arXiv subjects

Subhodeep Dey

Publications and source records attributed to Subhodeep Dey.

7 recordsLinked to original sources

arXiv2026

Linear Regression: Inference Based on Cluster Estimates

This article proposes a novel estimator for regression coefficients in clustered data that explicitly accounts for within-cluster dependence. We study the asymptotic properties of the proposed estimator under both finite and infinite cluster sizes. The analysis is then extended to a standard random coefficient model, where we derive asymptotic results for the average (common) parameters and develop a Wald-type test for general linear hypotheses. We also investigate the performance of the conventional pooled ordinary least squares (POLS) estimator within the random coefficients framework and show that it can be unreliable across a wide range of empirically relevant settings. Furthermore, we introduce a new test for parameter stability at a higher (superblock; Tier 2, Tier 3,...) level, assuming that parameters are stable across clusters within that level. Extensive simulation studies demonstrate the effectiveness of the proposed tests, and an empirical application illustrates their practical relevance.

stat.ME↗

arXiv2026

Anomalous Dynamical Heterogeneity in Active Glasses as a Signature of Violation of Mermin-Wagner-Hohenberg Theorem

Two-dimensional (2D) systems have attracted renewed interest within the scientific community due to their anomalous dynamical behaviors, which arise from long-wavelength density fluctuations as predicted by the Mermin-Wagner-Hohenberg (MWH) theorem. In equilibrium, it is well established that continuous spontaneous symmetry breaking (SSB) in 2D is prohibited at any finite temperature ($T > 0$), resulting in the absence of true long-range positional order and establishing $d_l = 2$ as the lower critical dimension. Recent studies have demonstrated that, in active systems, the lower critical dimension can shift from $d_l = 2$ to $3$. This study examines the impact of MWH theorem violation in active systems on dynamical heterogeneity (DH). As a minimal model, glassy systems of active particles undergoing run-and-tumble (RT) motion are considered. Glass-like dynamical behavior, including anomalously enhanced DH, is observed in various biological systems such as collective cell migration, bacterial cytoplasm, and ant colonies. Furthermore, the study investigates the influence of local positional order, or medium-range crystalline order (MRCO), on DH in the presence of activity. The results indicate that the growth of DH with increasing activity differs significantly between systems with and without MRCO. These findings may have important implications, as many biological systems exhibit local structural ordering, and DH could serve as a useful indicator for quantifying the degree of ordering.

cond-mat.soft↗

arXiv2024

Scaling Description of the Relaxation Dynamics and Dynamical Heterogeneity of an Active Glass-forming Liquid

Active glasses refer to a class of driven non-equilibrium systems that share remarkably similar dynamical behavior as conventional glass-formers in equilibrium. Glass-like dynamical characteristics have been observed in various biological systems from micro to macro length scales. As activity induces additional fluctuations in the system, studying how they couple with density fluctuations is an interesting question to address. Via extensive molecular dynamics simulations, We show that activity enhances density fluctuations more strongly than its passive counterpart. Increasing activity beyond a limit results in the sub-Arrhenieus-type relaxation behavior in active glasses. We also propose a unified scaling theory that can rationalize the relaxation spectrum over a broad parameter range using the concept of an effective temperature. In particular, we show that our scaling theory can capture the dynamical crossover from super to sub-Arrhenius relaxation behavior by changing activity from small to large values. Furthermore, We present non-trivial system size dependencies of the relaxation time at large activity limits that have not been found in any passive systems or even in active systems at small activities.

cond-mat.soft↗

arXiv2024

Cross Sectional Regression with Cluster Dependence: Inference based on Averaging

We re-investigate the asymptotic properties of the traditional OLS (pooled) estimator, $\hat{\beta} _P$, in the context of cluster dependence. The present study considers various scenarios under various restrictions on the cluster sizes and number of clusters. It is shown that $\hat{\beta}_P$ could be inconsistent in many realistic situations. We propose a simple estimator, $\hat{\beta}_A$ based on data averaging. The asymptotic properties of $\hat{\beta}_A$ are studied. It is shown that $\hat{\beta}_A$ is consistent even when $\hat{\beta}_P$ is inconsistent. It is further shown that the proposed estimator $\hat{\beta}_A$ is more efficient than $\hat{\beta}_P$ in many practical scenarios. As a consequence of averaging, we show that $\hat{\beta}_A$ retains consistency, asymptotic normality under classical measurement error problem circumventing the use of Instrumental Variables (IV). A detailed simulation study shows the efficacy of $\hat{\beta}_A$. It is also seen that $\hat{\beta}_A$ yields better goodness of fit.

stat.ME↗

arXiv2024

A perspective on active glassy dynamics in biological systems

Dynamics is central to living systems. In the last two decades, experiments have revealed that the dynamics in diverse biological systems - from intracellular cytoplasm to cellular and organismal aggregates - are remarkably similar to that in dense systems of inanimate particles in equilibrium. They show a glass transition from a solid-like jammed state to a fluid-like flowing state, where a moderate change in control parameter leads to an enormous variation in relaxation time. However, biological systems have crucial differences from the equilibrium systems: the former have activity that drives them out of equilibrium, novel control parameters, and enormous levels of complexity. These active systems showing glassy dynamics are known as active glasses. The field is at the interface of physics and biology, freely borrowing tools from both disciplines and promising novel, fascinating discoveries. We review the experiments that started this field, simulations that have been instrumental for insights, and theories that have helped unify diverse phenomena, reveal correlations, and make novel quantitative predictions. We discuss the primary characteristics that define a glassy system. For most concepts, we first discuss the known equilibrium scenario and then present the key aspects when activity is introduced. We end the article with a discussion of the challenges in the field and possible future directions.

cond-mat.soft↗

arXiv2024

Enhanced Long Wavelength Mermin-Wagner Fluctuations in Active Crystals and Glasses

In two-dimensions (2D), the Mermin-Wagner-Hohenberg (MWH) fluctuation plays a significant role, giving rise to striking dimensionality effects marked by long-range density fluctuations leading to the singularities of various dynamical properties. According to the MWH theorem, a 2D equilibrium system with continuous degrees of freedom cannot achieve long-range crystalline order at non-zero temperatures. Recently, MWH fluctuations have been observed in glass-forming liquids, evidenced by the logarithmic divergence in the plateau value of mean squared displacement (MSD). Our research investigates long-wavelength fluctuations in crystalline and glassy systems influenced by non-equilibrium active noises. Active systems serve as a minimal model for understanding diverse non-equilibrium dynamics, such as those in biological systems and self-propelled colloids. We demonstrate that fluctuations from active forces can strongly couple with long-wavelength density fluctuations, altering the lower critical dimension ($d_l$) from $2$ to $3$ and leading to a novel logarithmic divergence of the MSD plateau with system size in 3D.

cond-mat.soft↗

arXiv2021

Enhanced Phonon Peak in Four-point Dynamic Susceptibility in the Supercooled Active Glass-forming Liquids

Active glassy systems can be thought of as simple model systems that imitate complex biological systems. Sometimes, it becomes crucial to estimate the amount of the activity present in such biological systems, such as predicting the progression rate of the cancer cells or the healing time of the wound. In this work, we study a model active glassy system to understand a possible quantification of the degree of activity from the collective, long-range phonon response in the system. We find that the four-point dynamic susceptibility, $\chi_4(t)$ at the phonon timescale, grows with increased activity. We then show how one can estimate the degree of the activity at such a small timescale by measuring the growth of $\chi_4(t)$ with changing activity. A detailed finite size analysis of this measurement, shows that the peak height of $\chi_4(t)$ at this phonon timescale increases strongly with increasing system size suggesting a possible existence of an intrinsic dynamic length scale that grows with increasing activity. Finally, we show that this peak height is a unique function of effective activity across all system sizes, serving as a possible parameter for characterizing the degree of activity in a system.

cond-mat.soft↗