Paper proposes active learning for structured output design, improving Gaussian process model predictions.
problem Finding optimal input parameters for achieving desired structured outputs.
method Developed new acquisition functions to minimize prediction error of Gaussian process model, incorporating output correlations.
result Effectiveness demonstrated in synthetic and real data experiments, including materials informatics.
For any given C∞ immersion r:S1→R2 such that the set NSr=R2−∪s∈S1(r(s)+drs(Ts(S1))) is not empty, a simple geometric model of crystal growth is constructed. It is shown that our geometric model of crystal growth never form…
The paper proves the regularity of solutions to a specific differential equation describing physical phenomena.
problem Understanding the regularity of solutions to a curvature-dependent differential equation.
method Weaves together analysis and geometry to prove the optimal regularity of solutions.
result The second derivative of solutions is continuous only in very rigid situations.
Researchers created curved carbon crystals using standard lattice methods.
problem Creating physically stable negatively curved cubic carbon structures.
method Standard realization of abstract crystal lattices.
result Constructed physically stable sp2 negatively curved cubic carbon structures.
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.
Deep learning classifies over 94% of crystallization images accurately.
problem Classifying macromolecular crystallization outcomes from various experiments.
method Deep convolutional neural networks trained on a large annotated dataset.
result More than 94% of test images correctly labeled, regardless of origin.
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.
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.
New method uses space-filling curves to represent crystal structures for machine learning.
problem Representing molecular crystals for machine learning.
method SFC-M feature representations based on Morton curves, reduced by LSI.
result Promising results in predicting crystal properties.
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.
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.
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.
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. 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. 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…
New method calculates genus of PL 4-manifolds accurately.
problem Calculating the genus of PL 4-manifolds accurately.
method Introducing weak semi-simple crystallization and proving genus formula.
result Regular genus of PL 4-manifolds equals a specific formula.
Minimal crystallizations bound for 3-manifolds with boundary.
problem Bounding the gem-complexity of 3-manifolds with boundary.
method Proving bounds on gem-complexity and using crystallization properties.
result Sharp bounds for gem-complexity of 3-manifolds with boundary.
Study on defect topology in smectic liquid crystals.
problem Topological classification and combination rules of smectic defects.
method Topological analysis of point defects and disclination lines in 2D and 3D smectic liquid crystals.
result Combination rules for smectic point defects in 2D and 3D, showing path dependence.
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…
Machine learning predicts perovskite formability and classifies crystal structures.
problem Predicting and classifying perovskite formability and crystal structures.
method Machine learning, specifically Random Forest, with 5-fold cross-validation.
result 98.57% accuracy in predicting perovskite formability and 90.53% in classifying crystal structures.
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.
problem Mathematical analysis of phase transition between isotropic and nematic states of liquid crystals.
method Rigorous mathematical analysis using the Ericksen model and Γ-convergence theory.
result Γ-limit provides geometric description and anchoring conditions for liquid crystal orientations.
Generative models encode and decode 3D crystal structures from a large dataset.
problem Challenges in encoding and decoding 3D crystal structures from large datasets.
method Training two neural networks on a dataset of over 120,000 crystal structures to encode and decode 3D atom positions.
result Ability to generate compressed, continuous latent space representations and decode molecules accurately.
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…
The paper connects tensor models to crystallization theory to study manifold properties.
problem Understanding topological and geometrical properties of tensor models.
method Using crystallization theory to analyze colored tensor models and their PL-manifold representations.
result The G-degree of PL-manifolds is finite-to-one in any dimension, and classification theorems are obtained for specific dimensions.
Theory of packing diabolic domains in liquid crystals.
problem Understanding the packing of diabolic domains in liquid crystals.
method Lorentz transformations and geometric analysis.
result Diabolic domains can lower the elastic energy of the system.
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…
New approach proves crystallization theorem using discrete curvature and Gauss-Bonnet theorem.
problem Proving crystallization theorem for two-dimensional atom systems.
method Introducing discrete curvature to bond graphs and applying discrete Gauss-Bonnet theorem.
result Exact geometric decomposition of Heitmann-Radin energy into various terms.
We investigate the well-posedness of (i) the heat flow of harmonic maps from Rn to a compact Riemannian manifold without boundary for initial data in BMO; and (ii) the hydrodynamic flow (u,d) of nematic liquid crystals on Rn for initial data in BMO−1×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…
COM finds shared minima in multiple cost functions.
problem Optimizing multiple cost functions with different local minima.
method Exploring common minima shared by all cost functions without metaheuristics.
result High success rate in finding correct crystal structures.
FlowMM models stable crystal structures efficiently.
problem Predicting and proposing stable crystalline structures.
method Riemannian Flow Matching generalized to crystal symmetries.
result 3x more efficient at finding stable materials.
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.
New normalizing flows model molecular crystal structures.
problem Modeling positions and orientations of molecules in crystals.
method Smooth flows on unit quaternions for rigid body motion, using double cover property.
result Trained flows can generate Boltzmann distributions of molecules.
New methods reveal compatible liquid crystal phases in 3D.
problem Understanding compatible director fields in 3D liquid crystals.
method Re-derived compatibility conditions using vector calculus.
result Characterized a wide range of compatible liquid crystal phases.
DRNets combine deep learning and reasoning for complex tasks.
problem Solving complex tasks, especially in scientific discovery, with limited supervision.
method DRNets integrate logic and neural network optimization to encode structured latent spaces constrained by prior knowledge.
result DRNets outperform state-of-the-art models in scientific discovery tasks, recovering more precise crystal structures.
New metrics reveal how Majoranas crystallize in a particle model.
problem Understanding how Majoranas crystallize in particle models.
method Analyzing metrics on su(n) for n=4,8 and finding kam metrics. result Found kam metrics on su(4) and su(8) that adhere to a penalty schedule. EBM predicts protein conformations at atomic scale using crystallized data.
problem Predicting the conformation of a side chain from its context within a protein structure.
method Energy-based model trained on crystallized protein data, evaluating performance on rotamer recovery task.
result EBM achieves performance close to state-of-the-art methods, including Rosetta energy function.
Smectic liquid crystals are materials formed by stacking deformable, fluid layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary conditions can impose curvature on the layers. Since the layer spacing and curvature are intertwined, the problem of finding minimal configurations for the layers bec…
Within crystallization theory, two interesting PL invariants for d-manifolds have been introduced and studied, namely {\it gem-complexity} and {\it regular genus}. In the present paper we prove that, for any closed connected PL 4-manifold M, its gem-complexity k(M) and its regular genus $ \mathcal G(M)…