Mathematics

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This paper deals with representing in concrete fashion those Hilbert spaces that are vector subspaces of the Hardy spaces Hp(Dn)(1≤p≤∞) that remain invariant under the action of coordinate wise multiplication by an n-tuple (TB1,…,TBn) of operators where each Bi,1≤i≤n, is a finite Blaschke factor on the open unit disc. The critical point to be noted is that these TBi are assumed to be weaker than isometries as operators. Thus our main theorems extends the principal result of [10] in the following three directions: (i) from one to several variables; (ii) from multiplication with the coordinate function z to an n-tuple of multiplication by finite Blaschke factors Bi,1≤i≤n; (iii) from vector subspaces of H2(D) to the case of vector subspaces of Hp(Dn),1≤p≤∞. We further derive a generalization of Slocinski's well known Wold type decomposition of a pair of doubly commuting isometries to the case of n-tuple of doubly commuting operators whose actions are weaker than isometries. © 2022

(SoNS) School of Natural Sciences

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Journal of Mathematical Analysis and Applications

Multivariable sub-Hardy Hilbert spaces invariant under the action of n-tuple of finite Blaschke factors

The emergence of antimicrobial resistance has raised great concern for public health in many lower-income countries including India. Socio-economic determinants like poverty, health expenditure and awareness accelerate this emergence by influencing individuals' attitudes and healthcare practices such as self-medication. This self-medication practice is highly prevalent in many countries, where antibiotics are available without prescriptions. Thus, complex dynamics of drug- resistance driven by economy, human behaviour, and disease epidemiology poses a serious threat to the community, which has been less emphasized in prior studies. Here, we formulate a game-theoretic model of human choices in self-medication integrating economic growth and disease transmission processes. We show that this adaptive behaviour emerges spontaneously in the population through a self-reinforcing process and continual feedback from the economy, resulting in the emergence of resistance as externalities of human choice under resource constraints situations. We identify that the disparity between social-optimum and individual interest in self-medication is primarily driven by the effectiveness of treatment, health awareness and public health interventions. Frequent multiple-peaks of resistant strains are also observed when individuals imitate others more readily and self-medication is more likely. Our model exemplifies that timely public health intervention for financial risk protection, and antibiotic stewardship policies can improve the epidemiological situation and prevent economic collapse. © 2022 The Authors.

Royal Society Open Science

Disparity in socio-economic status explains the pattern of self-medication of antibiotics in India: Understanding from game-theoretic perspective

Let GL3(Zn) denote the set of 3 × 3 invertible matrices with entries from Zn, the ring of integers modulo n. We study the distribution of a matrix function called the permanent, restricting its domain to GL3(Zn). Given x ∈ Z, we count the number of elements in the set G3(n, x) = {M ∈ GL3(Zn) | perm(M) ≡ x (mod n)}. © 2022, Colgate University. All rights reserved.

Integers

PERMANENTS OF 3 × 3 INVERTIBLE MATRICES MODULO N

Insecticide-treated net (ITN) is the most applicable and cost-effective malaria intervention measure in sub-Saharan Africa and elsewhere. Although ITNs have been widely distributed to malaria-endemic regions in the past, their success has been threatened by misuses (in fishing, agriculture etc.) and decay in ITN efficacy. Decision-making in using the ITNs depends on multiple coevolving factors: malaria prevalence, mosquito density, ITN availability and its efficacy, and other socio-economic determinants. While ITN misuse increases as the efficacy of ITNs declines, high efficacy also impedes proper use due to free-riding. This irrational usage leads to increased malaria prevalence, thereby worsening malaria control efforts. It also remains unclear if the optimum ITN use for malaria elimination can be achieved under such an adaptive social learning process. Here, we incorporate evolutionary game theory into a disease transmission model to demonstrate these behavioural interactions and their impact on malaria prevalence. We show that social optimum usage is a function of transmission potential, ITN efficacy and mosquito demography. Under specific parameter regimes, our model exhibits patterns of ITN usage similar to observed data from parts of Africa. Our study suggests that the provision of financial incentives as prompt feedback to improper ITN use can reduce misuse and contribute positively towards malaria elimination efforts in Africa and elsewhere. © 2022 The Authors.

An evolutionary game model of individual choices and bed net use: Elucidating key aspect in malaria elimination strategies

When a connected component of the set of singular points of the maxface X consists of only generalized cone-like singular point, we construct a sequence of maxfaces Xn, with an increasing number of swallowtails, converging to the maxface X. We include the general discussion toward this. © 2022, Indian Academy of Sciences.

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Swallowtails and cone-like singularities on a maxface

A real square matrix is a Z-matrix if it’s off diagonal elements are nonpositive. A Z-matrix with nonnegative principal minors is called an M-matrix. The problem of testing whether a given matrix is an M-matrix or not is an important research problem in matrix theory as M-matrices arise naturally in a wide range of applications including finite difference methods for partial differential equations, input-output models in economics, linear complementarity problems in operations research, and Markov processes in probability and statistics. In this paper, we present a polynomial-time algorithm for testing whether a Z-matrix is an M-matrix based on modified simplex method. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Annals of Operations Research

On testing nonnegativity of principal minors of Z -matrices using simplex method

Introduction: Assessment of myelodysplasia (MDS) by flow cytometry (FCM) includes elaborate panels, and interpretation is observer-dependent. This study evaluates single tube 10-color FCM in a test cohort of clinically suspected MDS patients. Methods: We analyzed fifty-six bone marrow (BM) samples from clinically suspected MDS patients in a morphology-blinded manner along with controls using a 10-color single tube flow cytometry. We analyzed the reproducibility of Ogata score and modified FCM scores, additionally incorporating the proportion of CD15, CD11b, CD56, and CD38MFI on CD34+CD19-cluster for each patient. Patients were grouped as proven-MDS, suspected-MDS, and non-MDS groups based on morphology and cytogenetics. Optimized multi-axial radar-plots were also used to analyze maturation patterns in the granulocytic, monocytic, and blast progenitor compartments of proven-MDS cases and controls. Results: Flow cytometric abnormalities ≥3 were present in proven-MDS (n = 23) with a sensitivity and specificity of 78 % and 94 %, respectively, as per Ogata score. The addition of CD38 MFI to the score yielded sensitivity and specificity of 82 % and 88 %, respectively. Additional analysis of aberrant expression of CD15, CD11b, and CD56 increased the diagnostic power of the FCM score. A qualitative analysis of data also showed differences in maturation patterns in proven-MDS compared to the control group. Conclusion: Single tube 10-color FCM scoring, including Ogata score, modified-FCM scores, and radar plots pattern analysis, showed significant abnormalities in proven-MDS cases in this pilot study. Large databases, including FCM-scoring and pattern-based analysis for normal BM maturation, could be further validated and standardized for screening MDS. © 2021 Elsevier Ltd

Leukemia Research

The utility of a single tube 10-color flow cytometry for quantitative and qualitative analysis in myelodysplastic syndrome- a pilot study

Let (Formula presented.) be an abelian extension of the Lie superalgebra (Formula presented.). In this article we consider the problems of extending endomorphisms of (Formula presented.) and lifting endomorphisms of (Formula presented.) to certain endomorphisms of (Formula presented.). We connect these problems to the cohomology of (Formula presented.) with coefficients in (Formula presented.) through construction of two exact sequences which are our main results. The first exact sequence is obtained using the Hochschild–Serre spectral sequence corresponding to the above extension while to prove the second we rather take a direct approach. As an application of our results we obtain descriptions of certain automorphism groups of semidirect product Lie superalgebras. © 2021 Informa UK Limited, trading as Taylor & Francis Group.

Linear and Multilinear Algebra

Exact sequences in the cohomology of a Lie superalgebra extension

In this paper, we explore mutual information based stock networks to build regular vine copula structure on high frequency log returns of stocks and use it for the estimation of Value at Risk (VaR) of a portfolio of stocks. Our model is a data driven model that learns from a high frequency time series data of log returns of top 50 stocks listed on the National Stock Exchange (NSE) in India for the year 2014. The Ljung-Box test revealed the presence of Autocorrelation as well as Heteroscedasticity in the underlying time series data. Analysing the goodness of fit of a number of variants of the GARCH model on each working day of the year 2014, that is, 229 days in all, it was observed that ARMA(1,1)-EGARCH(1,1) demonstrated the best fit. The joint probability distribution of the portfolio is computed by constructed an R-Vine copula structure on the data with the mutual information guided minimum spanning tree as the key building block. The joint PDF is then fed into the Monte- Carlo simulation procedure to compute the VaR. If we replace the mutual information by the Kendall's Tau in the construction of the R-Vine copula structure, the resulting VaR estimations were found to be inferior suggesting the presence of non-linear relationships among stock returns. © 2021 Sharma, Sahni. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

PLoS ONE

A mutual information based R-vine copula strategy to estimate VaR in high frequency stock market data

Since the recent introduction of several viable vaccines for SARS-CoV-2, vaccination uptake has become the key factor that will determine our success in containing the COVID-19 pandemic. We argue that game theory and social network models should be used to guide decisions pertaining to vaccination programmes for the best possible results. In the months following the introduction of vaccines, their availability and the human resources needed to run the vaccination programmes have been scarce in many countries. Vaccine hesitancy is also being encountered from some sections of the general public. We emphasize that decision-making under uncertainty and imperfect information, and with only conditionally optimal outcomes, is a unique forte of established game-theoretic modelling. Therefore, we can use this approach to obtain the best framework for modelling and simulating vaccination prioritization and uptake that will be readily available to inform important policy decisions for the optimal control of the COVID-19 pandemic. © 2021 The Authors.