Model predicts multiple material properties with reduced error.
problem Limited materials data and lack of universal material descriptors.
method Integrates CGCNN with multi-task learning.
result Reduces test error by up to 8% for correlated properties.
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…
Study on crystallized polyominoes with minimum tiles and structural properties.
problem Finding the minimum number of tiles for polyominoes with holes.
method Developed a dynamical method to create sequences of polyominoes invariant with crystallization.
result Proved uniqueness of crystallized polyominoes with specific hole count.
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…
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…
The article studies crystallizations of small covers over simple polytopes and finds unique crystallizations for the n-simplex.
problem Understanding crystallizations of small covers over simple polytopes.
method Examining crystallizations of small covers over the n-simplex and prism, proving uniqueness and counting equivalence classes. result Proves uniqueness of crystallization for RPn over n-simplex and counts equivalence classes for prism. We extend to dimension n≥3 the concept of ρ-pair in a coloured graph and we prove the existence theorem for minimal rigid crystallizations of handle-free, closed n-manifolds.
The aim of this paper is twofold. On the one hand, it provides a review of the links between random tensor models, seen as quantum gravity theories, and the PL-manifolds representation by means of edge-colored graphs (crystallization theory). On the other hand, the core of the paper is to establish results about the to…
Lecture notes on crystallography and discrete surfaces.
problem Mathematical modeling of crystal structures.
method Variational principle and discrete surface theory.
result Most symmetric crystal structures identified.
Graph-CNN for 3D point cloud classification tackles non-regular graph topology.
problem Classifying 3D point cloud data with non-regular graph topology.
method Developed PointGCN combining localized graph convolutions and graph downsampling.
result Achieves competitive performance on 3D object classification benchmark ModelNet.
GWNN uses graph wavelets for efficient graph CNNs.
problem Spectral graph CNNs' high computational cost and lack of interpretability.
method Graph wavelet transform for efficient graph convolution.
result GWNN significantly outperforms spectral graph CNNs.
Researchers create crystallizations of lens spaces.
problem Understanding crystallizations of lens spaces.
method Quotients of triangulations of the sphere.
result Natural crystallizations of generalized lens spaces created.
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…
Machine learning predicts molecular crystal stability.
problem Predicting the stability of molecular crystals.
method Supervised and unsupervised machine learning techniques to classify and predict lattice energy.
result Data-driven assessment of chemical groups' contribution to crystal stability.
ShotgunCSP predicts crystal structures using machine learning, achieving high accuracy with minimal computation.
problem Predicting stable or metastable crystal structures of large systems.
method Noniterative screening using transfer learning and generative models.
result ShotgunCSP achieves 93.3% accuracy in benchmark tests with 90 different crystal structures.
Paper revisits graph-CNNs using Laplace-Beltrami spectral filters and polynomials.
problem Improving spectral graph convolutional neural networks (graph-CNNs).
method Developed Laplace-Beltrami CNN (LB-CNN) by replacing graph Laplacian with LB operator and approximating spectral filters using Chebyshev, Laguerre, and Hermite polynomials.
result Classification accuracy of LB-CNN is not dependent on the type of polynomials or operators.
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…
A grid layout method for graph classification using CNNs.
problem How to project graphs onto grids for CNNs to work effectively.
method Proposes a novel graph-preserving grid layout (GPGL) using integer programming to minimize topological loss, and solves it approximately with a regularized Kamada-Kawai algorithm.
result Demonstrates the success of the method for graph classification using multi-scale maxout CNNs.
Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and con…
Numerous pattern recognition applications can be formed as learning from graph-structured data, including social network, protein-interaction network, the world wide web data, knowledge graph, etc. While convolutional neural network (CNN) facilitates great advances in gridded image/video understanding tasks, very limit…
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…
Classifies defects in ordered media using homotopy theory.
problem Classifying defects in ordered media like liquid crystals.
method Using homotopy theory and continuous maps from ordered media to quotient spaces.
result Equivalence classes of defects are enumerated by subgroups of the quaternion group.
New minimal surfaces found from vortex crystals.
problem Minimal surfaces and vortex crystals.
method Gluing helicoids into minimal surfaces.
result New minimal surfaces and vortex crystals discovered.
New graph CNN layers improve accuracy on graph datasets.
problem Graph data relations are better represented as graphs, not grids.
method Proposed new graph CNN layers for vertex and edge features.
result Improved classification accuracy on graph datasets.
Ego-CNN detects critical structures in graphs efficiently.
problem Lack of precise detection of critical structures in existing graph embedding models.
method Ego-CNN uses ego-convolutions at each layer and stacks them in an ego-centric way.
result Ego-CNN achieves comparable task performance to state-of-the-art models and can incorporate scale-free priors.
Extends knotted defect classification to bounded domains using handlebodies.
problem Classifying knotted defects in bounded domains.
method Using continuous maps and monodromies around meridional loops, global defects are described in terms of planar diagrams.
result Classification scheme for defects in handlebodies.
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 paper studies special crystallizations of 4-manifolds to minimize certain PL-invariants.
problem Minimizing combinatorially defined PL-invariants in crystallizations of compact 4-manifolds.
method Analysis of semi-simple and weak semi-simple crystallizations to minimize regular genus, Gurau degree, gem-complexity, and trisection genus.
result An original theorem on the minimization of PL-invariants for compact 4-manifolds with weak semi-simple crystallizations.
DeepFreak learns crystal diffraction patterns from synthetic and real images.
problem Classifying crystallography diffraction patterns.
method End-to-end CNN architecture (DeepFreak) for classification on DiffraNet dataset.
result Best model achieves 98.5% accuracy on synthetic images and 94.51% on real images.
Machine learning and complexity-entropy methods estimate liquid crystal properties from textures.
problem Extracting physical properties from liquid crystal textures.
method Combining permutation entropy, statistical complexity, and machine learning.
result Significant precision in predicting physical properties of liquid crystals.
One-dimensional crystals have convex shapes under certain conditions.
problem Determining if one-dimensional crystals have convex shapes.
method Analyzing the free energy under mass constraints and convexity assumptions.
result In one dimension, crystals have convex shapes under given conditions.
Monopole dynamics linked to crystal volumes via moduli space geometry.
problem Understanding the motion of monopoles and their impact on crystal structures.
method Relating geodesic motion on a hyperkaehler moduli space to crystal volume calculations.
result Established a connection between monopole dynamics and crystal volume via moduli space geometry.
CRYSPNet predicts crystal structures from chemical compositions.
problem Predicting crystal structures of solids is challenging and computationally expensive.
method CRYSPNet uses a neural network to predict crystal properties from chemical composition.
result CRYSPNet outperforms alternative methods and is robustly validated.
Convolutional neural networks (CNNs) can be applied to graph similarity matching, in which case they are called graph CNNs. Graph CNNs are attracting increasing attention due to their effectiveness and efficiency. However, the existing convolution approaches focus only on regular data forms and require the transfer of …
FlowLLM uses LLMs and flow matching to efficiently generate novel materials.
problem Challenging material discovery due to vast chemical space.
method Combines LLMs and Riemannian flow matching to design novel crystalline materials.
result Significantly increases generation rate of stable materials and unique crystals.
Combines CNN and LSTM for spatio-temporal graph networks.
problem Improving spatio-temporal feature extraction.
method Proposes a new architecture combining CNN and LSTM temporal blocks.
result Empirical comparison shows our model outperforms existing models.
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…
Graph-based CNN for spherical data with equivariance.
problem Efficiently learning from non-uniformly distributed spherical data.
method Discretized sphere as graph, graph convolutions, equivariance using Defferrard's graph neural network.
result Good performance on rotation-invariant learning problems.
We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (R. C. Heitmann, C. Radin, J. Stat. Phys. 22, 281-287, 1980), which concerns a system of N identical at…
GNNs generalize CNNs for graph data, showing equivariance and stability.
problem Processing signals on graphs.
method Graph convolutional filters, nonlinearities, stacked layers.
result GNNs converge to graphon neural networks under graph convergence.
Paper proposes a robust deep graph-based classifier for noisy labels.
problem Difficulty in feature learning with noisy training labels.
method Convolutional neural networks with graph Laplacian regularization (GLR).
result Proposed method outperforms state-of-the-art classifiers on noisy datasets.
CHILI datasets tackle inorganic nanomaterials, advancing graph machine learning.
problem Challenges in modelling inorganic crystalline materials and nanomaterials with graph ML.
method Presented two large-scale datasets of inorganic nanomaterials, defined property and structure prediction tasks.
result Benchmarked performance of graph ML methods on inorganic nanomaterials, highlighting areas for future work.
Machine learning predicts band gaps for large organic crystals.
problem Predicting band gaps for complex organic crystal structures.
method Released a dataset of 12,500 crystal structures and their band gaps. Trained two state-of-the-art models to achieve a mean absolute error of 0.388 eV.
result Trained models predict band gaps with 13% error for an average gap of 3.05 eV.
We have defined weight of the pair (⟨S∣R⟩,R) for a given presentation ⟨S∣R⟩ 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.
problem Understanding if minimizing free energy with convex potential and mass constraint generates a convex crystal.
method Utilized a stability theorem, convexity, and a new maximum principle approach to prove a three-dimensional convexity theorem.
result Completely settled the Almgren problem in R3 under generic conditions. Proposes a new CNN for meshes that can handle orientation.
problem Isotropic kernels in graph convolutions are insensitive to mesh geometry.
method Introduces gauge equivariant kernels and geometric message passing.
result Significantly improved expressivity over conventional GCNs.
DFNets uses feedback-looped filters for better graph CNN performance.
problem Improving CNN performance on graph structured data.
method DFNets incorporates feedback-looped spectral graph filters.
result DFNets outperforms state-of-the-art methods in document and entity classification tasks.
The task of representing entire graphs has seen a surge of prominent results, mainly due to learning convolutional neural networks (CNNs) on graph-structured data. While CNNs demonstrate state-of-the-art performance in graph classification task, such methods are supervised and therefore steer away from the original pro…