Gaussian process regression cuts energy evaluations for atomic rearrangement paths.
problem Reducing computational effort for minimum energy paths in complex systems.
method Gaussian process regression to approximate energy surfaces and converge to minimum energy paths.
result Significant reduction in energy evaluations (less than a fifth for a test problem).
Gaussian process regression speeds up nudged elastic band calculations for transitions.
problem Reducing computational effort for calculating minimum energy paths in thermalized systems.
method Approximate energy surface generation and refinement using Gaussian process regression.
result The number of energy and force evaluations can be reduced by an order of magnitude.
The paper shows how to rearrange arcs to form closed curves.
problem Creating closed curves from planar arcs.
method Splitting a curve into arcs and rearranging them to form a closed curve.
result Closed curves can be formed by rearranging arcs under weak assumptions.
Simplified and extended a method for rearranging infinite configurations of cubes.
problem Constructing homotopies for isotopically rearranging cubes.
method Simplified and extended Eda and Kawamura's procedure.
result Simplified and extended the construction of homotopies.
This note proves a Gaussian version of a Pólya-Szegö conjecture using rearrangement techniques.
problem Finding the domain with the minimum Gaussian principal frequency when the Gaussian torsional rigidity is fixed.
method Adapted Kohler-Jobin rearrangement technique to the Gauss space, considering a modified torsional rigidity and rearranging layers to half-spaces.
result The Gaussian principal frequency is minimized for the half-space when the Gaussian torsional rigidity is fixed.
Paper explores closedness properties of convex sets in rearrangement invariant spaces.
problem Closedness properties of law-invariant convex sets in rearrangement invariant spaces.
method Analyzes equivalence of different closedness types in rearrangement invariant spaces.
result Order closedness, σ(X,Xn∼)-closedness and σ(X,L∞)-closedness of a law-invariant convex set are equivalent. Numerical challenges inherent in algorithms for computing worst Value-at-Risk in homogeneous portfolios are identified and solutions as well as words of warning concerning their implementation are provided. Furthermore, both conceptual and computational improvements to the Rearrangement Algorithm for approximating wors…
Graphs represent gene segment organization, revealing complex interrelationships in a scrambled genome.
problem Understanding gene segment organization and interrelationships in a scrambled genome.
method Directed graphs representing gene segments and their relationships, with graph properties mapped to higher-dimensional space for analysis.
result Emerging star-like structures indicate complex interrelationships, including segments from multiple genes interleaving or overlapping.
Paper develops polynomial approximations for complex probability densities.
problem Approximating high-dimensional concentrated probability densities.
method Tensor-product spectral polynomials and KR rearrangements.
result Efficient approximation of complex densities using composite maps.
The paper proves a Moser-Trudinger inequality on metric spaces with curvature-dimension conditions.
problem Proving a Moser-Trudinger inequality on metric measure spaces.
method Rearrangement of functions on CD(k,n)-spaces satisfying a Polya-Szegö type inequality.
result Characterization of manifolds with lower bounded Ricci curvature admitting a Moser-Trudinger inequality.
Method calibrates basket options using rearranged samples from constituent processes.
problem Calibrate basket options with non-linear dependency structure.
method Propose a method to extract dependency structure from market data through systematic sampling rearrangement, then calibrate a local volatility model.
result Efficiently calibrates basket options with near-perfect accuracy.
The paper extends geometric inequalities from Euclidean space to Riemannian manifolds.
problem Proving geometric inequalities on smooth oriented Riemannian manifolds.
method Introducing symmetric decreasing rearrangement inequalities and testing their applicability to Riemannian manifolds.
result Smooth co-area formula and re-formulated geometric inequalities on Riemannian manifolds.
New proof of rearrangement lemma for noncommutative tori using hypergeometric functions.
problem Proving rearrangement lemma in noncommutative tori.
method Using Lauricella functions of type D and Gauss hypergeometric functions.
result Full reduction of spectral functions to Gauss hypergeometric functions.
The strong Fatou property is crucial for risk measures' dual representations.
problem Ensuring nice dual representations of risk measures.
method Exploring Fatou-type properties and inf-convolutions of law-invariant or surplus-invariant risk measures.
result Every quasiconvex law-invariant functional on a rearrangement invariant space with the strong Fatou property is σ(X, L∞)-lower semicontinuous.
Study fine Pólya-Szegő inequalities in metric spaces with applications.
problem Fine Pólya-Szegő rearrangement inequalities in metric spaces.
method Theory of Sobolev and BV functions, synthetic Ricci bounds, isoperimetric inequality.
result New geometric and functional inequalities under Ricci lower bounds.
Pixle attacks images by rearranging pixels, bypassing neural networks.
problem Vulnerability of neural networks to black-box adversarial attacks.
method A novel attack that rearranges a small number of pixels in images.
result Successfully attacks a high percentage of samples on various datasets and models.
Paper compares solutions of Poisson equations on Riemannian manifolds with Robin boundary.
problem Comparing solutions of Poisson equations on Riemannian manifolds with Robin boundary.
method Using Schwarz rearrangement and isoperimetric inequalities.
result Extends results on Poisson equations with Ric≥(n−1)κ. Unified theory linking atom-centered and message-passing models for molecular properties.
problem Combining atom-centered and message-passing models for accurate molecular property prediction.
method Generalizing ACDC framework to include multi-centered information, providing a complete linear basis for regression.
result Unified understanding of atom-centered and message-passing models, providing a coherent foundation.
Proposes atomic swaptions for trustless cryptocurrency derivatives.
problem Lack of trustless derivatives for cryptocurrency exchanges.
method Extends atomic swap protocol to include derivatives without oracles.
result Atomic swaptions enable trustless exchange of derivative assets.
Researchers use manifold learning to analyze 4D-STEM data of graphene, revealing atomic structure details.
problem Challenges in processing and interpreting large 4D-STEM datasets, especially for light materials.
method Data-driven manifold learning approaches for visualization and exploration of 4D-STEM datasets.
result Extracted patterns relate to individual atom sites and sublattice structures, effectively discriminating single dopant anomalies.
Machine learning predicts atomization energies accurately from low-fidelity calculations.
problem Predicting accurate atomization energies of organic molecules efficiently.
method Machine learning models trained on low-fidelity B3LYP energies to predict high-fidelity G4MP2 energies.
result Predicted G4MP2 atomization energies within 0.012 eV for molecules with 10-14 heavy atoms.
Study Hamiltonian diffeomorphisms on symplectic manifolds and properties of invariant convex functions.
problem Properties of invariant convex functions under Hamiltonian diffeomorphisms.
method Analysis of the adjoint action and properties of invariant convex functions.
result Continuous convex functions invariant under Hamiltonian diffeomorphisms are also invariant under strict rearrangements.
New features for quantum calculations learn N-center Hamiltonian matrix elements.
problem Quantum calculations need features for N-center Hamiltonians, not just atom-centered ones.
method Developed fully equivariant N-center features for machine learning.
result Learned matrix elements of N-center Hamiltonians efficiently.
Frank and Lieb proved sharp Sobolev inequalities without rearrangements.
problem Proving sharp Sobolev inequalities for function spaces.
method Using conformal covariance and commutator identities from the Fefferman-Graham ambient metric.
result Direct proof of sharp Sobolev inequalities and new nonlinear inequality.
Neural network learns atomic coordinates from Patterson maps in a simplified case.
problem Training a neural network to infer atomic coordinates from Patterson maps.
method Synthetic data training, centering output maps, removing centrosymmetric inversion, and adding empty space.
result The network can generalize to infer atom positions from Patterson maps not in the training set.
Study compares atom representations in graph neural networks for molecular properties.
problem Incorrect attribution of results in molecular property prediction due to varying atom features.
method Evaluated multiple atom representations on free energy, solubility, and metabolic stability predictions.
result Different atom representations can lead to varying predictive performance in graph neural networks.
We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schrödinger equation is mapped onto a non-linear statistical regression problem of reduced complexity. Regression models a…
LC-GAP uses localized Coulomb descriptors for accurate molecular potential predictions.
problem Creating accurate molecular potentials for large molecules.
method Combining localized Coulomb matrix representations with Gaussian approximation potential.
result LC-GAP generates accurate potentials for molecules larger than training data with chemical accuracy.
We prove that the introduction of the class of geometrically atomic bundle maps by Harvey and Lawson in their theory of singular connections is not necessary because an arbitrary map satisfies the conditions of geometric atomicity.
ASLA learns atomic structures using neural networks and reinforcement learning.
problem Designing materials and drugs with desired properties.
method Atomistic structure learning algorithm (ASLA) using a convolutional neural network and reinforcement learning.
result ASLA can predict optimal structural arrangements of atoms for various target properties.
Machine learning models simulate molecular spectra and reactions in solvents.
problem Accurate simulation of molecular spectra and reactions in solvent environments.
method Introduced FieldSchNet, a deep neural network for modeling molecular interactions with external fields.
result Demonstrated significant lowering of Claisen rearrangement reaction activation barrier using FieldSchNet.
PAM models generate dependent random distributions across groups with overlapping clusters.
problem Generating dependent random distributions across multiple groups.
method Atom skipping in an infinite mixture model.
result Interpretable posterior inference of cluster exclusivity and sharing.
Non-atomic arbitrage exploits price differences on Ethereum and other blockchains, accounting for over 10% of Ethereum's block value.
problem Price differences on decentralized exchanges and centralized exchanges lead to MEV.
method Analyzed non-atomic arbitrage on Ethereum's largest DEXes, identifying its prevalence and impact.
result More than 10% of Ethereum's block value is attributed to non-atomic arbitrage, involving over $132 billion.
Extends subspace detour method to Gromov-Wasserstein problem.
problem Matching shapes using Gromov-Wasserstein distance.
method Project measures onto a subspace, then compute optimal transport plan.
result Connections with Knothe-Rosenblatt rearrangement.
Graph neural network predicts protonation energies of oxygen atoms in bio-oil molecules.
problem Predicting protonation energies of oxygen atoms in bio-oil molecules for chemical upgrading.
method Site-specific graph neural network approach using iterative local nonlinear embedding.
result Effective prediction of protonation energies of individual oxygen atoms in bio-oil molecules.
ATOMO reduces communication in distributed learning by sparsifying gradients.
problem Communication overheads in distributed model training.
method ATOMO framework for atomic sparsification of stochastic gradients.
result Sparsifying singular value decomposition can lead to faster distributed training.
Improved chemical predictions through compressed atomic species representations.
problem Intractable chemical space of molecules and materials.
method Introducing elemental modes for compressed representation of atomic species.
result Elemental modes enable improvements in machine learning tasks for chemical predictions.
Unified approach to invariants in equivariant geometry.
problem Constructing invariants in G-equivariant birational geometry. method Combining atom theory and modular symbols.
result Developed new geometric invariants for orbifolds and surfaces.
Improves molecular activity prediction using graph convolutional neural networks considering graph distances.
problem Predicting molecular activity using graph convolutional neural networks with improved distance representation.
method Proposed three improvements: modified graph distances, distance-dependent weight matrices, and weighted sum conversion.
result The proposed method slightly outperforms the original weave module in compound activity prediction.
GRAPE uses graph kernels to predict molecular energies efficiently.
problem Efficiently predicting molecular energies with physical constraints.
method GRAPE approach based on graph theory incorporating symmetries.
result GRAPE predicts atomization energies accurately on organic molecules.
Develops conformal Bayes for two-sided censored Gaussian regression under label shift.
problem Prediction under label shift with censored responses.
method Combines posterior predictive tilting with weighted conformal calibration.
result Restores marginal coverage with smaller prediction sets.
In many signal processing applications, the aim is to reconstruct a signal that has a simple representation with respect to a certain basis or frame. Fundamental elements of the basis known as "atoms" allow us to define "atomic norms" that can be used to formulate convex regularizations for the reconstruction problem. …
Geometric GNNs model 3D atomic systems with rotations and translations.
problem Modeling 3D atomic systems with geometric graphs and machine learning.
method Invariant, equivariant, and unconstrained GNN architectures.
result Geometric GNNs leverage physical symmetries and chemical properties.
Proposes an algorithm for infinite-dimensional sparse learning in system identification.
problem System identification without known model structures.
method Atomic norm regularization and greedy algorithm for solving an infinite-dimensional group lasso problem.
result The proposed algorithm outperforms benchmark methods in impulse response fitting and pole location estimation.
Examines how algorithms affect user autonomy and information choice.
problem Impact of algorithmic recommendations on user autonomy and free choice.
method Double dichotomy analysis of user intentions and actions, prior and posterior information rearrangement.
result Algorithms can expand or limit user cognitive and social horizons.
Optimizes ligand binding poses using CNNs and atomic grids.
problem Improving the accuracy of docking predictions for drug discovery.
method Differentiable atomic grid representation, CNN for scoring and optimization.
result Iteratively-trained CNNs outperform single CNNs in optimizing poses.
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.
New method learns histograms using optimal transport barycenters.
problem Nonlinear dictionary learning for histograms.
method Optimal transport theory, displacement interpolations, entropic regularization, gradient descent.
result Efficient and tractable method for nonlinear dictionary learning.