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Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…
Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields. Most existing methods, normally relying on tensor nuclear norm minimization, need to pay an expensive computational cost…
Topological Data Analysis (TDA) is a rapidly growing field, which studies methods for learning underlying topological structures present in complex data representations. TDA methods have found recent success in extracting useful geometric…
Proteins are biomolecules of life. They fold into a great variety of three-dimensional (3D) shapes. Underlying these folding patterns are many recurrent structural fragments or building blocks (analogous to `LEGO bricks'). This paper…
Amino acid sequence portrays most intrinsic form of a protein and expresses primary structure of protein. The order of amino acids in a sequence enables a protein to acquire a particular stable conformation that is responsible for the…
Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…
The Automated Protein Structure Analysis (APSA) method, which describes the protein backbone as a smooth line in 3-dimensional space and characterizes it by curvature kappa and torsion tau as a function of arc length s, was applied on 77…
Recent advancements in diffusion models have demonstrated significant success in unsupervised anomaly segmentation. For anomaly segmentation, these models are first trained on normal data; then, an anomalous image is noised to an…
Motivation Protein fold recognition is an important problem in structural bioinformatics. Almost all traditional fold recognition methods use sequence (homology) comparison to indirectly predict the fold of a tar get protein based on the…
Structure-based drug design (SBDD) leverages the three-dimensional geometry of proteins to identify potential drug candidates. Traditional approaches, rooted in physicochemical modeling and domain expertise, are often resource-intensive.…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
One of the most powerful methods of color image recognition is the two-dimensional principle component analysis (2DQPCA) approach, which is based on quaternion representation and preserves color information very well. However, the current…
Due to the lack of a method to efficiently represent the multimodal information of a protein, including its structure and sequence information, predicting compound-protein binding affinity (CPA) still suffers from low accuracy when applying…
How and where proteins interface with one another can ultimately impact the proteins' functions along with a range of other biological processes. As such, precise computational methods for protein interface prediction (PIP) come highly…
Protein structure representation is an important tool in structural biology. There exists different methods of representing the protein 3D structures and different biologists favor different methods based on the information they require.…
We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…
The dynamic mode decomposition (DMD) is a simple and powerful data-driven modeling technique that is capable of revealing coherent spatiotemporal patterns from data. The method's linear algebra-based formulation additionally allows for a…
Motivation: 3D structures of proteins provide rich information for understanding their biochemical roles. Identifying the representative protein structures for protein sequences is essential for analysis of proteins at proteome scale.…
Motivation: RNA design aims to find RNA sequences that fold into a given target secondary structure, a problem also known as RNA inverse folding. However, not all target structures are designable. Recent advances in RNA designability have…
We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a…