arXiv subjects

Subhash Chandra

Publications and source records attributed to Subhash Chandra.

12 recordsLinked to original sources

arXiv2026

Some topological properties and bi-Lipschitz equivalence of graph-directed attractors

In this paper, we discuss some topological properties of the graph-directed iterated function system (GDIFS) of injective contractions. Further, we establish the existence of a Lipschitz bijection between two different bi-Lipschitz graph-directed attractors. In general, two different bi-Lipschitz graph-directed attractors defined on the same graph need not be bi-Lipschitz equivalent. However, under suitable conditions, we prove that these graph-directed attractors are bi-Lipschitz equivalent.

math.DS↗

arXiv2026

Comparative Analysis of Differential and Collision Entropy for Finite-Regime QKD in Hybrid Quantum Noisy Channels

In this work, a comparative study between three fundamental entropic measures, differential entropy, quantum Renyi entropy, and quantum collision entropy for a hybrid quantum channel (HQC) was investigated, where hybrid quantum noise (HQN) is characterized by both discrete and continuous variables (CV) noise components. Using a Gaussian mixture model (GMM) to statistically model the HQN, we construct as well as visualize the corresponding pointwise entropic functions in a given 3D probabilistic landscape. When integrated over the relevant state space, these entropic surfaces yield values of the respective global entropy. Through analytical and numerical evaluation, it is demonstrated that the differential entropy approaches the quantum collision entropy under certain mixing conditions, which aligns with the Renyi entropy for order $\alpha = 2$. Within the HQC framework, the results establish a theoretical and computational equivalence between these measures. This provides a unified perspective on quantifying uncertainty in hybrid quantum communication systems. Extending the analysis to the operational domain of finite key QKD, we demonstrated that the same $10\%$ approximation threshold corresponds to an order-of-magnitude change in Eves success probability and a measurable reduction in the secure key rate.

eess.SP↗

arXiv2025

Set Valued Riemann-Liouville integral and some Regular Selections

In this article, we introduce the notion of the Riemann-Liouville fractional integral of set-valued mappings via integrable selections. We establish fundamental properties of this fractional integral, including convexity, boundedness, and continuity with respect to the Hausdorff metric. The investigation of preservation of regularity under fractional integration with respect to the Hausdorff metric is given. We show that bounded variation and Lipschitz continuity of a set-valued mapping are inherited by its Riemann-Liouville fractional integral. We discuss the existence of regular selections for the fractional integral under the corresponding regularity assumptions on the original mapping. In the scalar case, we further identify extremal selections given by the pointwise minimum and maximum of the fractional integral and show that they possess the same regularity properties. Finally, we discuss possible applications in differential inclusion and directions for future research.

math.DS↗

arXiv2025

On the Achievable Rate of Satellite Quantum Communication Channel using Deep Autoencoder Gaussian Mixture Model

We present a comparative study of the Gaussian mixture model (GMM) and the Deep Autoencoder Gaussian Mixture Model (DAGMM) for estimating satellite quantum channel capacity, considering hybrid quantum noise (HQN) and transmission constraints. While GMM is simple and interpretable, DAGMM better captures non-linear variations and noise distributions. Simulations show that DAGMM provides tighter capacity bounds and improved clustering. This introduces the Deep Cluster Gaussian Mixture Model (DCGMM) for high-dimensional quantum data analysis in quantum satellite communication.

eess.SP↗

arXiv2025

Deformation Due to Non-planar Fault Movement in Fractional Maxwell Medium

In earthquake-prone regions, the accumulation of geophysical stress during the aseismic period plays a critical role in determining which faults are more likely to be reactivated in future seismic events. In this model, we consider an infinite non-planar fault located in a viscoelastic half-space of a fractional Maxwell medium representing the lithosphere-asthenosphere system comprising three interconnected planar sections. The problem is formulated as a two-dimensional boundary value problem with discontinuities along the fault surface. A numerical solution is obtained using a Laplace transformation, fractional derivative, correspondence principle and Green's function technique. The outcomes are demonstrated graphically using appropriate model parameters. The computational findings highlight the significant influence of fault motion and geometry in shaping the displacement, stress and strain fields in the vicinity of the fault zone. A study has been carried out to investigate how non-planar faults influence displacement and the accumulation of stress and strain. Analysis of these results can provide insights into subsurface deformation and its impact on fault movement, which may contribute to the study of earthquake activity.

physics.geo-ph↗

arXiv2024

A Hybrid Noise Approach to Modelling of Free-Space Satellite Quantum Communication Channel for Continuous-Variable QKD

This paper significantly advances the application of Quantum Key Distribution (QKD) in Free- Space Optics (FSO) satellite-based quantum communication. We propose an innovative satellite quantum channel model and derive the secret quantum key distribution rate achievable through this channel. Unlike existing models that approximate the noise in quantum channels as merely Gaussian distributed, our model incorporates a hybrid noise analysis, accounting for both quantum Poissonian noise and classical Additive-White-Gaussian Noise (AWGN). This hybrid approach acknowledges the dual vulnerability of continuous variables (CV) Gaussian quantum channels to both quantum and classical noise, thereby offering a more realistic assessment of the quantum Secret Key Rate (SKR). This paper delves into the variation of SKR with the Signal-to-Noise Ratio (SNR) under various influencing parameters. We identify and analyze critical factors such as reconciliation efficiency, transmission coefficient, transmission efficiency, the quantum Poissonian noise parameter, and the satellite altitude. These parameters are pivotal in determining the SKR in FSO satellite quantum channels, highlighting the challenges of satellitebased quantum communication. Our work provides a comprehensive framework for understanding and optimizing SKR in satellite-based QKD systems, paving the way for more efficient and secure quantum communication networks.

eess.SP↗

arXiv2024

Hybrid Quantum Noise Approximation and Pattern Analysis on Parameterized Component Distributions

Noise is a vital factor in determining the accuracy of processing the information of the quantum channel. One must consider classical noise effects associated with quantum noise sources for more realistic modelling of quantum channels. A hybrid quantum noise model incorporating both quantum Poisson noise and classical additive white Gaussian noise (AWGN) can be interpreted as an infinite mixture of Gaussians with weightage from the Poisson distribution. The entropy measure of this function is difficult to calculate. This research developed how the infinite mixture can be well approximated by a finite mixture distribution depending on the Poisson parametric setting compared to the number of mixture components. The mathematical analysis of the characterization of hybrid quantum noise has been demonstrated based on Gaussian and Poisson parametric analysis. This helps in the pattern analysis of the parametric values of the component distribution, and it also helps in the calculation of hybrid noise entropy to understand hybrid quantum noise better.

eess.SP↗

arXiv2024

An Unsupervised Machine Learning to Optimize Hybrid Quantum Noise Clusters for Gaussian Quantum Channel

This work focuses on optimizing the hybrid quantum noise model to improve the capacity of Gaussian quantum channels using Machine Learning (ML) generated clusters. The work specifically leverages Gaussian Mixture Model (GMM) and the Expectation-Maximization (EM) algorithm to model the complex noise characteristics of quantum channels. Hybrid quantum noise, which includes both quantum shot noise and classical Additive-White-Gaussian Noise (AWGN), is modeled as an infinite mixture of Gaussian distributions weighted by Poissonian parameters. The study proposes a method to reduce the number of clusters within this noise model, simplifying visualization and improving the accuracy of channel capacity estimations without compromising essential noise characteristics. Key contributions include the reduction of Gaussian clusters while maintaining error tolerances and using the EM algorithm to update quantum channel parameters, leading to more accurate channel capacity. The approach is validated through simulations, demonstrating that ML-enhanced quantum noise clustering significantly improves the channels performance in satellite-based quantum communication systems, specifically for Quantum Key Distribution (QKD). The work demonstrates that GMM and EM algorithms provide a practical solution for modeling quantum noise in real-time applications, advancing the optimization of quantum communication networks.

eess.SP↗

arXiv2023

Construction of Fractal Functions Using Kannan Mappings and Smoothness Analysis

Let T be a self-map on a metric space (X, d). Then T is called the Kannan map if there exists \alpha, 0 < \alpha < 1/2, such that d(T(x), T(y)) <= \alpha[d(x, T(x)) + d(y, T(y))], for all x, y in X. This paper aims to introduce a new method to construct fractal functions using Kannan mappings. First, we give the rigorous construction of fractal functions with the help of the Kannan iterated function system (IFS). We also show the existence of a Borel probability measure supported on the attractor of the Kannan IFS satisfying the strong separation condition. Moreover, we study the smoothness of the constructed fractal functions. We end the paper with some examples and graphical illustrations.

math.DS↗

arXiv2021

Analysis of Fractal Dimension of Mixed Riemann-Liouville Fractional Integral

In this article, we investigate the fractal dimension of the graph of the mixed Riemann-Liouville fractional integral for various choice of continuous functions on a rectangular region. We estimate bounds for the box dimension and the Hausdorff dimension of the graph of the mixed Riemann-Liouville fractional integral of the functions which belong to the class of continuous functions and the class of Holder continuous functions. We also show that the box dimension of the graph of the mixed Riemann-Liouville fractional integral of two-dimensional continuous functions is also two. Furthermore, we give construction of unbounded variational continuous functions. Later, we prove that the box dimension and the Hausdorff dimension of the graph of the mixed Riemann-Liouville fractional integral of unbounded variational continuous functions are also two.

math.CA↗

arXiv2021

Box Dimension of Mixed Katugampola Fractional Integral of Two-Dimensional Continuous Functions

The goal of this article is to study the box dimension of the mixed Katugampola fractional integral of two-dimensional continuous functions on [0; 1]X[0; 1]. We prove that the box dimension of the mixed Katugampola fractional integral having fractional order (\alpha = (\alpha_1; \alpha_2); \alpha_1 > 0; \alpha_2 > 0) of two-dimensional continuous functions on [0; 1]X[0; 1] is still two. Moreover, the results are also established for the mixed Hadamard fractional integral.

math.CA↗

arXiv2020

The Calculus Of Bivariate Fractal Interpolation Surfaces

In this article, we investigate partial integrals and partial derivatives of bivariate fractal interpolation functions. We prove also that the mixed Riemann-Liouville fractional integral and derivative of order $\gamma = (p, q); p > 0,q > 0$, of bivariate fractal interpolation functions are again bivariate interpolation functions corresponding to some iterated function system (IFS). Furthermore, we discuss the integral transforms and fractional order integral transforms of the bivariate fractal interpolation functions.

math.DS↗