arXiv research

Framework separates chemical and structural contributions to aqueous solubility.

A framework separates chemical and structural contributions to aqueous solubility.

Solvents can induce helical knots in simulated biopolymer tubes.

It is known that every ribbon category with unimodality allows symmetrized $6j$-symbols with full tetrahedral symmetries while a spherical category does not in general. We give an explicit counterexample for this, namely the category $\mathcal{E}$. We define the mirror conjugate symmetry of $6j$-symbols instead and sho…

We consider a natural question: "Is it true that each homotopy domination of a polyhedron over itself is a homotopy equivalence?" and a strongly related problem of K. Borsuk (1967): "Is it true that two ANR's homotopy dominating each other have the same homotopy type?" The answer was earlier known to be positive for ma…

Study compares atom representations in graph neural networks for molecular properties.

Let M be a compact surface, either orientable or non-orientable. We study the lower central and derived series of the braid and pure braid groups of M in order to determine the values of n for which B\_n(M) and P\_n(M) are residually nilpotent or residually soluble. First, we solve this problem for the case where M is …

We give an overview about finiteness properties of soluble S-arithmetic groups. Both, the number field case and the function field case are covered. The main result is: If B is a Borel subgroup in a Chevalley group and R is an S-arithmetic ring, then the group B(R) has finiteness length |S|-1 in the function field case…

Chemical databases store information in text representations, and the SMILES format is a universal standard used in many cheminformatics software. Encoded in each SMILES string is structural information that can be used to predict complex chemical properties. In this work, we develop SMILES2vec, a deep RNN that automat…

Let $(M^{n},g_{0})$ be a $n=3,4,5$ dimensional, closed Riemannian manifold of positive Yamabe invariant. For a smooth function $K>0$ on $M$ we consider a scalar curvature flow, that tends to prescribe $K$ as the scalar curvature of a metric $g$ conformal to $g_{0}$. We show global existence and in case $M$ is not confo…

Local solubility of Bao--Ratiu equations proven for surfaces with specific curvature conditions.

Sharp regularity for Pfaff system leads to isometric immersions in arbitrary dimensions.

Let G be a Chevalley group scheme and B<=G a Borel subgroup scheme, both defined over Z. Let K be a global function field, S be a finite non-empty set of places over K, and O_S be the corresponding S-arithmetic ring. Then, the S-arithmetic group B(O_S) is of type F_{|S|-1} but not of type FP_{|S|}. Moreover one can der…

Complete criterion for VoI in multi-decision influence diagrams established.

Extended dual Coxeter and Artin groups theory to rank-three systems.

The efficacy of family-based approaches to mixture model-based clustering and classification depends on the selection of parsimonious models. Current wisdom suggests the Bayesian information criterion (BIC) for mixture model selection. However, the BIC has well-known limitations, including a tendency to overestimate th…

We prove that the profinite completion of the fundamental group of a compact 3-manifold $M$ satisfies a Tits alternative: if a closed subgroup $H$ does not contain a free pro-$p$ subgroup for any $p$, then $H$ is virtually soluble, and furthermore of a very particular form. In particular, the profinite completion of th…

Manifold methods improve amino acid classification in LIBS spectra.

Graph networks struggle with multi-task learning due to varying property loss surface curvatures.

BERT learns molecular substructures for chemistry problems.

Bio-oil molecule assessment is essential for the sustainable development of chemicals and transportation fuels. These oxygenated molecules have adequate carbon, hydrogen, and oxygen atoms that can be used for developing new value-added molecules (chemicals or transportation fuels). One motivation for our study stems fr…

Molecular structure-property relationships are key to molecular engineering for materials and drug discovery. The rise of deep learning offers a new viable solution to elucidate the structure-property relationships directly from chemical data. Here we show that the performance of graph convolutional networks (GCNs) for…

Novel deep learning method predicts reaction coordinates and future MD trajectories.

Recently, machine learning (ML) has established itself in various worldwide benchmarking competitions in computational biology, including Critical Assessment of Structure Prediction (CASP) and Drug Design Data Resource (D3R) Grand Challenges. However, the intricate structural complexity and high ML dimensionality of bi…

In the majority of molecular optimization tasks, predictive machine learning (ML) models are limited due to the unavailability and cost of generating big experimental datasets on the specific task. To circumvent this limitation, ML models are trained on big theoretical datasets or experimental indicators of molecular s…

This work improves molecular design by efficiently selecting diverse candidate molecules.

The paper proves unboundedness of a functional on G2 forms and describes manifold limits.

Superintegrable systems are classical and quantum Hamiltonian systems which enjoy much symmetry and structure that permit their solubility via analytic and even, algebraic means. They include such well-known and important models as the Kepler potential, Calogero-Moser model, and harmonic oscillator, as well as its inte…

Extending isometric immersions with low regularity, especially supercritical.

ProtTrans models predict protein features without evolutionary info.

DOCKSTRING simplifies docking simulations for better drug design benchmarks.

The objective of this work is to study the applicability of various Machine Learning algorithms for prediction of some rock properties which geoscientists usually define due to special lab analysis. We demonstrate that these special properties can be predicted only basing on routine core analysis (RCA) data. To validat…

Extract common latent factors from graphs for better representation learning.