Related papers: Geometric combinatorics and computational molecula…
A new statistical method of alignment of two heteropolymers which can form hierarchical cloverleaf-like secondary structures is proposed. This offers a new constructive algorithm for quantitative determination of binding free energy of two…
Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and…
Ground-state 3D geometries of molecules are essential for many molecular analysis tasks. Modern quantum mechanical methods can compute accurate 3D geometries but are computationally prohibitive. Currently, an efficient alternative to…
Due to the hierarchical organization of RNA structures and their pivotal roles in fulfilling RNA functions, the formation of RNA secondary structure critically influences many biological processes and has thus been a crucial research topic.…
Crystalline materials are widely used in technological applications, yet their discovery remains a significant challenge. As their properties are driven by structure, crystal structure prediction (CSP) methods play a central role in…
Reciprocal best matches play an important role in numerous applications in computational biology, in particular as the basis of many widely used tools for orthology assessment. Nevertheless, very little is known about their mathematical…
Biomolecular graph analysis has recently gained much attention in the emerging field of geometric deep learning. Here we focus on organizing biomolecular graphs in ways that expose meaningful relations and variations between them. We…
The main problems in modeling interacting galaxies are the extended parameter space and the fairly high CPU costs of self-consistent N-body simulations. Therefore, traditional modeling techniques suffer from either extreme CPU demands or…
Finding the best configuration of algorithms' hyperparameters for a given optimization problem is an important task in evolutionary computation. We compare in this work the results of four different hyperparameter tuning approaches for a…
Optimal sequence alignments depend heavily on alignment scoring parameters. Given input sequences, {\em parametric alignment} is the well-studied problem that asks for all possible optimal alignment summaries as parameters vary, as well as…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
The RNA inverse folding problem, a key challenge in RNA design, involves identifying nucleotide sequences that can fold into desired secondary structures, which are critical for ensuring molecular stability and function. The inherent…
In recent years, there has been notable interest in investigating combinatorial optimization (CO) problems by neural-based framework. An emerging strategy to tackle these challenging problems involves the adoption of graph neural networks…
We introduce genetic algorithms as a means to estimate the accuracy required to discriminate among different models using experimental observables. We exemplify the technique in the context of the minimal supersymmetric standard model. If…
Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…
For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…
Many of today's most interesting questions involve understanding and interpreting complex relationships within graph-based structures. For instance, in materials science, predicting material properties often relies on analyzing the…
Accurately modeling and designing protein complex structures is a central problem in computational structural biology, with broad implications for understanding cellular function and developing therapeutics. This thesis investigates two…