Geometric QCD framework establishes stable vacuum for quark confinement.
problem Quark confinement in QCD.
method Geometric construction of stable vacuum using Hodge-dual surfaces.
result Existence and stability of the Hodge-dual surface in 4D ensures quark confinement.
In this paper the dynamics of the classical chiral QCD2 currents is studied. We describe how the dynamics of the theory can be summarized in an equation of the Lax form, thereby demonstrating the existence of an infinite set of conserved quantities. Next, the r matrix of a fundamental Poisson relation is obtaine…
Supervised learning with a deep convolutional neural network is used to identify the QCD equation of state (EoS) employed in relativistic hydrodynamic simulations of heavy-ion collisions from the simulated final-state particle spectra ρ(pT,Φ). High-level correlations of ρ(pT,Φ) learned by the neural network act a…
Geometric QHD tests improve hub detection in correlated data.
problem Detecting hubs in correlated data with evolving correlations.
method Geometric QHD tests combining QCD and QHD, clustering.
result Improved hub detection in correlated data.
Study finds almost contact structures in thermal QCD-like theories at intermediate coupling.
problem Understanding (Almost) Contact Structures in thermal QCD-like theories.
method Explicitly obtained (Almost) Contact Structures and SU(3) structures.
result Subspaces of C3S and AC3S are not mutually 'N-path connected' in the Infra-Red.
Study of M-theory dual of thermal QCD-like theories at intermediate coupling.
problem Missing top-down holographic dual for thermal QCD-like theories at intermediate 't Hooft coupling.
method Analysis of O(R4) corrections and O(lp6) corrections in the MQGP background. result Discovery of O(R4) corrections and G-structure classification of underlying geometries. We show that the baryon number of N=2 supersymmetric QCD can be twisted in order to couple the topological field theory of non-abelian monopoles to Spinc-structures. To motivate the construction, we also consider some aspects of the twisting procedure as a gauging of global currents in two and four dimensions, in pa…
Compactification of AdS5 allows studying meson behavior in QCD.
problem Understanding meson behavior in Quantum Chromodynamics (QCD).
method Deforming AdS5 metric to model Coulomb interaction between charges.
result Proposed conformal deformation provides a quantum mechanical description of mesons.
Many four-dimensional supersymmetric compactifications of F-theory contain gauge groups that cannot be spontaneously broken through geometric deformations. These "non-Higgsable clusters" include realizations of SU(3), SU(2), and SU(3)×SU(2), but no SU(n) gauge groups or factors with n>3. We study poss…
We obtain the best known quantitative estimates for the Lp-Poincaré and log-Sobolev inequalities on domains in various sub-Riemannian manifolds, including ideal Carnot groups and in particular ideal generalized H-type Carnot groups and the Heisenberg groups, corank 1 Carnot groups, the Grushin plane, and various H…
New method uses neural maps to efficiently sample lattice QCD distributions.
problem Challenges in sampling Boltzmann distributions of lattice field theories.
method Sparse triangular transport maps exploiting conditional independence structure of lattice graphs.
result Sparse triangular maps achieve efficient sampling with linear time complexity in lattice size.
Jets from boosted heavy particles have a typical angular scale which can be used to distinguish them from QCD jets. We introduce a machine learning strategy for jet substructure analysis using a spectral function on the angular scale. The angular spectrum allows us to scan energy deposits over the angle between a pair …
Recent progress in applying machine learning for jet physics has been built upon an analogy between calorimeters and images. In this work, we present a novel class of recursive neural networks built instead upon an analogy between QCD and natural languages. In the analogy, four-momenta are like words and the clustering…
Non-parametric estimators improve quickest changepoint detection under irregular sequence lengths.
problem Limited and irregular sequence lengths hinder application of ARL and ADD in QCD.
method Analogies with survival analysis to model detection probabilities under truncation.
result KM-ARL and KM-ADD non-parametric estimators are asymptotically unbiased.
Improved diffusion models for manifold learning.
problem Learning distributions on general manifolds with geometric complexity.
method Revised approximations for score matching on symmetric spaces.
result Improved performance and scalability to high dimensions.
Deep learning enhances Hamiltonian Monte Carlo for sampling gauge field configurations.
problem Sampling from complex gauge field topologies efficiently.
method Stacked neural networks to generalize Hamiltonian Monte Carlo.
result Significantly reduces computational cost for generating gauge field configurations.
We study the path integral of a twisted N=2 supersymmetric Yang-Mills theory coupled with hypermultiplet having the bare mass. We explicitly compute the topological correlation functions for the SU(2) theory on a compact oriented simply connected simple type Riemann manifold with b2+≥3. As the corollaries,…
Non-trivial obstructions found for topological solitons in Yang-Mills-Chern-Simons theories.
problem Existence of topological solitons in Yang-Mills-Chern-Simons theories on compact manifolds.
method Cohomological formulations of the calculus of variations, focusing on Yang-Mills-Chern-Simons theories on compact manifolds in odd dimensions.
result Non-trivial obstructions leading to a strong non-existence theorem for topological solitons.
Anomaly Awareness detects anomalies in particle physics and computer vision.
problem Detect anomalies in complex data sets.
method Modifies cost function to learn normal events and anomalies.
result Effective at identifying new anomalies not previously seen.
Study topological twists of massive SQCD with gauge group SU(2) and 3 or fewer fundamental hypermultiplets.
problem Evaluate topological partition functions of massive SQCD with arbitrary gauge bundles and hypermultiplet masses.
method Develop techniques for evaluating low-energy path integrals on the Coulomb branch.
result Formulate theories for arbitrary gauge bundles on compact four-manifolds.
New quantum integrals discovered for a spin chain model.
problem Exploring quantum integrals for a spin chain model.
method Using surface defects and observables in 4D N=2 super-QCD. result First construction of quantum integrals and their joint eigenvectors.
We study solutions of the Bogomolny equation on R^2\times S^1$ with prescribed singularities. We show that Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particu…
Foundation models trained on collider data improve jet generation tasks.
problem Improving foundation models for jet generation tasks.
method Pre-training OmniJet-α model on AspenOpenJets dataset. result Pre-trained model improves performance on jet generation tasks with domain shift.
Study evaluates topological contributions in massive SQCD on compact 4-manifolds.
problem Analyzing topological path integrals for massive SQCD with up to 3 massive hypermultiplets.
method Decouples hypermultiplets, evaluates massless limit, and merges singularities at Argyres-Douglas points. Uses mass expansions for P2 and K3. result Physical partition functions match mathematical results on Segre numbers of instanton moduli spaces.
We propose a regression algorithm that utilizes a learned dictionary optimized for sparse inference on a D-Wave quantum annealer. In this regression algorithm, we concatenate the independent and dependent variables as a combined vector, and encode the high-order correlations between them into a dictionary optimized for…
Optimizes latency and false alarm probability in change detection problems.
problem Balancing latency and false alarms in non-stationary environments.
method Develops order-optimal change detectors under specified latency and false alarm levels.
result Derives a universal lower bound on latency and develops order-optimal detectors.
Lossy compression of statistical data using quantum annealing.
problem Efficiently compressing statistical floating-point data.
method Representation learning with binary variables, classical optimization of basis vectors, quantum annealing for coefficients, bias correction.
result Quantum annealing shows promising results with 3.5x better compression than neural-network autoencoders.
VAE improves anomaly detection for jet tagging at the LHC.
problem Anomaly detection in jet tagging at the LHC.
method Variational Autoencoder (VAE) trained on background QCD jets, with latent space learning for anomaly detection.
result Outlier Exposed VAE (OE-VAE) achieves excellent results in both sensitivity and decorrelation of jet mass.
Interprets AI model for identifying boosted H → b̄b jets.
problem Difficulty in explaining AI model decisions due to complexity.
method Exploring Interaction Network (IN) model and Neural Activation Pattern (NAP) diagrams.
result NAP diagrams reveal important information about hidden layers' activity.
New construction reveals SU(2)-flavor fields in heterotic M5-brane model.
problem Tackles the emergence of SU(2)-flavor fields in heterotic M5-brane models.
method Classifies super-exceptional field content and works out interactions.
result SU(2)xU(1)-valued scalar and vector fields emerge from probe M2- and M5-branes.
Geometric GNNs improve graph discrimination through GWL.
problem Discriminating geometric graphs embedded in Euclidean space.
method Proposed a geometric version of the Weisfeiler-Leman test (GWL) for geometric graphs.
result Characterized the expressive power of geometric GNNs based on physical symmetries.
Geometric Algebra Transformer (GATr) handles various geometric data types efficiently.
problem Lack of a single architecture for diverse geometric data types.
method GATr uses projective geometric algebra, equivariant to E(3), and is a Transformer architecture.
result GATr outperforms non-geometric and equivariant baselines in various geometric tasks.
Geometric methods study 3-manifold splittings.
problem Studying Heegaard splittings of 3-manifolds.
method Geometric approaches.
result Recent advances in geometric methods.
The differential geometric aspects of Geometric Phases are reviewed.
A geometric triangulation of a Riemannian manifold is a triangulation where the interior of each simplex is totally geodesic. Bistellar moves are local changes to the triangulation which are higher dimensional versions of the flip operation of triangulations in a plane. We show that geometric triangulations of a compac…
Expanding on previous work, this note generalizes geometric structures results.
problem Generalizing geometric structures results.
method Generalization to a class of geometric structures including integrable almost-complex structures.
result Main results generalized to a broader class of geometric structures.
tf_geometric simplifies graph deep learning in TensorFlow.
problem Efficient graph deep learning in TensorFlow.
method Kernel libraries and infrastructures for GNNs.
result tf_geometric supports various graph tasks and provides efficient GNN models.
Geometric Bass martingales linked to Brownian motion and geometric Brownian motion.
problem Modeling continuous martingales with prescribed initial and terminal distributions.
method Developed geometric Bass martingales and established their properties.
result Explicit bijection and representation of geometric Bass martingales.
Study geometric bounds on generalized Ricci flow.
problem No specific problem stated; focuses on bounds.
method Analogous geometric quantities and bounds proven.
result Geometric and analytic bounds established.
Researchers geometrically define asymptotic coordinates in General Relativity.
problem Understanding the asymptotic behavior of relativistic initial data sets.
method Geometrization of asymptotic flatness and analysis of geometric invariants.
result Geometrically defined asymptotic coordinates for mass, energy, momentum, and angular momentum.
GDB bridges geometric states with improved accuracy and generality.
problem Challenges in predicting geometric state evolution in complex systems.
method Geometric Diffusion Bridge (GDB) framework using equivariant diffusion bridges.
result GDB surpasses existing methods in accurately bridging geometric states.
Estimates small eigenvalues for geometrically finite manifolds.
problem Estimating small eigenvalues of Schrödinger operators.
method Geometrically finite manifolds, Riemannian vector bundles.
result Estimates the number of small eigenvalues.
We show that for a strongly convergent sequence of geometrically finite Kleinian groups with geometrically finite limit, the Cannon-Thurston maps of limit sets converge uniformly. If however the algebraic and geometric limits differ, as in the well known examples due to Kerckhoff and Thurston, then provided the geometr…
In this paper we study a collection of jet geometrical concepts, we refer to d-tensors, relativistic time dependent semisprays, harmonic curves and nonlinear connections on the 1-jet space J1(R;M), necessary to the construction of a Miron's-like geometrization for Lagrangians depending on a relativistic time. The geome…
Survey on conservation laws for geometric PDEs.
problem Modeling polyharmonic maps.
method Conservation law approach.
result Overview of conservation laws in geometric PDEs.
Sharp geometric inequalities for free boundary hypersurfaces in balls.
problem Understanding geometric properties of free boundary hypersurfaces in balls.
method Proving a family of sharp geometric inequalities.
result Family of sharp geometric inequalities for free boundary hypersurfaces in balls.
Equivariant networks improve geometric prediction without scalar approximations.
problem Efficiently predicting geometric tensors in real-world scenarios.
method Equivariant networks for geometric prediction.
result Equivariant networks can generalize to unseen systems for geometric prediction.
Combines topological and geometric approaches to data analysis.
problem Understanding when and how geometric objects intersect.
method Connects topological and geometric concepts of curvature.
result Reconceptualizes curvature and links it to hyperconvexity.