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Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by considering a suitable family of filtering functions…
Various approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between two input sequences. Haubold {\em et al.} (2009) showed how the average number of substitutions between two DNA…
Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. Persistence barcode is a graphical representation of such information. A filtration might be determined by time in a set…
Proteins have evolved to perform diverse cellular functions, from serving as reaction catalysts to coordinating cellular propagation and development. Frequently, proteins do not exert their full potential as monomers but rather undergo…
Semantic matching aims to establish pixel-level correspondences between instances of the same category and represents a fundamental task in computer vision. Existing approaches suffer from two limitations: (i) Geometric Ambiguity: Their…
We develop topological methods for analyzing difference topology experiments involving 3-string tangles. Difference topology is a novel technique used to unveil the structure of stable protein-DNA complexes involving two or more DNA…
Multiple sequence alignment is a basic procedure in molecular biology, and it is often treated as being essentially a solved computational problem. However, this is not so, and here I review the evidence for this claim, and outline the…
Background Nucleotide sequences contain multiple codes responsible for organism's functioning and structure. They can be investigated by various signal processing methods. These techniques are well suited for indication of frequently…
We consider a novel approach of measuring the homology of DNA sequences based of the variety of optimal alignments in the longest common subsequence sense. The proposed approach is compared with BLAST in measuring the homology of four…
Gene finding is the task of identifying the locations of coding sequences within the vast amount of genetic code contained in the genome. With an ever increasing quantity of raw genome sequences, gene finding is an important avenue towards…
Understanding how protein mutations affect protein-nucleic acid binding is critical for unraveling disease mechanisms and advancing therapies. Current experimental approaches are laborious, and computational methods remain limited in…
Predicting protein properties is paramount for biological and medical advancements. Current protein engineering mutates on a typical protein, called the wild-type, to construct a family of homologous proteins and study their properties.…
Feature matching between image pairs is a fundamental problem in computer vision that drives many applications, such as SLAM. Recently, semi-dense matching approaches have achieved substantial performance enhancements and established a…
Many biological questions, including the estimation of deep evolutionary histories and the detection of remote homology between protein sequences, rely upon multiple sequence alignments (MSAs) and phylogenetic trees of large datasets.…
We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…
Aligning protein-protein interaction (PPI) networks of different species has drawn a considerable interest recently. This problem is important to investigate evolutionary conserved pathways or protein complexes across species, and to help…
Nuclear Magnetic Resonance (NMR) Spectroscopy is a widely used technique to predict the native structure of proteins. However, NMR machines are only able to report approximate and partial distances between pair of atoms. To build the…
Molecular and morphological characters, as important parts of biological taxonomy, are contradictory but need to be integrated. Organism's image recognition and bioinformatics are emerging and hot problems nowadays but with a gap between…
Directed evolution as a widely-used engineering strategy faces obstacles in finding desired mutants from the massive size of candidate modifications. While deep learning methods learn protein contexts to establish feasible searching space,…
Despite advances in representation learning, high-dimensional classification remains challenging in low-sample-size regimes, where the dominant signal may vary across applications and labeled data are often limited. We propose a…