arXiv subjects

Vivek Vijay

Publications and source records attributed to Vivek Vijay.

10 recordsLinked to original sources

arXiv2026

Collisional energy transfer in ethanimine + He system

The ethanimine molecule, CH3CHNH, is one of the prebiotic molecules detected by astronomers in chemically-rich molecular clouds in the Galactic Center. The observations indicate a non-equilibrium distribution of rotational state populations in both the E- and Z-isomers of ethanimine, resulting from the competition between radiative processes and collisions with background gases such as He and H2. Accurate interpretation of these observations requires the use of radiative transfer models with collisional state-to-state transition processes included. Here, in order to compute cross sections for state-to-state transitions in both ethanimine isomers, accurate potential energy surfaces for their interaction with a He atom were constructed and three complementary methods for inelastic scattering were utilized: full-quantum coupled-channel and coupled-states methods, and the mixed quantum/classical theory. Strong propensities of transitions toward $\Delta j = 0$ and either $\Delta k_a = 0$ (with $\Delta k_c = \pm 1$) or $\Delta k_c = 0$ (with $\Delta k_a = \pm 1$) are reported and the origin of this effect is identified. Small but non-negligible differences between energy transfer in the two isomers, on the order of 10%, were found. The utility of the mixed quantum/classical approach to collisional energy transfer at higher collision energies is discussed.

physics.chem-ph↗

arXiv2025

A heavy-tail arctan-based mixture model for modelling and measuring actuarial risk

Heavy-tailed probability distributions are extremely useful and play a crucial role in modeling different types of financial data sets. This study presents a two-pronged methodology. First, a mixture probability distribution is created by combining Gaussian and Rayleigh distributions using the arctangent transformation, aimed at producing heavier-tailed features and enhancing alignment with real market data. Some statistical properties of the proposed model are also discussed. Furthermore, essential actuarial risk evaluation instruments, such as value-at-risk (VaR), tail value-at-risk (TVaR) and tail variance (TV) are employed for efficient risk management practices. Lastly, an application is provided using an insurance dataset to demonstrate the applicability of the proposed model. The proposed model demonstrates superior fitting performance compared to current baseline distributions, showcasing its practical value in financial risk evaluation. The combination of Gaussian and Rayleigh distributions through arctangent transformation is particularly successful in representing extreme market behaviour and tail dependencies that are frequently found in real-world financial data.

stat.AP↗

arXiv2025

Crystal Systems Classification of Phosphate-Based Cathode Materials Using Machine Learning for Lithium-Ion Battery

The physical and chemical characteristics of cathodes used in batteries are derived from the lithium-ion phosphate cathodes crystalline arrangement, which is pivotal to the overall battery performance. Therefore, the correct prediction of the crystal system is essential to estimate the properties of cathodes. This study applies machine learning classification algorithms for predicting the crystal systems, namely monoclinic, orthorhombic, and triclinic, related to Li P (Mn, Fe, Co, Ni, V) O based Phosphate cathodes. The data used in this work is extracted from the Materials Project. Feature evaluation showed that cathode properties depend on the crystal structure, and optimized classification strategies lead to better predictability. Ensemble machine learning algorithms such as Random Forest, Extremely Randomized Trees, and Gradient Boosting Machines have demonstrated the best predictive capabilities for crystal systems in the Monte Carlo cross-validation test. Additionally, sequential forward selection (SFS) is performed to identify the most critical features influencing the prediction accuracy for different machine learning models, with Volume, Band gap, and Sites as input features ensemble machine learning algorithms such as Random Forest (80.69%), Extremely Randomized Tree (78.96%), and Gradient Boosting Machine (80.40%) approaches lead to the maximum accuracy towards crystallographic classification with stability and the predicted materials can be the potential cathode materials for lithium ion batteries.

cond-mat.mtrl-sci↗

arXiv2025

Kolmogorov Arnold Networks (KANs) for Imbalanced Data -- An Empirical Perspective

Kolmogorov Arnold Networks (KANs) are recent architectural advancement in neural computation that offer a mathematically grounded alternative to standard neural networks. This study presents an empirical evaluation of KANs in context of class imbalanced classification, using ten benchmark datasets. We observe that KANs can inherently perform well on raw imbalanced data more effectively than Multi-Layer Perceptrons (MLPs) without any resampling strategy. However, conventional imbalance strategies fundamentally conflict with KANs mathematical structure as resampling and focal loss implementations significantly degrade KANs performance, while marginally benefiting MLPs. Crucially, KANs suffer from prohibitive computational costs without proportional performance gains. Statistical validation confirms that MLPs with imbalance techniques achieve equivalence with KANs (|d| < 0.08 across metrics) at minimal resource costs. These findings reveal that KANs represent a specialized solution for raw imbalanced data where resources permit. But their severe performance-resource tradeoffs and incompatibility with standard resampling techniques currently limits practical deployment. We identify critical research priorities as developing KAN specific architectural modifications for imbalance learning, optimizing computational efficiency, and theoretical reconciling their conflict with data augmentation. This work establishes foundational insights for next generation KAN architectures in imbalanced classification scenarios.

cs.LG↗

arXiv2025

Extropy Rate: Properties and Application in Feature Selection

Extropy, a complementary dual of entropy, (proposed by Lad et al. \cite{lad2015extropy} in 2015) has attracted considerable interest from the research community. In this study, we focus on discrete random variables and define conditional extropy, establishing key properties of joint and conditional extropy such as bounds, uncertainty reduction due to additional information, and Lipschitz continuity. We further introduce the concept of extropy rate for a stochastic process of discrete random variables as a measure of the average uncertainty per random variable within the process. It is observed that for infinite stationary and ergodic stochastic processes, as well as for identically and independently distributed sequences, the extropy rate exhibits asymptotic equivalence. We explore the extropy rate for finite stochastic processes and numerically illustrate its effectiveness in capturing the underlying information across various distributions, quantifying complexity in time series data, and characterizing chaotic dynamics in dynamical systems. The behaviour of estimated extropy rate is observed to be closely aligned with Simpson's diversity index. The real-life applicability of the extropy rate is presented through a novel feature selection method based on the fact that features with higher extropy rates contain greater inherent information. Using six publicly available datasets, we show the superiority of the proposed feature selection method over some other existing popular approaches.

cs.IT↗

arXiv2025

Entropy measures and their applications: A comprehensive review

Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical foundations and practical applications, is crucial to advance research across disciplines. This review article provides motivation, fundamental properties, and constraints of various entropy measures. These measures are categorized with time evolution ranging from Shannon entropy generalizations, distribution function theory, fuzzy theory, fractional calculus to graph theory, all explained in a simplified and accessible manner. These entropy measures are selected on the basis of their usability, with descriptions arranged chronologically. We have further discussed the applicability of these measures across different domains, including thermodynamics, communication theory, financial engineering, categorical data, artificial intelligence, signal processing, and chemical and biological systems, highlighting their multifaceted roles. A number of examples are included to demonstrate the prominence of specific measures in terms of their applicability. The article also focuses on entropy-based applications in different disciplines, emphasizing openly accessible resources. Furthermore, this article emphasizes the applicability of various entropy measures in the field of finance. The article may provide a good insight to the researchers and experts working to quantify uncertainties, along with potential future directions.

math.PR↗

arXiv2025

Rebalancing the Scales: A Systematic Mapping Study of Generative Adversarial Networks (GANs) in Addressing Data Imbalance

Machine learning algorithms are used in diverse domains, many of which face significant challenges due to data imbalance. Studies have explored various approaches to address the issue, like data preprocessing, cost-sensitive learning, and ensemble methods. Generative Adversarial Networks (GANs) showed immense potential as a data preprocessing technique that generates good quality synthetic data. This study employs a systematic mapping methodology to analyze 3041 papers on GAN-based sampling techniques for imbalanced data sourced from four digital libraries. A filtering process identified 100 key studies spanning domains such as healthcare, finance, and cybersecurity. Through comprehensive quantitative analysis, this research introduces three categorization mappings as application domains, GAN techniques, and GAN variants used to handle the imbalanced nature of the data. GAN-based over-sampling emerges as an effective preprocessing method. Advanced architectures and tailored frameworks helped GANs to improve further in the case of data imbalance. GAN variants like vanilla GAN, CTGAN, and CGAN show great adaptability in structured imbalanced data cases. Interest in GANs for imbalanced data has grown tremendously, touching a peak in recent years, with journals and conferences playing crucial roles in transmitting foundational theories and practical applications. While with these advances, none of the reviewed studies explicitly explore hybridized GAN frameworks with diffusion models or reinforcement learning techniques. This gap leads to a future research idea develop innovative approaches for effectively handling data imbalance.

cs.AI↗

arXiv2025

Certified Interpolation Oversampling: Per-Instance Safety Guarantees for Imbalanced Learning

Synthetic minority oversampling is typically designed and evaluated against a predictive objective, generating samples that improve downstream classification. This paper pursues a second objective by generating samples that carry a stated safety property, established for each instance by construction rather than assumed. We introduce Certified Interpolation Safe Oversampling (CISO), a three-phase interpolation framework built for this objective. A safety-guided distribution selects where synthesis occurs, a locality-and clearance-weighted distribution selects with whom each anchor interpolates, and a q-Gaussian placement density determines how far along the resulting segment each instance is placed. The framework provides three guarantees. Each synthetic instance seeded by a sufficiently safe anchor carries a certified distance from the majority class; a signed temperature parameter provably and monotonically shifts synthesis between boundary-seeking and interior-seeking regimes; and selection weights are strictly positive by construction, so no degenerate case arises. Certification is obtained alongside competitive predictive performance rather than in place of it. Under a protocol preregistered before evaluation, across 45 datasets, four classifiers, and eleven competing methods, CISO is statistically equivalent to SMOTE on precision-recall AUC, ranks second of eleven under gradient boosting, and completes every one of 11,460 fold-level evaluations without failure. A parameter sweep further reveals a continuous fidelity-safety trade-off that competing methods occupy only as isolated points.

cs.LG↗

arXiv2024

Estimation of Tsallis entropy for exponentially distributed several populations

We study the estimation of Tsallis entropy of a finite number of independent populations, each following an exponential distribution with the same scale parameter and distinct location parameters for $q>0$. We derive a Stein-type improved estimate, establishing the inadmissibility of the best affine equivariant estimate of the parameter function. A class of smooth estimates utilizing the Brewster technique is obtained, resulting in a significant improvement in the risk value. We computed the Brewster-Zidek estimates for both one and two populations, to illustrate the comparison with best affine equivariant and Stein-type estimates. We further derive that the Bayesian estimate, employing an inverse gamma prior, which takes the best affine equivariant estimate as a particular case. We provide a numerical illustration utilizing simulated samples for a single population. The purpose is to demonstrate the impact of sample size, location parameter, and entropic index on the estimates.

math.ST↗

arXiv2018

Algorithm for $\mathcal{B}$-partitions, parameterized complexity of the matrix determinant and permanent

Every square matrix $A=(a_{uv})\in \mathcal{C}^{n\times n}$ can be represented as a digraph having $n$ vertices. In the digraph, a block (or 2-connected component) is a maximally connected subdigraph that has no cut-vertex. The determinant and the permanent of a matrix can be calculated in terms of the determinant and the permanent of some specific induced subdigraphs of the blocks in the digraph. Interestingly, these induced subdigraphs are vertex-disjoint and they partition the digraph. Such partitions of the digraph are called the $\mathcal{B}$-partitions. In this paper, first, we develop an algorithm to find the $\mathcal{B}$-partitions. Next, we analyze the parameterized complexity of matrix determinant and permanent, where, the parameters are the sizes of blocks and the number of cut-vertices of the digraph. We give a class of combinations of cut-vertices and block sizes for which the parametrized complexities beat the state of art complexities of the determinant and the permanent.

cs.CC↗