The paper studies quaternionic Monge-Ampère equations in weighted energy classes.
problem Characterizing the finite energy range of quaternionic Monge-Ampère operator.
method Proving well-definedness and fine property of the operator in weighted energy classes.
result Explicit characterization of the finite energy range of quaternionic Monge-Ampère operator.
Study complex Monge-Ampère equations on compact Kähler manifolds.
problem Finite energy range of complex Monge-Ampère operator.
method Survey and general answer to Guedj-Zeriahi's question.
result General answer to Guedj-Zeriahi's question about finite energy range.
This paper generalizes neural transport learning for free energy estimation in arbitrary state spaces.
problem Efficient estimation of free energy in various state spaces.
method Generalized neural transport learning approach for arbitrary state spaces.
result Validation of the proposed method's effectiveness and efficiency in diverse settings.
We introduce and study an approximate solution of the p-Laplace equation, and a linearlization Lε of a perturbed p-Laplace operator. By deriving an Lε-type Bochner's formula and a Kato type inequality, we prove a Liouville type theorem for weakly p-harmonic functions with finite p-energy on a complete noncompact …
In this article we introduce and investigate a new two-parameter family of knot energies TP(p,q) that contains the tangent-point energies. These energies are obtained by decoupling the exponents in the numerator and denominator of the integrand in the original definition of the tangent-point energies. We will firs…
In this article we study the regularity of stationary points of the knot energies Eα introduced by O'Hara in the range α∈(2,3). In a first step we prove that Eα is C1 on the set of all regular embedded closed curves belonging to H(α+1)/2,2 and calculate its derivative. After that we use the structure…
We generalize the notion of integral Menger curvature introduced by Gonzalez and Maddocks by decoupling the powers in the integrand. This leads to a new two-parameter family of knot energies intMp,q. We classify finite-energy curves in terms of Sobolev-Slobodeckij spaces. Moreover, restricting to the range of para…
Researchers confirm scalar-flatness for critical metrics in 5-9 dimensions.
problem Verifying scalar-flatness for critical metrics in specific dimensions.
method Analyzing complete Riemannian manifolds with critical metrics of the L2-scalar curvature functional. result The conjecture that all complete noncompact critical metrics with finite energy are scalar-flat is confirmed for dimensions 5 to 9.
Study Hessian equations on compact Kähler manifolds with prescribed singularities.
problem Characterize finite energy ranges of the Hessian operator and solutions of degenerate complex Hessian equations.
method Reformulate pluripotential results to Hessian setting and use a new method.
result Prove solutions of degenerate complex Hessian equations have the same singularity type as the model potential.
Proves energy expression on Poincaré-Einstein spaces.
problem Computing renormalized Yang-Mills energy on Poincaré-Einstein manifolds.
method Generalizes Chang-Qing-Yang method for renormalized volumes and uses scattering theory for Schrödinger operators.
result Agrees with anomaly boundary integrand in seven dimensions.
Study on finite entropy and energy in Kähler geometry.
problem Finite entropy and energy measures in Kähler geometry.
method Refined Moser-Trudinger inequalities for quasi-plurisubharmonic functions.
result Quasi-plurisubharmonic potentials with finite entropy belong to the finite energy class En−1n. The problem of recovering the asymptotics of a short range perturbation of the Euclidean metric on R^n from fixed energy scattering data is studied. It is shown that if two such metrics, g1, g2, have scattering data at some fixed energy which are equal up to smoothing, then there exists a diffeomorphism ψ`fixing infini…
Synthetic approach to pluripotential theory measures finite energy.
problem Global pluripotential theory on compact Kähler manifolds and projective Berkovich spaces.
method Definition and study of measures of finite energy, introduction of twisted and free energy functionals.
result Coercivity of energy functionals is an open condition with respect to polarization.
Suppressing bones on chest X-rays such as ribs and clavicle is often expected to improve pathologies classification. These bones can interfere with a broad range of diagnostic tasks on pulmonary disease except for musculoskeletal system. Current conventional method for acquisition of bone suppressed X-rays is dual ener…
We investigate probability measures with finite pluricomplex energy. We give criteria insuring that a given measure has finite energy and test these on various examples. We show that this notion is a biholomorphic but not a bimeromorphic invariant.
New calibration energy measures deviation from calibrated geometry, enabling mean curvature flow in infinite volumes.
problem Mean curvature flow in infinite volumes with finite energy.
method Introducing calibration energy and proving its dissipation identity for mean curvature flows.
result Every proper self-expander with finite calibration energy is a plane in all dimensions and codimensions.
D-LinOSS models learn to dissipate energy, improving performance on long-range tasks.
problem Representational limitations of LinOSS models in long-range reasoning.
method Introducing Damped Linear Oscillatory State-Space models (D-LinOSS) that learn to dissipate latent state energy on arbitrary time scales.
result D-LinOSS consistently outperforms previous LinOSS methods on long-range learning tasks, achieving faster convergence and reducing hyperparameter search space.
EBM model for functional data using path measure tilting.
problem Modeling distributions of functions from irregularly sampled data.
method Spectral decomposition of an energy-based model with a Gaussian Process path measure to reweight the distribution.
result Effective approach to up-scaling functional data.
Uniform small energy regularity for fractional geometric problems proved.
problem Proving regularity for fractional geometric problems.
method Analyzing parabolic boundary reaction Ginzburg-Landau problems and fractional harmonic maps to spheres.
result Uniform small energy regularity results for s∈(0,1), answering a posed question. This study examines biases in flow matching samplers using finite-sample estimation.
problem Biases in flow matching samplers when using finite-sample surrogates.
method Finite-sample plug-in estimation and hierarchy of empirical FM models.
result Exact empirical minimizer and smoothed plug-in regime identified for affine conditional flows.
In this paper, we study the critical case of the Allard regularity theorem. Combining with Reifenberg's topological disk theorem, we get a critical Allard-Reifenberg type regularity theorem. As a main result, we get the topological finiteness for a class of properly immersed surfaces in Rn with finite Willm…
Finite energy solutions of 4-harmonic and ES-4-harmonic maps are trivial.
problem Characterizing the qualitative behavior of 4-harmonic and ES-4-harmonic maps.
method Proving triviality of finite energy solutions for both maps.
result Finite energy solutions of both 4-harmonic and ES-4-harmonic maps are trivial.
We study degenerate complex Monge-Ampère equations on a compact Kähler manifold (X,ω). We show that the complex Monge-Ampère operator (ω+ddc⋅)n is well-defined on the class E(X,ω) of ω-plurisubharmonic functions with finite weighted Monge-Ampère energy. The class E(X,ω) is the la…
Study on finite energy SU(2) monopoles on AC 3-manifolds, proving integrality of charge and curvature decay.
problem Understanding the asymptotic behavior of finite energy SU(2) monopoles on AC 3-manifolds.
method Analysis of critical points of the SU(2) Yang--Mills--Higgs energy on asymptotically conical 3-manifolds.
result Proves integrality of the monopole number and quadratic decay of curvature, among other findings.
Study finite-energy metrics over complex manifold degenerations.
problem Finite-energy metrics on complex manifolds with singularities.
method Investigate spaces of plurisubharmonic metrics with finite-energy conditions.
result Complete and geodesic metric structure on finite-energy metrics space.
We study approximations of non-Gaussian stationary processes having long range correlations with microcanonical models. These models are conditioned by the empirical value of an energy vector, evaluated on a single realization. Asymptotic properties of maximum entropy microcanonical and macrocanonical processes and the…
In this paper, we establish compactness for various geometric curvature energies including integral Menger curvature, and tangent-point repulsive potentials, defined a priori on the class of compact, embedded m-dimensional Lipschitz submanifolds in Rn. It turns out that due to a smoothing effect any seq…
Geodesics in non-Archimedean metrics are continuous.
problem Understanding geodesics in spaces of non-Archimedean metrics.
method Maximal psh segments are geodesics, and continuity of these segments is proven.
result Maximal psh segments joining continuous psh metrics are continuous.
New energy measure for isolated systems in general relativity.
problem Quantifying energy in isolated systems in general relativity.
method Optimal isometric embedding and conformal Killing fields.
result Finite quasi-local energies for asymptotically flat spacetimes.
Extends finite entropy measures in Kähler geometry.
problem Analyzing finite entropy measures on compact Kähler manifolds.
method Defining finite p-entropy and demonstrating their inclusion in an energy class. result Stability result for the complex Monge-Ampère equation.
Study generalizes Möbius energy to non-smooth sets in arbitrary dimensions.
problem Investigate Möbius-invariant energies on non-smooth subsets of arbitrary dimensions.
method Show local finite energy implies embedded Lipschitz submanifold, and low fractional Sobolev regularity guarantees finite energy.
result Local graph structure of low fractional Sobolev regularity on a set is sufficient to guarantee finite energy.
Paper explores sustainable machine learning with energy harvesting.
problem Energy-efficient distributed machine learning in resource-constrained devices.
method Developed a practical learning framework with theoretical guarantees for distributed learning over energy-harvesting devices.
result Demonstrated significant performance improvement over non-harvesting benchmarks.
The paper classifies energy-minimizing sets in specific domains.
problem Classifying volume-constraint local energy-minimizing sets.
method Proved a Poincaré-type inequality for stable sets.
result Relative boundary of energy-minimizing sets is smooth.
New taxonomy and improved solvers for discrete energy minimization.
problem Maximum-a-posteriori inference in discrete graphical models.
method Dual block-coordinate ascent rule, theoretical analysis, new solver variants.
result Improved state-of-the-art solver outperforming existing methods on all test instances.
Proves conditions for minimal surfaces in complex hyperbolic space.
problem Conditions for finite energy equivariant minimal surfaces in complex hyperbolic space.
method Analyzes peripheral holonomy and uses Higgs bundles.
result Explicit parametrization and construction of minimal surfaces.
Proves convergence of gradient Ricci shrinkers with uniform bounds.
problem Compactness and energy concentration in gradient Ricci shrinkers.
method Bubble-tree convergence and local energy analysis.
result No energy concentrates in neck regions, leading to a local diffeomorphism finiteness theorem.
We introduce different Finsler metrics on the space of smooth Kähler potentials that will induce a natural geometry on various finite energy classes Eχ~(X,ω). Motivated by questions raised by R. Berman, V. Guedj and Y. Rubinstein, we characterize the underlying topology of these spaces in terms of c…
Extends denoising and score estimation to energy models via Tweedie's formula.
problem Linking denoising and score estimation for a wider range of distributions.
method Derives a fundamental identity connecting energy score derivatives and scores.
result Establishes a new identity for energy scores analogous to Tweedie's formula.
Compact DNNs increase memory footprint and reduce energy efficiency.
problem Designing compact deep neural networks (DNNs) for improved energy efficiency.
method Evaluation of recently proposed compact DNNs on a Tesla P100 GPU.
result Higher number of activations and memory footprint lead to reduced energy efficiency.
Estimates for Schrödinger operators on manifolds with bounded Ricci curvature.
problem Quantifying unique continuation for Schrödinger operators on manifolds with specific curvature conditions.
method Proving quantitative unique continuation estimates for Schrödinger operators on manifolds with Ricci curvature bounded below.
result Upper bound for energy range and constant in terms of Ricci curvature and parameters of relatively dense set.
Study calculates the elastic energy of curves on a sphere.
problem Elastic energy of curves on a sphere.
method Introduced p-curvature functional for rectifiable curves in the sphere and proved its finiteness. result The p-curvature functional agrees with the integral of geodesic curvature raised to the power p for curves in W2,p. The paper proves a finite diffeomorphism theorem for manifolds with lower Ricci curvature and bounded energy.
problem Proving a finite number of diffeomorphism types for manifolds with specific curvature and energy bounds.
method Analyzing the space of closed manifolds with lower Ricci curvature, volume, diameter, and energy bounds.
result The space of manifolds has at most a finite number of diffeomorphism types.
Gradient Ricci solitons can be extended to non-gradient Ricci solitons using energy function.
problem Extending the geometry of gradient Ricci solitons to non-gradient Ricci solitons.
method Using energy function E to study the geometry. result A non-steady Ricci soliton with symmetric covariant derivative is gradient.
We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then such a map is harmonic. We then give applications to isometric immersions and horizontally conformal submersions.
EB-RANSAC uses energy-based model for robust estimation without complex sampling.
problem Robust estimation of parameters in noisy data.
method EB-RANSAC combines RANSAC's sampling scheme with an energy-based model, simplifying the process and reducing hyperparameter requirements.
result EB-RANSAC effectively solves linear regression and maximum likelihood estimation problems.
The paper proves the existence of finite-energy solutions to a specific elliptic equation on Riemannian manifolds.
problem Existence of finite-energy solutions to a singular elliptic equation on Riemannian manifolds.
method ε-regularized problems, mountain pass arguments, and limiting procedures.
result Existence of nonnegative finite-energy supersolutions under certain conditions.
New approach proves existence of gravitating vortices on Riemann surfaces.
problem Existence of gravitating vortices on Riemann surfaces.
method Symplectic reduction by stages and reduced α-K-energy. result Existence of solutions implies polystability of effective divisors.
Probabilistic models can be defined by an energy function, where the probability of each state is proportional to the exponential of the state's negative energy. This paper considers a generalization of energy-based models in which the probability of a state is proportional to an arbitrary positive, strictly decreasing…