arXiv subjects

Vivek Kumar Singh

Publications and source records attributed to Vivek Kumar Singh.

At least 19 recordsLinked to original sources

arXiv2026

ChurnBench: A Drift-Aware Benchmark Demonstrating That Refresh Scheduling, Not Cache Age, Governs Staleness in Agentic AI

In production, agentic systems answer questions over data that lives in several places and keeps changing: licenses are reassigned, users offboarded, prices changed, contracts renewed. Existing retrieval benchmarks freeze the data, so they cannot ask whether an agent's answer is still true, only whether it found the right passage. We present ChurnBench, an open-source benchmark that generates a four-source enterprise data fabric as a timeline rather than a snapshot. Every change is written to an append-only ground-truth ledger, and gold answers are computed from that ledger, never from the live stores. An answer that was correct when its data was retrieved but wrong when evaluated is therefore detected and labeled a freshness error, distinct from a reasoning error; we validate this by resolving ground truth at both timestamps for every case reported. Using the instrument, we find that when a system refreshes on a schedule, cache age does not predict staleness. Across cache ages of 1, 14, and 28 days, freshness errors were 7, 4, and 4, because scheduled refresh bounds staleness by time-to-live, and no TTL lapse was observed in any window. A controlled ablation confirms the mechanism: disabling tiered refresh raises freshness errors from 4 to 45 at 28 days and leaves them identical at one day. The variable a drift benchmark should sweep is therefore TTL configuration against each entity's rate of change, not drift-window length. ChurnBench, the evaluation harness, and all per-error data are released open source.

cs.SE↗

arXiv2026

Technical Report on Resilient and Secure Large-Scale Energy Internet Systems

This IEEE PES Task Force report examines the security and resilience of large-scale Energy Internet (EI) systems, in which electricity, information, and market layers are tightly coupled through pervasive digitalization. The report characterizes the EI cyber-physical threat landscape and surveys detection, assurance, and mitigation techniques, presents modeling, control, and decision-making frameworks that capture cyber-physical interdependencies, including storage integration, multi-dimensional resilience, and electricity price forecasting, examines adversarial risks and trustworthy deployment of artificial intelligence, and introduces graph-based, attack-resilient information routing. The report closes with recommendations for research, standardization, and regulatory efforts needed to realize a resilient and secure large-scale EI.

eess.SY↗

arXiv2026

PROSLEX: A Novel Dataset for Expert-Annotated Legal Statute Prediction for Indian Judiciary

Legal Statute Prediction (LSP) involves automatically identifying relevant legal statutes given factual descriptions in legal documents, typically framed as a multi-label classification task within natural language processing and information retrieval research. While recent advances have begun incorporating Large Language Models (LLMs) for statute prediction, current approaches primarily focus on accuracy metrics without addressing the critical need for legal reasoning, a fundamental requirement in judicial contexts where decisions must be explainable and justifiable. To address this research gap, we present PROSLEX (PRediction Of Statutes and LEgal eXplanation), a comprehensive dataset comprising 1,623 expert-annotated legal documents from the Indian context. Each document is paired with statute predictions and detailed explanations, totaling 7,450 explanations, capturing the underlying legal reasoning. Using this dataset, we systematically evaluate various prompting strategies, including zero-shot, few-shot, chain-of-thought, and tree-of-thoughts approaches, to generate both statute predictions and their corresponding legal rationales. Our evaluation framework measures not only predictive performance but also the coherence and legal validity of generated explanations, positioning PROSLEX as a benchmark for developing explainable AI systems that can support legal practitioners while advancing research in interpretable legal NLP. To ensure reproducibility, we have made our PROSLEX dataset and model code available on GitHub: https://github.com/subinay494/Legal_Statute_Prediction_Explanation.

cs.AI↗

arXiv2026

A TQFT-based Platform for Efficient Computation of Knot Invariants

We present an interactive web platform that unifies the construction Feynman ribbon diagrams (FRDs), the evaluation of higher-rank Chern--Simons knot invariants, and the identification of FRD-like knots at higher crossing numbers. These tree-structured diagrams naturally represent arborescent knots, which we refer to throughout as FRD-like knots. Within a single visual environment, users can construct an FRD as a tensor network, evaluate its associated Chern--Simons invariants, and use the resulting invariant data to distinguish and identify the corresponding knot. To our knowledge, this is the first platform to combine diagrammatic construction, tensor-network evaluation, invariant computation, and knot identification within a unified workflow.

math.GT↗

arXiv2025

Panhandle polynomials of torus links and geometric applications

We use a decomposition of the tensor of the fundamental representation of the quantum group $U_q(\mathfrak{sl}_N)$ and the Rosso-Jones formula to establish a peculiar ``panhandle'' shape of the HOMFLY-PT polynomial of the reverse parallel of torus knots and links. Due to their panhandle-like intrinsic properties, the HOMFLY-PT polynomial is referred to as a ``panhandle polynomial''. With the help of the $\ell$-invariant, this extends to links the Etnyre-Honda result about the arc index and maximal Thurston-Bennequin invariant of torus knots. It has further geometric consequences, related to the braid index, the existence of minimal string Bennequin surfaces for banded and Whitehead doubled links, the Bennequin sharpness problem, and the equivalence of their quasipositivity and strong quasipositivity. We extend these properties to torus links, which relate to the classification of their component-wise Thurston-Bennequin invariants. Finally, we discuss the definition of the $\ell$-invariant for general links.

math.GT↗

arXiv2025

Torus Knots in Adjoint Representation

We derive a closed-form expression for the adjoint polynomials of torus knots and investigate their special properties. The results are presented in the very explicit double sum form and provide a deeper insight into the structure of adjoint invariants essential for the Vogel's universality of Chern-Simons theory.

hep-th↗

arXiv2025

Clifford Solver for the Tetrahedron Equation and its Variants

The different forms of the tetrahedron equation appear when all possible ways to label the scattering process of infinitely long straight lines are considered in three dimensional spacetime. This is expected to lead to three dimensional integrability, analogous to the Yang-Baxter equation. Among the three possibilities, we consider two of them and their variants. We show that Clifford algebras solve both the constant and the spectral parameter dependent versions of all of them. We also present a scheme for canonically solving higher simplex equations using tetrahedron solutions.

hep-th↗

arXiv2025

Full twists and stability of knots and quivers

We relate the stability of knot invariants under twisting a pair of strands to the stability of symmetric quivers under unlinking (or linking) operation. Starting from the HOMFLY-PT skein relations, we confirm the stable growth of $Sym^r$-coloured HOMFLY-PT polynomials under the addition of a~full twist to the knot. On the other hand, we show that symmetric quivers exhibit analogous stable growth under unlinking or linking of the quiver augmented with the extra node; in some cases this augmented quiver captures the spectrum of motivic Donaldson-Thomas invariants of all quivers in the sequence. Combining these two versions of the stable growth, we conjecture that performing a~full twist on any knot corresponds to appropriate unlinking or linking of the corresponding augmented quiver -- this statement is an important step towards a~direct definition of the knot-quiver correspondence based on the knot diagram. We confirm the conjecture for all twist knots, $(2,2p+1)$ torus knots, and all pretzel knots up to 15 crossings with an~odd number of twists in each twist region.

hep-th↗

arXiv2025

Data to Decisions: A Computational Framework to Identify skill requirements from Advertorial Data

Among the factors of production, human capital or skilled manpower is the one that keeps evolving and adapts to changing conditions and resources. This adaptability makes human capital the most crucial factor in ensuring a sustainable growth of industry/sector. As new technologies are developed and adopted, the new generations are required to acquire skills in newer technologies in order to be employable. At the same time professionals are required to upskill and reskill themselves to remain relevant in the industry. There is however no straightforward method to identify the skill needs of the industry at a given point of time. Therefore, this paper proposes a data to decision framework that can successfully identify the desired skill set in a given area by analysing the advertorial data collected from popular online job portals and supplied as input to the framework. The proposed framework uses techniques of statistical analysis, data mining and natural language processing for the purpose. The applicability of the framework is demonstrated on CS&IT job advertisement data from India. The analytical results not only provide useful insights about current state of skill needs in CS&IT industry but also provide practical implications to prospective job applicants, training agencies, and institutions of higher education & professional training.

cs.CY↗

arXiv2025

Colored Jones Polynomials and the Volume Conjecture

Using the vertex model approach for braid representations, we compute polynomials for spin-1 placed on hyperbolic knots up to 15 crossings. These polynomials are referred to as 3-colored Jones polynomials or adjoint Jones polynomials. Training a subset of the data using a fully connected feedforward neural network, we predict the volume of the knot complement of hyperbolic knots from the adjoint Jones polynomial or its evaluations with 99.34% accuracy. A function of the adjoint Jones polynomial evaluated at the phase $q=e^{ 8 πi / 15 }$ predicts the volume with nearly the same accuracy as the neural network. From an analysis of 2-colored and 3-colored Jones polynomials, we conjecture the best phase for $n$-colored Jones polynomials, and use this hypothesis to motivate an improved statement of the volume conjecture. This is tested for knots for which closed form expressions for the $n$-colored Jones polynomial are known, and we show improved convergence to the volume.

math.GT↗

arXiv2025

Non-invertible symmetry breaking in a frustration-free spin chain

A nearest-neighbor, frustration-free spin $\frac{1}{2}$ chain can be constructed {\it via} projectors of various ranks á la Bravyi-Gosset. We show that in the rank 1 case this system is gapped and has two ground states resembling ferromagnetic states. These states spontaneously break the non-invertible symmetry connecting them. The latter is proved using the machinery of algebraic quantum theory. The non-invertible symmetries of this system do not come from a duality.

hep-th↗

arXiv2025

Algebraic classification of Hietarinta's solutions of Yang-Baxter equations~:~invertible $4\times 4$ operators

In order to examine the simulation of integrable quantum systems using quantum computers, it is crucial to first classify Yang-Baxter operators. Hietarinta was among the first to classify constant Yang-Baxter solutions for a two-dimensional local Hilbert space (qubit representation). Including the one produced by the permutation operator, he was able to construct eleven families of invertible solutions. These techniques are effective for 4 by 4 solutions, but they become difficult to use for representations with more dimensions. To get over this limitation, we use algebraic ansätze to generate the constant Yang-Baxter solutions in a representation independent way. We employ four distinct algebraic structures that, depending on the qubit representation, replicate 10 of the 11 Hietarinta families. Among the techniques are partition algebras, Clifford algebras, Temperley-Lieb algebras, and a collection of commuting operators. Using these techniques, we do not obtain the $(2,2)$ Hietarinta class.

hep-th↗

arXiv2024

Institutional Shifts in Contribution to Indian Research Output during the last two decades

In the past few decades, India has emerged as a major knowledge producer, with research output being contributed by a diverse set of institutions ranging from centrally funded to state funded, and from public funded to private funded institutions. A significant change has been witnessed in Indian institutional actors during the last two decades, with various new private universities being set up and several new IITs, NITs, IISERs being established. Therefore, it is important to identify whether the composition of the list of the top 100 research output producing institutions of India has changed significantly during the recent two decades. This study attempted to analyse the changes during the two 10-year periods (2004-13 and 2014-23). The institutions which retain their position within top 100 during both periods are identified, along with the change in their positions. Similarly, institutions that were there in top 100 list during first time period (2004-13) and go out of top 100 list during second time period (2014-23) are also identified. In the same line, the new entrant institutions in the top 100 list during second time period (2014-23) are identified too. The results obtained indicate towards an institutional shift in the contribution to Indian research output.

cs.DL↗

arXiv2024

Who is Funding Indian Research? A look at major funding sources acknowledged in Indian research papers

Science and scientific research activities, in addition to the involvement of the researchers, require resources like research infrastructure, materials and reagents, databases and computational tools, journal subscriptions and publication charges etc. In order to meet these requirements, researchers try to attract research funding from different funding sources, both intramural and extramural. Though some recent reports provide details of the amount of funding provided by different funding agencies in India, it is not known what quantum of research output resulted from such funding. This paper, therefore, attempts to quantify the research output produced with the funding provided by different funding agencies to Indian researchers. The major funding agencies that supported Indian research publications are identified and are further characterized in terms of being national or international, and public or private. The analytical results not only provide a quantitative estimate of funded research from India and the major funding agencies supporting the research, but also discusses the overall context of research funding in India, particularly in the context of upcoming operationalization of Anusandhan National Research Foundation (ANRF).

cs.DL↗

arXiv2024

Indo-US Research Collaboration: strengthening or declining?

Despite the importance of Indo-US research collaboration, it is intriguing to note that measurement and characterization of dynamics of Indo-US research collaboration is relatively underexplored. Therefore, in this work, we investigate major patterns in Indo-US collaboration with respect to certain key aspects using suitable scientometric notions and indicators. The research publication data for the last three decades (1990-2020) is obtained from Web of Science and analysed for the purpose. Results indicate an increase in absolute number of Indo-US collaborated papers over time, with an impressive share of about 1/3rd of India's total internationally collaborated research output. However, the proportionate share of Indo-US collaborated papers in India's internationally collaborated papers has declined over the time, as Indian researchers find new collaborating partners. Nevertheless, the collaboration with US is found to be highly rewarding in terms of citations and boost measures. Important insights and recommendations that may be helpful for shaping up new perspective on Indo-US collaboration policy are presented in this work.

cs.DL↗

arXiv2024

BPS Spectra of complex knots

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.

hep-th↗

arXiv2024

Unitary tetrahedron quantum gates

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.

quant-ph↗

arXiv2024

A Hybrid Transformer-Sequencer approach for Age and Gender classification from in-wild facial images

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.

cs.CV↗