arXiv research

ShotgunCSP predicts crystal structures using machine learning, achieving high accuracy with minimal computation.

CRYSPNet predicts crystal structures from chemical compositions.

Machine learning predicts molecular crystal stability.

Machine learning predicts perovskite formability and classifies crystal structures.

A fundamental problem in applying machine learning techniques for chemical problems is to find suitable representations for molecular and crystal structures. While the structure representations based on atom connectivities are prevalent for molecules, two-dimensional descriptors are not suitable for describing molecula…

Machine-learning models are capable of capturing the structure-property relationship from a dataset of computationally demanding ab initio calculations. Over the past two years, the Organic Materials Database (OMDB) has hosted a growing number of calculated electronic properties of previously synthesized organic crysta…

EBM predicts protein conformations at atomic scale using crystallized data.

We constructed physically stable sp2 negatively curved cubic carbon structures which reticulate a Schwarz P-like surface. The method for constructing such crystal structures is based on the notion of the standard realization of abstract crystal lattices. In this paper, we expound on the mathematical method to construct…

FlowMM models stable crystal structures efficiently.

We present a novel optimization method, named the Combined Optimization Method (COM), for the joint optimization of two or more cost functions. Unlike the conventional joint optimization schemes, which try to find minima in a weighted sum of cost functions, the COM explores search space for common minima shared by all …

We give a complete solution to the extremal topological combinatorial problem of finding the minimum number of tiles needed to construct a polyomino with $h$ holes. We denote this number by $g(h)$ and say that a polyomino is crystallized if it has $h$ holes and $g(h)$ tiles. We analyze structural properties of crystall…

In this paper, we propose an active learning method for an inverse problem that aims to find an input that achieves a desired structured-output. The proposed method provides new acquisition functions for minimizing the error between the desired structured-output and the prediction of a Gaussian process model, by effect…

Minimal crystallizations of simply connected PL 4-manifolds are very natural objects. Many of their topological features are reflected in their combinatorial structure which, in addition, is preserved under the connected sum operation. We present a minimal crystallization of the standard PL K3 surface. In combination w…

The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the case of two-dimensional nematic liquid crystals coating a toroidal particle. Our…

Imaging techniques are essential tools for inquiring a number of properties from different materials. Liquid crystals are often investigated via optical and image processing methods. In spite of that, considerably less attention has been paid to the problem of extracting physical properties of liquid crystals directly …

Developing accurate, transferable and computationally inexpensive machine learning models can rapidly accelerate the discovery and development of new materials. Some of the major challenges involved in developing such models are, (i) limited availability of materials data as compared to other fields, (ii) lack of unive…

Materials discovery is crucial for making scientific advances in many domains. Collections of data from experiments and first-principle computations have spurred interest in applying machine learning methods to create predictive models capable of mapping from composition and crystal structures to materials properties. …

Researchers create crystallizations of lens spaces.

Computational chemists typically assay drug candidates by virtually screening compounds against crystal structures of a protein despite the fact that some targets, like the $μ$ Opioid Receptor and other members of the GPCR family, traverse many non-crystallographic states. We discover new conformational states of $μOR$…

Lecture notes on crystallography and discrete surfaces.

The Machine Recognition of Crystallization Outcomes (MARCO) initiative has assembled roughly half a million annotated images of macromolecular crystallization experiments from various sources and setups. Here, state-of-the-art machine learning algorithms are trained and tested on different parts of this data set. We fi…

New minimal surfaces found from vortex crystals.

We introduce Deep Reasoning Networks (DRNets), an end-to-end framework that combines deep learning with reasoning for solving complex tasks, typically in an unsupervised or weakly-supervised setting. DRNets exploit problem structure and prior knowledge by tightly combining logic and constraint reasoning with stochastic…

The paper studies special crystallizations of 4-manifolds to minimize certain PL-invariants.

New normalizing flows model molecular crystal structures.

Generative models have achieved impressive results in many domains including image and text generation. In the natural sciences, generative models have led to rapid progress in automated drug discovery. Many of the current methods focus on either 1-D or 2-D representations of typically small, drug-like molecules. Howev…

One-dimensional crystals have convex shapes under certain conditions.

New metrics reveal how Majoranas crystallize in a particle model.

Study of knotted defects in smectic liquid crystals using topological knot theory.

This paper is devoted to the problem of choosing the most suitable model of a geometrical system for describing the real crystallographic space. It has been shown that all 230 crystallographic groups used to describe the crystalline structures in a Euclidean space can be presented by elliptic motions in the closed spac…

CHILI datasets tackle inorganic nanomaterials, advancing graph machine learning.

Model predicts EMF of Ni-Mn-Ga MSMA, improved with GRNN.

Researchers create topologically protected knots in a realizable system.

The article studies crystallizations of small covers over simple polytopes and finds unique crystallizations for the $n$-simplex.

We have defined weight of the pair $(\langle S \mid R \rangle, R)$ for a given presentation $\langle S \mid R \rangle$ of a group, where the number of generators is equal to the number of relations. We present an algorithm to construct crystallizations of 3-manifolds whose fundamental group has a presentation with two …

The paper solves a thermodynamics problem about crystal shape.

Consider a finite connected graph possibly with multiple edges and loops. In discrete geometric analysis, Kotani and Sunada constructed the crystal associated to the graph as a standard realization of the maximal abelian covering of the graph. As an application of what the author showed in an earlier paper with Seshadr…

We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper arXiv:0811.2801. In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the par…

For $d\geq 2$, the regular genus of a closed connected PL $d$-manifold $M$ is the least genus (resp., half of the genus) of an orientable (resp., a non-orientable) surface into which a crystallization of $M$ imbeds regularly. The regular genus of every orientable surface equals its genus, and the regular genus of every…

Simple crystallizations are edge-coloured graphs representing PL 4-manifolds with the property that the 1-skeleton of the associated triangulation equals the 1-skeleton of a 4-simplex. In the present paper, we prove that any (simply-connected) PL $4$-manifold $M$ admitting a simple crystallization admits a special hand…

Study phase transition in liquid crystal droplets using mathematical analysis.

Theory of packing diabolic domains in liquid crystals.

We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid non-bipartite crystallizations up to 30 vertices.

By means of a slight modification of the notion of GM-complexity, the present paper performs a graph-theoretical approach to the computation of (Matveev's) complexity for closed orientable 3-manifolds. In particular, the existing crystallization catalogue C^{28}, due to Lins, is used to obtain upper bounds for the comp…

Topologically protected vortex knots and links are proposed and proven.

We investigate the well-posedness of (i) the heat flow of harmonic maps from $R^n$ to a compact Riemannian manifold without boundary for initial data in BMO; and (ii) the hydrodynamic flow $(u,d)$ of nematic liquid crystals on $\mathbb R^n$ for initial data in $BMO^{-1}\times BMO$.

This expository paper is a tribute to Ekkehart Kröner's results on the intrinsic non-Riemannian geometrical nature of a single crystal filled with point and/or line defects. A new perspective on this old theory is proposed, intended to contribute to the debate around the still open Kröner's question: "what are the dyna…

The present paper follows the computational approach to 3-manifold classification via edge-coloured graphs, already performed by several authors with respect to orientable 3-manifolds up to 28 coloured tetrahedra, non-orientable 3-manifolds up to 26 coloured tetrahedra, genus two 3-manifolds up to 34 coloured tetrahedr…