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Sudhir Singh

Publications and source records attributed to Sudhir Singh.

13 recordsLinked to original sources
arXiv2026

A Hybrid Architecture for Benign-Malignant Classification of Mammography ROIs

Accurate characterization of suspicious breast lesions in mammography is important for early diagnosis and treatment planning. While Convolutional Neural Networks (CNNs) are effective at extracting local visual patterns, they are less suited to modeling long-range dependencies. Vision Transformers (ViTs) address this limitation through self-attention, but their quadratic computational cost can be prohibitive. This paper presents a hybrid architecture that combines EfficientNetV2-M for local feature extraction with Vision Mamba, a State Space Model (SSM), for efficient global context modeling. The proposed model performs binary classification of abnormality-centered mammography regions of interest (ROIs) from the CBIS-DDSM dataset into benign and malignant classes. By combining a strong CNN backbone with a linear-complexity sequence model, the approach achieves strong lesion-level classification performance in an ROI-based setting.

cs.CV↗
arXiv2025

Computing the Dynamics of Multi-Lumps in Nonlinearity-Managed Spatial-Symmetric Dispersive Wave Framework

We investigate the dynamics of multi-lump waves in a new version of a generalized spatial-symmetric higher-dimensional nonlinear dispersive water wave model using an analytical approach. This involves the proposition of a new spatial-symmetric nonlinear model in (3+1)-dimensions and the construction of its explicit solutions for multi-lump waves through a systematic analytical framework by employing Hirota's bilinear method and generalized polynomial expansions. Analyzing the resultant explicit solutions in terms of their dynamical characteristics reveals that the obtained multi-lump waves are non-interacting and exhibit different geometrical patterns. The observed results demonstrate the significance of new higher-dimensional nonlinear dispersive models in enhancing our understanding of the dynamics of various types of localized waves.

nlin.PS↗
arXiv2025

Generalized Gottesman-Kitaev-Preskill States on a Quantum Torus

We introduce a novel formulation of a Generalized Gottesman-Kitaev-Preskill (GKP) state that resolves all of its foundational pathologies, such as infinite energy, non-normalizability, and orthogonality. We demonstrate that these issues are artifacts of defining the code on an unbounded phase-space. By considering the compact quantum-phase-space intrinsic to systems like coupled quantum harmonic oscillators, we have obtained a Generalized GKP (GGKP) state that is both exact and physically realizable. This is achieved by applying an obtained Quantum Zak Transform (QZT) to Squeezed Coherent States, which reveals that Riemann-Theta functions are the natural representation of these states on the quantum torus phase-space. This framework not only provides a well-behaved quantum state, but also reveals a deep connection between quantum error correction, non-commutative geometry, and the theory of generalized Theta functions. This opens a new avenue for fault-tolerant photonic quantum computing.

quant-ph↗
arXiv2023

Exploring the Dynamics of Nonlocal Nonlinear Waves: Analytical Insights into the Extended Kadomtsev-Petviashvili Model

The study of nonlocal nonlinear systems and their dynamics is a rapidly increasing field of research. In this study, we take a closer look at the extended nonlocal Kadomtsev-Petviashvili (enKP) model through a systematic analysis of explicit solutions. Using a superposed bilinearization approach, we obtained a bilinear form of the enKP equation and constructed soliton solutions. Our findings show that the nature of the resulting nonlinear waves, including the amplitude, width, localization, and velocity, can be controlled by arbitrary solution parameters. The solutions exhibited both symmetric and asymmetric characteristics, including localized bell-type bright solitons, superposed kink-bell-type and antikink-bell-type soliton profiles. The solitons arising in this nonlocal model only undergo elastic interactions while maintaining their initial identities and shifting phases. Additionally, we demonstrated the possibility of generating bound-soliton molecules and breathers with appropriately chosen soliton parameters. The results of this study offer valuable insights into the dynamics of localized nonlinear waves in higher-dimensional nonlocal nonlinear models.

nlin.PS↗
arXiv2023

Lump and Soliton on Certain Spatially-varying Backgrounds for an Integrable (3+1) Dimensional Fifth-order Nonlinear Oceanic Wave Model

The dynamics of nonlinear waves with controllable dispersion, nonlinearities, and background continues to be an exciting line of research in recent years. In this work, we focus to investigate an integrable (3+1)-dimensional nonlinear model describing the evolution of {water waves} with higher-order temporal dispersion by characterizing the dynamics of lump and soliton waves on different spatially-varying backgrounds. We construct explicit lump wave and kink-soliton solutions for the considered model through its trilinear and bilinear equations with appropriate forms of the polynomial and exponential-type initial seed solutions, respectively. Additionally, we obtain hyperbolic and periodic waves through bilinear Bäcklund transformation. We explore their propagation and transformation dynamics with spatial backgrounds through a categorical analysis and clear graphical demonstrations to fully understand the resulting solutions. Our analysis shows that the lump solution results into a simultaneous existence of well-localized spike and declining (coupled bright-dark type wave) structures on a constant background, while the soliton solution exhibits kink and anti-kink wave patterns along different spatio-temporal domains with controllable properties. When the arbitrary spatial background is incorporated appropriately, we can witness the manifestation of soliton into periodic and interacting dynamical structures. On the other hand, the lump wave results into the coexistence, interacting wave and breather formation due to periodic and localized type spatial backgrounds. The results will be an important addition to the context of nonlinear waves with controllable backgrounds in higher-dimensional models. Further, the present study can be extended to investigate several other nonlinear systems to understand the physical insights of the variable background in their dynamics.

nlin.PS↗
arXiv2022

Transverse Spectral Instabilities in Konopelchenko-Dubrovsky Equation

We study the transverse spectral stability of the one-dimensional small-amplitude periodic traveling wave solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky (KD) equation. We show that these waves are transversely unstable with respect to two-dimensional perturbations that are periodic in both directions with long wavelength in the transverse direction. We also show that these waves are transversely stable with respect to perturbations which are either mean-zero periodic or square-integrable in the direction of the propagation of the wave and periodic in the transverse direction with finite or short wavelength. We discuss the implications of these results for special cases of the KD equation - namely, KP-II and mKP-II equations.

math.AP↗
arXiv2022

Painlevé Analysis and Higher-Order Rogue Waves of a Generalized(3+1)-dimensional Shallow Water Wave Equation

Considering the importance of ever-increasing interest in exploring localized waves, we investigate a generalized (3+1)-dimensional Hirota-Satsuma-Ito equation describing the unidirectional propagation of shallow-water waves and perform Painlevé analysis to understand its integrability nature. We construct the explicit form of higher-order rogue wave solutions by adopting Hirota's bilinearization and generalized polynomial functions. Further, we explore their dynamics in detail, depicting different pattern formation that reveal potential advantages with available arbitrary constants in their manipulation mechanism. Particularly, we demonstrate the existence of singly-localized line-rogue waves and doubly-localized rogue waves with multiple (single, triple, and sextuple) structures generating triangular and pentagon type geometrical patterns with controllable orientations that can be altered appropriately by tuning the parameters. The presented analysis will be an essential inclusion in the context of rogue waves in higher-dimensional systems.

nlin.SI↗
arXiv2022

Localized Nonlinear Waves on Spatio-Temporally Controllable Backgrounds for a (3+1)-Dimensional Kadomtsev-Petviashvili-Boussinesq Model in Water Waves

Physics of nonlinear waves on variable backgrounds and the relevant mathematical analysis continues to be the challenging aspect of the study. In this work, we consider a (3+1)-dimensional nonlinear model describing the dynamics of {water waves} and construct nonlinear wave solutions on spatio-temporally controllable backgrounds for the first time by using a simple mathematical tool auto-Bäcklund transformation. Mainly, we unravel physically interesting features to control and manipulate the dynamics of nonlinear waves through the background. Adapting an exponential function and general polynomial of degree two as initial seed solutions, we construct single kink-soliton and rogue wave, respectively. We choose arbitrary periodic, localized and combined wave backgrounds by incorporating Jacobi elliptic functions and investigate the modulation of these two nonlinear waves with a clear analysis and graphical demonstrations. The solutions derived in this work give us sufficient freedom to generate exotic nonlinear coherent structures on variable backgrounds and open up an interesting direction to explore the dynamics of various other nonlinear waves propagating through inhomogeneous media.

nlin.PS↗
arXiv2020

Dynamics of Higher-order Bright and Dark Rogue Waves in a New (2+1)-Dimensional Integrable Boussinesq Model

This work deals with the dynamics of higher-order rogue waves in a new integrable (2+1)-dimensional Boussinesq equation governing the evolution of high and steep gravity water waves. To achieve this objective, we construct rogue wave solutions by employing Bell polynomial and Hirota's bilinearization method, along with the generalized polynomial function. Through the obtained rogue wave solutions, we explore the impact of various system and solution parameters in their dynamics. Primarily, these parameters determine the characteristics of rogue waves, including the identification of their type, bright or dark type doubly-localized rogue wave structures and spatially localized rational solitons, and manipulation of their amplitude, depth, and width. Reported results will be encouraging to the studies on the rogue waves in higher dimensional systems as well as to experimental investigations on the controlling mechanism of rogue waves in optical systems, atomic condensates, and deep water oceanic waves.

nlin.SI↗
arXiv2020

Benjamin-Ono equation: Rogue waves, generalized breathers, soliton bending, fission, and fusion

In this work, we construct various interesting localized wave structures of the Benjamin-Ono equation describing the dynamics of deep water waves. Particularly, we extract the rogue waves and generalized breather solutions with the aid of bilinear form and by applying two appropriate test functions. Our analysis reveals the control mechanism of the rogue waves with arbitrary parameters to obtain both bright and dark type first and second-order rogue waves. Additionally, a generalization of the homoclinic breather method, also known as the three-wave method, is used for extracting the generalized breathers along with bright, dark, anti-dark, rational solitons. Interestingly, we have observed the manipulation of breathers along with soliton interaction, bending, fission, and fusion. Our results are discussed categorically with the aid of clear graphical demonstrations.

nlin.SI↗
arXiv2020

Higher dimensional localized and periodic wave dynamics in a new integrable (2+1)-dimensional Kundu-Mukherjee-Naskar model

In this article, a new integrable (2+1)-dimensional Kundu-Mukherjee-Naskar model which is a variant of the well known nonlinear Schrödinger equation is investigated. Bright-dark optical solitons along with periodic waves, complexiton and rational solutions are constructed by employing a generalized traveling wave analysis, Jacobian-elliptic function, Riccati equation and ansatz approach. Further, the dynamics of these bright/dark optical solitons and complexiton/periodic waves are studied by exploring the importance of arbitrary physical parameters with graphical demonstrations for a clear understanding. The obtained higher dimensional nonlinear wave solutions of this integrable system shall have useful applications in different physical systems including the dynamics of beam propagation in optical fibers, ion-acoustic waves in magnetized plasma and deep water oceanic rogue waves.

nlin.PS↗
arXiv2019

Brain-inspired automated visual object discovery and detection

Despite significant recent progress, machine vision systems lag considerably behind their biological counterparts in performance, scalability, and robustness. A distinctive hallmark of the brain is its ability to automatically discover and model objects, at multiscale resolutions, from repeated exposures to unlabeled contextual data and then to be able to robustly detect the learned objects under various nonideal circumstances, such as partial occlusion and different view angles. Replication of such capabilities in a machine would require three key ingredients: (i) access to large-scale perceptual data of the kind that humans experience, (ii) flexible representations of objects, and (iii) an efficient unsupervised learning algorithm. The Internet fortunately provides unprecedented access to vast amounts of visual data. This paper leverages the availability of such data to develop a scalable framework for unsupervised learning of object prototypes--brain-inspired flexible, scale, and shift invariant representations of deformable objects (e.g., humans, motorcycles, cars, airplanes) comprised of parts, their different configurations and views, and their spatial relationships. Computationally, the object prototypes are represented as geometric associative networks using probabilistic constructs such as Markov random fields. We apply our framework to various datasets and show that our approach is computationally scalable and can construct accurate and operational part-aware object models much more efficiently than in much of the recent computer vision literature. We also present efficient algorithms for detection and localization in new scenes of objects and their partial views.

cs.CV↗