Synthetic proof shows globally hyperbolic Lorentzian spaces with specific curvature are warped products.
problem Synthetic proof of rigidity for globally hyperbolic Lorentzian spaces.
method Synthetic geometry and warped product analysis.
result Spaces with specific curvature and distance realizer are warped products.
The article classifies and realizes globally exceptional Z2 × Z2-symmetric spaces.
problem Classifying and realizing globally symmetric spaces with specific symmetry groups.
method Detailed classification and realization of exceptional Z2 × Z2-symmetric spaces using Lie groups and Lie algebras.
result A concrete realization of globally exceptional Z2 × Z2-symmetric spaces is provided.
We give a direct global proof for the existence of symplectic realizations of arbitrary Poisson manifolds.
Graph Signal Processing improves stock market volatility forecasting.
problem Forecasting realized volatility in a global stock market context.
method Integrating Graph Signal Processing into the HAR model.
result The proposed model outperforms HAR-type benchmarks.
The paper explores embedding Ricci flow solutions in flag manifolds.
problem Realizing Ricci flow solutions as embedded submanifolds.
method Investigation of invariant metrics in flag manifolds, proving global attractors and non-realizable collapses.
result Certain Ricci flow collapses cannot be embedded in Euclidean spaces.
We consider globally hyperbolic maximal anti de Sitter 3-manifolds M with a closed Cauchy surface S of genus greater than one and prove that any pair of hyperbolic metrics on S can be realized as the boundary metrics of the convex core of a maximal globally hyperbolic anti de Sitter 3-manifold structure on M. T…
The paper constructs and analyzes globally exceptional Z3 x Z3-symmetric spaces for specific Lie groups.
problem Understanding and constructing symmetric spaces for exceptional Lie groups.
method Introduced and used the concept of Γ-symmetric spaces, constructed automorphisms, and determined group structures.
result Explicit constructions and structures of exceptional Z3 x Z3-symmetric spaces for G2, F4, and E6.
We describe the unitary globalization of cohomologically induced modules $A_{\fq}(λ)$. The purpose of the paper is to give a geometric realization of the unitarizable modules. Our results do not constitute a proof of unitarity.
We prove that each special Lorentzian holonomy group (with the exception of those including the isotropy groups of Kähler symmetric spaces with rank greater than one) can be realized as the holonomy group of a globally hyperbolic Lorentzian manifold.
Bayesian realized-GARCH models forecast financial tail risks using two-sided Weibull distribution.
problem Forecasting financial tail risks in volatile markets.
method Adaptive Bayesian Markov Chain Monte Carlo for estimation and forecasting, incorporating sub-sampled realized range and variance.
result Realized-GARCH models with two-sided Weibull distribution outperform other models in tail risk forecasting.
Integrates C-bracket and Vaisman algebroid structures in double field theory.
problem Integration problem of C-bracket and Vaisman algebroid structures in double field theory.
method Introduces pre-rackoid as a global group-like object for infinitesimal algebroid structures, proposes two realizations, and shows reduction to rackoid under strong constraint.
result Reduces pre-rackoid to rackoid under strong constraint of double field theory.
The compact simply connected Riemannian 4-symmetric spaces were classified by J.A. Jim{é}nez. As homogeneous manifolds, these spaces are of the G/H, where G is a connected compact simple Lie group with an automorphism γ~ of oder 4 and H is a fixed points subgroup Gγ of G. In the present article, for t…
Improved tail risk forecasting using realized measures and Bayesian methods.
problem Forecasting tail risk in financial markets.
method Extended Taylor's model with realized measures, using maximum likelihood and Bayesian MCMC methods.
result Bayesian approach outperforms maximum likelihood in forecasting accuracy.
Proofs non-realizability of mapping class group via homeomorphisms, resolves Thurston's conjecture.
problem Non-realizability of mapping class group via homeomorphisms
method Short and elementary proof, rigidity results for actions on Euclidean spaces
result Proof of non-realizability of mapping class group via homeomorphisms
Geometric operators link solutions on different spacetimes.
problem Comparing solutions on different globally hyperbolic manifolds.
method Intertwining operators preserving Hermitian forms.
result Existence of Hadamard states on globally hyperbolic manifolds.
The paper constructs Levi flat structures using structure sheaves and differential complexes.
problem Global solvability and regularity of Levi flat structures.
method Employing formal integrability and differential complexes, the paper constructs a resolution for the structure sheaf.
result Global exactness and Sobolev regularity of the differential complex for Levi flat structures.
The study examines how global economic policy uncertainty affects crude oil futures volatility.
problem Predicting crude oil futures volatility using global economic policy uncertainty.
method Established single-factor and two-factor models under the GARCH-MIDAS framework, tested with rolling-window and fixed-span specifications.
result GEPU changes have stronger predictive power than the GEPU index for crude oil futures volatility.
New method solves Cartan's problem for Lie algebroids and groupoids.
problem Classification of extremal Kähler metrics on surfaces.
method New theory of Lie algebroids and groupoids with structure group and connection.
result Local and complete solutions, symmetries, and moduli spaces determined.
In this paper we discuss the highest weight kr-finite representations of the pair (gr,kr) consisting of gr, a real form of a complex basic Lie superalgebra of classical type g (g=A(n,n)), and the maximal compact subalgebra kr of gr,0, together …
We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifolds, based on Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a vector bundle with flat connection.
We show that the metrical connection can be introduced in the two-dimensional Finsler space such that entailed parallel transports along curves joining points of the underlying manifold keep the two-vector angle as well as the length of the tangent vector, thereby realizing isometries of tangent spaces under the parall…
Model forecasts global stock market volatility using dynamic graphs and all trading days.
problem Enhance forecasting accuracy and practical utility in global stock market volatility.
method Spatial-temporal graph neural network architecture to capture volatility spillover effect.
result Forecasting performance surpasses baseline models in all scenarios.
We present a systematic study of symmetries, invariants and moduli spaces of classes of coframes. We introduce a classifying Lie algebroid to give a complete description of the solution to Cartan's realization problem that applies to both the local and the global versions of this problem.
New method for private density estimation of high-dimensional Gaussian mixtures.
problem Private density estimation for mixtures of unrestricted high-dimensional Gaussians.
method Exploits list global stability to prove upper bound on sample complexity.
result First upper bound on sample complexity for agnostic private density estimation.
For an almost complex structure J in dimension 6 with nondegenerate Nijenhuis tensor NJ, the automorphism group G=Aut(J) of maximal dimension is the exceptional Lie group G2. In this paper we establish that the sub-maximal dimension of automorphism groups of almost complex structures with nondegenerate NJ,…
New ambient metrics reveal properties of Walker metrics.
problem Characterizing Walker metrics using ambient metrics.
method Developed Fefferman-Graham ambient metrics for Walker metrics.
result Walker metrics have vanishing Q-curvature.
The paper solves curvature problems on graphs using a special flow.
problem Solving curvature problems on finite graphs.
method Defined the Calabi flow for a specific curvature type and established its global existence and convergence.
result The solution to the Calabi flow exists globally and converges under certain conditions.
Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra combinatorial structures on T. We then analyze how to change these extra structures…
New systemic risk indicator measures stock market reactions globally.
problem Analyzing systemic risk in diverse financial markets.
method Implied and realized volatility approach, focusing on historical and long-term volatility.
result IVRVSRI shows varying stock market reactions and shock persistence across locations.
Characterizes conical angles for metrics with dihedral symmetry.
problem Understanding metrics with specific symmetry properties.
method Using recent results on local invariants of quadratic differentials.
result Complete characterization of conical angles for dihedral spherical metrics.
We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface S can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover such a polyhedron is unique, up to global isometries, among convex polyhedra invar…
Deep ReLU networks with extra parameters have mostly good loss landscapes.
problem Finding good local minima in the loss landscape of deep neural networks.
method Analyzing shallow and deep ReLU networks with extra parameters on a generic dataset.
result Most activation patterns correspond to regions with no bad local minima.
A complex structure on a subset of S^6 cannot be extended to a global integrable structure.
problem Non-integrability of complex structures on subsets of S^6.
method Proving the non-integrability of extensions of a specific complex structure on a subset of S^6.
result It is impossible to deform a non-integrable structure to an integrable one on S^6 while fixing it on a subset.
We bound two global invariants of cusped hyperbolic manifolds: the length of the shortest closed geodesic (the systole), and the radius of the biggest embedded ball (the inradius). We give an upper bound for the systole, expressed in terms of the dimension and simplicial volume. We find a positive lower bound on the in…
We present a constructive approach to surface comparison realizable by a polynomial-time algorithm. We determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solut…
This paper improves land cover classification using global spatial features in CNN.
problem Limited classification accuracy and universality of traditional remote sensing image classification methods.
method Integrates global spatial features into a dual-branch CNN for hyperspectral/SAR imagery classification.
result The proposed method outperforms traditional single-channel CNN methods.
The paper proves a smooth Birman-Hilden theorem for hyperkähler manifolds.
problem Understanding the smooth mapping class groups of certain 4-manifolds.
method Geometric and Teichmüller-theoretic methods.
result Proves a global Torelli theorem for generalized Enriques manifolds.
Polynomial chaos surrogates handle intrinsic noise in stochastic models.
problem Handling intrinsic noise in stochastic models with parametric uncertainty.
method Developed a PCE surrogate on a joint space of intrinsic and parametric uncertainty using Rosenblatt transformations and Karhunen-Loeve expansion.
result Quantified intrinsic noise contribution to model output variance using PCE Sobol indices.
Develops a neural network for global minimum variance portfolio optimization.
problem Minimizing portfolio variance for large equity covariance matrices.
method Rotation-invariant neural network that learns lag-transformed returns and covariance regularization.
result End-to-end trained model outperforms competitors in realized volatility and Sharpe ratios.
AEN-RBF kernel improves robustness in Bayesian optimization for complex systems.
problem Bayesian optimization struggles with outliers in RBF kernel, leading to poor performance.
method Proposes AEN-RBF kernel function, demonstrating improved robustness and convergence.
result The AEN-RBF kernel function reduces mean squared prediction error and improves convergence.
The paper addresses rigid alignment of noisy patches, providing a polynomial time algorithm and convergence conditions.
problem Finding a rigid alignment of overlapping local views (patches) that minimizes alignment error in a noisy setting.
method Characterizes non-degeneracy based on kernel and positivity of a matrix, provides polynomial time algorithm for testing non-degeneracy, and uses Riemannian gradient descent for alignment.
result The algorithm converges locally linearly to a non-degenerate perfect alignment under certain conditions.
In this paper, finite type domains with hyperbolic orbit accumulation points are studied. We prove, in case of C2, it has to be a (global) pseudoconvex domain, after an assumption of boundary regularity. Moreover, one of the applications will realize the classification of domains within this class, precisel…
Study convex hyperbolic cone-metrics on 3-manifold boundaries, proving unique bent realizations.
problem Convex hyperbolic cone-metrics on 3-manifold boundaries and their bent realizations.
method Alexandrov-Weyl-type problem, bent metrics, controllably polyhedral, Lipschitz topology.
result Unique bent realizations for convex hyperbolic cone-metrics on 3-manifold boundaries.
The study examines attractors in Cartan foliations and their properties.
problem Existence of attractors in Cartan foliations.
method Reduction of the problem to the action of Lie groups and holonomy groups.
result Conditions for the existence of attractors in reductive Cartan foliations.
New counterexamples found to cosmic censor conjecture in 4D.
problem Cosmic censor conjecture in 4D physics.
method Constructing non-globally hyperbolic Lorentzian 4-manifolds using exotic and self-dual spaces.
result Found physical counterexamples to the strong cosmic censor conjecture.
This paper tackles global Nash equilibrium in non-convex multi-player games.
problem Challenges in finding global Nash equilibrium due to non-convexity.
method Conjugate transformation and variational inequality formulation to prove existence and design algorithms.
result Designs an ODE-based algorithm with exponential convergence rate and proves its effectiveness in practical scenarios.
Optimization geometrodynamics simplifies adaptive optimizer dynamics.
problem Hidden states in adaptive optimizers complicate gradient-based learning.
method Develops a variational theory to eliminate hidden states and compose across hierarchies.
result Yields interaction curvature that integrates to finite contrasts.
The paper formalizes and analyzes multi-agent Q-learning with value factorization.
problem Understanding and improving the convergence of multi-agent Q-learning with value factorization.
method Formalized a multi-agent fitted Q-iteration framework for analyzing factorized multi-agent Q-learning.
result Multi-agent Q-learning with linear value factorization can converge under certain conditions.