arXiv subjects

Anirban Mondal

Publications and source records attributed to Anirban Mondal.

18 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.

stat.ME↗

arXiv2026

Vortex-Beam Transient Absorption Microspectroscopy Resolves Ultrafast Free-Exciton and Polaron Diffusion in 2D Perovskites

Two-dimensional (2D) Ruddlesden Popper perovskites are promising optoelectronic materials with strongly confined excitonic properties; however, probing their ultrafast carrier transport dynamics, particularly the initial nonequilibrium diffusion regime, remains challenging because conventional transient absorption microscopy requires complex spatial imaging and lacks sufficient temporal sensitivity to resolve early time diffusion dynamics. Here, we demonstrate a vortex beam based transient absorption microspectroscopy platform (VTAM) enabling imaging free measurement of carrier transport by encoding spatial diffusion information into the mode dependent pump probe signal. By employing vortex probes with different topological charges, VTAM provides mode selective spatial sensitivity to excitonic dynamics with subpicosecond temporal resolution. Using VTAM, we resolved rapid free exciton (FE) diffusion followed by relaxation toward a slower steady state transport regime. A theoretically derived time dependent diffusion model separated transient and steady state transport contributions, yielding a transient diffusion enhancement (68.84 cm2 per s) and a steady state diffusion coefficient (1.85 cm2 per s), thus providing an initial diffusion coefficient (70.69 cm2 per s), and a cooling time of 0.35 ps. Measurements at the exciton-polaron (EP) resonance revealed strongly suppressed diffusion with nearly time independent signal ratios, indicating lattice-coupled EP transport. These parameters were extracted without spatial scanning or image reconstruction, establishing V-TAM as a powerful imaging free platform for investigating carrier transport in perovskites and other semiconductor systems.

physics.optics↗

arXiv2026

Locally stationary Argo ocean heat content estimates: Modeling, validation and uncertainty quantification

Argo profiling floats measure seawater temperature and salinity in the upper 2000 meters of the ocean. These floats are uniquely capable of measuring the global Ocean Heat Content (OHC), a quantity that is of central importance for understanding Earth Energy Imbalance. Yet, producing Argo-based OHC estimates with reliable uncertainties is statistically challenging due to the complex structure and large size of the Argo dataset. Here we present an end-to-end mapping and uncertainty quantification framework for Argo-based OHC estimation using state-of-the-art methods from spatio-temporal statistics. The framework is based on modeling vertically integrated Argo temperature profiles as a locally stationary Gaussian process defined over space and time. This enables us to produce computationally tractable OHC anomaly maps based on data-driven decorrelation scales estimated from the Argo observations. Our modeling choices are validated using statistical cross-validation, which demonstrates the importance of including a climatological time trend in the mean field and accounting for time in the covariance function. We quantify the uncertainty of these maps using local conditional simulation ensembles, a novel approach that leads to principled spatially and temporally correlated uncertainty quantification. A new paired cross-validation technique is presented to validate these uncertainties. The mapping framework is implemented in an open-source codebase that is designed to be modular, reproducible and extensible. To demonstrate the mapping and uncertainty quantification capabilities of this approach, we present new Argo OHC maps with uncertainties for 2004-2022 and report on various downstream climatological estimates and their uncertainties.

stat.AP↗

arXiv2026

An Improved Milstein Method for the Numerical Solution of Multidimensional Stochastic Differential Equations

Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems. However, analytical solutions for many SDEs are often unavailable, necessitating the use of numerical approximation methods. The rate of convergence of such numerical methods is of great importance, as it directly influences both computational efficiency and accuracy. This paper presents a proposed theorem, along with its proof, that facilitates the numerical evaluation of the strong (and weak) order of convergence of a numerical scheme for an SDE when the analytical solution is unavailable. Additionally, we address the challenge of numerically computing the multiple stochastic integrals required by the Milstein method to achieve improved convergence rates for multidimensional SDEs. In this context, two newly proposed numerical techniques for computing these multiple stochastic integrals are introduced and compared with existing approaches in terms of efficiency and effectiveness. The methodologies are further illustrated through simulation studies and applications to widely used financial models.

math.ST↗

arXiv2025

Ultrafast exciton polaron dynamics in 2D Ruddlesden Popper lead halide perovskites

Two dimensional Ruddlesden Popper (2D) RP hybrid perovskites exhibit substantially higher chemical and structural stability than their three dimensional (3D) counterparts, positioning them as promising candidates for next generation optoelectronics. While quasiparticle dynamics in 3D perovskites are well studied, their 2D analogues remain comparatively underexplored. Here we systematically investigate the branching, dynamics, and interactions of free excitons (FEs) and exciton polarons EPs in monolayer 2D RP perovskites using visible range femtosecond transient absorption TA spectroscopy. We prepared monolayer 2D RP perovskite thin films with varied organic spacers and distinct fabrication routes for comparative analysis. We find that the EP binding energy is 50 65 meV in (BA)2PbI4 and 37 39 meV in (PEA)2PbI4, consistent with spacer layer dependent coupling as corroborated by FTIR. We reveal a dynamic equilibrium between FEs and EPs that persists for tens of picoseconds. Notably, the TA signatures differ by fabrication route films from the newly developed process show weaker Auger annihilation and a reduced hot phonon bottleneck than those from the conventional route trends consistent with fewer traps and impurities in the former. Coupled rate equation modeling reproduces the transients and quantifies the processes of hot carrier relaxation, exciton exciton annihilation, exciton phonon coupling, and FE EP interconversion. These results demonstrate that the chemical synthetic process (fabrication route) and spacer choice significantly influence EP stability and population balance, offering practical levers for engineering ultrafast photophysics in 2D perovskites and guiding the design of advanced optoelectronic devices.

cond-mat.mtrl-sci↗

arXiv2024

A CNN Approach to Polygenic Risk Prediction of Kidney Stone Formation

Kidney stones are a common and debilitating health issue, and genetic factors play a crucial role in determining susceptibility. While Genome-Wide Association Studies (GWAS) have identified numerous single nucleotide polymorphisms (SNPs) linked to kidney stone risk, translating these findings into effective clinical tools remains a challenge. In this study, we explore the potential of deep learning techniques, particularly Convolutional Neural Networks (CNNs), to enhance Polygenic Risk Score (PRS) models for predicting kidney stone susceptibility. Using a curated dataset of kidney stone-associated SNPs from a recent GWAS, we apply CNNs to model non-linear genetic interactions and improve prediction accuracy. Our approach includes SNP selection, genotype filtering, and model training using a dataset of 560 individuals, divided into training and testing subsets. We compare our CNN-based model with traditional machine learning models, including logistic regression, random forest, and support vector machines, demonstrating that the CNN outperforms these models in terms of classification accuracy and ROC-AUC. The proposed model achieved a validation accuracy of 62%, with an ROC-AUC of 0.68, suggesting its potential for improving genetic-based risk prediction for kidney stones. This study contributes to the growing field of genomics-driven precision medicine and highlights the promise of deep learning in enhancing PRS models for complex diseases.

q-bio.GN↗

arXiv2022

Bayesian Uncertainty Quantification of Local Volatility Model

Local volatility is an important quantity in option pricing, portfolio hedging, and risk management. It is not directly observable from the market; hence calibrations of local volatility models are necessary using observable market data. Unlike most existing point-estimate methods, we cast the large-scale nonlinear inverse problem into the Bayesian framework, yielding a posterior distribution of the local volatility, which naturally quantifies its uncertainty. This extra uncertainty information enables traders and risk managers to make better decisions. To alleviate the computational cost, we apply Karhunen--Lòeve expansion to reduce the dimensionality of the Gaussian Process prior for local volatility. A modified two-stage adaptive Metropolis algorithm is applied to sample the posterior probability distribution, which further reduces computational burdens caused by repetitive numerical forward option pricing model solver and time of heuristic tuning. We demonstrate our methodology with both synthetic and market data.

stat.AP↗

arXiv2021

Spline-Based Bayesian Emulators for Large Scale Spatial Inverse Problems

A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is developed, where the Bayesian multivariate adaptive regression splines (BMARS) are used to model the function that maps the inputs to the outputs. Discrete cosine transformation (DCT) is used for dimension reduction of the input spatial field. The posterior sampling is carried out using trans-dimensional Markov Chain Monte Carlo (MCMC) methods. Numerical results are presented by analyzing simulated as well as real data on hydrocarbon reservoir characterization.

stat.AP↗

arXiv2021

Two-dimensional ReS2: Solution to the Unresolved Queries on Its Structure and Inter-layer Coupling Leading to Potential Optical Applications

Over the last few years, ReS2 has generated a myriad of unattended queries regarding its structure, the concomitant thickness dependent electronic properties and apparently contrasting experimental optical response. In this work, with elaborate first-principles investigations, using density functional theory (DFT) and time-dependent DFT (TDDFT), we identify the structure of ReS2, which is capable of reproducing and analyzing the layer-dependent optical response. The theoretical results are further validated by an in-depth structural, chemical, optical and optoelectronic analysis of the large-area ReS2 thin films, grown by chemical vapor deposition (CVD) process. Micro-Raman (MR), X-ray photoelectron spectroscopy (XPS), cross-sectional transmission electron microscopy (TEM) and energy-dispersive X-ray analysis (EDAX) have enabled the optimization of the uniform growth of the CVD films. The correlation between the layer-dependent optical and electronic properties of the excited states was established by static photoluminescence (PL) and transient absorption (TA) measurements. Sulfur vacancy-induced localized mid-gap states render a significantly long life-time of the excitons in these films. The ionic gel top-gated photo-detectors, fabricated from the as-prepared CVD films, exhibit a large photo-response of ~ 5 A/W and a remarkable detectivity of ~ 1011 Jones. The outcome of the present work will be useful to promote the application of vertically grown large-area films in the field of optics and opto-electronics.

cond-mat.mtrl-sci↗

arXiv2021

Pulse-duration dependence of saturable and reverse saturable absorption in ZnCo2O4 microflowers

We employed open-aperture Z-scan technique to unveil the third-order optical nonlinearity in ZnCo2O4 (ZCO) microflowers. Our results indicate that intersystem crossing (ISC) lifetime can be used as simple tool to demonstrate remarkably contrasting optical nonlinearity in ZCO. Ultrafast transient absorption measurements reveal that ISC from singlet to triplet state takes place in 5 ps. For femtosecond laser pulses, when the pulse duration is shorter than ISC lifetime, saturable absorption (SA) takes place for all intensities. On the contrary, when the pulse duration is longer than ISC for nanosecond excitation, we observe transition from SA to reverse SA (RSA) at higher intensities via excited-state absorption. We envisage that benefiting from SA and RSA, ZCO emerges as potential candidate for mode locking and optical limiting devices.

physics.optics↗

arXiv2021

Combinatorial Large-area MoS2/Anatase-TiO2 interface: A Pathway to Emergent Optical and Opto-electronic Functionalities

Interface of transition metal dichalcogenide (TMDC) and high-k dielectric transition metal oxides (TMO) had triggerred umpteen discourses due to the indubitable impact of TMO in reducing the contact resistances and restraining the Fermi-level pinning for the metal-TMDC contacts. In the present work, we focus on the unresolved tumults of large-area TMDC/TMO interfaces, grown by adopting different techniques. Here, on a pulsed laser deposited (PLD) MoS2 thin film, a layer of TiO2 is grown by using both atomic layer deposition (ALD) and PLD. These two different techniques emanate TiO2 layers with different crystalline properties, thicknesses and interfacial morphologies, subsequently influencing the electronic and optical properties of the interfaces. In addition, they manifest a boost in the extent of p-type doping with increasing thickness of TiO2, as emerged after analyzing the core-level shifts of the X-ray photoelectron spectra (XPS). Density functional analysis of the MoS2/Anatase-TiO2 interfaces, for pristine and in presence of a wide range of interfacial defects, could explain the interdependence of doping and the terminating atomic-surface of TiO2 on MoS2. The optical properties of the interface, encompassing the photoluminescence, transient absorption and z-scan two-photon absorption indicate the presence of defect-induced localized mid-gap levels in MoS2/TiO2 (PLD), resulting quenched exciton signals. On the contrary, the relatively defect-free interface in MoS2/TiO2 (ALD) demonstrates a clear presence of both A and B excitons of MoS2. From the investigation of optical properties, we indicate that MoS2/TiO2 (PLD) interface may act as a promising saturable absorber. Moreover, MoS2/TiO2 (PLD) interface had resulted a better photo-transport. A potential application of MoS2/TiO2 (PLD) is demonstrated by the fabrication of a p-type photo-transistor with the ionic-gel top gate.

cond-mat.mtrl-sci↗

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.

stat.CO↗

arXiv2020

The influence of impurities on the charge carrier mobility of small molecule organic semiconductors

Amorphous organic semiconductors based on small molecules and polymers are used in many applications, most prominently organic light emitting diodes (OLEDs) and organic solar cells. Impurities and charge traps are omnipresent in most currently available organic semiconductors and limit charge transport and thus device efficiency. The microscopic cause as well as the chemical nature of these traps are presently not well understood. Using a multiscale model we characterize the influence of impurities on the density of states and charge transport in small-molecule amorphous organic semiconductors. We use the model to quantitatively describe the influence of water molecules and water-oxygen complexes on the electron and hole mobilities. These species are seen to impact the shape of the density of states and to act as explicit charge traps within the energy gap. Our results show that trap states introduced by molecular oxygen can be deep enough to limit the electron mobility in widely used materials.

cond-mat.soft↗

arXiv2020

Computer Model Emulation with High-Dimensional Functional Output in Large-Scale Observing System Uncertainty Experiments

Observing system uncertainty experiments (OSUEs) have been recently proposed as a cost-effective way to perform probabilistic assessment of retrievals for NASA's Orbiting Carbon Observatory-2 (OCO-2) mission. One important component in the OCO-2 retrieval algorithm is a full-physics forward model that describes the mathematical relationship between atmospheric variables such as carbon dioxide and radiances measured by the remote sensing instrument. This forward model is complicated and computationally expensive but large-scale OSUEs require evaluation of this model numerous times, which makes it infeasible for comprehensive experiments. To tackle this issue, we develop a statistical emulator to facilitate large-scale OSUEs in the OCO-2 mission with independent emulation. Within each distinct spectral band, the emulator represents radiances output at irregular wavelengths via a linear combination of basis functions and random coefficients. These random coefficients are then modeled with nearest-neighbor Gaussian processes with built-in input dimension reduction via active subspace. The proposed emulator reduces dimensionality in both input space and output space, so that fast computation is achieved within a fully Bayesian inference framework. Validation experiments demonstrate that this emulator outperforms other competing statistical methods and a reduced order model that approximates the full-physics forward model.

stat.AP↗

arXiv2020

Analyzing Stochastic Computer Models: A Review with Opportunities

In modern science, computer models are often used to understand complex phenomena, and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer models -- providing a catalogue of statistical methods for practitioners, an introductory view for statisticians (whether familiar with deterministic computer models or not), and an emphasis on open questions of relevance to practitioners and statisticians. Gaussian process surrogate models take center stage in this review, and these, along with several extensions needed for stochastic settings, are explained. The basic issues of designing a stochastic computer experiment and calibrating a stochastic computer model are prominent in the discussion. Instructive examples, with data and code, are used to describe the implementation of, and results from, various methods.

stat.ME↗

arXiv2020

Preconditioning Markov Chain Monte Carlo Method for Geomechanical Subsidence using multiscale method and machine learning technique

In this paper, we consider the numerical solution of the poroelasticity problem with stochastic properties. We present a Two-stage Markov Chain Monte Carlo method for geomechanical subsidence. In this work, we study two techniques of preconditioning: (MS) multiscale method for model order reduction and (ML) machine learning technique. The purpose of preconditioning is the fast sampling, where a new proposal is first testes by a cheap multiscale solver or using fast prediction of the neural network and the full fine grid computations will be conducted only if the proposal passes the first step. To construct a reduced order model, we use the Generalized Multiscale Finite Element Method and present construction of the multiscale basis functions for pressure and displacements in stochastic fields. In order to construct a machine learning based preconditioning, we generate a dataset using a multiscale solver and use it to train neural networks. The Karhunen-Loeve expansion is used to represent the realization of the stochastic field. Numerical results are presented for two- and three-dimensional model examples.

math.NA↗

arXiv2019

Stratified Random Sampling for Dependent Inputs

A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations of functions of the corresponding output variables. The advantage of the proposed method over the existing methods is that it preserves the exact form of the joint distribution on the input variables. The asymptotic distribution of the new estimator is derived. Asymptotically, the variance of the estimator using the proposed method is less than that obtained using the simple random sampling, with the degree of variance reduction depending on the degree of additivity in the function being integrated. This technique is applied to a practical example related to the performance of the river flood inundation model.

stat.ME↗

arXiv2019

Computer model calibration based on image warping metrics: an application for sea ice deformation

Arctic sea ice plays an important role in the global climate. Sea ice models governed by physical equations have been used to simulate the state of the ice including characteristics such as ice thickness, concentration, and motion. More recent models also attempt to capture features such as fractures or leads in the ice. These simulated features can be partially misaligned or misshapen when compared to observational data, whether due to numerical approximation or incomplete physics. In order to make realistic forecasts and improve understanding of the underlying processes, it is necessary to calibrate the numerical model to field data. Traditional calibration methods based on generalized least-square metrics are flawed for linear features such as sea ice cracks. We develop a statistical emulation and calibration framework that accounts for feature misalignment and misshapenness, which involves optimally aligning model output with observed features using cutting edge image registration techniques. This work can also have application to other physical models which produce coherent structures.

stat.AP↗