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Quantum computing is poised to solve practically useful problems which are computationally intractable for classical supercomputers. However, the current generation of quantum computers are limited by errors that may only partially be…

Human societies continuously transform scattered information into collective judgments and coordinated action, whether through markets discovering prices, governments allocating resources, communities enforcing norms, or science converging…

The main challenge addressed in this paper is to identify individual terms in a superposition of heat kernels on a graph. We establish geometric conditions on the vertices at which these heat kernels are centered and find bounds on the time…

Four chapters of the synthesis represent four major areas of my research interests: 1) data analysis in molecular biology, 2) mathematical modeling of biological networks, 3) genome evolution, and 4) cancer systems biology. The first…

The use of machine learning to develop intelligent software tools for interpretation of radiology images has gained widespread attention in recent years. The development, deployment, and eventual adoption of these models in clinical…

Support vector machines and kernel methods are increasingly popular in genomics and computational biology, due to their good performance in real-world applications and strong modularity that makes them suitable to a wide range of problems,…

A computationally challenging classical elimination theory problem is to compute polynomials which vanish on the set of tensors of a given rank. By moving away from computing polynomials via elimination theory to computing pseudowitness…

Cell segmentation is a critical step for quantitative single-cell analysis in microscopy images. Existing cell segmentation methods are often tailored to specific modalities or require manual interventions to specify hyper-parameters in…

The topological analysis of four-dimensional (4D) image-type data is challenged by the immense size that these datasets can reach. This can render the direct application of methods, like persistent homology and convolutional neural networks…

Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can…

Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…

Cell formation problem is among the first obstacles the designer of cellular production systems must overcome. This paper presents a critical analysis of the various criteria and constraints considered in the literature. The objective is to…

Reproducibility in research remains hindered by complex systems involving data, models, tools, and algorithms. Studies highlight a reproducibility crisis due to a lack of standardized reporting, code and data sharing, and rigorous…

Statistical analysis of DNA mixtures is known to pose computational challenges due to the enormous state space of possible DNA profiles. We propose a Bayesian network representation for genotypes, allowing computations to be performed…

This paper studies the notion of computational entropy. Using techniques from convex optimization, we investigate the following problems: (a) Can we derandomize the computational entropy? More precisely, for the computational entropy, what…

A key challenge in modern computing is to develop systems that address complex, dynamic problems in a scalable and efficient way, because the increasing complexity of software makes designing and maintaining efficient and flexible systems…

The integration of machine learning techniques in materials discovery has become prominent in materials science research and has been accompanied by an increasing trend towards open-source data and tools to propel the field. Despite the…

Crystallization is a key step in macromolecular structure determination by crystallography. While a robust theoretical treatment of the process is available, due to the complexity of the system, the experimental process is still largely one…

We review a recent trend in computational systems biology which aims at using pattern recognition algorithms to infer the structure of large-scale biological networks from heterogeneous genomic data. We present several strategies that have…

Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a…