arXiv subjects

Abhijit Mandal

Publications and source records attributed to Abhijit Mandal.

At least 19 recordsLinked to original sources

arXiv2026

Robust K-means Clustering using the Density Power Divergence Measure

We introduce a robust clustering method, MK-means DPD, that estimates cluster centers and covariance matrices using density power divergence (DPD) measures combined with Mahalanobis distance, making it resistant to outliers and adaptable to heterogeneous, elliptical clusters, unlike the classical K-means algorithm. Since Mahalanobis distance-based K-means lacks a general convergence guarantee, we further introduce a convergent variant, Density-Consistent MK-means DPD (DC-MK-means DPD), which redefines the cluster assignment step in terms of a pointwise DPD loss. We prove a formal theorem establishing that the resulting algorithm converges in a finite number of steps. We also propose two new robust internal evaluation indices, a Median Davies-Bouldin Index and a Trimmed Calinski-Harabasz Index, to ensure that performance comparisons are not themselves distorted by outliers. The efficacy of the proposed methods is demonstrated on simulated data, showing superiority over existing methods, and on two real datasets: Iris data, to identify similar species, and COVID-19 case fatality rate and infection rate data for countries worldwide, examining the resulting clusters' geographic and socio-economic patterns.

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arXiv2026

Basis-Independent Coherence Dynamics of Tripartite States under Pure Dephasing

Quantum coherence is a fundamental quantum resource whose preservation under environmental interactions is essential for quantum information processing. While most studies have focused on basis-dependent coherence measures, the dynamics of intrinsic coherence quantified by basis-independent measures remain largely unexplored. In this work, we investigate the dynamics of basis-independent quantum coherence for several representative tripartite pure and mixed states subjected to local and common dephasing environments in both Markovian and non-Markovian regimes. We show that Markovian local dephasing leads to state-dependent coherence degradation, whereas collective dephasing significantly enhances coherence preservation through decoherence-free sectors. More importantly, non-Markovian environments give rise to nearly frozen coherence dynamics for both pure and mixed states, demonstrating the remarkable robustness of intrinsic coherence against dephasing environment. A comparison with the measure of relative entropy of coherence reveals that basis-independent coherence measure exhibits substantially greater resilience and qualitatively different dynamical behaviour than its basis-dependent counterpart. These results provide new insights into the preservation of intrinsic multipartite coherence in open quantum systems and highlight basis-independent coherence as a robust quantum resource for realistic noisy quantum technologies.

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arXiv2026

Coherence thermometry using multipartite quantum systems

Accurate temperature measurement at the quantum scale is becoming increasingly important for emerging quantum technologies, motivating the development of quantum thermometry based on quantum resources. In this work, we investigate how finite environmental temperature influences the coherence dynamics of multipartite quantum systems and examine whether quantum coherence can serve as a temperature sensitive observable. We consider a tripartite spin-boson model interacting with finite temperature dephasing environments under two physically distinct reservoir configurations, namely local and common environments. The dynamics of representative tripartite pure and mixed states are quantified using the relative entropy of coherence. Our results show that local dephasing produces a universal monotonic decay of coherence, with increasing temperature accelerating decoherence for all states. In contrast, common dephasing generates a markedly state dependent thermal response. Under common dephasing, the $\vert GHZ \rangle$ and $\vert Star\rangle$ states undergo complete coherence loss, the $\vert W\rangle$ state exhibits temperature independent stationary coherence, and the $\vert W\overline{W}\rangle$ state retains finite residual coherence at long times. Similar state dependent behaviour is also observed for mixed states. These results demonstrate that the thermal susceptibility of quantum coherence is governed jointly by the environmental configuration and the internal architecture of the multipartite quantum state. Furthermore, we establish a direct coherence temperature correspondence through representative thermometry tables, providing a \textit{proof-of-principle} foundation for coherence based quantum thermometry.

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arXiv2025

Understanding How Network Geometry Influences Diffusion Processes in Complex Networks: A Focus on Cryptocurrency Blockchains and Critical Infrastructure Networks

This study provides essential insights into how diffusion processes unfold in complex networks, with a focus on cryptocurrency blockchains and infrastructure networks. The structural properties of these networks, such as hub-dominated, heavy-tailed topology, network motifs, and node centrality, significantly influence diffusion speed and reach. Using epidemic diffusion models, specifically the Kertesz threshold model and the Susceptible-Infected (SI) model, we analyze key factors affecting diffusion dynamics. To assess the uncertainty in the fraction of infected nodes over time, we employ bootstrap confidence intervals, while Bayesian credible intervals are constructed to quantify parameter uncertainties in the SI models. Our findings reveal substantial variations across different network types, including Erdős--Rényi networks, Geometric Random Graphs, and Delaunay Triangulation networks, emphasizing the role of network architecture in failure propagation. We identify that network motifs are crucial in diffusion. We highlight that hub-dominated networks, which dominate blockchain ecosystems, provide resilience against random failures but remain vulnerable to targeted attacks, posing significant risks to network stability. Furthermore, centrality measures such as degree, betweenness, and clustering coefficient strongly influence the transmissibility of diffusion in both blockchain and critical infrastructure networks.

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arXiv2025

Teleporting single qutrit using symmetric-anti symmetric two-qutrit basis states as quantum channels

This work presents a deterministic scheme for the teleportation of a single qutrit state, held by the sender Alice, using maximally entangled two-qutrit states as resource channels. These states have been constructed from symmetric and anti-symmetric bases by Leslie, Devin and Lynn (LDL). Leveraging the higher information capacity of qutrits compared to qubits, we employ these nine distinct two-qutrit entangled channels by LDL, for our protocol. For each channel, explicit unitary operations at the receiver Bob's end are derived, ensuring perfect recovery of the unknown qutrit state, initially in possesion of the sender Alice, after the sender performs joint measurements on her qutrits and communicates the outcomes through a classical channel. The proposed framework confirms teleportation with unit fidelity, thereby extending conventional teleportation schemes beyond qubits into higher-dimensional systems. This not only enriches the available toolkit for quantum communication but also highlights the utility of structured entangled states in advancing quantum information processing. The results open new avenues for secure and efficient quantum networks, higher-dimensional cryptographic schemes, and the design of novel quantum algorithms, while laying the groundwork for experimental realizations of deterministic qutrit teleportation.

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arXiv2025

Teleportation of unknown qubit via Star type tripartite states

Eylee Jung \textit{et.al}\cite{jung2008} had conjectured that $P_{max}=\frac{1}{2}$ is a necessary and sufficient condition for the perfect two-party teleportation and consequently the Groverian measure of entanglement for the entanglement resource must be $\frac{1}{\sqrt{2}}$. It is also known that prototype $W$ state is not useful for standard teleportation. Agrawal and Pati\cite{pati2006} have successfully executed perfect (standard) teleportation with non-prototype $W$ state. Aligned with Pati's protocol\cite{pati2006} we have considered here $Star$ type tripartite states and have shown that perfect teleportation is suitable with such states. Moreover, we have taken the linear superposition of non-prototype $W$ state and its spin-flipped version and shown that it belongs to $Star$ class. Also, standard teleportation is possible with these states. It is observed that genuine tripartite entanglement is not necessary requirement for a state to be used as a channel for successful standard teleportation. We have also shown that these $Star$ class states are $P_{max}=\frac{1}{4}$ states and their Groverian entanglement is $\frac{\sqrt{3}}{2}$, thus concluding that Jung conjecture is not a necessary condition.

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arXiv2025

Robust Variable Selection in High-dimensional Nonparametric Additive Model

Additive models belong to the class of structured nonparametric regression models that do not suffer from the curse of dimensionality. Finding the additive components that are nonzero when the true model is assumed to be sparse is an important problem, and it is well studied in the literature. The majority of the existing methods focused on using the $L_2$ loss function, which is sensitive to outliers in the data. We propose a new variable selection method for additive models that is robust to outliers in the data. The proposed method employs a nonconcave penalty for variable selection and considers the framework of B-splines and density power divergence loss function for estimation. The loss function produces an M-estimator that down weights the effect outliers. Our asymptotic results are derived under the sub-Weibull assumption, which allows the error distribution to have an exponentially heavy tail. Under regularity conditions, we show that the proposed method achieves the optimal convergence rate. In addition, our results include the convergence rates for sub-Gaussian and sub-Exponential distributions as special cases. We numerically validate our theoretical findings using simulations and real data analysis.

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arXiv2025

Dephasing-Induced Distribution of Entanglement in Tripartite Quantum Systems

Preserving multipartite entanglement amidst decoherence poses a pivotal challenge in quantum information processing. However, assessing multipartite entanglement in mixed states amid decoherence presenting a formidable task. Employing reservoir memory offers a means to attenuate the decoherence dynamics impacting multipartite entanglement, thereby slowing its degradation. One of the important measures which can be implemented to quantify entanglement is the relative entropy of entanglement. Although this measure is not monogamous \cite{horodeckirev2009}, it can universally be applied to both pure and mixed states. Based on this fundamental novelty, in this work, therefore, we introduce a quantifier which will investigate how entanglement remain distributed among the qubits of multipartite states when these states are exposed to multipartite dephasing setting. For our study we use various pure and mixed tripartite states subjected to finite temperature in both Markovian and non-Markovian local/common bath. Here, we consider situations where the three qubits interact with a common reservoir as well as a local bosonic reservoir. We also show that the robustness of a quantum system to decoherence depends on the distribution of entanglement and its interaction with various configurations of the bath. When each qubit has its own local environment, the system exhibits different distribution dynamics compared to when all three qubits share a common environment with one exception regarding a mixed state.

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arXiv2025

Resilience of Quantum Teleportation Fidelity for Bipartite Mixed States near Schwarzschild and Dilaton Black Holes

We investigate the robustness of quantum teleportation in the presence of strong gravitational fields by analysing bipartite mixed states derived from tripartite GHZ and W-class states near black hole event horizons. Considering a scenario where two observers approach the horizon of either a Schwarzschild or a Garfinkle Horowitz Strominger (GHS) Dilaton black hole while a third remains in flat space, we quantify the teleportation fidelity of the resulting bipartite channels after tracing out one party. Through the quantization of Dirac fields and Bogoliubov transformations, we compute the teleportation fidelity under the influence of Hawking radiation and spacetime curvature. Our results show that while entanglement degrades, teleportation fidelity remains above the classical threshold of $f>\frac{2}{3}$ for channels derived from W-class states, but not for GHZ-derived states. This indicates that quantum teleportation can remain feasible near black holes provided the initial entangled state retains useful bipartite entanglement.

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arXiv2024

Spatial function-on-function regression

We introduce a spatial function-on-function regression model to capture spatial dependencies in functional data by integrating spatial autoregressive techniques with functional principal component analysis. The proposed model addresses a critical gap in functional regression by enabling the analysis of functional responses influenced by spatially correlated functional predictors, a common scenario in fields such as environmental sciences, epidemiology, and socio-economic studies. The model employs a spatial functional principal component decomposition on the response and a classical functional principal component decomposition on the predictor, transforming the functional data into a finite-dimensional multivariate spatial autoregressive framework. This transformation allows efficient estimation and robust handling of spatial dependencies through least squares methods. In a series of extensive simulations, the proposed model consistently demonstrated superior performance in estimating both spatial autocorrelation and regression coefficient functions compared to some favorably existing traditional approaches, particularly under moderate to strong spatial effects. Application of the proposed model to Brazilian COVID-19 data further underscored its practical utility, revealing critical spatial patterns in confirmed cases and death rates that align with known geographic and social interactions. An R package provides a comprehensive implementation of the proposed estimation method, offering a user-friendly and efficient tool for researchers and practitioners to apply the methodology in real-world scenarios.

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arXiv2024

Robust function-on-function interaction regression

A function-on-function regression model with quadratic and interaction effects of the covariates provides a more flexible model. Despite several attempts to estimate the model's parameters, almost all existing estimation strategies are non-robust against outliers. Outliers in the quadratic and interaction effects may deteriorate the model structure more severely than their effects in the main effect. We propose a robust estimation strategy based on the robust functional principal component decomposition of the function-valued variables and $τ$-estimator. The performance of the proposed method relies on the truncation parameters in the robust functional principal component decomposition of the function-valued variables. A robust Bayesian information criterion is used to determine the optimum truncation constants. A forward stepwise variable selection procedure is employed to determine relevant main, quadratic, and interaction effects to address a possible model misspecification. The finite-sample performance of the proposed method is investigated via a series of Monte-Carlo experiments. The proposed method's asymptotic consistency and influence function are also studied in the supplement, and its empirical performance is further investigated using a U.S. COVID-19 dataset.

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arXiv2024

Enhancing Spatial Functional Linear Regression with Robust Dimension Reduction Methods

This paper introduces a robust estimation strategy for the spatial functional linear regression model using dimension reduction methods, specifically functional principal component analysis (FPCA) and functional partial least squares (FPLS). These techniques are designed to address challenges associated with spatially correlated functional data, particularly the impact of outliers on parameter estimation. By projecting the infinite-dimensional functional predictor onto a finite-dimensional space defined by orthonormal basis functions and employing M-estimation to mitigate outlier effects, our approach improves the accuracy and reliability of parameter estimates in the spatial functional linear regression context. Simulation studies and empirical data analysis substantiate the effectiveness of our methods, while an appendix explores the Fisher consistency and influence function of the FPCA-based approach. The rfsac package in R implements these robust estimation strategies, ensuring practical applicability for researchers and practitioners.

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arXiv2021

Robust Density Power Divergence Estimates for Panel Data Models

The panel data regression models have become one of the most widely applied statistical approaches in different fields of research, including social, behavioral, environmental sciences, and econometrics. However, traditional least-squares-based techniques frequently used for panel data models are vulnerable to the adverse effects of the data contamination or outlying observations that may result in biased and inefficient estimates and misleading statistical inference. In this study, we propose a minimum density power divergence estimation procedure for panel data regression models with random effects to achieve robustness against outliers. The robustness, as well as the asymptotic properties of the proposed estimator, are rigorously established. The finite-sample properties of the proposed method are investigated through an extensive simulation study and an application to climate data in Oman. Our results demonstrate that the proposed estimator exhibits improved performance over some traditional and robust methods in the presence of data contamination.

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arXiv2021

A robust specification test in linear panel data models

The presence of outlying observations may adversely affect statistical testing procedures that result in unstable test statistics and unreliable inferences depending on the distortion in parameter estimates. In spite of the fact that the adverse effects of outliers in panel data models, there are only a few robust testing procedures available for model specification. In this paper, a new weighted likelihood based robust specification test is proposed to determine the appropriate approach in panel data including individual-specific components. The proposed test has been shown to have the same asymptotic distribution as that of most commonly used Hausman's specification test under null hypothesis of random effects specification. The finite sample properties of the robust testing procedure are illustrated by means of Monte Carlo simulations and an economic-growth data from the member countries of the Organisation for Economic Co-operation and Development. Our records reveal that the robust specification test exhibit improved performance in terms of size and power of the test in the presence of contamination.

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arXiv2021

A Two Stage Adaptive Metropolis Algorithm

We propose a new sampling algorithm combining two quite powerful ideas in the Markov chain Monte Carlo literature -- adaptive Metropolis sampler and two-stage Metropolis-Hastings sampler. The proposed sampling method will be particularly very useful for high-dimensional posterior sampling in Bayesian models with expensive likelihoods. In the first stage of the proposed algorithm, an adaptive proposal is used based on the previously sampled states and the corresponding acceptance probability is computed based on an approximated inexpensive target density. The true expensive target density is evaluated while computing the second stage acceptance probability only if the proposal is accepted in the first stage. The adaptive nature of the algorithm guarantees faster convergence of the chain and very good mixing properties. On the other hand, the two-stage approach helps in rejecting the bad proposals in the inexpensive first stage, making the algorithm computationally efficient. As the proposals are dependent on the previous states the chain loses its Markov property, but we prove that it retains the desired ergodicity property. The performance of the proposed algorithm is compared with the existing algorithms in two simulated and two real data examples.

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arXiv2020

Robust Inference Using the Exponential-Polynomial Divergence

Density-based minimum divergence procedures represent popular techniques in parametric statistical inference. They combine strong robustness properties with high (sometimes full) asymptotic efficiency. Among density-based minimum distance procedures, the methods based on the Bregman-divergence have the attractive property that the empirical formulation of the divergence does not require the use of any non-parametric smoothing technique such as kernel density estimation. The methods based on the density power divergence (DPD) represent the current standard in this area of research. In this paper, we will present a more generalized divergence that subsumes the DPD as a special case and produces several new options providing better compromises between robustness and efficiency.

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arXiv2020

Robust Wald-type test in GLM with random design based on minimum density power divergence estimators

We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and use this estimator to propose robust Wald-type tests for testing any general composite null hypothesis about the GLM. The asymptotic and robustness properties of the proposed tests are also examined for the GLM with random design. Application of the proposed robust inference procedures to the popular Poisson regression model for analyzing count data is discussed in detail both theoretically and numerically through simulation studies and real data examples.

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arXiv2019

Robust Variable Selection Criteria for the Penalized Regression

We propose a robust variable selection procedure using a divergence based M-estimator combined with a penalty function. It produces robust estimates of the regression parameters and simultaneously selects the important explanatory variables. An efficient algorithm based on the quadratic approximation of the estimating equation is constructed. The asymptotic distribution and the influence function of the regression coefficients are derived. The widely used model selection procedures based on the Mallows's $C_p$ statistic and Akaike information criterion (AIC) often show very poor performance in the presence of heavy-tailed error or outliers. For this purpose, we introduce robust versions of these information criteria based on our proposed method. The simulation studies show that the robust variable selection technique outperforms the classical likelihood-based techniques in the presence of outliers. The performance of the proposed method is also explored through the real data analysis.

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