arXiv subjects

Kumar Abhinav

Publications and source records attributed to Kumar Abhinav.

At least 19 recordsLinked to original sources

arXiv2026

Isospectral potentials with Dirac delta interaction: Constrained Spectra

We study quantum potentials containing Dirac delta function (DDF) within its supersymmetric (isospectral) construction via a discontinuous superpotential, instead of being simply an added part. This construction comprises of two independently solvable sectors joined at the singular point by matching conditions imposed by the corresponding self-adjoint extension. Needing careful regularization, these boundary conditions impose independent algebraic constraints on each of the eigenstates, that restrict and truncate the spectrum. The number of surviving bound states, which are required to be parity-even, is thus fixed by the available system parameters rather than by the usual quantization rule. The specific cases of the Harmonic oscillator and the Rosen-Morse potential isospectrally infused with the DDF demonstrate such highly restrictive spectra, while the similar combination of the DDF with a Calogero-type singularity turns out to be largely incompatible as the regularization breaks down. Therefore, localized singularities are capable of controlling and engineering the discrete spectrum of quantum systems, with possible use in myriads of physical systems with very localized interactions.

quant-ph↗

arXiv2026

Gabor Orthonormal Bases with Maximal Localization and Gabor Frame Operator on Local Fields

We provide an explicit construction of a Gabor orthonormal bases for a local field $K$ that provides maximal localization in both time and frequency. Such a localization is not true in case of $\mathbb{R}$ due to the uncertainty principle. In particular, we construct examples of functions $f \in L^2(K)$ such that the support of the ambiguity function of $f$ is of minimum measure. Moreover, we establish a quantitative uncertainty principle for local fields, which follows as a consequence of Lieb's inequalities for general locally compact abelian group. In addition, we develop fundamental operator representations for Gabor systems defined over local fields.

math.FA↗

arXiv2026

Career-Aware Resume Tailoring via Multi-Source Retrieval-Augmented Generation with Provenance Tracking: A Case Study

AI-assisted resume tailoring systems commonly operate on a single uploaded resume, which limits their ability to recover relevant experience omitted from the current draft and makes it difficult for users to distinguish grounded edits from model-generated suggestions. This paper presents Resume Tailor, an agentic resume-tailoring system that maintains a longitudinal career vault in a vector database and uses multi-source retrieval-augmented generation (RAG) to assemble job-specific resume content from historical resumes and structured career records. The system is implemented as a 12-node LangGraph pipeline with typed state management, hybrid semantic-lexical confidence scoring, provenance-aware fallback generation, anti-hallucination guardrails, and a conditional review loop. We report a pilot evaluation on nine job descriptions (JDs) across software engineering, data analytics, and business analysis roles using a single candidate's career history. For six JDs where the candidate held at least one prior role in the same occupational category, enabling the career vault improved Applicant Tracking System (ATS)-style fit scores by an average of 7.8 points. For two JDs requiring domain-specific expertise absent from the vault, scores decreased by an average of 8.0 points. One partially overlapping role showed a modest gain of 2 points. These results suggest that longitudinal retrieval can improve resume tailoring when relevant prior experience exists, while also highlighting the need for confidence-gated retrieval when domain overlap is weak.

cs.IR↗

arXiv2025

Quasi-integrability from PT-symmetry

Parity and time-reversal (PT ) symmetry is shown as the natural cause of quasi-integrability of deformed integrable models, crucial to represent real physical systems as they posses various irregularities. The condition for asymptotic conservation of quasi-conserved charges appear as a direct consequence of the PT -symmetric phase of the system, ensuring definite PT -properties of the corresponding Lax pair as well as that of the anomalous contribution, consistent with the Wilson-loop criterion for integrability-like behavior. As a result, the quasi-deformed charge densities always acquire definite PT -properties suitable for the asymptotic conservation, as the Abelianization approach to construct them also preserves the definite PT -behavior of the Lax pair. This PT -symmetry based origin of quasi-conservation is general and has been demonstrated for quasi-deformations of multiple systems such as KdV, NLSE and non-local NLSE.

nlin.SI↗

arXiv2025

Wavelet Coorbit Spaces over Local Fields

This paper studies wavelet coorbit spaces on disconnected local fields $K$, associated to the quasi-regular representation of $G = K \rtimes K^*$ acting on $L^2(K)$. We show that coorbit space theory applies in this context, and identify the homogeneous Besov spaces $\dot{B}_{\alpha,s,t}(K)$ as coorbit spaces. We identify a particularly convenient space $\mathcal{S}_0(K)$ of wavelets that give rise to tight wavelet frames via the action of suitable, easily determined discrete subsets $R \subset G$, and show that the resulting wavelet expansions converge simultaneously in the whole range of coorbit spaces. For orthonormal wavelet bases constructed from elements of $\mathcal{S}_0(K)$, the associated wavelet bases turn out to be unconditional bases for all coorbit spaces. We give explicit constructions of tight wavelet frames and wavelet orthonormal bases to which our results apply.

math.FA↗

arXiv2023

Quantizing a Non-locally Massive 2-form Model

A non-local yet gauge-invariantly massive 2-form model is considered that leads to local and unitary dynamics upon proper gauge-fixing. Since canonical momenta cannot be defined owing to the non-locality, consistent quantization of this system warrants particular care. We construct the Dirac brackets and covariant commutators for this model, followed by its path integral quantization, leading to consistent results. These treatments underline the most efficient way to extract the physical modes and the subsequent spectrum free from infrared ambiguity. Physically the massive 2-form represents a spin-1 excitation, with potential application to string theory and cosmology, that can mediate a screened interaction when topologically coupled to fermions.

hep-th↗

arXiv2022

Non-holonomic and Quasi-integrable deformations of the AB Equations

For the first time, both non-holonomic and quasi-integrable deformations are obtained for the AB system of coupled equations. The AB system models geophysical and atmospheric fluid motion along with ultra-short pulse propagation in nonlinear optics and serves as a generalization of the well-known sine-Gordon equation. The non-holonomic deformation retains integrability subjected to higher-order differential constraints whereas the quasi-AB system, which is partially deviated from integrability, is characterized by an infinite subset of quantities (charges) that are conserved only asymptotically given the solution possesses definite space-time parity properties. Particular localized solutions to both these deformations of the AB system are obtained, some of which are qualitatively unique to the corresponding deformation, displaying similarities with physically observed excitations.

math-ph↗

arXiv2021

On Quasi-integrable Deformation Scheme of The KdV System

We put forward a general approach to quasi-deform the KdV equation by deforming the corresponding Hamiltonian. Following the standard Abelianization process based on the inherent $sl(2)$ loop algebra, an infinite number of anomalous conservation laws are obtained, which yield conserved charges if the deformed solution has definite space-time parity. Judicious choice of the deformed Hamiltonian leads to an integrable system with scaled parameters as well as to a hierarchy of deformed systems, some of which possibly being quasi-integrable. As a particular case, one such deformed KdV system maps to the known quasi-NLS soliton in the already known weak-coupling limit, whereas a generic scaling of the KdV amplitude $u \to u^{1+\epsilon}$ also goes to possible quasi-integrability under an order-by-order expansion. Following a generic parity analysis of the deformed system, these deformed KdV solutions need to be parity-even for quasi-conservation which may be the case here following our analytical approach. From the established quasi-integrability of RLW and mRLW systems [Nucl. Phys. B 939 (2019) 49-94], which are particular cases of the present approach, exact solitons of the quasi-KdV system could be obtained numerically.

nlin.SI↗

arXiv2020

AI Assisted Apparel Design

Fashion is a fast-changing industry where designs are refreshed at large scale every season. Moreover, it faces huge challenge of unsold inventory as not all designs appeal to customers. This puts designers under significant pressure. Firstly, they need to create innumerous fresh designs. Secondly, they need to create designs that appeal to customers. Although we see advancements in approaches to help designers analyzing consumers, often such insights are too many. Creating all possible designs with those insights is time consuming. In this paper, we propose a system of AI assistants that assists designers in their design journey. The proposed system assists designers in analyzing different selling/trending attributes of apparels. We propose two design generation assistants namely Apparel-Style-Merge and Apparel-Style-Transfer. Apparel-Style-Merge generates new designs by combining high level components of apparels whereas Apparel-Style-Transfer generates multiple customization of apparels by applying different styles, colors and patterns. We compose a new dataset, named DeepAttributeStyle, with fine-grained annotation of landmarks of different apparel components such as neck, sleeve etc. The proposed system is evaluated on a user group consisting of people with and without design background. Our evaluation result demonstrates that our approach generates high quality designs that can be easily used in fabrication. Moreover, the suggested designs aid to the designers creativity.

cs.CV↗

arXiv2019

Analysis and comparative study of non-holonomic and quasi-integrable deformations of the Nonlinear Schrödinger Equation

The non-holonomic deformation of the nonlinear Schrödinger equation, uniquely obtained from both the Lax pair and Kupershmidt's bi-Hamiltonian [Phys. Lett. A 372, 2634 (2008)] approaches, is compared with the quasi-integrable deformation of the same system [Ferreira et. al. JHEP 2012, 103 (2012)]. It is found that these two deformations can locally coincide only when the phase of the corresponding solution is discontinuous in space, following a definite phase-modulus coupling of the non-holonomic inhomogeneity function. These two deformations are further found to be not gauge-equivalent in general, following the Lax formalism of the nonlinear Schrödinger equation. However, asymptotically they converge for localized solutions as expected. Similar conditional correspondence of nonholonomic deformation with a non-integrable deformation, namely, due to local scaling of the amplitude of the nonlinear Schrödinger equation is further obtained.

nlin.SI↗

arXiv2019

Space Curves from Nonlinear Schr\"odinger Solutions: A Direct Approach

The connection between vortex filament evolution in the local induction approximation and non-linear Schr\"odinger (NLS) equation by Hasimoto [H. Hasimoto, J. Fluid Mechanics 51, (1972) 477] has led to space curves corresponding to NLS solitons in the past. Utilizing this map, we propose a direct construction of parametric curve evolution from any NLS solution. It includes ordered (or nested) integrals of products of local matrices akin to the causal evolution of quantum theory, necessitating the implementation of the Magnus expansion. Such a straightforward mapping may be a simple tool to study the evolution of various systems of physical concern, although the actual computation can be a challenge for most NLS solutions.

nlin.SI↗

arXiv2018

Trustworthiness in Enterprise Crowdsourcing: a Taxonomy & evidence from data

In this paper we study the trustworthiness of the crowd for crowdsourced software development. Through the study of literature from various domains, we present the risks that impact the trustworthiness in an enterprise context. We survey known techniques to mitigate these risks. We also analyze key metrics from multiple years of empirical data of actual crowdsourced software development tasks from two leading vendors. We present the metrics around untrustworthy behavior and the performance of certain mitigation techniques. Our study and results can serve as guidelines for crowdsourced enterprise software development.

cs.SE↗

arXiv2018

Inhomogeneous Heisenberg Spin Chain and Quantum Vortex Filament as Non-Holonomically Deformed NLS Systems

Through the Hasimoto map, various dynamical systems can be mapped to different integrodifferential generalizations of Nonlinear Schrodinger (NLS) family of equations some of which are known to be integrable. Two such continuum limits, corresponding to the inhomogeneous XXX Heisenberg spin chain [Balakrishnan, J. Phys. C 15, L1305 (1982)] and that of a thin vortex filament moving in a superfluid with drag [Shivamoggi, Eur. Phys. J. B 86, 275 (2013) 86; Van Gorder, Phys. Rev. E 91, 053201 (2015)], are shown to be particular non-holonomic deformations (NHDs) of the standard NLS system involving generalized parameterizations. Crucially, such NHDs of the NLS system are restricted to specific spectral orders that exactly complements NHDs of the original physical systems. The specific non-holonomic constraints associated with these integrodifferential generalizations additionally posses distinct semi-classical signature.

math-ph↗

arXiv2017

Study of quasi-integrable and non-holonomic deformation of equations in the NLS and DNLS hierarchy

The hierarchy of equations belonging to two different but related integrable systems, the Nonlinear Schrödinger and its derivative variant, DNLS are subjected to two distinct deformation procedures, viz. quasi-integrable deformation (QID) that generally do not reserve the integrability, only asymptotically integrable, and non-holonomic deformation (N HD) that does. QID is carried out generically for the NLS hierarchy while for the DNLS hierarchy, it is first done on the Kaup-Newell system followed by other members of the family. No QI anomaly is observed at the level of EOMs which suggests that at that level the QID may be identified as some integrable deformation. NHD is applied to the NLS hierarchy generally as well as with the specific focus on the NLS equation itself and the coupled KdV type NLS equation. For the DNLS hierarchy, the Kaup-Newell(KN) and Chen-Lee-Liu (CLL) equations are deformed non-holonomically and subsequently, different aspects of the results are discussed.

math-ph↗

arXiv2017

Image Segmentation of Multi-Shaped Overlapping Objects

In this work, we propose a new segmentation algorithm for images containing convex objects present in multiple shapes with a high degree of overlap. The proposed algorithm is carried out in two steps, first we identify the visible contours, segment them using concave points and finally group the segments belonging to the same object. The next step is to assign a shape identity to these grouped contour segments. For images containing objects in multiple shapes we begin first by identifying shape classes of the contours followed by assigning a shape entity to these classes. We provide a comprehensive experimentation of our algorithm on two crystal image datasets. One dataset comprises of images containing objects in multiple shapes overlapping each other and the other dataset contains standard images with objects present in a single shape. We test our algorithm against two baselines, with our proposed algorithm outperforming both the baselines.

cs.CV↗

arXiv2017

Chern-Simons Gauge Invariance and Boundary Conformal Fields

The topological non-Abelian Chern-Simons theory with a boundary is shown to require a scalar field companion in order to preserve overall gauge-invariance both in the 3 dimensional manifold, as well as on its boundary. This scalar field, originally being a pure-gauge Chern-Simons excitation that indicates the most general topological gauge structure in the bulk, is found to be crucial for dynamic scalar excitation on the 2 dimensional generic boundary manifold, the latter naturally representing a conformal mode. This gauge/CFT correspondence is general, for a compact gauge group.

hep-th↗

arXiv2017

Quasi-Integrability of The KdV System

The quasi-integrable KdV equation has been obtained from the corresponding deformation of the Hamiltonian for the usual KdV system. Following suitable gauge-fixing, it has been found that the quasi-conservation condition is satisfied and an infinite number of anomalous conservation laws are obtained, with some containing possible conserved charges. Judicious choice of deformation of the Hamiltonian clearly leads to a conserved charge, manifesting quasi-integrability, but also creates a hierarchy of higher-derivative equations with at least one conserved charge. A particular quasi-deformation parameterization of the Hamiltonian is found to complement the same of the NLS system, following an approximate equivalence of the two systems obtained earlier, in the weak coupling limit. Single-soliton solutions for all these cases are obtained, with manifest scaling due to the quasi-integrable deformation. Finally, quasi-conservation formulation for the complex coupled generalized KdV system is obtained.

math-ph↗

arXiv2017

Bäcklund Transformation and Quasi-Integrable Deformation of Mixed Fermi-Pasta-Ulam and Frenkel-Kontorova Models

In this paper we study a non-linear partial differential equation (PDE), proposed by N. Kudryashov [arXiv:1611.06813v1[nlin.SI]], using continuum limit approximation of mixed Fermi-Pasta-Ulam and Frenkel-Kontorova Models. This generalized semi-discrete equation can be considered as a model for the description of non-linear dislocation waves in crystal lattice and the corresponding continuous system can be called mixed generalized potential KdV and sine-Gordon equation. We obtain the Bäcklund transformation of this equation in Riccati form in inverse method. We further study the quasi-integrable deformation of this model.

math-ph↗