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In spite of decades of research, much remains to be discovered about folding: the detailed structure of the initial (unfolded) state, vestigial folding instructions remaining only in the unfolded state, the interaction of the molecule with…
The application of molecular dynamics (MD) simulations to the interpretation of Raman scattering spectra is hindered by inability of atomistic simulations to account for the dynamic evolution of electronic polarizability, requiring the use…
Designing a neural network architecture for molecular representation is crucial for AI-driven drug discovery and molecule design. In this work, we propose a new framework for molecular representation learning. Our contribution is threefold:…
An algebraic method especially suited to describe strongly anharmonic vibrational spectra in molecules may be an appropriate framework to study vibrational spectra of Na$^+_n$ clusters, where nearly flat potential energy surfaces and the…
Bimolecular binding rate constants are often used to describe the association of large molecules, such as proteins. In this paper, we analyze a model for such binding rates that includes the fact that pairs of molecules can bind only in…
We derive the statistical limit of the spectral autocorrelation function and of the survival probability for the indirect photodissociation of molecules in the regime of non-overlapping resonances. The results are derived in the framework…
The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out…
High-performance machine learning tools in particle physics rest on two complementary directions: encoding symmetries explicitly in the architecture, and implicitly learning the structure of the data through large-scale (pre-) training. We…
Surface roughness of particle monolayer is one of its fundamental characteristics, conventionally described in terms of power spectral density. We derive a general equation for this function and demonstrate its similarity to those applied…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
Alignment and orientation of molecules by intense, ultrashort laser fields are crucial for a variety of applications in physics and chemistry. These include control of high harmonics generation, molecular orbitals tomography, control of…
Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each…
Developing the analysis of the distribution of the so-called posmom xp to the spherical harmonics that represents some molecular rotational states for such as diatomic molecules and spherical cage molecules, we obtain posmometry (introduced…
Through the introduction of a class of trial wave functions portraying combined rotations and vibrations of molecules formed through particle localization in concentric polygonal rings, a correlated basis is constructed that spans the…
Spectroscopy is the most important method for probing the structure of molecules. However, predicting molecular spectra on classical computers is computationally expensive, with the most accurate methods having a cost that grows…
In the context of NMR spectroscopy and MRI, the principle of reciprocity provides a convenient method for determining the reception sensitivity from the transmitted rf field pattern. The reciprocity principle for NMR was originally…
We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals. Some comparisons and analogies are drawn to the fields of signal processing, harmonic analysis and sparse…
Application of circularly polarized beams in interferometric illumination of colloid sphere monolayers enables the direct fabrication of rectangular patterns consisting of circular nanohole miniarrays in metal films. The spectral and…
Recognizing symmetries in data allows for significant boosts in neural network training. In many cases, however, the underlying symmetry is present only in an idealized dataset, and is broken in the training data, due to effects such as…
Machine learning over-fitting caused by data scarcity greatly limits the application of machine learning for molecules. Due to manufacturing processes difference, big data is not always rendered available through computational chemistry…