Pseudomechanics of supersymmetric oscillators

In this note, we study some classical aspects of supersymmetric oscillators, in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket, which emerges as a classical counterpart to commutators and anticommutators from supersymmetric quantum mechanics. In one dimension, i.e. in presence of one bosonic and one fermionic coordinate, the Hamiltonian admits a $U(1,1)$ symmetry for which we explicitly compute the first integrals. It is found that the supercharges emerge from the formalism in a natural way as fermionic conserved quantities. Following this, we describe classical supercharge operators based on the generalized Poisson bracket, which define supersymmetry transformations. The results are generalized to two spatial dimensions, where there is a $U(2,2)$ symmetry in the Hamiltonian. We comment on supersymmetric generalizations of the Pais-Uhlenbeck and isotonic oscillators. The possibility of defining a generalized Nambu bracket in this framework is also discussed

Study of price variation analysis of fluoroquinolones eye drops manufactured by various pharmaceutical companies in India

Background: Fluoroquinolone eye drops is being prescribed by Opthalmologist in many ocular diseases as conjunctivitis, keratitis, bacterial corneal ulcers etc in more and more amount. There are many brands of fluoroquinolones drugs available in Indian market. Costly drugs can lead to economic burden on patients. Modifications in pharmaceutical policy are required, and prices of the drug should be controlled in effective way for all the drugs. Hence this study was done to assess the cost variation of fluoroquinolones opthalmic solutions available in Indian market.Methods: The maximum and minimum price of each brand of the drug in INR was noted by using CIMS January to April 2020 edition and Drug Today April to June 2020 volume 1. The cost ratio and the percentage cost variation for individual drug brands was calculated. The cost of each eye drop was calculated. At last the cost ratio and percentage cost variation of various brands was compared.Results: Percentage variation in cost for fluoroquinolones eye preparations marketed in India was found to be Eye drop Ciprofloxacin (0.3%) of 5 ml:210.39, Eye drop Ciprofloxacin (0.3%) of 10 ml:162, Eye drop Gatifloxacin (0.3%) of 5 ml:156, Eye drop Moxifloxacin (0.5%) of 5 ml:196.95, Eye drop Ofloxacin (0.3%) of 5 ml:245.16, Eye drop Ofloxacin (0.3%) of 10 ml:62.5, Eye drop Norfloxacin (0.3%) of 5 ml:120.68, Eye drop Sparfloxacin (0.3%):8.31, Eye drop Lomefloxacin (0.3%):16.17.Conclusions: There is a wide difference in the cost of different brands of fluoroquinolones eye preparations available in India. The clinicians prescribing these drugs should be aware of these variations in cost to reduce the cost of drug therapy

The role of skeletal muscle energetics in the symptoms and metabolic characteristics of growth hormone deficiency and vitamin D deficiency :a functional MRS approach

PhD ThesisBoth growth hormone deficient (GHD) and vitamin D deficient adults complain of fatigue. Suboptimal skeletal muscle mitochondrial function has been implicated in several disorders where fatigue is a prominent feature. I examined in vivo dynamic skeletal muscle metabolism in GHD and vitamin D deficient adults using a non-invasive tool called phosphorus-31 magnetic resonance spectroscopy (31P MRS). 31P MRS can quantify abnormalities in metabolic work-cost relationship during exercise. In the first study, skeletal muscle metabolism was assessed in age, gender and physical activity matched untreated GHD adults, GH treated GHD adults and healthy volunteers. Fatigue perception was compared across the 3 groups using specific domains within a validated quality of life questionnaire (QoL-AGHDA). Whilst untreated GHD adults experienced more fatigue compared to treated GHD adults and normal volunteers, they did not demonstrate any perturbations in peripheral skeletal muscle metabolism as determined by 31P MRS: maximal mitochondrial oxidative function, anaerobic glycolysis and proton clearance. In the second study, the effect of cholecalciferol therapy on skeletal muscle mitochondrial function in vitamin D deficient adults who had presented to their local primary care team with fatigue was examined. 31P MRS assessments were undertaken in 12 symptomatic, severely vitamin D deficient subjects before and after treatment with cholecalciferol. Cholecalciferol therapy was found to augment skeletal muscle mitochondrial oxidative phosphorylation in these individuals. To summarise, I have examined dynamic skeletal muscle metabolism in two common endocrine disorders with contrasting results. There was no detectable perturbation in skeletal muscle metabolism in untreated GHD patients when compared to both matched GH replaced GHD patients and healthy controls. On the other hand, I have found that maximal mitochondrial function is improved and altered by vitamin D repletion in symptomatic vitamin D deficient adults, thereby suggesting a peripheral mechanism for fatigue in vitamin D deficiency. This is the first time that a link has been identified between vitamin D and the mitochondria in human skeletal muscle using 31P MRS.Pfizer and Serono Inc. for funding the 1st and 2nd year of this study including my salary. British Society of Paediatric Endocrinology for awarding me the money to undertake the Vitamin D study

Mathematical Modelling and Theoretical Exploration of Hybrid Blood-Nano-fluid Flow in a Stenosed Artery with Magnetization Effect

In this study, we investigate the effects of hybrid blood-nano-fluid flow in stenosis arteries under the influence of magnetization. The governing equations are expressed and solved using the standard finite difference method, and the key parameters, such as the flow parameter,  Prandtl’s number,  blood flow rate, and skin friction, are computed to detect the behavior of blood flow in stenosis arteries. The mathematical model uses blood as a Newtonian fluid and assumes that it is two-dimensional (2D).In order to give a thorough understanding of the physiological dynamics, the differences between these parameters are illustrated graphically. The results demonstrate that while a larger nano-particle volume fraction and Prandtl number result in a decrease in blood temperature, an increase in the flow parameter increases velocity. With the tailored use of nanoparticles, nanotechnology displays great promise from a biomedical perspective, especially in chemotherapy. For a more thorough and correct description of blood rheology, this study emphasizes the necessity for future modifications by adding more factors

Disorder-free localisation in permutation symmetric fermionic quantum walks

We investigate the phenomenon of disorder-free localisation in a quantum system with a global permutation symmetry and the exchange symmetry for identical particles. We start with a systematic construction of many-fermion Hamiltonians with a global permutation symmetry using the conjugacy classes of the permutation group $S_N$, with $N$ being the total number of fermions. The resulting Hamiltonians are interpreted as generators of continuous-time quantum walk of indistinguishable fermions. In this setup we analytically solve the simplest example and show that for large $N$ all the states are localised without the introduction of any disorder coefficients. The localisation is also time-independent and is not the result of any emergent disorder. This seems to be an important distinction from other mechanisms of disorder-free localisation. Furthermore, we show that the localisation is stable to interactions that preserve the global $S_N$ symmetry making these systems potential candidates for a quantum memory. By marking sites and reducing the symmetry to subgroups of $S_N$, the localisation can be obtained for any $N$ by tuning the symmetry-reducing parameters in the Hamiltonian. Finally we show that similar localisation also occurs for spin systems governed by a $S_N$-symmetric Heisenberg chain and we make a few comments about $S_N$-symmetric bosonic systems. The models we propose feature all-to-all connectivity and can be realised on superconducting quantum circuits and trapped ion systems.Comment: 24 pages, 2 figures ; v2- 27 pages, 2 figures, slight modifications in the abstract and introductio

Jacobi last multiplier and two-dimensional superintegrable oscillators

In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit-mass oscillators admitting a separable Hamiltonian description, i.e., $H = H_1 + H_2$, where $H_1$ and $H_2$ are the Hamiltonians of two one-dimensional unit-mass oscillators; it is shown that there exists a third functionally-independent first integral $Θ$, thereby ensuring superintegrablility. Various examples are explicitly worked out. We then consider position-dependent-mass oscillators and the Bateman pair, where the latter consists of a pair of dissipative linear oscillators. Quite remarkably, the Bateman pair is found to be superintegrable, despite admitting a Hamiltonian which cannot be separated into those of two isolated (non-interacting) one-dimensional oscillators.v1: Preliminary version, comments are welcome; v2: Revised version with some new examples and few errors corrected; V3: To appear in Praman

Dyck Paths and Topological Quantum Computation

The fusion basis of Fibonacci anyons supports unitary braid representations that can be utilized for universal quantum computation. We show a mapping between the fusion basis of three Fibonacci anyons, $\{|1\rangle, |\tau\rangle\}$, and the two length 4 Dyck paths via an isomorphism between the two dimensional braid group representations on the fusion basis and the braid group representation built on the standard $(2,2)$ Young diagrams using the Jones construction. This correspondence helps us construct the fusion basis of the Fibonacci anyons using Dyck paths as the number of standard $(N,N)$ Young tableaux is the Catalan number, $C_N$ . We then use the local Fredkin moves to construct a spin chain that contains precisely those Dyck paths that correspond to the Fibonacci fusion basis, as a degenerate set. We show that the system is gapped and examine its stability to random noise thereby establishing its usefulness as a platform for topological quantum computation. Finally, we show braidwords in this rotated space that efficiently enable the execution of any desired single-qubit operation, achieving the desired level of precision($\sim 10^{-3}$).Comment: 30 pages, 20 figure

CLIPSyntel: CLIP and LLM Synergy for Multimodal Question Summarization in Healthcare

In the era of modern healthcare, swiftly generating medical question summaries is crucial for informed and timely patient care. Despite the increasing complexity and volume of medical data, existing studies have focused solely on text-based summarization, neglecting the integration of visual information. Recognizing the untapped potential of combining textual queries with visual representations of medical conditions, we introduce the Multimodal Medical Question Summarization (MMQS) Dataset. This dataset, a major contribution to our work, pairs medical queries with visual aids, facilitating a richer and more nuanced understanding of patient needs. We also propose a framework, utilizing the power of Contrastive Language Image Pretraining(CLIP) and Large Language Models(LLMs), consisting of four modules that identify medical disorders, generate relevant context, filter medical concepts, and craft visually aware summaries. Our comprehensive framework harnesses the power of CLIP, a multimodal foundation model, and various general-purpose LLMs, comprising four main modules: the medical disorder identification module, the relevant context generation module, the context filtration module for distilling relevant medical concepts and knowledge, and finally, a general-purpose LLM to generate visually aware medical question summaries. Leveraging our MMQS dataset, we showcase how visual cues from images enhance the generation of medically nuanced summaries. This multimodal approach not only enhances the decision-making process in healthcare but also fosters a more nuanced understanding of patient queries, laying the groundwork for future research in personalized and responsive medical careComment: AAAI 202

Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator

Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which incorporates two fermionic oscillators together with bilinear-coupling terms that do not conserve particle number. We determine the eigenvalues and eigenvectors, and expose the appearance of exceptional points where two of the eigenstates coalesce with the corresponding eigenvectors exhibiting self-orthogonality with respect to the bi-orthogonal inner product. The model admits a quantum phase transition - we discuss the two phases and also demonstrate that the ground-state entanglement entropy exhibits a discontinuous jump indicating the transition between the two phases.v1: Comments are welcome; v2: This version contains some new calculations and corrects some errors from the older version; v3: Substantially revised and to appear in Physica Script

Phosphate Solubilizing Bacteria: A Promising Approach For Improving Phosphorus In Agricultural Soils

One of the most crucial elements for crop growth and advancement is phosphorus (P), a key macronutrient in soil. Plant yields are decreased as a result of the P shortage caused by the insolubility of P resources in the soil. Fertilisers containing phosphate are widely used to remedy soil P deficiency. P deficiency in soils is caused by a decrease in the overall P content of the soil as well as the fixation of extra P from chemical fertilisers and other organic sources, such as manures. Even in the presence of an acceptable level of P stress, plants don't react very significantly. P's availability is primarily constrained by its solubilization because P is fixed in both acidic and alkaline soils. These PSMs' capability to solubilize P varies and is mostly influenced by the solubilization process employed, their molecular makeup, and their ability to release P in soil. A healthy way to alleviate the P deficiency in the soil is to employ PSMs as biofertilizers. The investigation of efficient PSM cultivars for use as biofertilizers is one of the key focus areas for improving agricultural productivity by reducing P scarcity. The goal of this review was to understand the ecology and diversity of PSMs, how P is soluble, and how PSMs are used as biofertilizers