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…
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48 results for “integral couplings”
New integrable systems derived from Nijenhuis geometry.
problem Developing new integrable systems from Nijenhuis geometry.
method Constructing a new series of multicomponent integrable PDE systems.
result Many famous integrable systems are contained within the new series.
The coupled KdV-mKdV system arises as the classical part of one of superextensions of the KdV equation. For this system, we prove its complete integrability, i.e., existence of a recursion operator and of infinite series of symmetries.
New equations reveal moduli space rigidity in geometric deformations.
problem Understanding moduli space rigidity in geometric deformations.
method Coupled Hitchin-He equations, Lax pair, nonlinear embedding.
result Moduli space is analytically isomorphic to the classical case for small deformations.
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.
Coupled nonlinear integrable systems are generated from usual zero curvature equation. The relevant Maurer-Cartan forms are constructed by combining suitably chosen matrices (nilpotent, Hadamard, idempotent and k-idempotent) and Lie algebraic elements via Kronecker product. In each case a closure type property among th…
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.
Deep-learning method solves BSVIEs and coupled systems.
problem High-dimensional, time-inconsistent stochastic control problems.
method Trains a neural network to approximate solution fields directly.
result Non-asymptotic error bound and scalable performance.
Finite-dimensional reductions and finite-gap type solutions of multicomponent integrable PDEsmath-ph
The paper solves integrable systems of PDEs, including famous equations.
problem Constructing solutions for multicomponent integrable PDEs.
method Reduction to a finite-dimensional system, using Nijenhuis geometry.
result Animations of multi-component soliton and cnoidal solutions.
Coupled Flow Matchingstat.ML
CPFM integrates dimensionality reduction and reconstruction with flow networks.
problem Learning coupled continuous flows for data and embeddings.
method Coupled flow matching framework with Gromov-Wasserstein objective and dual-conditional flow network.
result CPFM preserves and recovers residual information in latent space.
We recently outlined the vision of "Learning Everywhere" which captures the possibility and impact of how learning methods and traditional HPC methods can be coupled together. A primary driver of such coupling is the promise that Machine Learning (ML) will give major performance improvements for traditional HPC simulat…
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 …
Improved KLMC for sampling under various conditions.
problem Stable simulation of kinetic Langevin dynamics under different parameters.
method Revisited synchronous Wasserstein coupling analysis with stochastic exponential Euler discretization.
result Exponential integrator can simulate kinetic Langevin dynamics in the overdamped regime with proper time acceleration.
We prove that Hamiltonian characteristic classes defined as fibre integrals of powers of the coupling class are algebraically independent for generic coadjoint orbits.
Efficiently factorizes coupled matrix tensor data for better accuracy and speed.
problem Poor computation efficiency in existing N-CMTF algorithms.
method Column-wise element selection to prevent frequent gradient updates.
result More accurate and computationally efficient factorization.
We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's splitting theorem for the integrable system is also studied giving some examples in whic…
BalLOT uses optimal transport for balanced k-means clustering.
problem Balanced -means clustering of data.
method BalLOT is an optimal transport approach to alternating minimization.
result BalLOT provides theoretical guarantees for exact and partial recoveries of planted clusters.
A new model integrates LSTM and copulas for high-dimensional financial data.
problem Modeling high-dimensional dependencies across financial markets.
method Variational LSTM with regular vine copulas.
result Outperforms benchmarks in cross-market portfolio forecasting.
In this paper, we analyze Nash equilibria between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity production. We set out a…
In this note, we present an existence result of a Nash equilibrium between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity…
LR and L+R Systemsmath-ph
We consider coupled nonholonomic LR systems on the product of Lie groups. As examples, we study -dimensional variants of the spherical support system and the rubber Chaplygin sphere. For a special choice of the inertia operator, it is proved that the rubber Chaplygin sphere, after reduction and a time reparametrizat…
We define a non-degenerated Monge-Ampere structure on a 6-manifold associated with a Monge-Ampere equation as a couple (Ω,ω), such that Ωis a symplectic form and ωis a 3-differential form which satisfies ω\wedgeΩ=0 and which is non-degenerated in the sense of Hitchin. We associate with such a couple an almost (pseudo) …
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.
Study predicts electricity prices using LSTM models with feature selection, considering market coupling.
problem Accurate day-ahead electricity price forecasting in coupled markets.
method Hybrid LSTM-based deep learning models with feature selection algorithms.
result Proposed models achieve considerably accurate results in Nordic market.
A new watermarking method corrects bias in language models using maximal coupling.
problem Correcting bias in language model token distributions.
method Maximal coupling to balance bias correction and text quality.
result Outperforms prior techniques in preserving text quality and detectability.
Develop a framework for barycentric projections of optimal transport plans on Riemannian manifolds.
problem Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps.
method Develop a framework for barycentric projections of transport couplings on Riemannian manifolds.
result The intrinsic projection maps each source point to the conditional Fréchet mean of its destination law and is shown to be the best deterministic representative under squared geodesic loss.
We study partition functions of random Bergman metrics, with the actions defined by a class of geometric functionals known as `stability functions'. We introduce a new stability invariant - the critical value of the coupling constant - defined as the minimal coupling constant for which the partition function converges.…
MUSIC learns coupled systems with sparse data and incomplete physics.
problem Learning coupled systems with incomplete physical constraints and missing data.
method Sparsity induced multitask neural network framework integrating partial physical constraints with data-driven learning.
result MUSIC accurately learns solutions to complex coupled systems under data-scarce and noisy conditions.
N=2 Supersymmetric QCD and Four Manifolds; (I) the Donaldson and the Seiberg-Witten Invariantshep-th
We study the path integral of a twisted supersymmetric Yang-Mills theory coupled with hypermultiplet having the bare mass. We explicitly compute the topological correlation functions for the theory on a compact oriented simply connected simple type Riemann manifold with . As the corollaries,…
Jacobi's solution for geodesics on a triaxial ellipsoidphysics.geo-ph
Jacobi solved geodesics on triaxial ellipsoids.
problem Finding the shortest path on a triaxial ellipsoid.
method Numerical evaluation of integrals and solving coupled equations.
result Solution for geodesics on triaxial ellipsoids.
We consider the optimal control problem for null curves in de Sitter 3-space defined by a functional which is linear in the curvature of the trajectory. We show how techniques based on the method of moving frames and exterior differential systems, coupled with the reduction procedure for systems with a Lie group of sym…
We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its application to integration problems. First, we introduce piecewise-polynomial couplin…
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.
New asymmetric kernel methods improve feature learning.
problem Improving feature learning with asymmetric kernels.
method Coupled covariance eigenproblem and Nyström method.
result Empirical evaluations show benefits of KSVD.
The paper characterizes integrability of tensors on manifolds.
problem Analyzing integrability conditions for various tensor types on manifolds.
method Analytical and geometric characterizations of integrability for different tensor types, using Nijenhuis tensors.
result Integrability of tensors is equivalent to algebraic constancy coupled with vanishing of Nijenhuis-type tensors.
We construct a path integral based on the coupling of the Liouville action and the Mabuchi K-energy on a one-dimensional complex manifold. To the best of our knowledge this is the first rigorous construction of such an object and this is done by means of probabilistic tools. Both functionals play an important role resp…
Mathematical structures of non-perturbative topological string theory: from GW to DT invariantshep-th
Mathematical structures link Gromov-Witten to Donaldson-Thomas invariants.
problem Understanding non-perturbative topological string theory.
method Borel summation of Gromov-Witten potential and analysis of Stokes phenomena.
result Stokes phenomena encode Donaldson-Thomas invariants of the resolved conifold.
We give the global mathematical formulation of a class of generalized four-dimensional theories of gravity coupled to scalar matter and to Abelian gauge fields. In such theories, the scalar fields are described by a section of a surjective pseudo-Riemannian submersion over space-time, whose total space carries a Lo…
We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the…
Study of correlated Wigner matrices with BBP transitions.
problem Understanding spectral transitions in correlated Wigner matrices.
method Analyzes a Wigner-type matrix with row/column correlations, decomposes into bulk and outliers, and uses integral operators to model transitions.
result Correlated Wigner matrices exhibit multiple BBP transitions at critical points.
In this study, we introduce a new approach to curve pairs by using integral curves. We consider the direction curve and donor curve to study curve couples such as involute-evolute curves, Mannheim partner curves and Bertrand partner curves. We obtain new methods to construct partner curves of a unit speed curve and giv…
This study compares direct and indirect methods for estimating own funds in life insurance, finding indirect methods more effective under realistic asset-liability coupling.
problem Computing own funds for life insurers using direct and indirect methods in a risk-neutral pricing framework.
method Introduced a novel family of mixed estimators including both direct and indirect methods, integrated into a control variate framework for variance reduction.
result The indirect method is more effective under realistic asset-liability coupling, but neither method is universally superior.
We consider the semi-classical Dirac operator coupled to a magnetic potential on a large class of manifolds including all metric contact manifolds. We prove a sharp local Weyl law and a bound on its eta invariant. In the absence of a Fourier integral parametrix, the method relies on the use of almost analytic continuat…
Study of characteristic numbers in 24-dimensional String manifolds.
problem Characterizing and understanding characteristic numbers of 24-dimensional String manifolds.
method Using Pontryagin numbers, integral basis of String cobordism group, and divisibility results.
result Established 2- and 3-primary divisibilities of characteristic numbers.
It is shown that superpositions of path integrals with arbitrary Hamiltonians and different scaling parameters v ("variances") obey the Chapman-Kolmogorov relation for Markovian processes if and only if the corresponding smearing distributions for v have a specific functional form. Ensuing "smearing" distributions subs…
Simplified uHMC with time integration improves accuracy and efficiency.
problem Improving the efficiency and accuracy of Hamiltonian Monte Carlo algorithms.
method Randomized time integrator for uHMC with stratified Monte Carlo.
result Achieves more accurate approximations with fewer gradient evaluations.
In this paper, we introduce a new approach to non-lightlike curve pairs by using integral curves in Minkowski 3-space. We consider direction curve and donor curve to study non-lightlike curve couples such as involute-evolute curves, Mannheim partner curves and Bertrand partner curves. We obtain new methods to construct…
Covariance shrinkage via stochastic interpolation
problem High-dimensional covariance estimation
method Recasting shrinkage as empirical risk minimization
result Reduces statistical risk through scheduling, flow maps, and early stopping