We review coupled -structures, also known in the literature as restricted half-flat structures, in relation to supersymmetry. In particular, we study special classes of examples admitting such structures and the behaviour of flows of -structures with respect to the coupled condition.
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48 results for “Structured Couplings”
Paper discusses conditions for deforming coupled Kähler-Einstein metrics.
problem Conditions for deforming coupled Kähler-Einstein metrics.
method Analyzes deformation of coupled Kähler-Einstein metrics on Fano manifolds.
result Necessary and sufficient condition for deformation of coupled Kähler-Einstein metrics.
Coupling Dirac structures are Dirac structures defined on the total space of a fibration, generalizing hamiltonian fibrations from symplectic geometry, where one replaces the symplectic structure on the fibers by a Poisson structure. We study the associated Poisson gauge theory, in order to describe the presymplectic g…
The paper studies properties of group relations induced by compatible coarse structures.
problem Properties of asymptotic resemblance relations on groups.
method Generalization of asymptotic dimension and introduction of set theoretic coupling.
result Groups with compatible coarse structures that admit a set theoretic coupling are asymptotic equivalent.
Study Poisson structures on fibered 5-manifolds with compatibility conditions.
problem Understanding Poisson structures on fibered 5-manifolds.
method Using almost coupling condition and bigraded factorization of the Jacobi identity.
result Describe global behavior and singularities of almost coupling Poisson tensors.
In this paper, we consider half-flat -structures and the subclasses of coupled and double structures. In the general case we show that the intrinsic torsion form is constant in each of the two subclasses. We then consider the problem of finding half-flat structures inducing Einstein metrics on homogeneou…
New model predicts electricity spot and forward prices in coupled markets.
problem Predicting electricity prices in markets with limited interconnection.
method Structural approach to model link between prices, consumption, and production.
result Explicit formulas for forward prices and transmission rights values.
Study of coupled Sasaki-Einstein and solitons metrics.
problem Existence and properties of coupled Sasaki-Einstein and solitons metrics.
method Isomorphism between Lie algebra and space of coupled basic functions, use of coupled twisted Laplacians, reduction to Kähler-Einstein metrics, existence of toric coupled Sasaki-Einstein metrics.
result Existence and properties of coupled Sasaki-Einstein and solitons metrics, reduction to known cases when applicable.
We give sufficient conditions for the existence of a Dirac structure on the total space of a Poisson fiber bundle endowed with a compatible connection. We also show that Cartan and Cartan-Hannay-Berry connections give rise to coupling Dirac structures.
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.
This paper analyzes microstructure dynamics in coupled markets using CFMMs.
problem Quantifying contributions of CFMMs to market dynamics in coupled markets.
method Examined constant function market makers (CFMMs) in coupled markets, focusing on basket inflation/deflation.
result CFMMs contribute significantly to basket inflation/deflation in coupled markets.
New method for faster, scalable inference in coupled Gaussian Processes.
problem Coupled Gaussian Processes require scalable inference methods for posterior uncertainty.
method Structured variational inference for multi-Gaussian Processes.
result Fast and scalable inference capturing posterior dependencies.
New method infers coupling in distributed dynamical systems.
problem Learning structure of coupled dynamical systems.
method Information-theoretic approach using time delay embedding theorems.
result Globally optimal approximations of distribution found.
DS2CF-Net learns hierarchical representations with deep coupled factorization and enriched prior.
problem Learning deep hierarchical representations from data.
method Dual-constrained Deep Semi-Supervised Coupled Factorization Network (DS2CF-Net) with enriched prior.
result DS2CF-Net achieves state-of-the-art performance in representation learning and clustering.
Unified Jacobi coupling construction for various geometric settings.
problem Constructing Jacobi structures on associated bundles.
method Extending Sternberg--Weinstein coupling to Jacobi geometry.
result Associated bundles inherit Jacobi structures from base spaces.
The paper characterizes metallic pseudo-Riemannian manifolds using conjugate connections and tensor structures.
problem Characterizing metallic pseudo-Riemannian manifolds.
method Using conjugate connections and tensor structures, the paper derives new characterizations and conditions for these manifolds.
result A necessary and sufficient condition for a non-integrable metallic pseudo-Riemannian manifold to be a quasi metallic pseudo-Riemannian manifold is derived.
The paper constructs examples of coupled Dirac-Yang-Mills pairs on Riemannian manifolds.
problem Constructing coupled Dirac-Yang-Mills pairs on Riemannian manifolds.
method Constructing spherically symmetric Dirac-Yang-Mills pairs on Riemannian 3-manifolds with SU(2) structure group.
result The construction yields coupled solutions, including on S^1(r_1) x S^2(r_2) for certain radii.
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
In our previous paper (arXiv:1306.5449) we have given a sufficient and necessary condition when the coupling between Lie algebra bundle (LAB) and the tangent bundle exists in the sense of Mackenzie (\cite{Mck-2005}, Definition 7.2.2) for the theory of transitive Lie algebroids. Namely we have defined a new topology on …
The paper maps time-series onto networks to reveal hidden joint information.
problem Extract hidden joint information from uncorrelated time-series.
method Discretize time-series amplitudes, map onto networks, measure coupling deviations, and compare with Gaussian distributions.
result Markets may possess joint patterns even if initially uncorrelated.
New insights connect strong coupling SYM amplitudes to hyperkähler geometry.
problem Understanding strong coupling SYM amplitudes.
method Integrable systems, pseudo-hyperkähler geometry, twistor theory.
result Remainder function is a pseudo-Kähler scalar in hyperkähler geometry.
New equations derived for Kähler metrics, linking stability and curvature.
problem Finding metrics with constant scalar curvature in Kähler geometry.
method Introduced coupled cscK equations and defined K-polystability.
result Proved existence of coupled cscK metrics for small perturbations.
New method identifies network structure without regularization for sparse teacher couplings.
problem Identifying network structure in inverse Ising problems with model mismatch.
method Ridge linear regression with two-stage estimator.
result Perfect identification of network structure possible without regularization for sparse teacher couplings.
Optimal coupling among random vectors with known statistics and correlation structure found using minimum spanning tree over measure-valued vertices.
problem Finding the optimal coupling among random vectors with known statistics and correlation structure.
method Formulating the problem as a minimum spanning tree over measure-valued vertices and solving it in two steps.
result Optimal coupling found using the minimum spanning tree approach.
Deep Learning of Vortex Induced Vibrationsphysics.flu-dyn
Deep neural nets predict vortex-induced vibrations from limited flow data.
problem Predicting lift and drag forces on structures from scattered velocity field data.
method Extended deep neural networks solving coupled Navier-Stokes and structural dynamics equations.
result Deep neural networks can accurately infer structural parameters, pressure field, and velocity field from limited flow data.
Unified framework for coupled tensor completion improves recovery accuracy.
problem Improving recovery accuracy in coupled tensor completion.
method Unified framework using tensor ring (TR) decomposition with shared latent factors and novel optimization model.
result The proposed method achieves superior recovery accuracy on real-world data compared to state-of-the-art methods.
New method designs joint initial noises for diffusion models to improve diversity and alignment.
problem Independent initial noises limit diversity in generated images.
method Coupling of initial noises, maintaining Gaussian distribution while allowing dependence.
result Repulsive Gaussian coupling improves diversity without increasing sampling cost.
The paper analyzes the non-Gaussian behavior of inflation and unemployment over 70 years using multifractal methods.
problem Capturing unusual fluctuations in inflation and unemployment over long periods.
method Coupled multifractal approach to analyze non-Gaussian distributions of inflation and unemployment over 70 years.
result The non-Gaussianity of unemployment is noticeable only for periods smaller than 1 year, while inflation's non-Gaussianity persists across all time scales.
A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplingscs.LG
Flexible framework for CMTF with ADMM for various constraints and couplings.
problem Challenges in data fusion from multiple sources with varying characteristics.
method Flexible algorithmic framework using AO and ADMM for various constraints, loss functions, and couplings.
result Accurate and computationally efficient results for various loss functions, including KL divergence.
Structured Optimal Transportstat.ML
Develops a new optimal transport model capturing complex structures.
problem Limited ability of optimal transport to capture complex structures.
method Develops a nonlinear generalization of optimal transport.
result Demonstrates improved performance in tasks like domain adaptation and natural language processing.
Optimal martingale transport plans without structural assumptions.
problem Finding optimal martingale transport plans.
method Left-monotone martingale coupling and Skorokhod embedding.
result Left-monotone coupling is optimal under specific conditions.
This paper shows how to approximate any log-concave distribution using well-conditioned affine coupling flows.
problem Understanding the representational power of affine coupling flows for log-concave distributions.
method Leveraging connections between affine coupling architectures, Langevin dynamics, and Hénon maps to prove log-concave approximation.
result Any log-concave distribution can be approximated using well-conditioned affine-coupling flows.
New model captures state-dependent variability in partially observed systems.
problem Structured stochasticity not captured by constant-variance models.
method State-coupled stochastic volatility framework with particle expectation-maximization.
result Model consistently reduces recovery bias under partial observation.
In this work we define a deformation theory for the Coupled Kähler-Yang-Mills equations in arXiv:1102.0991, generalizing work of Székelyhidi on constant scalar curvature Kähler metrics. We use the theory to find new solutions of the equations via deformation of the complex structure of a polarised manifold endowed with…
Study infers evolutionary interactions from protein sequences using regularization methods.
problem Inferring evolutionary interactions from protein sequences.
method Regularization methods, including for fields and group for couplings, with parameter tuning.
result Effective regularization parameters for sparse couplings improve accuracy.
Study of -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 corrections and corrections in the MQGP background.
result Discovery of corrections and -structure classification of underlying geometries.
Study lift metrics and connections on tangent bundles of Riemannian manifolds.
problem Investigate geometric properties of tangent bundles and their lifts.
method Analyze lift metrics and connections on of , and study statistical and Codazzi couples.
result Prove a result on -Stein and Osserman structures on .
Proves solutions to Einstein and scalar field constraints form a Hilbert manifold.
problem Proving the structure of solutions to coupled Einstein and scalar field equations.
method Used weighted Sobolev spaces and Implicit Function Theorem.
result The set of solutions has a Hilbert manifold structure.
Improved VAE model enhances image accuracy and robustness.
problem Enhancing accuracy and robustness of VAE models.
method Coupled VAE method with generalized entropy function.
result Improved accuracy and robustness of output images.
We study the moduli space of torsion-free G2-structures on a fixed compact manifold, and define its associated universal intermediate Jacobian J. We define the Yukawa coupling and relate it to a natural pseudo-Kahler structure on J. We consider natural Chern-Simons type functionals, whose critical points give associati…
We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters in…
Study on structures and their moduli space in 7D.
problem Understanding moduli space of structures with torsion.
method Solving a system of partial differential equations related to the Bianchi identity.
result Moduli space of solutions is finite-dimensional.
We define higher genus Gromov-Witten invariants and establish a mathematical theory of sigma model coupled with gravity over any semi-positive symplectic manifolds. As applications, we verify the stablizing conjecture of symplectic 4-manifolds for simply connected elliptic surfaces and construct smooth 6-manifolds admi…
Equations link metrics with tensors, revealing curvature constraints.
problem Understanding curvature properties of geometric structures.
method Formal analogies to Einstein-Maxwell equations, studying Codazzi and conformal Killing equations.
result Constraints on scalar curvature of metrics in solutions.
Efficiently models tree-like data with coupled branches using HMMs.
problem Modeling sequential data with coupled branches in biological systems.
method Developed a dynamic programming algorithm for tree-based HMMs with coupled branches.
result Efficiently solves likelihood, decoding, and parameter learning problems for tree-based HMMs with coupled branches.
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and sufficient additional integrability conditions on a solution. We then discuss a procedure for coupling known solutions of …
Abstract: Geometrically describes Poisson cohomology groups around symplectic leaves.
problem Understanding the first Poisson cohomology groups around symplectic leaves.
method Splitting theorems for infinitesimal automorphisms of coupling Poisson structures.
result Derives criteria for vanishing of first Poisson cohomology groups.
Study reveals geometric context of second-order superintegrable systems.
problem Understanding second-order superintegrable systems and their Weylian geometry.
method Re-examined second-order maximally conformally superintegrable Hamiltonian systems, revealing their Weyl structure.
result Extended conformal superintegrability to Weyl structures, interpreting systems as semi-Weyl structures.