Related papers: PepCompass: Navigating peptide embedding spaces us…
Conjugate gradient (CG) methods are widely acknowledged as efficient for minimizing continuously differentiable functions in Euclidean spaces. In recent years, various CG methods have been extended to Riemannian manifold optimization, but…
Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
Peptides are formed by the dehydration condensation of multiple amino acids. The primary structure of a peptide can be represented either as an amino acid sequence or as a molecular graph consisting of atoms and chemical bonds. Previous…
We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…
Cell-penetrating peptides (CPPs) are powerful vectors for the intracellular delivery of a diverse array of therapeutic molecules. Despite their potential, the rational design of CPPs remains a challenging task that often requires extensive…
The application of Riemannian geometry in the decoding of brain-computer interfaces (BCIs) has swiftly garnered attention because of its straightforwardness, precision, and resilience, along with its aptitude for transfer learning, which…
Ligand-based virtual screening aims to reduce the cost and duration of drug discovery campaigns. Shape similarity can be used to screen large databases, with the goal of predicting potential new hits by comparing to molecules with known…
Decentralized optimization on Riemannian manifolds is foundational for many modern machine learning and signal processing applications in which data are non-Euclidean and generated and processed in a distributed manner. Although intrinsic…
Although Deep Learning (DL) has achieved success in complex Artificial Intelligence (AI) tasks, it suffers from various notorious problems (e.g., feature redundancy, and vanishing or exploding gradients), since updating parameters in…
We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…
Understanding peptide properties is often assumed to require modeling long-range molecular interactions, motivating the use of complex graph neural networks and pretrained transformers. Yet, whether such long-range dependencies are…
Peptides are recognized for their varied self-assembly behaviors, forming a wide array of structures and geometries, such as spheres, fibers, and hydrogels, each presenting a unique set of material properties. The functionalities of these…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
Protein-protein interactions (PPIs) are crucial in regulating numerous cellular functions, including signal transduction, transportation, and immune defense. As the accuracy of multi-chain protein complex structure prediction improves, the…
We consider the fundamental task of optimising a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in…
The protein-protein interactions (PPIs) are crucial for understanding the majority of cellular processes. PPIs play important role in gene transcription regulation, cellular signaling, molecular basis of immune response and more. Moreover,…
We present Extended Riemannian Stochastic Derivative-Free Optimization (Extended RSDFO), a novel population-based stochastic optimization algorithm on Riemannian manifolds that addresses the locality and implicit assumptions of manifold…
Antimicrobial peptides (AMPs) are promising therapeutic approaches against drug-resistant pathogens. Recently, deep generative models are used to discover new AMPs. However, previous studies mainly focus on peptide sequence attributes and…
The symplectic Stiefel manifold, denoted by $\mathrm{Sp}(2p,2n)$, is the set of linear symplectic maps between the standard symplectic spaces $\mathbb{R}^{2p}$ and $\mathbb{R}^{2n}$. When $p=n$, it reduces to the well-known set of $2n\times…