Related papers: MGOS: A Library for Molecular Geometry and its Ope…
Quantum geometrical molecular dynamics provides a quantum geometric picture for understanding reactive dynamics, especially excited-state conical intersection dynamics, and also a numerically exact method for strongly correlated…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
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…
Machine learning methods have shown promise in predicting molecular properties, and given sufficient training data machine learning approaches can enable rapid high-throughput virtual screening of large libraries of compounds. Graph-based…
We introduce a novel concept, the minimal molecular surface (MMS), as a new paradigm for the theoretical modeling of biomolecule-solvent interfaces. When a less polar macromolecule is immersed in a polar environment, the surface free energy…
Geometric integration theory can be employed when numerically solving ODEs or PDEs with constraints. In this paper, we present several one-step algorithms of various orders for ODEs on a collection of spheres. To demonstrate the versatility…
Silicon-oxygen compounds are among the most important ones in the natural sciences, occurring as building blocks in minerals and being used in semiconductors and catalysis. Beyond the well known silicon dioxide, there are phases with…
In this work, we address the systematic biases and random errors stemming from finite step sizes encountered in diffusion simulations. We introduce the Effective Geometry Monte Carlo (EG-MC) simulation algorithm which modifies the geometry…
We introduced the concept of a metric value set (MVS) in an earlier paper \cite{GM}. In this paper we study the algebraic structure of MVSs. For an MVS $M$ we define the concept of $M$-metrizability of a topological space and prove some…
Despite their ability to understand chemical knowledge, large language models (LLMs) remain limited in their capacity to propose novel molecules with desired functions (e.g., drug-like properties). In addition, the molecules that LLMs…
Recently, we presented a framework for understanding protein structure based on the idea that simple constructs of holding hands or touching of objects can be used to rationalize the common characteristics of globular proteins. We developed…
Mathematics has many useful properties for developing of complex software systems. One is that it can exactly describe a physical situation of the object or outcome of an action. Mathematics support abstraction and this is an excellent…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…
In a world made of atoms, the computer simulation of molecular systems, such as proteins in water, plays an enormous role in science. Software packages that perform these computations have been developed for decades. In molecular…
We study the notion of molecules in coorbit spaces. The main result states that if an operator, originally defined on an appropriate space of test functions, maps atoms to molecules, then it can be extended to a bounded operator on coorbit…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
The applications of machine learning techniques to chemistry and materials science become more numerous by the day. The main challenge is to devise representations of atomic systems that are at the same time complete and concise, so as to…
Molecular dynamics (MD) simulations allow atomistic insights into chemical and biological processes. Accurate MD simulations require computationally demanding quantum-mechanical calculations, being practically limited to short timescales…