We characterize how to vary the Abel-Jacobi map in terms of Schiffer variation. From this characterization, we will interpret the relation of hyperellipticity of curves with Schiffer variation and describe the deformation of elliptic solitons under Schiffer variation.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
Trend · papers per month
48 results for “Variational characterization”
Characterizes obstacles to variational formulation of Dirac dynamics.
problem Obstacles to variational formulation of Dirac dynamics.
method Characterizes using basic cohomology for Dirac structures and Lie algebroids.
result Characterizes the obstruction to variational formulation.
The study characterizes complex structures using calculus of variations.
problem Variational characterization of complex structures.
method Calculus of variations for real vector bundle valued differential forms.
result Obtains variational characterization of complex structures.
Sheng and Zuo's characteristic forms are invariants of a variation of Hodge structure. We show that they characterize Gross's canonical variations of Hodge structure of Calabi-Yau type over (Hermitian symmetric) tube domains.
This paper characterizes VAE training pathologies and their effects on tasks.
problem Characterizing VAE training pathologies and their impact on downstream tasks.
method Concretely characterizing conditions for VAE training pathologies and their connection to specific downstream tasks.
result Connects VAE training pathologies to specific downstream tasks like learning compressed and disentangled representations, adversarial robustness, and semi-supervised learning.
Variational characterization of calibrated submanifolds in different contexts.
problem Characterize calibrated submanifolds using variational principles.
method Variational approach with special variations of ambient metrics and calibrations.
result Critical points of volume functional correspond to calibrated submanifolds.
New curves defined by curvature powers studied for variational properties.
problem Characterizing translating solitons in curve flows.
method Variational characterization of generalized elastic curves.
result New variational characterization of grim reaper curve.
Characterizes curves for minimal surfaces in de Sitter space.
problem Minimal surfaces in de Sitter space.
method Variational problem to find critical points of center of mass.
result Curves are critical points of center of mass.
We show that degenerate complex Monge-Ampere equations in a big cohomology class of a compact Kaehler manifold can be solved using a variational method independent of Yau's theorem. Our formulation yields in particular a natural pluricomplex analogue of the classical logarithmic energy of a measure. We also investigate…
We define a new formal Riemannian metric on a conformal class in the context of the -Yamabe problem. Our construction leads to a new variational characterization and a new parabolic flow approach to this problem. Moreover, this variational framework suggests that solutions to this problem are unique in…
Variational properties of the total inverse mean curvature in the plane under boundary constraintsmath.DG
Study variational properties of curves in half-plane with area constraints.
problem Characterize critical points of inverse mean curvature.
method Variational analysis of curves with boundary constraints.
result Existence and stability of critical points with prescribed area.
We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and automated variational Gaussian copula approach, in which the parametric Gaussian copul…
New characterization limits sampling with inexact scores.
problem Limiting sampling with inexact scores for unbiased results.
method Characterized types of inexact score oracle access.
result Weaker error assumptions rule out tractability of unbiased sampling.
Characterizing and modeling cyclic behavior in non-stationary time series through multi-resolution analysisphysics.data-an
A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic splines, are well captured by genetic programming in the form of dynamical equations. …
Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as minimization and nuclear norm minimization are…
Variational reduction simplifies Lagrangian systems with scaling symmetries.
problem Simplifying Lagrangian systems with scaling symmetries.
method Defining a variational reduction procedure for homogenous Lagrangian systems.
result Reconstructing trajectories from critical points of reduced variational principle.
Elliptically-Contoured Tensor-variate Distributions with Application to Improved Image Learningstat.ME
Improved image learning using elliptically contoured tensor-variate distributions.
problem Inadequate statistical analysis for tensor-valued data, especially with heavier or lighter tails.
method Developed a family of elliptically contoured tensor-variate distributions and derived their properties and procedures for estimation.
result Tensor-variate classification rules and tensor-on-tensor regression better predict and characterize data than TVN-based methods.
Study variation spaces for neural networks, linking them to approximation theory.
problem Understanding the variation spaces of shallow neural networks.
method Examined variation spaces defined by convex hulls and integral representations for a dictionary of functions.
result Found that Barron space, spectral Barron space, and Radon BV space are variation spaces for certain neural networks.
New methods model gamma-ray data to better understand Galactic emissions.
problem Uncertain diffuse Galactic gamma-ray emissions bias data interpretation.
method Gaussian processes and variational inference for flexible modeling.
result More robust interpretation of gamma-ray sky, especially dark matter signals.
Combines deep generative models with ensemble methods for subsurface property estimation.
problem Estimating spatially distributed subsurface properties from sparse measurements.
method Wasserstein Generative Adversarial Network (WGAN-GP) and Ensemble Smoother with Multiple Data Assimilation (ES-MDA).
result The proposed method outperforms variational inversion methods, especially for channelized and fractured fields.
In this note, we use a result of Osserman and Schiffer \cite{OS} to give a variational characterization of the catenoid. Namely, we show that subsets of the catenoid minimize area within a geometrically natural class of minimal annuli. To the best of our knowledge, this fact has gone unremarked upon in the literature. …
The paper calculates variations of Einstein-Hilbert action on CR manifolds.
problem Variation of the Einstein-Hilbert action in pseudohermitian geometry.
method Computed first and second variations on CR manifolds, characterized critical points as pseudo-Einstein structures, and analyzed second variation on standard spheres.
result In three dimensions, the second variation of the Einstein-Hilbert action on CR structures differs from the Riemannian case due to embeddability.
After establishing some new global facts (like a measure theoretic structure theorem and approximation results) about complex-valued functions with bounded variation on arbitrary noncompact Riemannian manifolds, we extend results of Miranda/the second author/Paronetto/Preunkert and of Carbonaro/Mauceri on the heat semi…
A triangulated piecewise-linear minimal surface in Euclidean 3-space defined using a variational characterization is critical for area amongst all continuous piecewise-linear variations with compact support that preserve the simplicial structure. We explicitly construct examples of such surfaces that are embedded and a…
Study variational problems in Kähler geometry to construct metrics.
problem Maximizing/minimizing Monge--Ampère energy on Kähler potentials.
method Prove existence and uniqueness of extremals, use them to construct metrics.
result Existence and uniqueness of extremals with simple characterization.
The paper classifies surfaces with constant skew curvature in 3-space forms.
problem Classifying surfaces with constant skew curvature in 3-space forms.
method Variational characterization and flow of binormal vector field.
result Classification of rotational surfaces with constant skew curvature.
In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference, a tractable way to approximate Bayesian posteriors: the loss to optimize contain…
Integrative analysis of disparate data blocks measured on a common set of experimental subjects is a major challenge in modern data analysis. This data structure naturally motivates the simultaneous exploration of the joint and individual variation within each data block resulting in new insights. For instance, there i…
Boosting Variational Inference improves posterior approximations with adaptive step-sizes.
problem Limited resources hinder the widespread adoption of Boosting Variational Inference.
method Characterized global curvature impact, introduced local curvature, and developed an approximate backtracking algorithm.
result New theoretical convergence rates and experimental validation demonstrate improved performance.
Survey on discrete minimal surfaces and their properties.
problem Discretizing minimal surfaces in Euclidean space.
method Polyhedral surfaces with parallel face offsets and circle patterns.
result All simply connected discrete minimal surfaces can be constructed from circle patterns.
We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restric…
Copula variational inferencestat.ML
We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the dependency that is not captured by the original variational distribution, and thus …
We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under similar "prior mass and testing" conditions considered in the literature, the rat…
Variational inference is an umbrella term for algorithms which cast Bayesian inference as optimization. Classically, variational inference uses the Kullback-Leibler divergence to define the optimization. Though this divergence has been widely used, the resultant posterior approximation can suffer from undesirable stati…
We (1) characterize the Schubert varieties that arise as variations of Hodge structure (VHS); (2) show that the isotropy orbits of the infinitesimal Schubert VHS `span' the space of all infinitesimal VHS; and (3) show that the cohomology classes dual the Schubert VHS form a basis of the invariant characteristic cohomol…
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley [2013], Galley, Tsang, and Stein [2014]. We show that this construction is useful to…
Solves wealth maximization problem using variational analysis.
problem Maximizing expected utility of terminal wealth.
method Variational analysis, forward-backward stochastic differential equation (FBSDE).
result Characterization and solutions for various utility functions.
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear whether the fixed point identified by the variational inference algorithm is a local…
The paper defines new geometric concepts on Riemannian manifolds and applies them to optimization problems.
problem Optimization problems on Riemannian manifolds.
method Strongly geodesic preinvexity, strongly η-invexity, and strongly invariant η-monotonicity definitions.
result Characterization of strict η-minimizers and solutions to variational like-inequality problems.
Current variational inference methods for hierarchical Bayesian nonparametric models can neither characterize the correlation structure among latent variables due to the mean-field setting, nor infer the true posterior dimension because of the universal truncation. To overcome these limitations, we propose the conditio…
Characterizes Lévy-driven Ornstein-Uhlenbeck processes linked to tempered stable distributions.
problem Understanding Lévy-driven Ornstein-Uhlenbeck processes and their properties.
method Characterizes the Lévy triplet and deduces transition laws for finite variation Ornstein-Uhlenbeck processes associated with tempered stable distributions.
result Provides algorithms for generating skeleton of Ornstein-Uhlenbeck processes related to exponentially-modulated tempered stable laws.
Gradient flows and Evolution Variational Inequalities in metric spaces. I: structural propertiesmath.FA
This is the first of a series of papers devoted to a thorough analysis of the class of gradient flows in a metric space that can be characterized by Evolution Variational Inequalities. We present new results concerning the structural properties of solutions to the formulation, such as co…
New method classifies hypersurfaces that can bend infinitesimally.
problem Classifying hypersurfaces that can be slightly deformed while preserving the Möbius metric.
method Introducing infinitesimal Moebius variations and characterizing isometric immersions.
result Classification of hypersurfaces that can be infinitesimally Moebius bendable.
The extragradient method fails for hypomonotone variational inequalities.
problem The convergence of the extragradient method for hypomonotone variational inequalities.
method Application of the extragradient method to hypomonotone linear operators.
result The extragradient method diverges for hypomonotone variational inequalities.
We first generalize the operation of formal exterior differential in the case of finite dimensional fibered manifolds and then we extend it to certain bundles of smooth maps. In order to characterize the operator order of some morphisms between our bundles of smooth maps, we introduce the concept of fiberwise -j…
In this short note we prove that, in dimension three, flat metrics are the only complete metrics with non-negative scalar curvature which are critical for the -curvature functional.
This paper deals with numerical solutions of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of t…
The paper analyzes uncertainty quantification in sparse Gaussian process regression with a Brownian motion prior.
problem Analyzing uncertainty in sparse Gaussian process regression with a Brownian motion prior.
method Theoretical guarantees and limitations for pointwise credible sets are derived for a rescaled Brownian motion prior with a sparse variational Gaussian process method.
result Theoretical characterization of asymptotic frequentist coverage for credible sets, distinguishing conservative and overconfident cases.