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The complexity of molecular dynamics simulations necessitates dimension reduction and coarse-graining techniques to enable tractable computation. The generalized Langevin equation (GLE) describes coarse-grained dynamics in reduced…
Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
Diabetes mellitus affects over 537 million adults worldwide and remains a major challenge in preventive healthcare. Existing machine-learning studies primarily formulate diabetes prediction as a binary classification problem, while…
Determining atomistic structures from characterization data is one of the most common yet intricate problems in materials science. Particularly in amorphous materials, proposing structures that balance realism and agreement with experiments…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
This paper aims to investigate a full numerical approximation of non-autonomous semilnear parabolic partial differential equations (PDEs) with nonsmooth initial data. Our main interest is on such PDEs where the nonlinear part is stronger…
The detection of new multiple sclerosis (MS) lesions is an important marker of the evolution of the disease. The applicability of learning-based methods could automate this task efficiently. However, the lack of annotated longitudinal data…
Modern applications of strong gravitational lensing require the ability to use precise and varied observational data to constrain complex lens models. I discuss two sets of computational methods for lensing calculations. The first is a new…
The recent development of high-throughput sequencing creates a large collection of multi-omics data, which enables researchers to better investigate cancer molecular profiles and cancer taxonomy based on molecular subtypes. Integrating…
We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear…
With recent advances in sequencing technologies, large amounts of epigenomic data have become available and computational methods are contributing significantly to the progress of epigenetic research. As an orthogonal approach to methods…
We establish an explicit data-driven criterion for identifying the solid-liquid transition of two-dimensional self-propelled colloidal particles in the far from equilibrium parameter regime, where the transition points predicted by…
Machine learning (ML) research has yielded powerful tools for training accurate prediction models despite complex multivariate associations (e.g. interactions and heterogeneity). In fields such as medicine, improved interpretability of ML…
High-dimensional biomedical studies require models that are simultaneously accurate, sparse, and interpretable, yet exact best subset selection for generalized linear models is computationally intractable. We develop a scalable method that…
Particle identification in large high-energy physics experiments typically relies on classifiers obtained by combining many experimental observables. Predicting the probability density function (pdf) of such classifiers in the multivariate…
The diffusion of tracer particles immersed in a granular gas under uniform shear flow (USF) is analyzed within the framework of the inelastic Boltzmann equation. Two different but complementary approaches are followed to achieve exact…
The behaviour of molecules in space is to a large extent governed by where they freeze out or sublimate. The molecular binding energy is thus an important parameter for many astrochemical studies. This parameter is usually determined with…
Although many real-world applications, such as disease prediction, and fault detection suffer from class imbalance, most existing graph-based classification methods ignore the skewness of the distribution of classes; therefore, tend to be…
Quantum many-body methods provide a systematic route to computing electronic properties of molecules and materials, but high computational costs restrict their use in large-scale applications. Due to the complexity in many-electron…