Motivated by the study of coupled Kähler-Einstein metrics by Hultgren and Witt Nyström and coupled Kähler-Ricci solitons by Hultgren, we study in this paper coupled Sasaki-Einstein metrics and coupled Sasaki-Ricci solitons. We first show an isomorphism between the Lie algebra of all transverse holomorphic vector fields…
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48 results for “coupling”
Coupled embeddabilitymath.GT
Defines coupled embeddability for maps on products of spaces, generating examples and nonexamples.
problem Understanding when maps on products of spaces can be embedded.
method Uses known results for nonsingular biskew and bilinear maps, studies genericity properties, extends Whitney embedding theorems, and relates to -coindex of embedding spaces.
result Generates strong obstructions to coupled embeddability in terms of combinatorics of triangulations.
Solves modified conjecture for Fano manifolds using Ding stability.
problem Finding Kähler-Einstein metrics on Fano manifolds.
method Interprets Ding semistability and solves modified conjecture.
result Solves modified conjecture for coupled Kähler-Einstein metrics on Fano manifolds.
UNTIE learns representations of coupled categorical data.
problem Challenges in learning from unlabeled categorical data with complex couplings.
method UNTIE approach for unsupervised representation learning of heterogeneous couplings.
result UNTIE significantly improves categorical data representations on 25 diverse datasets.
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.
Develops non-Markovian couplings for sub-Riemannian Brownian motions.
problem Constructing couplings for sub-Riemannian Brownian motions starting from points on the same vertical fiber.
method Uses global isometries to construct maximal couplings, satisfying a reflection principle.
result Estimates coupling time and applies to inequalities for the heat semigroup.
Numerical observations on martingale couplings are confirmed under certain conditions.
problem Understanding the validity of numerical observations on maximizers and minimizers of martingale couplings.
method Investigation of sufficient conditions and counterexamples for the property to hold.
result The non-decreasing property of martingale couplings is preserved for maximizers under specific conditions.
Compositional diffusion models simulate coupled PDEs efficiently.
problem Efficiently simulating long-horizon coupled PDE systems.
method Diffusion models trained on decoupled data are composed at inference time.
result Compositional diffusion models recover coupled trajectories with low error.
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and…
Unified analytic account of correlation emergence and Epps effect in coupled limit order books
problem Correlation emergence and Epps effect in coupled limit order books
method Discrete random-walk description of order flow with creation, cancellation, and diffusion, coupled reaction-diffusion equations with moving reaction boundary
result Realized correlations as a function of aggregation time
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.
We introduce the coupled Ricci-Calabi functional and the coupled H-functional which measure how far from a coupled Kähler-Einstein metric in the sense of Hultgren-Witt Nyström. We first give corresponding moment weight type inequalities which estimate each functional in terms of algebraic invariants. Secondly, we give …
Vortices and coupled vortices arise from Yang-Mills-Higgs theories and can be viewed as generalizations or analogues to Yang-Mills connections and, in particular, Hermitian-Yang-Mills connections. We proved an analytic compactification of the moduli spaces of vortices and coupled vortices on hermitian vector bundles ov…
Two probability distributions and in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are al…
Paper proposes an algorithm for PARAFAC2-based CMTF models with various constraints.
problem Jointly analyze matrices and tensors with irregular/ragged data.
method Alternating Optimization (AO) and ADMM for fitting PARAFAC2-based CMTF models with various constraints.
result Accurately recovers underlying patterns using various constraints and linear couplings.
Coupled entropy corrects flaws in Tsallis entropy for complex systems.
problem Misinterpretation of generalized temperature and entropy.
method Derived from generalized Pareto and Student's t distributions.
result Provides balanced measure of uncertainty for complex systems.
The paper introduces new equations in Kähler geometry and proves their solutions and convexity.
problem Solving equations in Kähler geometry and understanding their geometric implications.
method Using moment map pictures to motivate and prove solutions for the equations.
result The Mabuchi functional for certain equations is shown to be convex.
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.
Using methods of statistical physics, we analyse the error of learning couplings in large Ising models from independent data (the inverse Ising problem). We concentrate on learning based on local cost functions, such as the pseudo-likelihood method for which the couplings are inferred independently for each spin. Assum…
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.
Stochastic Schwarz lemma on Kähler manifolds via couplings.
problem Develop a new Schwarz lemma for Kähler manifolds.
method Probabilistic approach using Markovian couplings.
result Improved gradient estimates for harmonic functions.
Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode properties, which ensures the uniformity of decomposed factors and mode attribut…
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.
Let be a solution to the Ricci flow coupled with the heat equation for a scalar field . We show that a complete, -noncollapsed solution to this coupled Ricci flow with a Type I singularity at time will converge to a non-trivial Ricci soliton after parabolic rescaling, if the base po…
Unified framework for Brownian motion distances on specific geometric manifolds.
problem Understanding Brownian motion distances on radially isoparametric manifolds.
method Developed a geometric framework and derived drift-window inequalities.
result Unified framework for coadapted Brownian couplings on RIM.
Paper proves convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
problem Proving convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
method Differentiation-based approach to handle Z process, uniformly controlling Lipschitz continuity of decoupling fields.
result Proves convergence of Markovian iteration method for FBSDEs with fully coupled drift and Z process.
Solves Dirac equation coupled to vector bundles.
problem Yang-Mills equations and vector bundles on Riemann surfaces.
method Analyzes coupled Dirac operators.
result Provides concrete solutions to the Dirac equation.
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.
The goal of this paper is to re-examine D-brane Ramond-Ramond field couplings in the presence of a B-field. We will argue that the generalised geometry induced on the world volume by the B-field results in an important but subtle change on the coupling. In order to explain this, we use the language of differential K-th…
New MCMC method tackles label-switching problem for clustering.
problem Label-switching problem impedes MCMC efficiency in discrete clustering.
method Formulated optimal transport couplings for partition space.
result Our method efficiently overcomes label-switching problem.
We present a coupled Variational Auto-Encoder (VAE) method that improves the accuracy and robustness of the probabilistic inferences on represented data. The new method models the dependency between input feature vectors (images) and weighs the outliers with a higher penalty by generalizing the original loss function t…
Study finds optimal martingale coupling between two distributions with minimal entropy.
problem Finding the optimal martingale coupling between two distributions with minimal relative entropy.
method Solving a dual problem to find the log-density of the optimal coupling, which represents the marginal and martingale constraints.
result The log-density of the optimal coupling is given by a triplet of real functions representing the marginal and martingale constraints.
Bounds on Hessian of heat equation coupled with Ricci flow.
problem Estimating the Hessian of a solution to the conjugate heat equation coupled with Ricci flow.
method Obtained upper bounds for the Hessian.
result Local and global upper bounds for the Hessian of a positive solution.
Weak Convergence of Approximate reflection coupling and its Application to Non-convex Optimizationmath.PR
Paper proposes a weak approximation of reflection coupling for non-convex optimization.
problem Non-convex optimization problems with different drift terms.
method Proposes an approximate reflection coupling (ARC) for stochastic differential equations (SDEs).
result ARC converges weakly to the reflection coupling and can be applied to non-convex optimization.
SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.
problem Proving geometric ergodicity of SGLD in nonconvex, log-concave settings.
method Reflection coupling technique to handle SGLD's time discretization and minibatch issues.
result SGLD has an invariant distribution and geometric ergodicity in distance.
New method uses coupled SDEs to edit images with high fidelity and consistency.
problem Challenges in editing image content with text-to-image models.
method Using coupled stochastic differential equations to guide generative model sampling.
result Achieves high prompt fidelity and near-pixel-level consistency.
5D SCFTs can have confining vacua with strings and unbroken symmetries.
problem Investigating phases of 5D SCFTs by varying couplings.
method Using geometric realisation of M-theory on metrically conical Calabi-Yau threefolds.
result Many 5D SCFTs have couplings leading to massive, confining vacua with strings and unbroken symmetries.
We provide a moment map interpretation for the coupled Kähler-Einstein equations introduced by Hultgren and Witt Nyström, and in the process introduce a more general system of equations, which we call coupled cscK equations. A differentio-geometric formulation of the corresponding Futaki invariant is obtained and a not…
Coupling by reflection of diffusion processes via discrete approximation under a backward Ricci flowmath.PR
A coupling by reflection of a time-inhomogeneous diffusion process on a manifold are studied. The condition we assume is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow. As in time-homogeneous cases, our coupling provides a gradient esti…
Study finds critical points of volume functionals on Sasaki manifolds.
problem Finding Kähler-Einstein metrics on Sasaki manifolds.
method Revisited moment polytopes, applied to volume minimization.
result Transverse coupled Kähler-Einstein metrics found as critical points.
We obtain a residue formula for an obstruction to the existence of coupled Kähler-Einstein metrics described by Futaki-Zhang. We apply it to an example studied separately by Futaki and Hultgren which is a toric Fano manifold with reductive automorphism, does not admit a Kähler-Einstein metric but still admits coupled K…
Novel framework detects lead-lag relationships in Chinese A-share market.
problem Detecting lead-lag relationships in the Chinese A-share market.
method Two-stage framework: long-term coupling via correlation, dynamic time warping, and rank-based metrics; high-frequency data analysis via cross-correlation, Granger causality, and regression models.
result Strongly coupled stock pairs often exhibit lead-lag effects, especially at finer time scales.
New examples found of complex manifolds with special metrics.
problem Existence of Kähler-Einstein metrics on certain complex manifolds.
method Using Hultgren's polytope formulation, constructing explicit examples of toric Fano manifolds.
result Found examples of projective bundles that admit coupled Kähler-Einstein metrics but no ordinary Kähler-Einstein metrics.
New proof shows coupling-based flows converge linearly to diagonalize data covariance.
problem Understanding convergence of coupling-based normalizing flows to arbitrary data distributions.
method Proved linear convergence rate for whitening of data distribution.
result Coupling-based flows achieve linear convergence to diagonalize data covariance.
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.
Paper proposes a coupling-based diagnostic for SGD stepsize optimization.
problem Optimizing stepsize for SGD convergence.
method Coupling-based convergence diagnostic for monitoring stationarity.
result Proposed stepsize scheme achieves superior performance across convex and non-convex problems.
Theory for gravity coupled with fields on manifolds with null-boundary.
problem Formulating a theory for gravity coupled with scalar, SU(n), and spinor fields on manifolds with null-boundary.
method Symplectic reduction of boundary fields and constraints analysis.
result The set of constraints does not form a first class system for the three couplings.
Coupled uncertainty provided by a multifractal random walkerphysics.data-an
The aim here is to study the concept of pairing multifractality between time series possessing non-Gaussian distributions. The increasing number of rare events creates "criticality". We show how the pairing between two series is affected by rare events, which we call "coupled criticality". A method is proposed for stud…