Arijit Dey

Bio: Arijit Dey is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Toric variety & Equivariant map. The author has an hindex of 7, co-authored 41 publications receiving 131 citations. Previous affiliations of Arijit Dey include Institute of Mathematical Sciences, Chennai & Islamic Azad University.

A Hybrid Meta-Heuristic Feature Selection Method Using Golden Ratio and Equilibrium Optimization Algorithms for Speech Emotion Recognition

Abstract: Speech is the most important media of expressing emotions for human beings. Thus, it has often been an area of interest to understand the emotion of a person out of his/her speech by using the intelligence of the computing devices. Traditional machine learning techniques are very much popular in accomplishing such tasks. To provide a less expensive computational model for emotion classification through speech analysis, we propose a meta-heuristic feature selection (FS) method using a hybrid of Golden Ratio Optimization (GRO) and Equilibrium Optimization (EO) algorithms, which we have named as Golden Ratio based Equilibrium Optimization (GREO) algorithm. The optimally selected features by the model are fed to the XGBoost classifier. Linear Predictive Coding (LPC) and Linear Prediction Cepstral Coefficients (LPCC) based features are considered as the input here, and these are optimized by using the proposed GREO algorithm. We have achieved impressive recognition accuracies of 97.31% and 98.46% on two standard datasets namely, SAVEE and EmoDB respectively. The proposed FS model is also found to perform better than their constituent algorithms as well as many well-known optimization algorithms used for FS in the past. Source code of the present work is made available at: https://github.com/arijitdey1/Hybrid-GREO .

COVID-19 Detection by Optimizing Deep Residual Features with Improved Clustering-Based Golden Ratio Optimizer.

Abstract: The COVID-19 virus is spreading across the world very rapidly. The World Health Organization (WHO) declared it a global pandemic on 11 March 2020. Early detection of this virus is necessary because of the unavailability of any specific drug. The researchers have developed different techniques for COVID-19 detection, but only a few of them have achieved satisfactory results. There are three ways for COVID-19 detection to date, those are real-time reverse transcription-polymerize chain reaction (RT-PCR), Computed Tomography (CT), and X-ray plays. In this work, we have proposed a less expensive computational model for automatic COVID-19 detection from Chest X-ray and CT-scan images. Our paper has a two-fold contribution. Initially, we have extracted deep features from the image dataset and then introduced a completely novel meta-heuristic feature selection approach, named Clustering-based Golden Ratio Optimizer (CGRO). The model has been implemented on three publicly available datasets, namely the COVID CT-dataset, SARS-Cov-2 dataset, and Chest X-Ray dataset, and attained state-of-the-art accuracies of 99.31%, 98.65%, and 99.44%, respectively.

On Harder-Narasimhan reductions for Higgs principal bundles

Abstract: The existence and uniqueness of H-N reduction for the Higgs principal bundles over nonsingular projective variety is shown. We also extend the notion of H-N reduction for (Γ,G)-bundles and ramifiedG-bundles over a smooth curve.

Tannakian classification of equivariant principal bundles on toric varieties

Abstract: Let X be a complete toric variety equipped with the action of a torus T, and G a reductive algebraic group, defined over an algebraically closed field K. We introduce the notion of a compatible ∑-filtered algebra associated to X, generalizing the notion of a compatible ∑-filtered vector space due to Klyachko, where ∑ denotes the fan of X. We combine Klyachko's classification of T-equivariant vector bundles on X with Nori's Tannakian approach to principal G-bundles, to give an equivalence of categories between T-equivariant principal G-bundles on X and certain compatible ∑-filtered algebras associated to X, when the characteristic of K is 0.

Transformation of Groups

Abstract: In this work, we have proved a number of purely geometric statements by algebraic methods. Also we have proved Sylvester’s law of Nullity and Exercise: the nullity of the product BA never exceeds the sum of the nullities of the factor and is never less than the nullity of A. Keywords: Transformation of Groups, Nullity, Kernel, Image, Non-Singular, Symmetry Group, Shear, Compression, Elongation Reflection Journal of the Nigerian Association of Mathematical Physics , Volume 20 (March, 2012), pp 27 – 30

Moduli of representations of the fundamental group of a smooth projective variety, II . Finite group actions and étale cohomology . A rank theorem for analytic maps between power series spaces . Some groups whose reduced C[*]-algebra is simple . Existence de 1-formes fermées non singulières dans une classe de cohomologie de de Rahm

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Wall-Crossing in Coupled 2d-4d Systems

Abstract: We introduce a new wall-crossing formula which combines and generalizes the Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d systems respectively. This 2d-4d wall-crossing formula governs the wall-crossing of BPS states in an N = 2 supersymmetric 4d gauge theory coupled to a supersymmetric surface defect. When the theory and defect are compactied on a circle, we get a 3d theory with a su- persymmetric line operator, corresponding to a hyperholomorphic connection on a vector bundle over a hyperkahler space. The 2d-4d wall-crossing formula can be interpreted as a smoothness condition for this hyperholomorphic connection. We explain how the 2d-4d BPS spectrum can be determined for 4d theories of classS, that is, for those theories ob- tained by compactifying the six-dimensional (0; 2) theory with a partial topological twist on a punctured Riemann surface C. For such theories there are canonical surface defects. We illustrate with several examples in the case of A1 theories of classS. Finally, we indi- cate how our results can be used to produce solutions to the A1 Hitchin equations on the Riemann surface C.