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Marino's conjecture remains underexplored within the framework of $SO(N )$ string dualities. In this article, we investigated the reformulated invariants of a one-parameter family of knots $\left[ K\right]_p$ derived from tangle surgery on Manolescu's quasi-alternating knot diagrams. Within topological string dualities, we have verified Marino's integrality conjecture for these families of knots up to the Young diagram representation ${\bf R}$, with ${|\bf R|}\leq 2$. Furthermore, through our analysis, we have conjectured the closed structure of extremal refined BPS integers for the torus knots $ \left[{\bf 3_1}\right]_{2p+1}$ and $ \left[{\bf 8_{20}}\right]_{2p+1}$, $p \in \mathbb{Z}_{\geq 0}$. As the parameter $p$ of the knot diagram increases, the total crossing number of a knot exceeds $16$, which we describe as a complex knot. Interestingly, we discovered a maximum number of gaps in the BPS spectra associated with complex knot families. Moreover, our observations indicated that as $p$ increases, the size of these gaps also expands., Comment: 19 pages, a few references are added. Other minor revisions are made

Chiral perturbation theory (ChPT) predicted scaling of the pion,~kaon decay constants $f_{\pi}, f_{K} $ and $M_{\eta}^2 = m_{\eta}^2 + m_{\eta^{\prime}}^2 $ has been used in the renormalized $2+1$ flavor quark-meson (RQM) model,~to find a consistent path to chiral limit as the $\pi \ \text{and} \ K $ meson masses approach zero.~The left side of the Columbia plot is generated free from any ambiguity or heuiristic adjustment in the model parameter fixing away from the physical point. The on-shell renormalization of parameters and consistent treatment of the divergent quark one-loop vacuum fluctuations in the RQM model,~make the axial $U_{A}(1)$ anomaly significantly stronger and the light (strange) explicit chiral symmetry breaking strength becomes weaker by a small (relatively large) amount.~The first order chiral transition region in the $m_{\pi}-m_{K}$ and $\mu-m_{K}$ planes of Columbia plot,~increases due to the above novel features of the RQM model.~Comparing the softening effect of quark one-loop vacuum fluctuation on the chiral transition,~it looks overestimated in a recent functional renormalization group study., Comment: 6-7 pages 4 Figures

Detecting anomalies in brain MRI scans using supervised deep learning methods presents challenges due to anatomical diversity and labor-intensive requirement of pixel-level annotations. Generative models like Denoising Diffusion Probabilistic Model (DDPM) and their variants like pDDPM, mDDPM, cDDPM have recently emerged to be powerful alternatives to perform unsupervised anomaly detection in brain MRI scans. These methods leverage frame-level labels of healthy brains to generate healthy tissues in brain MRI scans. During inference, when an anomalous (or unhealthy) scan image is presented as an input, these models generate a healthy scan image corresponding to the input anomalous scan, and the difference map between the generated healthy scan image and the original anomalous scan image provide the necessary pixel level identification of abnormal tissues. The generated healthy images from the DDPM, pDDPM and mDDPM models however suffer from fidelity issues and contain artifacts that do not have medical significance. While cDDPM achieves slightly better fidelity and artifact suppression, it requires huge memory footprint and is computationally expensive than the other DDPM based models. In this work, we propose an improved version of DDPM called Multichannel Conditional Denoising Diffusion Probabilistic Model (MCDDPM) for unsupervised anomaly detection in brain MRI scans. Our proposed model achieves high fidelity by making use of additional information from the healthy images during the training process, enriching the representation power of DDPM models, with a computational cost and memory requirements on par with DDPM, pDDPM and mDDPM models. Experimental results on multiple datasets (e.g. BraTS20, BraTS21) demonstrate promising performance of the proposed method. The code is available at https://github.com/vivekkumartri/MCDDPM., Comment: Accepted in CISP-BMEI 2024

Classifying Yang-Baxter operators is an essential first step in the study of the simulation of integrable quantum systems on quantum computers. One of the earliest initiatives was taken by Hietarinta in classifying constant Yang-Baxter solutions for a two-dimensional local Hilbert space (qubit representation). He obtained 11 families of invertible solutions, including the one generated by the permutation operator. While these methods work well for 4 by 4 solutions, they become cumbersome for higher dimensional representations. In this work, we overcome this restriction by constructing the constant Yang-Baxter solutions in a representation independent manner by using ans\"{a}tze from algebraic structures. We use four different algebraic structures that reproduce 10 of the 11 Hietarinta families when the qubit representation is chosen. The methods include a set of commuting operators, Clifford algebras, Temperley-Lieb algebras, and partition algebras. We do not obtain the $(2,2)$ Hietarinta class with these methods., Comment: 26 pages + References

Quantum simulations of many-body systems using 2-qubit Yang-Baxter gates offer a benchmark for quantum hardware. This can be extended to the higher dimensional case with $n$-qubit generalisations of Yang-Baxter gates called $n$-simplex operators. Such multi-qubit gates potentially lead to shallower and more efficient quantum circuits as well. Finding them amounts to identifying unitary solutions of the $n$-simplex equations, the building blocks of higher dimensional integrable systems. These are a set of highly non-linear and over determined system of equations making it notoriously hard to solve even when the local Hilbert spaces are spanned by qubits. We systematically overcome this for higher simplex operators constructed using two methods: from Clifford algebras and by lifting Yang-Baxter operators. The $n=3$ or the tetrahedron case is analyzed in detail. For the qubit case our methods produce 13 inequivalent families of unitary tetrahedron operators. 12 of these families are obtained by appending the 5 unitary families of 4 by 4 constant Yang-Baxter operators of Dye-Hietarinta, with a single qubit operator. As applications, universal sets of single, two and three qubit gates are realized using such unitary tetrahedron operators. The ideas presented in this work can be naturally extended to the higher simplex cases., Comment: 34 pages of main text + 4 pages of appendices + 8 pages of references; v2 Fixed minor typos, updated Acknowledgments

The advancements in computer vision and image processing techniques have led to emergence of new application in the domain of visual surveillance, targeted advertisement, content-based searching, and human-computer interaction etc. Out of the various techniques in computer vision, face analysis, in particular, has gained much attention. Several previous studies have tried to explore different applications of facial feature processing for a variety of tasks, including age and gender classification. However, despite several previous studies having explored the problem, the age and gender classification of in-wild human faces is still far from the achieving the desired levels of accuracy required for real-world applications. This paper, therefore, attempts to bridge this gap by proposing a hybrid model that combines self-attention and BiLSTM approaches for age and gender classification problems. The proposed models performance is compared with several state-of-the-art model proposed so far. An improvement of approximately 10percent and 6percent over the state-of-the-art implementations for age and gender classification, respectively, are noted for the proposed model. The proposed model is thus found to achieve superior performance and is found to provide a more generalized learning. The model can, therefore, be applied as a core classification component in various image processing and computer vision problems., Comment: 22 pages

We compute the $\text{PSL}(2,\mathbb{C})$ Chern-Simons partition function of a closed 3-manifold obtained from Dehn fillings of the link complement $\mathbf S^3\backslash {\mathcal{L}}$, where $\mathcal{L}=\mathcal{K}# H$ is the connected sum of the knot $\mathcal {K}$ with the Hopf link $H$. Motivated by our earlier work on topological entanglement and the reduced density matrix $\sigma$ for such link complements, we wanted to determine a choice of Dehn filling so that the trace of the matrix $\sigma$ becomes equal to the $\text{PSL}(2,\mathbb{C})$ partition function of the closed 3-manifold. We use the SnapPy program and numerical techniques to show this equivalence up to the leading order. We have given explicit results for all hyperbolic knots $\mathcal{K}$ up to six crossings., Comment: 25 pages, 5 figures, 5 tables

The innermost regions of Active Galactic Nuclei (AGN) are critical for understanding galaxy evolution and the dynamics of matter near a Supermassive Black Hole (SMBH). Yet, due to smaller angular projections, it is very difficult to resolve these regions. This thesis explores indirect methods to understand these objects. We use the reverberation mapping technique to estimate accretion disk sizes for a sample of AGN, finding that the computed disk sizes are, on average, 3.9 times larger than the Shakura Sunyev (SS) standard disk model predictions. We also find a weak correlation between the obtained accretion disk sizes and the SMBH mass. We present initial results from a new accretion disk monitoring program to probe the accretion disk structure of Super Eddington Accreting AGN. We report that the disk sizes are about 4 times larger than the SS disk model. We calibrate the narrow-band photometric reverberation mapping (PRM) technique to develop tools for a large systematic narrow-band PRM project. We use simulations to test the effect of cadence, variability of the light curves, and the length of light curves in recovering the reverberation lags. We study the dichotomy between AGNs with and without detected jets using the method of microvariability observed in the accretion disk continuum. We find that AGNs with confirmed jets are about 3 times more variable on short time scales than the AGNs without a confirmed jet. By performing statistical analysis on a large sample of low luminosity AGNs, we find that the NLSy1 galaxies are more likely to have outflow signatures than their broad-line counterparts, hinting toward the disk wind origin of the material in BLR. We find that the principal components for NLSy1 galaxies differ from the BLSy1 galaxies, suggesting that the NLSy1 galaxies could be occupying their own parameter space., Comment: PhD thesis. Submitted on 27th September 2023, Defended on 6th February 2024 at Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, India

We present here the information on the design and performance of the recently commissioned 2.5-meter telescope at the PRL Mount Abu Observatory, located at Gurushikhar, Mount Abu, India. The telescope has been successfully installed at the site, and the Site Acceptance Test (SAT) was completed in October 2022. It is a highly advanced telescope in India, featuring the Ritchey-Chr$\acute{e}$tien optical configuration with primary mirror active optics, tip-tilt on side-port, and wave front correction sensors. Along with the telescope, its two first light instruments {namely Faint Object Camera (FOC) and PARAS-2} were also integrated and attached with it in the June 2022. {FOC is a} camera that uses a 4096 X 4112 pixels detector SDSS type filters with enhanced transmission and known as u', g', r', i', z'. It has a limiting magnitude of 21 mag in 10 minutes exposure in the r'-band. The other first light instrument PARAS-2 is a state-of-the-art high-resolution fiber-fed spectrograph operates in 380-690 nm wave-band, aimed to unveil the super-Earth like worlds. The spectrograph works at a resolution of $\sim$107,000, making it the highest-resolution spectrograph in Asia to date, which is under {ultra}-stable temperature and pressure environment, at 22.5 $\pm$ 0.001 $^{\circ}$C and 0.005 $\pm$ 0.0005 mbar, respectively. Initial calibration tests of the spectrograph using a Uranium Argon Hollow Cathode Lamp (UAr HCL) have yielded intrinsic instrumental RV stability down to 30 cm s$^{-1}$., Comment: Accepted for publication in the Bulletin of Liege Royal Society of Sciences, Volume 93, 2024; 19 pages, 9 figures

Early diagnosis of Alzheimer's disease is a challenge because the existing methodologies do not identify the patients in their preclinical stage, which can last up to a decade prior to the onset of clinical symptoms. Several research studies demonstrate the potential of cerebrospinal fluid biomarkers, amyloid beta 1-42, T-tau, and P-tau, in early diagnosis of Alzheimer's disease stages. In this work, we used machine learning models to classify different stages of Alzheimer's disease based on the cerebrospinal fluid biomarker levels alone. An electronic health record of patients from the National Alzheimer's Coordinating Centre database was analyzed and the patients were subdivided based on mini-mental state scores and clinical dementia ratings. Statistical and correlation analyses were performed to identify significant differences between the Alzheimer's stages. Afterward, machine learning classifiers including K-Nearest Neighbors, Ensemble Boosted Tree, Ensemble Bagged Tree, Support Vector Machine, Logistic Regression, and Naive Bayes classifiers were employed to classify the Alzheimer's disease stages. The results demonstrate that Ensemble Boosted Tree (84.4%) and Logistic Regression (73.4%) provide the highest accuracy for binary classification, while Ensemble Bagged Tree (75.4%) demonstrates better accuracy for multiclassification. The findings from this research are expected to help clinicians in making an informed decision regarding the early diagnosis of Alzheimer's from the cerebrospinal fluid biomarkers alone, monitoring of the disease progression, and implementation of appropriate intervention measures.

The doping of lighter non-metals like boron and nitrogen into graphene represents a promising advancement in the field of nano-electronic devices, particularly in the development of field-effect transistors (FETs). These doped two-dimensional (2D) materials offer improved stability and enhanced adsorption characteristics compared to pure graphene. Notably, It displays semiconducting behavior, resulting in higher conductivity and carrier mobility. In this study, we investigate the structural, electronic, optical, and conductivity/carrier transport properties of 2D polymer sheets made of fullerene, both with and without boron and nitrogen doping. We employ density functional theory (DFT) with PBE and HSE functionals, considering the inclusion of van der Waals (vdW) interactions. The research findings indicate that the 2D sheets of C60, C58B1N1, and C54B3N3 exhibit band gaps of approximately 0.97 eV (1.5 eV), 1.08 eV (1.9 eV), and 1.05 eV (1.6 eV), respectively, as obtained from PBE (HSE) calculations. Moreover, according to the deformation potential theory, both doped sheets exhibit ultra-high conductivity at elevated temperature). These results are highly promising and underscore the significance of a single pair of BN dopants in fullerene (C58B1N1) monolayers for the advancement of next-generation 2D nanoelectronic and photonics applications.

In the innermost regions of Active Galactic Nuclei (AGN), matter is understood to be flowing onto the Supermassive black hole (SMBH), which forms an accretion disk. This disk is responsible for the optical/UV continuum emission observed in the spectra of AGN. Reverberation Mapping of the accretion disk using multiple bands can yield the structure of the disk. The emission is expected to be of the black body type peaking at different wavelengths. Hence, depending on the temperature of the disk, continuous, simultaneous monitoring in multiple wavelength ranges to cover hotter inner regions and cooler outer regions can yield the structure and temperature profile of the accretion disk itself. In this study, we present initial results from our accretion disk reverberation mapping campaign targeting AGN with Super High Eddington Accreting Black Holes (SEAMBH). Our analysis on one of the sources- IRAS 04416+1215; based on the broadband observations using the Growth India telescope (GIT), reveals that the size of the accretion disk for this source, calculated by cross-correlating the continuum light curves is larger than expected from the theoretical model. We fit the light curves directly using the thin disk model available in {\sc javelin} and find that the disk sizes are approximately 4 times larger than expected from the Shakura Sunyaev (SS) disk model. Further studies are needed to understand better the structure and physics of AGN accretion disks and their role in the evolution of galaxies., Comment: 11 pages,4 Figures. Accepted for publication in the Bulletin de la Soci\'et\'e Royale des Sciences de Li\`ege as proceeding of the 3rd Belgo-Indian Network for Astronomy and Astrophysics (BINA) workshop, held in Bhimtal, Uttarakhand (India) on 22-24 March 2023

This study provides a comprehensive time series analysis of daily industry-specific, country-wise CO$_2$ emissions from January 2019 to February 2023. The research focuses on the Power, Industry, Ground Transport, Domestic Aviation, and International Aviation sectors in European countries (EU27 & UK, Italy, Germany, Spain) and India, utilizing near-real-time activity data from the Carbon Monitor research initiative. To identify regular emission patterns, the data from the year 2020 is excluded due to the disruptive effects caused by the COVID-19 pandemic. The study then performs a principal component analysis (PCA) to determine the key contributors to CO$_2$ emissions. The analysis reveals that the Power, Industry, and Ground Transport sectors account for a significant portion of the variance in the dataset. A 7-day moving averaged dataset is employed for further analysis to facilitate robust predictions. This dataset captures both short-term and long-term trends and enhances the quality of the data for prediction purposes. The study utilizes Long Short-Term Memory (LSTM) models on the 7-day moving averaged dataset to effectively predict emissions and provide insights for policy decisions, mitigation strategies, and climate change efforts. During the training phase, the stability and convergence of the LSTM models are ensured, which guarantees their reliability in the testing phase. The evaluation of the loss function indicates this reliability. The model achieves high efficiency, as demonstrated by $R^2$ values ranging from 0.8242 to 0.995 for various countries and sectors. Furthermore, there is a proposal for utilizing scandium and boron/aluminium-based thin films as exceptionally efficient materials for capturing CO$_2$ (with a binding energy range from -3.0 to -3.5 eV). These materials are shown to surpass the affinity of graphene and boron nitride sheets in this regard., Comment: 38 pages, 16 figures

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 figures

Let G be a group and H a subgroup of G of finite index. In this article, it is proved that if the number of isomorphism classes of right transversals of H in G is 5, then the index of H in G is 6 and the permutation representation of G on right cosets of H in G is isomorphic to the alternating group on four symbols., Comment: some corrections are to be made

Augmenting the improved chiral effective potential of the on-shell renormalized 2+1 flavour quark-meson (RQM) model with the Polyakov-loop potential that accounts for the deconfinement transition,~we get the Quantum Chromodynamics (QCD) like framework of the renormalized Polyakov quark-meson (RPQM) model.~When the divergent quark one-loop vacuum term is included in the effective potential of the quark-meson (QM) model,~its tree level parameters or the parameters fixed by the use of meson curvature masses,~become inconsistent as the curvature masses involve the self energy evaluations at zero momentum.~Using the modified minimal subtraction method,~the consistent chiral effective potential for the RQM model has been calculated after relating the counterterms in the on-shell (OS) scheme to those in the $\overline{\text{MS}}$ scheme and finding the relations between the renormalized parameters of both the schemes where the physical (pole) masses of the $\pi, K, \eta$ and $\eta^{\prime}$ pseudo-scalar mesons and the scalar $\sigma$ meson,~the pion and kaon decay constants,~have been put into the relation of the running couplings and mass parameter.~Using the RPQM model and the PQM Model with different forms for the Polyakov-loop potentials in the presence or the absence of the quark back-reaction,~we have computed and compared the effect of the consistent quark one-loop correction and the quark back-reaction on the scaled chiral order parameter,~the QCD phase diagrams and the different thermodynamic quantities.~The results have been compared with the 2+1 flavor lattice QCD data from the Wuppertal-Budapest collaboration \{JHEP 09,73(2010); PLB 730,99(2014)\} and the HotQCD collaboration \{PRD 90,094503(2014)\}., Comment: 28 pages, 20 Figures. arXiv admin note: text overlap with arXiv:2211.11686, arXiv:2305.16180