Study calculates global sections on complex curves.
problem Global sections of chiral de Rham complexes on complex curves.
method Calculation on closed complex curves with genus g ≥ 2.
result Space of global sections determined.
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48 results for “global complexity”
Study describes global sections of chiral de Rham complex on compact Ricci-flat Kähler manifolds.
problem None explicitly stated; focuses on description of global sections.
method Complete description of vertex algebra of global sections.
result Complete description of vertex algebra of global sections of chiral de Rham complex.
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.
Study local and global aspects of complex plane curve embeddings.
problem Local and global problems of complex plane curve embeddings.
method Braid monodromy, local and global analysis.
result Historical progress in understanding complex plane curve embeddings.
Paper proves a quantitative estimate for transforming almost complex structures into standard ones.
problem Transforming almost complex structures into standard ones on bounded domains.
method Proves existence of global diffeomorphisms under Hölder-Zygmund conditions.
result Existence of a global diffeomorphism in a specified Hölder-Zygmund class.
In "Width complexes for knots and 3-manifolds," Jennifer Schultens defines the width complex for a knot in order to understand the different positions a knot can occupy in the 3-sphere and the isotopies between these positions. She poses several questions about these width complexes; in particular, she asks whether the…
Researchers found the global topology of the Eisenstein-Picard modular surface.
problem Understanding the global topology of the Eisenstein-Picard modular surface.
method Quotient space of the complex hyperbolic plane by the modular group.
result Determined the global topology of the Eisenstein-Picard modular surface as a 4-orbifold.
Groups with special properties always have fixed points.
problem Groups acting on finite CW-complexes without fixed points.
method Exhibited specific groups with strong fixed-point properties.
result Groups with finite generation and torsion-freeness have global fixed points.
The space of the global sections of chiral de Rham complex on a compact Ricci-flat Kähler manifold is calculated and it is expressed as an invariant subspace of a system under the action of certain Lie algebra.
Improved convergence for actor-critic algorithms in MDPs.
problem Global convergence analysis for actor-critic algorithms in MDPs.
method Introduced an analytical framework to handle complex recursions, established convergence to ε-close globally optimal policy with improved sample complexity.
result Converges to ε-close globally optimal policy with sample complexity of O(ε^(-3)) compared to O(ε^(-2)) for ε-close stationary policy.
Spherical arc-length as a global conformal parameter for analytic curves in the Riemann spheremath.CV
We prove that for every analytic curve in the complex plane, Euclidean and spherical arc-lengths are global conformal parameters. We also prove that for any analytic curve in the hyperbolic plane, hyperbolic arc-length is also a global parameter. We generalize some of these results to the case of analytic curves in Euc…
Global models outperform univariate benchmarks in complex time series forecasting.
problem Comparing global forecasting models to univariate benchmarks in various challenging scenarios.
method Simulated datasets with controlled characteristics, including homogeneity, complexity, and series lengths. Global forecasting models (RNN, LGBM) compared to univariate techniques.
result Global models like RNN and LGBM are competitive in complex scenarios with short series lengths and heterogeneous data.
New algorithm trains deep neural networks without global optimization.
problem Training deep neural networks efficiently and without global optimization.
method Uses random complex exponential activation functions and Markov Chain Monte Carlo sampling.
result Consistently attains theoretical approximation rate for residual networks.
We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local kinematic formulas on such spaces were recently obtained. While the local and global k…
The paper provides results regarding the computational complexity of hybrid system identification. More precisely, we focus on the estimation of piecewise affine (PWA) maps from input-output data and analyze the complexity of computing a global minimizer of the error. Previous work showed that a global solution could b…
We give nearly matching upper and lower bounds on the oracle complexity of finding -stationary points () in stochastic convex optimization. We jointly analyze the oracle complexity in both the local stochastic oracle model and the global oracle (or, statistical learning) model. This allows u…
New topological complexity measures for neural networks.
problem Measuring complexity of neural network functions.
method Generalized piecewise-linear Morse theory applied to ReLU networks.
result Local complexity can be arbitrarily high.
A classical result of D. McDuff asserts that a simply-connected complete Kaehler manifold with non positive sectional curvature admits global symplectic coordinates through a symplectomorphism (where is the complex dimension of ), satisfying the following property (proved by E.…
Let $M\subset{\complex}^n$ be a complex domain of ${\complex}^n$ endowed with a rotation invariant \K form . In this paper we describe sufficient conditions on the \K potential for to admit a symplectic embedding (explicitely described in terms of ) into a compl…
An application of Cartan's equivalence method to Hirschowitz's conjecture on the formal principlemath.AG
A conjecture of Hirschowitz's predicts that a globally generated vector bundle on a compact complex manifold satisfies the formal principle, i.e., the formal neighborhood of its zero section determines the germ of neighborhoods in the underlying complex manifold of the vector bundle . By applying Cartan's eq…
The paper proves global invertibility for certain local diffeomorphisms and biholomorphisms in higher dimensions.
problem Global invertibility of local diffeomorphisms and biholomorphisms in higher dimensions.
method The approach uses conformal geometry, complex analysis, elliptic PDEs, and topology.
result The main theorem guarantees global invertibility for specific local diffeomorphisms and biholomorphisms in higher dimensions.
Study presents a twistor correspondence for specific geometric structures.
problem Twistor theory for almost-Grassmannian manifolds.
method Utilizes moduli of curves-with-boundary for global correspondence.
result Foundational results in complex setting, global correspondence for real Grassmannian.
Complete complex parabolic geometries (including projective connections and conformal connections) are flat and homogeneous. This is the first global theorem on parabolic geometries.
Global methods outperform local in forecasting groups of time series, even in heterogeneous datasets.
problem Forecasting groups of time series, especially in heterogeneous datasets.
method Local methods consider each series separately, global methods fit a single model to all series.
result Global methods can outperform local methods in forecasting groups of time series, even in heterogeneous datasets.
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.
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.
This work develops a novel power control framework for energy-efficient power control in wireless networks. The proposed method is a new branch-and-bound procedure based on problem-specific bounds for energy-efficiency maximization that allow for faster convergence. This enables to find the global solution for all of t…
The paper develops residue currents for cohesive modules and proves a generalized Poincaré-Lelong formula.
problem Analyzing coherent sheaves on complex manifolds using global analytic methods.
method Developing residue currents for cohesive modules and proving their properties.
result Proves a generalized Poincaré-Lelong formula for cohesive modules.
Proof shows local convexity implies global convexity in special geometric spaces.
problem Proving convexity in CAT(0) cubed complexes from local convexity.
method Analyzes vertex link structures to determine convexity.
result Local combinatorial properties determine global convexity.
The article resolves complex structures in transport twistor spaces, proving a Newlander-Nirenberg theorem.
problem Degenerate complex structures in transport twistor spaces.
method Holomorphic blow-down structure maps to resolve degeneracy and gain insight into complex geometry.
result Global and local β-maps for various metrics, proving a Newlander-Nirenberg theorem for degenerate complex structures.
New method uses LP to achieve optimal sample complexity in multi-agent reinforcement learning.
problem Achieving global optimality in multi-agent reinforcement learning with average-cost criterion.
method Randomized Linear Programming and Stochastic Primal-Dual Methods for multi-agent saddle point problems.
result Sample complexity matches tight dependencies on state and action spaces, and scales with network size.
We apply ideas from viscosity theory to establish the existence of a unique global weak solution to the generalized Kahler-Ricci flow in the setting of commuting complex structures. Our results are restricted to the case of a smooth manifold with smooth background data. We discuss the possibility of extending these res…
Employing Morse theory for the global control of monodromy and the method of analytic discs for local extension, we establish a version of the global Hartogs extension theorem in a singular setting: for every domain D of an (n-1)-complete normal complex space X of pure dimension n >= 2 and for every compact set K in D …
Finite Sample Complexity of Sequential Monte Carlo Estimators on Multimodal Target Distributionsstat.CO
New bounds for SMC show its advantage over MCMC in multimodal distributions.
problem Estimating expectations under multimodal distributions with slow global mixing.
method Proves finite sample complexities for SMC with local mixing times, addressing bias through sequential resampling.
result SMC provides fully polynomial time approximation for multimodal problems.
Solves Calabi-Yau equation on symplectic manifolds using measurable Kahler metrics.
problem Solving the Calabi-Yau equation on symplectic manifolds.
method Global deformation of almost complex structures compatible with symplectic form, constructing measurable Lipschitz Kahler metric.
result Existence theorem for solutions to the one-form type Calabi-Yau equation on closed symplectic manifolds.
With globalization, countries are more connected than before by trading flows, which currently amount to at least 36 trillion dollars. Interestingly, approximately 30-60 percent of global exports consist of intermediate products. Therefore, the trade flow network of a particular product with high added values can be re…
Global Value Treesq-fin.GN
The fragmentation of production across countries has become an important feature of the globalization in recent decades and is often conceptualized by the term, global value chains (GVCs). When empirically investigating the GVCs, previous studies are mainly interested in knowing how global the GVCs are rather than how …
Study on Einstein metrics on complex projective spaces with specific group actions.
problem Finding Einstein metrics invariant under cohomogeneity one Lie group actions.
method Analyzing Einstein equation for diagonal invariant metrics under five Takagi models.
result Nonexistence of smooth globally defined invariant Einstein metrics in four models, necessary condition in the fifth.
Let be a close complex manifold and its holomorphic tangent bundle. We prove that if the global holomorphic sections of tangent bundle generate each fibre, then is a complex homogeneous manifold. Our proof depends on the complex version of Chow-Rashevskii theorem in Carnot-Caratheodory spaces.
Gradients help find global optima in complex functions.
problem Finding global optima in functions with many local minima.
method A principle for generating search directions from non-local quadratic approximants based on gradients.
result The proposed algorithm and CMA-ES perform better than random reinitialized BFGS.
Geometric approach to Dirac operator evolution on spacetimes.
problem Constructing the Cauchy evolution operator for Lorentzian Dirac operators.
method Realizing the operator as a sum of oscillatory integrals, relating to Feynman propagator.
result Relating Cauchy evolution operators to Feynman propagators and constructing Hadamard states.
Feature maps, that preserve the global topology of arbitrary datasets, can be formed by self-organizing competing agents. So far, it has been presumed that global interaction of agents is necessary for this process. We establish that this is not the case, and that global topology can be uncovered through strictly local…
Active learning method improves sensitivity analysis of complex models.
problem Limited model evaluations in global sensitivity analysis.
method Gradient-based active learning with Gaussian process.
result Improves sensitivity analysis accuracy with reduced evaluations.
Global Chern currents and Baum Bott currents defined on arbitrary complex manifolds.
problem Defining Chern classes and Baum Bott residues on complex manifolds without global resolutions.
method Combining Green's techniques with previous constructions to yield representatives of Chern classes and Baum Bott residues, using local resolutions and metrics.
result Transgression formula for the representatives, showing they differ by a current of the form .
We describe the global structure of holomorphic webs in codimension one, and in particular their singularity (caustic). Various concepts are introduced, which have no interest locally near a regular point, such as the type, the reducibility, the quasi-smoothness, the CI property (complete intersection), the dicriticity…
Study on stability and continuity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds.
problem Stability and continuity of solutions to degenerate complex Monge-Ampère equations.
method Analysis of Hölder continuity and global continuity of solutions.
result Established uniform diameter bound for the twisted Chern-Ricci flow.
We study compact complex 3-manifolds admitting holomorphic Riemannian metrics. We prove a uniformization result: up to a finite unramified cover, such a manifold admits a holomorphic Riemannian metric of constant sectionnal curvature.
FS&P uses birth-death process to ensure global convergence of stochastic conic particle gradient descent.
problem Global optimization of non-convex objective functions over measure space.
method Introduces Fast Spawn\&Prune (FS\&P) combining CPGD with birth-death process.
result First theoretical guarantee of global convergence for discrete-time stochastic algorithms.