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Antimagic labeling and its variations in graphs
Graph theory is a branch of discrete Mathematics with its results having significant applications in many areas of computing, social, and natural sciences. Graph labeling is one of the fascinating areas of graph theory with wide-ranging applications. The concept was first introduced in the 1960s where the vertices and edges are assigned real values or newlinesubsets of a set subject to certain conditions. The labeling dealt in the thesis is edge labeling basically, that is, assigning a label to the edges of the graph. Depending on the conditions applied in labeling give way to magic, super-magic, antimagic labelings. Hartsfield and Ringel introduced the notion of antimagic labeling in the year 1990. In this thesis, three variations in graph labeling are dealt namely, equitable antimagic labeling, equitable difference labeling and extension of equitable irregular labeling with an introduction of k-equitable irregular labeling. For a given graph G = (V,E), an equitable antimagic labeling (EAL) of G is a bijective edge-labeling f: E(G) and#8594; {1,2,3,...,m = |E(G)|} such that |W_f (u)-W_f (v)| and#8804; 1 for any pair of adjacent vertices u and v of G, where W_f (v) is the sum of the labels of the edges incident with the vertex v. A graph admitting an EAL is called an equitable antimagic graph (EAG). In Chapter 2, we initiate a study of this new edge labeling of graphs. A diand#64256;erence labeling of a graph G is realized by assigning distinct integer values to each vertex and then associating with each edge, the absolute diand#64256;erence of those values assigned to its end vertices. That is, it is an injective function f: V(G) and#8594; N together with function f^*: E(G) and#8594; N deand#64257;ned by f^* (uv)=|f(u)-f(v)|for any edge uv in G. The function f^* is called the weight function induced by f. An irregular labeling f: E(G) and#8594; N with the property that S_f (u) and#8800; S_f (v) for any two vertices u and v of G, where S_f (u) denotes the sum of the labels of the edges incident with the vertex u. The sum S_f (u) is called the vertex sum of u under f. -
A Study on Measures of Central Tendency of Some Distance Parameters of Connected Graphs
This dissertation sets out to examine the implications of various mea- sures of central tendencies of graphs by introducing the unique concept of ?graphs. A ?graph is defined as a simple, finite, connected and undirected graph in which the basic centrality measures: mean, median and mode of eccentricities are equal. It takes a formal approach to the exploration of ?graphs by applying the principles of Graph Theory. Various graphs are looked into to compare the centrality measures, and the possibility of those being ?graphs. Earlier graph theoretical research in notions of centrality, distance and eccentricity are reviewed. It describes the development of a new elicitation tool that examines the effect of measures of central tenden- cies in graphs, by analyzing their eccentricity sequences. Using this new ap- proach the central values of certain graphs are obtained. The concept found would be helpful to develop a more complex interpretation of the notion of centrality measures in graph theory. Keywords: Eccentricity; Eccentricity sequence; Distance; Degree; Cen- trality; Mean; Mode; Median; ?graph; Central value -
Quantum Computings Path toSupremacy: Progress in the NISQ Epoch
Quantum computing leverages the principles of quantum mechanics for information processing, with qubits serving as the fundamental units of quantum information. Qubits are quantum states where information processing can be engineered. Qubits possess the unique ability to encode, manipulate and extract information, enabling remarkable parallelism in computation. This enhanced computational speed, called quantum supremacy, promises to transcend established complexity boundaries. Significant strides have been made in demonstrating quantum supremacy through various experiments, most notably Googles 2019 experiment utilizing the Sycamore quantum processor to solve a problem that would stymie classical supercomputers for millennia. Other research groups, such as the Chinese team employing Jiuzhang and Zuchongzhi quantum processors, have achieved similar feats, showcasing the profound computational capabilities of quantum computers. It is essential to underscore that quantum supremacy does not signify quantum computers superiority across all tasks; current quantum computers remain constrained in their applicability, excelling primarily in specific problem domains. Nevertheless, recent advancements in quantum computing are noteworthy and ongoing development promises to expand their problem-solving capacities. This paper offers an introductory overview of quantum computing and an assessment of three prominent quantum supremacy experiments. The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024. -
On Statistical Tools in Finding Equitable Antimagic Labeling of Complete Graphs
Graph theory is a branch of mathematics that deals with representation of graphs with vertices and edges. Graph labeling is the assignment of integer labels to either vertices or edges. For a given graph G= (V, E), an edge-weighting is a function f:E(G)?{1,2,3,..,|E(G)|}. For a vertex v of G, let Wf(v) denotes the sum of edge-weights appearing on the edges incident at v under the edge-weighting f. A bijective edge-weighting f of G is said to be an equitable antimagic labeling (EAL) of G if |Wf(u) - Wf(v) | ? 1 for any pair of adjacent vertices u and v of G. A graph admitting an EAL is called an equitable antimagic graph (EAG). In this paper, the characterization of complete graphs Kn, for n? 6 is dealt using an algorithmic approach. 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. -
Faulty Node Detection Using Vertex Magic Total Labelling in Distributed System
Distributed system consists of huge number of nodes that are connected to a network, which is mainly intended and predominantly used for information sharing. Large users are prone to share data through the network and the stability and reliability of the nodes are remaining as the major concern in this system. Therefore, the inconsistent message transmission causes the nodes in the network to act differently, which would not be acceptable. A rapid method of malfunctioning nodes detection can improve the QoS of distributed computing environment. In this paper, a novel algorithm is proposed based on the calculation of vertex magic total labelling (VMTL) value for each and every node in the network. Upon receiving the message from the sender node, the receiver node will quickly detect the faulty node by comparing the VMTL pivot value (Pv). Experimental results show that the proposed approach leads to high true fault rate (TFR) detection accuracy compared to the false fault rate (FFR) detection. Finally, all the information related to the faulty nodes will be sent to the server node for further investigation and action. The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021. -
On some classes of equitable irregular graphs
Graph labeling techniques are used by data scientists to represent data points and their relationships with each other. The segregation/sorting of similar datasets/points are easily done using labeling of vertices or edges in a graph. An equitable irregular edge labeling is a function $$f: E(G) \rightarrow N$$ (not necessarily be injective) such that the vertex sums of any two adjacent vertices of $$G$$ differ by at most one, where vertex sum of a vertex is the sum of the labels under $$f$$ of the edges incident with that vertex. A graph admitting an equitable irregular edge labeling is called an equitable irregular graph (EIG). In this paper, more classes of equitable irregular graphs are presented. We further generalize the concept of equitable irregular edge labeling to $$k$$-equitable irregular edge labeling by demanding the difference of the vertex sum of adjacent vertices to be $$k \ge 1$$. The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd 2021. -
BUILDING A DATA ETHICAL FUTURE: Data Policies and Frameworks
Technology-driven choices are shaping the digital engagement of individuals and policymakers. Rapid technological advancements and the increasing utilisation of Big Data and Artificial Intelligence (AI) have presented profound ethical challenges concerning privacy, accountability, and transparency. Existing Data Acts, internet policies, and government frameworks fall short of protecting individuals and states from violations of their digital footprints. This article advocates for a human-centric approach to data ethics, drawing on the concept of the common good, as articulated by John Rawls. Through a systematic review of global data privacy laws, acts, guidelines, and practices, the article examines potential disparities and emphasises the need for universal data legislation, guidelines, and policies. It highlights the significance of data policies and frameworks in fostering ethical data usage, trust, and integrity. By applying Kants philosophy of respecting individuals autonomy, the article emphasises the importance of informed consent and recommends ethical guidelines for both users and content creators. 2023, Journal of Dharma: Dharmaram Journal of Religions and Philosophies (DVK, Bangalore) -
Photocatalytic and antioxidant potential of silver nanoparticles biosynthesized using Artemisia stelleriana leaf extracts
The antioxidant and photocatalytic activity of Artemisia stelleriana-based silver nanoparticles (AS-AgNPs) was investigated in this study. Microscopic, X-ray diffraction and spectroscopic studies were used to characterize the synthesized AS-AgNPs. UVvisible spectrophotometric examination revealed a peak at 425 nm. The phytocompounds involved in the transformation of silver ions into AS-AgNPs were confirmed using Fourier-transform infrared spectroscopy analysis. The crystalline nature of the AS-AgNPs was verified using the X-ray powder diffraction technique. Spherical-shaped AS-AgNPs with a size of 22.7 nm were proved using field emission scanning electron microscopy. The AS-AgNPs were top-notch photocatalysts for the degradation of Reactive Blue-222A (RB-222A) and Reactive Blue-220 (RB-220) dyes. After 80 min of UV light exposure, AS-AgNPs degraded RB-222A and RB-220 dyes by 94.6 and 90.8%, respectively. The phytotoxicity investigation in Vigna radiata and Arte-mia salina indicated that the hazardous dye can be degraded into innocuous chemicals by AS-AgNPs. The results suggest that AS-AgNPs are an excellent antioxidant and photocatalyst for the degradation of synthetic dyes. 2023 The Authors. -
Access to Justice Through Law Schools Legal AID Activities in India : An Empirical Study with Special Reference to Kerala
The provision of legal services is a fundamental human right and is integral to the maintenance of the rule of law. Ensuring Justice and the rule of law are unique sustainable development goals in the 2030 Agenda. Law school clinics provide a novel way to reach SDG-16. The legal aid system has been influenced by both international and national legislation, which has contributed to the establishment of its framework. The judiciary plays a pivotal role in ensuring the provision of free legal assistance to indigent people. Access to formal and informal justice institutions must be improved so that people can seek and get justice. Law school clinics provide potential and challenges as informal justice nstitutions, yet they are mostly ignored. Under CLE, law schools LACs engage in a variety of legal aid initiatives. Through this, students acquire professional skills while clients get legal services. That is the beauty of law school LACs. In the end, this "laboratory of lawyering" helps individuals find justice. In the Indian context, this thesis answered three research questions. 1) How do the legal aid programmes undertaken by law schools clinics promote SDG-16 and improve access to justice? 2) What are the current practices being undertaken by law schools LACs to guarantee access to justice? 3) What are the shortcomings that law schools LACs face in delivering appropriate legal services in Kerala? Two methodologies were used in answering these three questions: the doctrinal method for the first two research questions and the empirical method for the third. The doctrinal study examines the operation of LACs in general. The purpose of this empirical research on law school clinics in Kerala is to investigate the numerous legal aid activities and barriers to law school clinic operations in Kerala. No meticulous study was conducted in Kerala to evaluate how law schools LACs worked. National and international law school clinics' best practises and case studies were incorporated. The study examined the relationship between BCI, NALSA, SLSAs as well as CLE requirements along with law school performance. The LACs' commitment will be assessed based on their legal aid operations pre- and post-Covid-19, including legal representation, legal awareness, legal advice, paralegal services, PIL and ADR services to beneficiaries, and the effective implementation of BCI and NALSA's CLE requirements. This study explores the relationship between dependent and independent variables, such as how the improper implementation of BCI and NALSA regulations on CLE hindered law school LACs' commitments. The prevailing policy has restricted law school LACs' activity and is not enough to achieve access to justice (ATJ). Due to multiple factors, law school LACs failed to ensure effective service learning and did not reach the needy. This gap in the current CLE and its insufficient attention to promoting access to justice have been addressed. The empirical investigation demonstrates that while the number of law schools increased, legal aid activities decreased during the past decade. Current legal aid practices of law school LACs in Kerala are unsatisfactory and inconsistent in providing access to justice. BCI and LSAs ineffective control over LACs in law schools has contributed to a decline in legal aid activities and services. BCI and NALSA must reform their CLE rules and establish mandatory legal services to foster inclusive and effective LACs that give meaningful justice to the disadvantaged. -
Digital transformation in clinical legal education, virtual law clinics, and access to justice
Clinical legal education (CLE)promotes skill training and service learning. It provides an opening to comprehend the law and practice through practical training. Access to justice with lawyering skills is the fundamental objective of CLE. Law students can uphold the 'rule of law' and play the leading role in legal services to the needy. Millions of people continue to be denied access to the legal system. The success of the digital transformation in CLE depends on the availability and efficiency of the adoption of advanced technology. The main theme of this chapter is to examine how the law schools approached the mode of CLE amidst the COVID-19 pandemic and the challenges faced while delivering services through VLC and examine the various types of online pro bono works. This chapter is designed in both doctrinal and analytical in terms of methodology. It also focuses on the new experiences globally in using IT and the methods that law schools can use through technology to improve access to justice. 2023, IGI Global. All rights reserved. -
INCLUSIVE LAW SCHOOL CLINICS: Institutionalizing Effective and Accountable Justice for All
Poor people are often denied access to the courts due to expensive legal fees. Preventing free access to justice violates a fundamental constitutional principle and universal international norms. The recognition of access to justice and the rule of law as outcomes and facilitators of sustainable development is a unique feature of the 2030 Agenda. This study shows that providing affordable and timely access to justice institutions and legal aid services will help achieve the Sustainable Development Goals (SDG) 16 targets of peace, justice, and strong institutions. Indian law school clinics have a unique opportunity to achieve the goal through institutionalized clinical legal education. The Advocates Act of 1961 requires an amendment to allow law students and faculty to represent pro bono clients. The study infers that completely institutionalizing the law school legal aid clinics as part of clinical legal education is a powerful platform to promote equal access to justice to all. 2021, Dharma Research Association. All rights reserved. -
Electrochemical non-enzymatic strategy with green synthesized Fe2O3CuO nanocomposite for detection of amiprofos-methyl herbicide in industrial effluents and soils
Iron oxide-Copper oxide nanoparticles composite (Fe2O3CuO NPs) was synthesized through a green phytosynthetic approach using Ocimum sanctum Linn (commonly known as Tulsi) leaf extract. The evaluation of electrocatalytic properties were evaluated by carrying out electrochemical detection of amiprofos-methyl (APM), an organophosphorus herbicide. It is moderately toxic to mammals and aquatic biodiversity and is considered to be an acetylcholinesterase inhibitor. The presence of specific natural phytochemicals such as eugenol, naringenin, apigenin, quercetin, and high amount of ascorbic acid in the aqueous extract of Ocimum sanctum Linn plant parts, has been widely used for the synthesis of various metallic nanoparticles where these compounds serve as reducing, stabilizing, and capping agents. The synthesized Fe2O3CuO NPs were characterized using scanning electron microscope (SEM), energy dispersive X-ray analysis (EDX), X-ray diffraction analysis (XRD), UVVis spectroscopy, Fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis (TGA). The modified electrode was electrochemically characterized by cyclic voltammetry and differential pulse voltammetry (DPV) techniques for the detection of APM. The electrochemical signals have increased by three folds in the detection of APM with Fe2O3CuO nanocomposite compared to the bare glassy carbon electrode. The electrochemical sensor showed a linear range of 0.05 to 30 g/mL with a limit of detection of 0.0065 g/mL. The developed electrochemical sensor was successfully applied for the detection of APM in different water and soil samples with recoveries ranging from 96.00?99.00%. The electrode showed good stability and reproducibility over a period of 10 days with a 95% of peak current than the former. The newly synthesized nanoparticles, thus, proved to be an interesting material for electrochemical and biological studies. 2023 The Authors -
Potential of insect-based milk moiety from Pacific beetle cockroach, Diploptera punctata (Blattodea): Insights as superfood
Diploptera punctata is a viviparous cockroach and secretes a concoction of glycosylated proteins as a basis of nutrition for developing embryos termed as cockroach milk. The milk proteins were identified as the lipocalin-like milk proteins (Lili-Mip) which are present in the brood sac of the gestated female D. punctata. Blotting techniques and RNA transcriptome assays have reported analogous Lili-Mip in the midgut of D. puncta embryos, which proved the ingestion during development inside brood sac. Thermodynamics and kinetic studies augmented the stability of the milk crystals and their controlled release mechanism of sustenance. Gene ontogeny reported the evolution of the ovoviviparous to viviparous due to selective pressures posed during the development stages of the embryos. Molecular simulation modelling studied unveiled the binding efficacies of the milk protein to build strong affiliates to the ligands to form a stable milk protein complex. Ahead of its nutritional benefits, cockroach milk also offers environmental advantages compared to traditional dairy and plant-based milk production. Nevertheless, there are still important hurdles to overcome to include this unconventional superfood as staple in human diets which are also discussed in the review. This review explored the existing molecular, evolutionary and biochemical insights for understanding the phenomena of the production of milk crystals and addressed the research gaps for developing a novel nutrient prospective from insect source. 2024 Korean Society of Applied Entomology -
Occurrence, identification, and decontamination of potential mycotoxins in fruits and fruit by-products
The incidence of aflatoxins, ochratoxin A, and patulin in fruits and processed fruit products has been ever more challenging and gained additional focus on ecofriendly mitigation strategies. The onset of these toxins is due to several factors involving insect attacks, agricultural practices, and climate change. Acute and chronic health hazards are clinically proven after consuming contaminated foodstuffs, even at lower concentrations of mycotoxins. Synergistic, masked, and substantial occurrence in fruit matrices increase their complexity in detection and detoxification; apparently, this article reviewed the available information on the occurrence of mycotoxins in several fruits and their products, focused on the conventional and advanced methods of identification, quantification, and decontamination techniques. Strengthening and implementing stringent international and national guidelines are required for impactful, tangible measures in the future. Nevertheless, controlling the mycotoxins in fruits will certainly be challenging for scientists. Therefore, more impactful technologies are still needed to eliminate the toxins at the threshold level of the food chain and ensure sustainable global food safety. 2023 The Authors. Food Frontiers published by John Wiley & Sons Australia, Ltd and Nanchang University, Northwest University, Jiangsu University, Zhejiang University, Fujian Agriculture and Forestry University. -
The crux of bioactive metabolites in endophytic and thermophilic fungi and their proximal prospects in biotechnological and industrial domains
Fungi are ubiquitous in distribution and are found in grasses to hot springs. Their mode of nutrition provides sustenance for living and propagation. Ironically, varied fungal species have developed customized strategies for protection and survival by producing diverse secondary metabolites. The review aimed to project the contrasting potential features of the endophytic and thermophilic fungi groups. The metabolites and the enzymes of endophytic and thermophilic fungi served as the backbone to thrive and adapt within-host and in extreme conditions like higher pH, heat, and salinity, respectively. Identification, knowledge of their biochemistry and pathway, exploration, production, and utilization of these bioactive molecules in various commercial, industrial, and pharmaceutical domains were briefly discussed. The uniqueness of endophytes includes stress management and improved biomass production of the host, green fuel production, omnipresence, selected triple-symbiosis with the virus, synthesis of polyketides, and other active metabolites are widely used in biomedical applications and agriculture management. This review attempted to limelight the specific applications of thermophilic fungal metabolites and the roles of thermo-stable enzymes in bioprospecting. Moreover, probing the metabolites of thermophiles rendered novel antibiotic compounds, which were proven effective against multi-drug resistant bacteria and harboured the potential to curtail infectious diseases. 2022 Elsevier Ltd -
Nano- from nature to nurture: A comprehensive review on facets, trends, perspectives and sustainability of nanotechnology in the food sector
Nanotechnology has underpinned vital progress in current research and has immensely promoted the food production chain. This review projected the critical intervention of nano-based technologies like modern advancements of nano-based biosensors in detecting mycotoxins, microbial contaminations, antibiotics, pesticides, food additives, and dyes. It also highlighted the starring roles of nanotechnology in terms of active, intelligent food packaging and food safety. These approaches have certainly intensified the strength of food processing technology and improved food quality and maintenance standards during shelf life. Apart from these trending facets, this review throw light on the utilisation of food waste for the biogenic synthesis of nanoparticles and the application of nano-based materials for the recycling process in food production units to ensure a complete cleaner technology. However, monitoring the chronic exposure of food contact nanomaterials should be critically evaluated to ensure food safety. Nanotechnology embraced an influential role in the food sector by providing effective avenues for energy conservation, sustainability, and cues to improve the capital funds well. 2021 Elsevier Ltd -
Perspectives and Implications of Probiotics as Beneficial Mediators in Aquaculture Industry
The diseases and nutrient deficiency in fish and other cultured aquatic species are of crucial concern as they cause severe economic loss in aquaculture sectors. The use of probiotics has proven to be an effective option to reduce the infections improve the overall health and enhance the productivity. This review comprehensively brought out significance of probiotics, their mode of administration via encapsulation methods and their mechanism of action reported by several research works. We have also highlighted the other beneficial aspects of probiotics as potent functional agents influencing gut microbiota, competence with pathogenic bacteria, release of antimicrobial secretions and maintain the water quality in environmental friendly manner which ensures sustainable aquaculture and fish farming. This review has also covered up the role of probiotics in wide spectrum of functions such as antiviral and antifungal properties, reducing stress and diseases, modifying the gut microbiota, improving the fecundity, survival and modulating the immune system of the host. We have discussed every aspect of probiotics and correlated with the existing research and review articles till date. However, most of the studies are reported based on the laboratory trials and experiments; commercial and large-scale demonstration has to be scaled up and utilization of them in natural environments like ponds and lakes will be effective way to broaden aquaculture industry. The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022. -
Mucormycosis (black fungus) ensuing COVID-19 and comorbidity meets - Magnifying global pandemic grieve and catastrophe begins
Post COVID-19, mucormycosis occurred after the SARS-CoV-2 has rampaged the human population and is a scorching problem among the pandemic globally, particularly among Asian countries. Invasive mucormycosis has been extensively reported from mild to severe COVID-19 survivors. The robust predisposing factor seems to be uncontrolled diabetes mellitus, comorbidity and immunosuppression acquired through steroid therapy. The prime susceptive reason for the increase of mucormycosis cases is elevated iron levels in the serum of the COVID survivors. A panoramic understanding of the infection has been elucidated based on clinical manifestation, genetic and non- genetic mechanisms of steroid drug administration, biochemical pathways and immune modulated receptor associations. This review lime-lights and addresses the What, Why, How and When about the COVID-19 associated mucormycosis (CAM) in a comprehensive manner with a pure intention to bring about awareness to the common public as the cases are inevitably and exponentially increasing in India and global countries as well. The article also unearthed the pathogenesis of mucormycosis and its association with the COVID-19 sequela, the plausible routes of entry, diagnosis and counter remedies to keep the infection at bay. Cohorts of case reports were analysed to spotlight the link between the pandemic COVID-19 and the nightmare-mucormycosis. 2021 Elsevier B.V. -
Out of Box Thinking to Tangible Science: A Benchmark History of 3D Bio-Printing in Regenerative Medicine and Tissues Engineering
Advancements and developments in the 3D bioprinting have been promising and have met the needs of organ transplantation. Current improvements in tissue engineering constructs have enhanced their applications in regenerative medicines and other medical fields. The synergistic effects of 3D bioprinting have brought technologies such as tissue engineering, microfluidics, integrated tissue organ printing, in vivo bioprinted tissue implants, artificial intelligence and machine learning approaches together. These have greatly impacted interventions in medical fields, such as medical implants, multi-organ-on-chip models, prosthetics, drug testing tissue constructs and much more. This technological leap has offered promising personalized solutions for patients with chronic diseases, and neurodegenerative disorders, and who have been in severe accidents. This review discussed the various standing printing methods, such as inkjet, extrusion, laser-assisted, digital light processing, and stereolithographic 3D bioprinter models, adopted for tissue constructs. Additionally, the properties of natural, synthetic, cell-laden, dECM-based, short peptides, nanocomposite and bioactive bioinks are briefly discussed. Sequels of several tissue-laden constructs such as skin, bone and cartilage, liver, kidney, smooth muscles, cardiac and neural tissues are briefly analyzed. Challenges, future perspectives and the impact of microfluidics in resolving the limitations in the field, along with 3D bioprinting, are discussed. Certainly, a technology gap still exists in the scaling up, industrialization and commercialization of this technology for the benefit of stakeholders. 2023 by the authors.