arXiv subjects

Himanshu Shekhar

Publications and source records attributed to Himanshu Shekhar.

5 recordsLinked to original sources

arXiv2026

Spectral and Eigenvector Crossovers in Random Mixed Graphs

We study the spectral and eigenvector properties of random mixed graphs, combining undirected and directed interactions, using random matrix theory (RMT). The network is represented by a Hermitian adjacency matrix, with undirected links as real entries and directed links as purely imaginary conjugate pairs, ensuring a real spectrum. Network density is controlled by the connection probability, while directionality sets the fraction of directed edges. We focus on the GOE-to-GUE crossover: at fixed connectivity, increasing directionality breaks time-reversal symmetry and drives spectral statistics from GOE to GUE. We show that this transition requires sufficient connectivity. In sparse networks, weak level repulsion produces Poisson statistics regardless of directionality. At fixed directionality, increasing connectivity drives a Poisson-to-GUE crossover; only above a sparsity threshold does the directionality-induced GOE-to-GUE transition emerge. In the dense regime, where the spectral density follows the Wigner semicircle law, the crossover is characterized using spacing distributions, spacing ratios, and spectral rigidity. In sparse networks, where unfolding is unreliable, spacing-ratio statistics provide an unfolding-free characterization. Eigenvector structure is examined through multifractal dimensions and component distributions, while Kullback--Leibler divergence confirms the robustness of the transitions. Applied to S&P 500 mixed graphs, the framework reveals a GOE-to-GUE crossover across four major market crashes. Denser crisis periods show sharper crossovers than sparser recovery periods. The results provide a unified picture of how connectivity and symmetry breaking govern spectral and eigenvector universality, while providing a transparent probe of changing financial-market organization.

physics.comp-ph↗

arXiv2026

Spectral fluctuations and crossovers in multilayer network

We investigate spectral fluctuations in multilayer networks within the random matrix theory (RMT) framework to characterize universal and non-universal features. The adjacency matrix of a multilayer network exhibits a block structure, with diagonal blocks representing intra-layer connections and off-diagonal blocks encoding inter-layer connections. Applying appropriate scaling factors for these blocks, we equalize variances across inter- and intra-layers, enabling direct comparison of spectral statistics. We analyze eigenvalue spectra across multilayer network configurations with varying inter- and intra-layer connectivities. Introducing a crossover model for bilayer networks, we capture the smooth transition of spectral properties from block-diagonal (two independent GOEs) to single-layer (one GOE) statistics as the relative strength of inter-layer to intra-layer connection varies. Furthermore, we analyze interatomic distance networks derived from protein crystal structures, including 1EWT, 1EWK, and 1UW6, to demonstrate applicability. Our findings reveal that the universality of spectral fluctuations persists across multilayer network architectures and highlight RMT as a robust tool for probing topological and dynamical complexities of real-world networks.

math-ph↗

arXiv2025

Spectral statistics of interpolating random circulant matrix and its applications to random circulant graphs

We consider a versatile matrix model of the form ${\bf A}+i {\bf B}$, where ${\bf A}$ and ${\bf B}$ are real random circulant matrices with independent but, in general, nonidentically distributed Gaussian entries. For this model, we derive exact results for the joint probability density function and find that it is a multivariate Gaussian. Arbitrary order marginal density therefore also readily follows. It is demonstrated that by adjusting the averages and variances of the Gaussian elements of ${\bf A}$ and ${\bf B}$, we can interpolate between a remarkably wide range of eigenvalue distributions in the complex plane. In particular, we can examine the crossover between a random real circulant matrix and a random complex circulant matrix. We also extend our study to include Wigner-like and Wishart-like matrices constructed from our general random circulant matrix. To validate our analytical findings, Monte Carlo simulations are conducted, which confirm the accuracy of our results. Additionally, we compare our analytical results with the spectra of adjacency matrices from various random circulant graphs. Despite the difference in entry distributions-Gaussian in our model and non-Gaussian in the adjacency matrices-the densities show excellent agreement in the large-dimension limit.

math-ph↗

arXiv2024

A Performance Evaluation of Filtered Delay Multiply and Sum Beamforming for Ultrasound Localization Microscopy: Preliminary Results

Ultrafast ultrasound localization microscopy (ULM), which has shown promising results in microvascular imaging, overcomes the typical trade-off between resolution and penetration depth. Combining ultrasound contrast agents and high frame rate imaging enables ULM to visualize microvasculature and quantify flow. However, the quality of the microvascular maps obtained depends on the signal-to-noise ratio of the received signals, image reconstruction techniques, and the microbubble (MB) localization and tracking algorithms used. Most reported research in ULM employs the conventional delay and sum (DAS) beamforming technique for image reconstruction despite its limited contrast and resolution. In this work, a filtered delay multiply and sum (F-DMAS) beamforming approach with non-steered plane wave transmit was employed for ULM, and its performance was compared with the conventional DAS-based approach for the different localization algorithms available in the Localization and Tracking Toolbox for Ultrasound Localization Microscopy. We also introduce two novel image quality measures that can overcome the limitations of conventional quality metrics that require suitable targets for evaluation. We also report the preliminary in-vitro investigation of F-DMAS with B-mode and power Doppler maps for microvascular imaging. The results are promising with enhanced contrast and lateral resolution, and suggest that further experimental studies are warranted.

eess.SP↗

arXiv2020

Pulsed Ultrasound Assisted Thermo-therapy for Subsurface Tumor Ablation: A numerical investigation

High Intensity Focused Ultrasound (HIFU) is a promising therapy for thermal ablation and hyperthermia, characterised by it noninvasiveness, high penetration depth. Effective HIFU thermo-therapy requires the ability to accurately predict temperature elevation and corresponding thermal dose distribution in target tissues. We report a parametric numerical study of the thermal response and corresponding of thermal dose in a bio-tissue in response to ultrasound. We compared the predictions of tissue models with two, three and seven layers, to ultrasound induced heating at duty cycles ranging from 0.6 and 0.9. Further, two tumor sizes and transducer powers (10 W and 15 W) were considered. Inhomogeneous Helmholtz equation was coupled with Penne's bioheat equation to predict heating in response to pulsed ultrasound. Necrotic lesion size was calculated using the cumulative equivalent minute (CEM) thermal dose function. In-vitro experiments were performed with agar-based tissue phantoms as a preliminary validation of the numerical results. The simulations conducted with the seven layered model predicted up to 33.5% lower peak pressure amplitude than the three-layered model. As the ultrasound pulse width decreased with the equivalent sonication time fixed, the corresponding magnitude of the peak temperature and the rate of temperature rise decreased. Pulsed ultrasound resulted in increased the volume of necrotic lesions for equivalent time of sonication. The findings of this study highlight the dependence of HIFU-induced heating on target geometry and acoustic properties, and could help guide the choice of suitable ultrasound exposure parameters for further studies.

physics.med-ph↗