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Computational RNA secondary structure prediction is rather well established. However, such prediction algorithms always depend on a large number of experimentally measured parameters. Here, we study how sensitive structure prediction…

Predicting the structure of multi-protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage pre-defined structural…

Structure determination is key to understanding protein function at a molecular level. Whilst significant advances have been made in predicting structure and function from amino acid sequence, researchers must still rely on expensive,…

We study a reinforcement learning setting, where the state transition function is a convex combination of a stochastic continuous function and a deterministic function. Such a setting generalizes the widely-studied stochastic state…

A mutator is an allele that increases the mutation rate throughout the genome by disrupting some aspect of DNA replication or repair. Mutators that increase the mutation rate by the order of 100 fold have been observed to spontaneously…

We present results of testing of the ability of eleven popular scoring functions to predict native docked positions using a recently developed method [1] for estimation the entropy contributions of relative motions to protein-ligand binding…

Identification of critical residues of a protein is actively pursued, since such residues are essential for protein function. We present three ways of recognising critical residues of an example protein, the evolution of which is tracked…

This paper formulates two 3D stochastic differential equations (SDEs) of two microbial populations in a chemostat competing over a single substrate. The two models have two distinct noise sources. One is general noise whereas the other is…

Fast Adversarial Training (FAT) has proven effective in enhancing model robustness by encouraging networks to learn perturbation-invariant representations. However, FAT often suffers from catastrophic overfitting (CO), where the model…

The calculation of chemical shifts in solids has enabled methods to determine crystal structures in powders. The dependence of chemical shifts on local atomic environments sets them among the most powerful tools for structure elucidation of…

Neutral evolution is the simplest model of molecular evolution and thus it is most amenable to a comprehensive theoretical investigation. In this paper, we characterize the statistical properties of neutral evolution of proteins under the…

Stochastic gradient descent with momentum (SGDM) is the dominant algorithm in many optimization scenarios, including convex optimization instances and non-convex neural network training. Yet, in the stochastic setting, momentum interferes…

Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. (2016) provides strong…

Instruction tuning relies on large instruction-response corpora whose quality and composition strongly affect downstream performance. We propose Answer Divergence-Guided Selection (ADG), which selects instruction data based on the geometric…

A stochastic nonlinear partial differential equation is built for two different models exhibiting self-organized criticality, the Bak, Tang, and Wiesenfeld (BTW) sandpile model and the Zhang's model. The dynamic renormalization group (DRG)…

Despite exceptional achievements, training neural networks remains computationally expensive and is often plagued by instabilities that can degrade convergence. While learning rate schedules can help mitigate these issues, finding optimal…

Reliable uncertainty from deterministic single-forward pass models is sought after because conventional methods of uncertainty quantification are computationally expensive. We take two complex single-forward-pass uncertainty approaches, DUQ…

Predictive geometric models deliver excellent results for many Machine Learning use cases. Despite their undoubted performance, neural predictive algorithms can show unexpected degrees of instability and variance, particularly when applied…

Accurate prediction of protein-ligand binding affinities is an essential challenge in structure-based drug design. Despite recent advances in data-driven methods for affinity prediction, their accuracy is still limited, partially because…

The goal of structure-based drug discovery is to find small molecules that bind to a given target protein. Deep learning has been used to generate drug-like molecules with certain cheminformatic properties, but has not yet been applied to…