Browsing by Author "Biswas, R."
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Item Additive Properties of the generalized and pseudo n-strong Drazin Inverse in Banach Algebras(Indian National Science Academy, 2025) Biswas, R.; Roy, F.In this paper, we establish some necessary and sufficient conditions for generalized n-strong Drazin invertibility (gns-invertibility) and pseudo n-strong Drazin invertibility (pns-invertibility) of an element in a Banach algebra for n?N. Subsequently, these results are utilized to prove some additive properties of gns (pns)-Drazin inverse. This process produces a generalization of some recent results of H Chen, M Sheibani (Linear and Multilinear Algebra 70.1 (2022): 53-65) for gns and pns-Drazin inverse. © The Indian National Science Academy 2025.Item Comprehensive classification of the algebra generated by two idempotent matrices(Elsevier Inc., 2025) Biswas, R.; Roy, F.For two idempotent matrix P,Q?Cn×n, let alg(In,P,Q) denote the smallest subalgebra of Cn×n that contains P,Q and the identity matrix In. This paper provides a complete classification of alg(In,P,Q) without imposing any restrictions on P and Q. As a result of this classification, the issue of group invertibility within alg(In,P,Q) is fully resolved. © 2024 Elsevier Inc.Item Diseasomics: Actionable machine interpretable disease knowledge at the point-of-care(Public Library of Science, 2022) Talukder, A.K.; Schriml, L.; Ghosh, A.; Biswas, R.; Chakrabarti, P.; Haas, R.E.Physicians establish diagnosis by assessing a patient’s signs, symptoms, age, sex, laboratory test findings and the disease history. All this must be done in limited time and against the backdrop of an increasing overall workload. In the era of evidence-based medicine it is utmost important for a clinician to be abreast of the latest guidelines and treatment protocols which are changing rapidly. In resource limited settings, the updated knowledge often does not reach the point-of-care. This paper presents an artificial intelligence (AI)-based approach for integrating comprehensive disease knowledge, to support physicians and healthcare workers in arriving at accurate diagnoses at the point-of-care. We integrated different disease-related knowledge bodies to construct a comprehensive, machine interpretable diseasomics knowledge-graph that includes the Disease Ontology, disease symptoms, SNOMED CT, DisGeNET, and PharmGKB data. The resulting disease-symptom network comprises knowledge from the Symptom Ontology, electronic health records (EHR), human symptom disease network, Disease Ontology, Wikipedia, PubMed, textbooks, and symptomology knowledge sources with 84.56% accuracy. We also integrated spatial and temporal comorbidity knowledge obtained from EHR for two population data sets from Spain and Sweden respectively. The knowledge graph is stored in a graph database as a digital twin of the disease knowledge. We use node2vec (node embedding) as digital triplet for link prediction in disease-symptom networks to identify missing associations. This diseasomics knowledge graph is expected to democratize the medical knowledge and empower non-specialist health workers to make evidence based informed decisions and help achieve the goal of universal health coverage (UHC). The machine interpretable knowledge graphs presented in this paper are associations between various entities and do not imply causation. Our differential diagnostic tool focusses on signs and symptoms and does not include a complete assessment of patient’s lifestyle and health history which would typically be necessary to rule out conditions and to arrive at a final diagnosis. The predicted diseases are ordered according to the specific disease burden in South Asia. The knowledge graphs and the tools presented here can be used as a guide. © 2022 Talukder et al. 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.Item Drazin and group invertibility in algebras spanned by two idempotents(Elsevier Inc., 2024) Biswas, R.; Roy, F.For two given idempotents p and q from an associative algebra A, in this paper, we offer a comprehensive classification of algebras spanned by the idempotents p and q. This classification is based on the condition that p and q are not tightly coupled and satisfy (pq)m−1=(pq)m but (pq)m−2p≠(pq)m−1p for some m(≥2)∈N. Subsequently, we categorize all the group invertible elements and establish an upper bound for the Drazin index of any elements in these algebras spanned by p,q. Moreover, we formulate a new representation for the Drazin inverse of αp+q under two different assumptions, (pq)m−1=(pq)m and λ(pq)m−1=(pq)m, where α is a non-zero and λ is a non-unit real or complex number. © 2024 Elsevier Inc.Item Equivalency of Drazin and g-Drazin invertibility of elements in a Banach algebra(Indian National Science Academy, 2025) Biswas, R.; Roy, F.Consider a complex unital Banach algebra A. For x1,x2,x3?A, in this paper, we establish that under certain assumptions on x1,x2,x3, Drazin (resp. g-Drazin) invertibility of any three elements among x1,x2,x3 and x1+x2+x3(orx1x2+x1x3+x2x3) ensure the Drazin (resp. g-Drazin) invertibility of the remaining one. As a consequence for two idempotents p,q?A, this result indicates the equivalence between Drazin (resp. g-Drazin) invertibility of (Formula presented.) and (Formula presented.) where ?1,?i?C for i=1,2,?,m, with ?1?1?0; which extend the work of Barraa and Benabdi [1]. Furthermore, for x1,x2, we establish that the Drazin (resp. g-Drazin) invertibility of any two elements among x1,x2 and x1+x2 indicates the Drazin (resp. g-Drazin) invertibility of the remaining one, provided that x1x2=?(x1+x2) for some ??C. Additionally, if it exists, we furnish a new formula to represent the Drazin (resp. g-Drazin) inverse of any element among x1,x2 and x1+x2, by using the other two elements and their Drazin (resp. g-Drazin) inverse. © The Indian National Science Academy 2025.Item Novel materials for energy translation and storage(Nova Science Publishers, Inc., 2024) Biswas, R.; Mal, S.S.; Mazumder, N.Novel materials have come a long way. With the advent of sophisticated fabrication and allied processes, it has become easier to make these novel materials for various applications. These materials have become part and parcel of making storage devices, supercapacitors, fuel cells etc. With the growing automobile as well as allied industrial sectors, the demand for novel materials has skyrocketed of late. As such, there has been a surge of extensive research and development in this sector. Although, there is no dearth of technical papers in this area; however, the absence of synchronized and well-organized content pertinent to this domain is duly felt. In this regard, this proposed book is a unique contribution to filling this gap. With the aim of assimilating theory and practices, this proposed book will endeavor to provide a comprehensive glimpse of recent advancements with a strong unification of theory and practices. The book's topics will encompass the principles of development, fabrication, functionalization, integration, and implementation of these materials. With a plethora of handpicked and well-organized content, this book is believed to cater to the needs of novices, researchers and practitioners. © 2024 by Nova Science Publishers, Inc. All rights reserved.Item Objective Assessment of Pitch Accuracy in Equal-Tempered Vocal Music Using Signal Processing Approaches(2020) Biswas, R.; Murthy, Y.V.S.; Koolagudi, S.G.; Vishnu, S.G.This paper presents�an approach for assessing the pitch in vocal monophonic music objectively using various�signal processing techniques. A database�has been collected with 250 recordings containing�both arohan and avarohan patterns rendered by 25 different singers for 10 Hindustani classical ragas. The fundamental frequency (F0) values of the user renditions are estimated and analyzed with the original pitch values to quantify the level of variations in pitch initially the five-point moving window has been considered to smoothen the contour. Later, first order and second order differential techniques are applied to estimate the note onset. This process is computationally economical when compared with the available approaches. The technique of cents has been used to evaluate the variation among the target and singing pitch as cent is a unit of the most common tuning system for quantifying intonation in equal tempered music. From this analysis, it is observed that singers with professional training have deviations within 15�20 cents, and non-musicians have deviations above 50 cents. Five expert singers rated the global pitch accuracy from the recordings and these results were found to exhibit high correlation with the system�s assessments. Such an evaluation system with quantitative analysis coupled with visual representation will greatly aid the training process of singers. � 2020, Springer Nature Singapore Pte Ltd.Item Objective Assessment of Pitch Accuracy in Equal-Tempered Vocal Music Using Signal Processing Approaches(Springer, 2020) Biswas, R.; Vishnu Srinivasa Murthy, Y.V.S.; Koolagudi, S.G.; Vishnu, S.G.This paper presents an approach for assessing the pitch in vocal monophonic music objectively using various signal processing techniques. A database has been collected with 250 recordings containing both arohan and avarohan patterns rendered by 25 different singers for 10 Hindustani classical ragas. The fundamental frequency (F0) values of the user renditions are estimated and analyzed with the original pitch values to quantify the level of variations in pitch initially the five-point moving window has been considered to smoothen the contour. Later, first order and second order differential techniques are applied to estimate the note onset. This process is computationally economical when compared with the available approaches. The technique of cents has been used to evaluate the variation among the target and singing pitch as cent is a unit of the most common tuning system for quantifying intonation in equal tempered music. From this analysis, it is observed that singers with professional training have deviations within 15–20 cents, and non-musicians have deviations above 50 cents. Five expert singers rated the global pitch accuracy from the recordings and these results were found to exhibit high correlation with the system’s assessments. Such an evaluation system with quantitative analysis coupled with visual representation will greatly aid the training process of singers. © 2020, Springer Nature Singapore Pte Ltd.Item Synthesis and detailed characterization of sustainable starch-based bioplastic(John Wiley and Sons Inc, 2022) Chakraborty, I.; Pooja, N.; Banik, S.; Govindaraju, I.; Das, K.; Mal, S.S.; Zhuo, G.-Y.; Rather, M.A.; Mandal, M.; Neog, A.; Biswas, R.; Managuli, V.; Datta, A.; Mahato, K.K.; Mazumder, N.There is an urgent requirement of replacing the environmentally hazardous petroleum-based plastics with sustainable and efficient starch-based bioplastics. Development and detailed characterization of the biodegradable bioplastics from plant-based polysaccharides such as starch is essential to reduce plastic pollution in the environment. In this research, bioplastics were developed from an equivalent blend of starch from two different sources namely rice and potato (1:1, w/w), crosslinked with different concentrations of citric acid (CA). The effect of CA cross-linking of starch-based bioplastics was investigated on its physicochemical and functional properties. The X-ray diffraction (XRD) spectra revealed that the synthesized bioplastics were amorphous in nature with broad diffraction peaks. Further, the peak at 1716 cm−1 in Fourier transform infrared (FTIR) spectra indicated the formation of ester bonds in CA cross-linked bioplastics. Atomic force microscopy (AFM) revealed the surface roughness of the bioplastics decreased with increasing concentration of CA. Mechanical and thermal properties of bioplastics were characterized using universal testing machine, differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA), respectively. © 2022 Wiley Periodicals LLC.