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Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…

Predicting protein structure from amino acid sequence is one of the most important unsolved problems of molecular biology and biophysics.Not only would a successful prediction algorithm be a tremendous advance in the understanding of the…

Protein function and dynamics are closely related to its sequence and structure. However prediction of protein function and dynamics from its sequence and structure is still a fundamental challenge in molecular biology. Protein…

This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small…

Topological properties of networks are widely applied to study the link-prediction problem recently. Common Neighbors, for example, is a natural yet efficient framework. Many variants of Common Neighbors have been thus proposed to further…

Proteins are complex biomolecules that play a central role in various biological processes, making them critical targets for breakthroughs in molecular biology, medical research, and drug discovery. Deciphering their intricate, hierarchical…

Link prediction, as a frontier task in complex network topology analysis, aims to infer the existence of latent links between node pairs based on observed nodes and structural information. We propose an ensemble link prediction model that…

In this study, we present a novel molecular fingerprint generation method based on multiparameter persistent homology. This approach reveals the latent structures and relationships within molecular geometry, and detects topological features…

Is protein secondary structure primarily determined by local interactions between residues closely spaced along the amino acid backbone, or by non-local tertiary interactions? To answer this question we have measured the entropy densities…

Protein structure-based property prediction has emerged as a promising approach for various biological tasks, such as protein function prediction and sub-cellular location estimation. The existing methods highly rely on experimental protein…

Protein similarity searches are a routine job for molecular biologists where a query sequence of amino acids needs to be compared and ranked against an ever-growing database of proteins. All available algorithms in this field can be grouped…

Extracting complex structures from grid-based data is a common key step in automated medical image analysis. The conventional solution to recovering tree-structured geometries typically involves computing the minimal cost path through…

Computational protein structure determination involves optimization in a problem space much too large to exhaustively search. Existing approaches include optimization algorithms such as gradient descent and simulated annealing, but these…

Background:Prediction of protein three-dimensional structures from amino acid sequences is a long-standing goal in computational/molecular biology. The successful discrimination of protein folds would help to improve the accuracy of protein…

We review the recent progress in computational approaches to protein design which builds on advances in statistical-mechanical protein folding theory. In particular, we evaluate the degeneracy of the protein code (i.e. how many sequences…

Deep neural networks such as AlphaFold and RoseTTAFold predict remarkably accurate structures of proteins compared to other algorithmic approaches. It is known that biologically small perturbations in the protein sequence do not lead to…

We present a novel technique of sampling the configurations of helical proteins. Assuming knowledge of native secondary structure, we employ assembly rules gathered from a database of existing structures to enumerate the geometrically…

Motivation: Discovering functional modules in protein-protein interaction (PPI) networks by optimization methods remains a longstanding challenge in biology. Traditional algorithms simply consider strong protein complexes that can be found…

Determination of binding affinity of proteins in the formation of protein complexes requires sophisticated, expensive and time-consuming experimentation which can be replaced with computational methods. Most computational prediction…

Quantification and classification of protein structures, such as knotted proteins, often requires noise-free and complete data. Here we develop a mathematical pipeline that systematically analyzes protein structures. We showcase this…