Related papers: Geometric combinatorics and computational molecula…
This paper proposes a new mathematical framework that can be applied to biological problems such as analysis of the structures of proteins and protein complexes. In particular, it gives a new method for encoding the three-dimensional…
An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot…
A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed,…
We propose a novel framework for combining datasets via alignment of their intrinsic geometry. This alignment can be used to fuse data originating from disparate modalities, or to correct batch effects while preserving intrinsic data…
Predicting the 3D structure of a macromolecule, such as a protein or an RNA molecule, is ranked top among the most difficult and attractive problems in bioinformatics and computational biology. Its importance comes from the relationship…
Predicting protein secondary structure is a fundamental problem in protein structure prediction. Here we present a new supervised generative stochastic network (GSN) based method to predict local secondary structure with deep hierarchical…
We investigate artificial neural networks as a parametrization tool for stochastic inputs in numerical simulations. We address parametrization from the point of view of emulating the data generating process, instead of explicitly…
Graph neural networks (GNNs) have been proposed for a wide range of graph-related learning tasks. In particular, in recent years, an increasing number of GNN systems were applied to predict molecular properties. However, a direct impediment…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
The aims of this article are two-fold. First, we give a geometric characterization of the optimal basic solutions of the general linear programming problem (no compactness assumptions) and provide a simple, self-contained proof of it…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
Identification of clusters of co-expressed genes in transcriptomic data is a difficult task. Most algorithms used for this purpose can be classified into two broad categories: distance-based or model-based approaches. Distance-based…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big…
Raman spectroscopy is an important characterization tool with diverse applications in many areas of research. We propose a machine learning method for predicting polarizabilities with the goal of providing Raman spectra from molecular…
Linear and geometric mixtures are two methods to combine arbitrary models in data compression. Geometric mixtures generalize the empirically well-performing PAQ7 mixture. Both mixture schemes rely on weight vectors, which heavily determine…
Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…
Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…
Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe…
Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing…