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We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
A means to take advantage of molecular similarity to lower the computational cost of electronic structure theory is proposed, in which parameters are embedded into a low-cost, low-level (LL) ab initio theory and adjusted to obtain agreement…
For several decades, chemical knowledge has been published in written text, and there have been many attempts to make it accessible, for example, by transforming such natural language text to a structured format. Although the discovered…
Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional…
We consider an embedding of a $2$-dimensional CW complex into the $3$-sphere, and construct it's dual graph. Then we obtain a homogeneous system of linear equations from the $2$-dimensional CW complex in the first homology group of the…
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Determining the different conformational states of a protein and the transition paths between them is key to fully understanding the relationship between biomolecular structure and function. This can be accomplished by sampling protein…
We present a novel neural network architecture, termed Decomposer-Composer, for semantic structure-aware 3D shape modeling. Our method utilizes an auto-encoder-based pipeline, and produces a novel factorized shape embedding space, where the…
Computer-driven molecular design combines the principles of chemistry, physics, and artificial intelligence to identify novel chemical compounds and materials with desired properties for a specific application. In particular,…
As an efficient model for knowledge organization, the knowledge graph has been widely adopted in several fields, e.g., biomedicine, sociology, and education. And there is a steady trend of learning embedding representations of knowledge…
Recently, the first-named author gave a classification of 3D consistent 6-tuples of quad-equations with the tetrahedron property; several novel asymmetric 6-tuples have been found. Due to 3D consistency, these 6-tuples can be extended to…
Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces,…
The compression of geometric structures is a relatively new field of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are…
To facilitate rational molecular and materials design, this research proposes an integrated computational framework that combines stochastic simulation, ab initio quantum chemistry, and molecular docking. The suggested workflow allows…
Structure-based drug design involves finding ligand molecules that exhibit structural and chemical complementarity to protein pockets. Deep generative methods have shown promise in proposing novel molecules from scratch (de-novo design),…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, experimental determination of RNA structures through X-ray…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…