arXiv subjects

Arabind Swain

Publications and source records attributed to Arabind Swain.

4 recordsLinked to original sources

arXiv2025

Better Together: Cross and Joint Covariances Enhance Signal Detectability in Undersampled Data

Many data-science applications involve detecting a shared signal between two high-dimensional variables. Using random matrix theory methods, we determine when such signal can be detected and reconstructed from sample correlations, despite the background of sampling noise induced correlations. We consider three different covariance matrices constructed from two high-dimensional variables: their individual self covariance, their cross covariance, and the self covariance of the concatenated (joint) variable, which incorporates the self and the cross correlation blocks. We observe the expected Baik, Ben Arous, and P\'ech\'e detectability phase transition in all these covariance matrices, and we show that joint and cross covariance matrices always reconstruct the shared signal earlier than the self covariances. Whether the joint or the cross approach is better depends on the mismatch of dimensionalities between the variables. We discuss what these observations mean for choosing the right method for detecting linear correlations in data and how these findings may generalize to nonlinear statistical dependencies.

cond-mat.dis-nn↗

arXiv2025

Distribution of singular values in large sample cross-covariance matrices

For two large matrices ${\mathbf X}$ and ${\mathbf Y}$ with Gaussian i.i.d.\ entries and dimensions $T\times N_X$ and $T\times N_Y$, respectively, we derive the probability distribution of the singular values of $\mathbf{X}^T \mathbf{Y}$ in different parameter regimes. This extends the Marchenko-Pastur result for the distribution of eigenvalues of empirical sample covariance matrices to singular values of empirical cross-covariances. Our results will help to establish statistical significance of cross-correlations in many data-science applications.

math.ST↗

arXiv2024

Machine learning that predicts well may not learn the correct physical descriptions of glassy systems

The complexity of glasses makes it challenging to explain their dynamics. Machine Learning (ML) has emerged as a promising pathway for understanding glassy dynamics by linking their structural features to rearrangement dynamics. Support Vector Machine (SVM) was one of the first methods used to detect such correlations. Specifically, a certain output of SVMs trained to predict dynamics from structure, the distance from the separating hyperplane, was interpreted as being linearly related to the activation energy for the rearrangement. By numerical analysis of toy models, we explore under which conditions it is possible to infer the energy barrier to rearrangements from the distance to the separating hyperplane. We observe that such successful inference is possible only under very restricted conditions. Typical tests, such as the apparent Arrhenius dependence of the probability of rearrangement on the inferred energy and the temperature, or high cross-validation accuracy do not guarantee success. We propose practical approaches for measuring the quality of the energy inference and for modifying the inferred model to improve the inference, which should be usable in the context of realistic datasets.

cond-mat.soft↗

arXiv2020

A Stochastic model for dynamics of FtsZ filaments and the formation of Z-ring

Understanding the mechanisms responsible for the formation and growth of FtsZ polymers and their subsequent formation of the $Z$-ring is important for gaining insight into the cell division in prokaryotic cells. In this work, we present a minimal stochastic model that qualitatively reproduces {\it in vitro} observations of polymerization, formation of dynamic contractile ring that is stable for a long time and depolymerization shown by FtsZ polymer filaments. In this stochastic model, we explore different mechanisms for ring breaking and hydrolysis. In addition to hydrolysis, which is known to regulate the dynamics of other tubulin polymers like microtubules, we find that the presence of the ring allows for an additional mechanism for regulating the dynamics of FtsZ polymers. Ring breaking dynamics in the presence of hydrolysis naturally induce rescue and catastrophe events in this model irrespective of the mechanism of hydrolysis.

q-bio.SC↗