistic view for a developing economy, however, is not tenable anymore once the poverty index is found to follow a pareto distribution. Here although a rising mean income indicates a reduction in poverty, due to the presence of an inflexion point in the poverty function, there is a critical value of the variance below which poverty decreases with increasing variance while beyond this value, poverty undergoes a steep increase followed by a decrease with respect to higher variance. Following these results, we make quantitative predictions to correlate a developing with a developed economy., Comment: 13 pages in single spaced latex, 4 figures, submitted to 'Econometrica'

Measurement of lung ventilation is one of the most reliable techniques of diagnosing pulmonary diseases. The time consuming and bias prone traditional methods using hyperpolarized H${}^{3}$He and ${}^{1}$H magnetic resonance imageries have recently been improved by an automated technique based on multiple active contour evolution. Mapping results from an equivalent thermodynamic model, here we analyse the fundamental dynamics orchestrating the active contour (AC) method. We show that the numerical method is inherently connected to the universal scaling behavior of a classical nucleation-like dynamics. The favorable comparison of the exponent values with the theoretical model render further credentials to our claim., Comment: 4 pages, 4 figures

Internal haemorrhage, often leading to cardio-vascular arrest happens to be one of the prime sources of high fatality rates in mammals. We propose a simplistic model of fluid flow to specify the location of the haemorrhagic spots, which, if located accurately, could be operated upon leading to a possible cure. The model we employ for the purpose is inspired by fluid mechanics and consists of a viscous fluid, pumped by a periodic force and flowing through an elastic tube. The analogy is with that of blood, pumped from the heart and flowing through an arte ry or vein. Our results, aided by graphical illustrations, match reasonably well with experimental observations., Comment: 6 pages and 4 figures

We study analytically the effects of inhomogeneous pairing interactions in short coherence length superconductors, using a spatially varying Bogoliubov-deGennes model. Within the Born approximation, it reproduces all of the standard Abrikosov-Gor'kov pairbreaking and gaplessness effects, even in the absence of actual magnetic impurities. For pairing disorder on a single site, the T-matrix gives rise to bound states within the BCS gap. Our results are compared with recent scanning tunneling microscopy measurements on Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ with Zn or Ni impurities., Comment: 4 pages, 2 figures, submitted to PRL