Study on energy-minimizing structures in complex geometry.
problem Existence and regularity of harmonic almost complex structures.
method Inspired by harmonic map theory, proving results similar to Schoen-Uhlenbeck and Cheeger-Naber.
result Proved existence and regularity similar to harmonic map theory.
Characterizes complex Hessian equations for bounded energy functions.
problem Understanding degenerate complex Hessian equations for bounded energy functions.
method Proving sublevel set estimates and using Sobolev inequalities.
result Characterization of degenerate complex Hessian equations for bounded (p,m)-energy functions. Optimizes energy of mappings from complex projective spaces.
problem Finding energy-minimizing mappings between complex projective spaces and Riemannian manifolds.
method Establishes optimal lower bounds for energy functionals and characterizes optimal mappings.
result Optimal lower bounds for energy functionals are characterized for mappings from real and complex projective spaces.
Proves an energy gap for complex Yang-Mills equations under specific manifold conditions.
problem Proving an energy gap for complex Yang-Mills equations.
method Uses the energy gap result of pure Yang-Mills equations to derive a new result for complex Yang-Mills equations.
result Proves an energy gap for complex Yang-Mills equations under certain manifold conditions.
Study of mean curvature flow in hyperkähler manifolds leading to complex Lagrangian submanifolds.
problem Understanding the behavior of mean curvature flow in hyperkähler manifolds.
method Definition of twistor energy and analysis of mean curvature flow starting from hyper-Lagrangian submanifolds.
result Mean curvature flow converges to a complex Lagrangian submanifold for sufficiently small twistor energy.
Lower bound found for energy on specific Lagrangian tori in complex projective space.
problem Finding a lower bound for the energy functional on Lagrangian tori in CP2. method Analyzing the energy functional on a family of Hamiltonian minimal Lagrangian tori.
result Proved that the energy of certain Hamiltonian minimal Lagrangian tori is strictly larger than the Clifford torus.
Discretizes Helfrich-type energies on surfaces using triangular complexes.
problem Discretizing curvature energies on surfaces of specific type.
method Asymptotic lower bound combined with recovery sequence of triangulations and edge director fields.
result Valid discrete versions of integral curvature energies on surfaces.
Paper models uncertainty in electricity and gas markets to assess its impact.
problem Addressing uncertainties in coupled electricity and gas markets.
method Integrated and stochastic optimisation approaches for large-scale energy systems.
result Quantifies the value of encoding uncertainty in models.
Study energy-minimizing maps in projective spaces, proving sharp bounds.
problem Finding optimal mappings in projective spaces.
method Proving lower bounds and characterizing energy-minimizing maps.
result Sharp lower bounds and characterization of energy-minimizing maps.
Study shows neural networks have less complexity than expected.
problem Understanding the complexity of neural networks.
method Explored the energy landscape of a simple neural network.
result Neural networks have less complexity than expected, leading to better generalization.
Proves existence and regularity of energy-minimizing maps between ideal hyperbolic simplicial complexes.
problem Existence and regularity of energy-minimizing maps between ideal hyperbolic simplicial complexes.
method Proves existence and regularity results for energy minimizing maps between ideal hyperbolic 2-dimensional simplicial complexes.
result Establishes existence and regularity of energy-minimizing maps between ideal hyperbolic simplicial complexes.
Study on biharmonic almost complex structures on compact manifolds.
problem Existence and regularity of biharmonic almost complex structures.
method Analyzes biharmonic almost complex structures on compact almost Hermitian manifolds, focusing on dimension four.
result Existence of energy-minimizing biharmonic almost complex structures for various topologies and homotopy classes.
The paper studies Möbius energy gradient of helix pairs and finds limiting behavior as coiling ratio increases.
problem Characterizing the limiting behavior of Möbius energy gradient for symmetric helix pairs.
method Complex asymptotics
result The gradient diverges in opposing directions based on radius, approaching 1/2 as coiling ratio increases.
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.
Complex wrinkling patterns emerge in non-Euclidean elastic sheets due to energy minimization.
problem Understanding hierarchical buckling patterns in non-Euclidean elastic sheets.
method Minimizing elastic energy to explain complex wrinkling patterns.
result Branch-point singularities are key to generating complex wrinkling patterns.
Paper uses STPN for energy/power prediction in complex systems.
problem Predicting energy in complex dynamical systems.
method Spatiotemporal pattern network (STPN) framework with mutual information metric.
result Improved energy prediction accuracy in wind and residential energy contexts.
Establishes convexity and coercivity of K-energy functional for complex tori.
problem Convexity and coercivity of K-energy functional for complex tori.
method Geodesics in finite energy space, cone angle perturbations, stability of coercivity.
result Openness of coercivity under cone angle perturbations and existence of cscK cone metrics.
New sampler tackles complex discrete energy landscapes efficiently.
problem Stagnation in gradient-based discrete samplers for non-convex settings.
method DREXEL sampler with Replica Exchange and Adjusted Metropolis.
result Proves samplers satisfy detailed balance and converge to target distribution.
Energy trees handle complex data structures with multiple variable types.
problem Handling intricate data structures with various types of covariates.
method Energy trees, a regression and classification model, use energy statistics to accommodate structured covariates of different types.
result Energy trees maintain statistical foundations, interpretability, and robustness to overfitting.
Formula found for energy slope in complex geometry.
problem Calculating the asymptotic slope of a K-energy.
method Established a formula for the asymptotic slope.
result Found a formula for the asymptotic slope of α-K-energy.
Rectifies singular set of harmonic maps into complex.
problem Regularity of harmonic maps into complex manifolds.
method Proves (m−2)-rectifiability of singular set. result Singular set is (m−2)-rectifiable. Finite energy solutions classified for Seiberg-Witten equations on complex plane and Riemann surface.
problem Classifying solutions to Seiberg-Witten equations with finite energy.
method Established a classification theorem for solutions on X=CimesΣ with finite analytic energy. result Finite energy solutions correspond to polynomial maps from C to H0(Σ,L+,∂ˉ). New result on energy-genus bounds for 6D symplectic Calabi-Yau manifolds.
problem Energy-genus bounds for pseudo-holomorphic curves in almost complex manifolds.
method Compactness and regularity theorems for J-holomorphic currents.
result Established a new result in dimension 6 for symplectic Calabi-Yau 6-manifolds.
In this article we apply a Bochner type formula to show that on a compact conformally flat riemannian manifold (or half-conformally flat in dimension 4) certain types of orthogonal almost-complex structures, if they exist, give the absolute minimum for the energy functional. We give a few examples when such minimizers …
K-energy is not strictly convex on certain complex manifolds, but under specific conditions, it is.
problem The strict convexity of Mabuchi's K-energy on geodesically complete spaces of bounded positive forms.
method Simple toric example and further assumptions on toric manifolds.
result Strict convexity holds in the toric case under certain conditions, leading to a uniqueness result.
Study compact Willmore surfaces without complex structure convergence, computing energy loss and geodesic lengths.
problem Compactness of Willmore surfaces without complex structure convergence.
method Compute energy loss in neck and geodesic lengths in Grassmannian G(2,n). result Limit of Gauss map image is a geodesic in G(2,n) with computable length. DEEN learns energy and score functions from complex data.
problem Challenges in density estimation for high-dimensional data.
method Inference-free hierarchical framework using score matching and multilayer perceptrons.
result DEEN successfully learns energy and score functions from synthetic and high-dimensional data.
Researchers find optimal configurations of complex knots and links.
problem Finding the most efficient configurations of complex knots and links.
method Minimizing Möbius and Minimum Distance energies by describing them with a small number of free parameters.
result Optimal geometries for Hopf links, Borromean rings, and chain links are found.
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.
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.
Novel framework finds globally optimal energy-efficient power control in wireless networks.
problem Energy-efficient power control in wireless networks.
method Branch-and-bound procedure with problem-specific bounds for faster convergence.
result Global solution for common energy-efficient power control problems with reduced complexity.
Study on helix curves and their Möbius energy asymptotics.
problem Understanding the asymptotic behavior of Möbius energy for helix curves.
method Investigation of helix curves with fixed radius, focusing on energy decay and blow-up.
result Proven asymptotics for both uncoiling and coiling helix curves, revealing distinct strategies for each.
The study characterizes and studies stability of biharmonic hypersurfaces in complex space forms.
problem Characterizing and studying biharmonic hypersurfaces in complex space forms.
method Characterizing hypersurfaces as critical points of a higher order energy functional.
result Existence and non-existence results for CPn and CHn. Study conjugate points on generalized flag manifolds using geodesic energy analysis.
problem Understanding conjugate points on generalized flag manifolds.
method Analyzing the second variation of geodesic energy.
result Evolution of conjugate points in complex projective space via Ricci flow.
Adaptive approximations improve variational inference for complex models.
problem Efficiently approximate marginal distributions and partition functions in complex probabilistic models.
method Two classes of adaptive approximations that include Bethe, tree-reweighted, and convex free energies.
result Proposed approximations automatically adapt to a given model and outperform existing methods.
The paper proves that certain maps from complex space to Kahler manifolds are holomorphic.
problem Characterizing harmonic maps from complex space to Kahler manifolds.
method Proves that harmonic maps from Cn to any Kahler manifold must be holomorphic under a specific condition. result Harmonic maps from Cn to Kahler manifolds are holomorphic under an energy density assumption. The paper studies energy functionals for Lagrangian tori in complex projective space.
problem Investigating energy functionals for Lagrangian tori in complex projective space.
method Introducing an energy functional based on the potential of associated Schrödinger operators and studying its behavior on specific families of tori.
result Proposes that the minimum of the energy functional is achieved by the Clifford torus.
Optimizes quadratic bandits with tight Hessian-dependent sample complexity bounds.
problem Understanding optimal sample complexity for quadratic functions.
method Introduces energy allocation and optimal energy spectrum to prove tight lower bounds. Solves for Hessian-independent optimal algorithm.
result Proves optimal Hessian-dependent sample complexities and existence of a universally optimal algorithm.
Quantum computing offers energy savings over classical computing.
problem Energy efficiency in computing services.
method Cournot competition model constrained by energy usage.
result Quantum computing firms can outperform classical counterparts in energy efficiency.
In many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \emph{Energy Landscape Maps} (ELMs) which characterize and visualize an energy function with a tree structure, in which each leaf node re…
Geometric Occam's Razor shapes deep learning solutions.
problem Understanding the regularization in over-parameterized neural networks.
method Analyzing the geometric model complexity and Dirichlet energy in neural networks.
result Over-parameterized neural networks are implicitly regularized by geometric model complexity.
Paper proposes new loss functions for training energy networks.
problem Challenges in computing gradients for training energy networks.
method Proposes generalized Fenchel-Young losses for efficient gradient computation.
result Demonstrates the calibration of excess risk for linear-concave energies.
Study complex Monge-Ampère operator on weighted pluricomplex energy classes.
problem Characterize the range of the Complex Monge-Ampère Operator on weighted pluricomplex energy classes.
method Characterizations and a priori estimates on sub-level sets of solutions.
result A non-negative Borel measure is the Monge-Ampère of a unique function in \(\mathcal E_χ\) if and only if \(χ(\mathcal E_χ) \subset L^1(dμ)\).
New method bounds curvature of Calabi flow on complex tori.
problem Smoothness of Calabi flow on complex tori.
method Developed a new method to obtain explicit curvature bounds.
result Calabi flow starting from weak Kähler metric becomes smooth immediately on n=2 complex tori. We introduce certain energy functionals to the complex Monge-Ampere equation over a bounded domain with inhomogeneous boundary condition, and use these functionals to show the convergence of the solution to the parabolic Monge-Ampere equation.
STOIC improves energy demand forecasting with reliable uncertainty estimates.
problem Accurate point forecasts alone are insufficient for energy systems; reliable uncertainty estimates are needed.
method Integrates graph-based forecasting with tabular foundation models for zero-shot calibration of spatial-temporal residuals.
result STOIC delivers more reliable and robust uncertainty estimates for complex graph-structured energy time series.
Energy-efficient DL inference for IoT devices reduces power consumption and improves performance.
problem Energy inefficiency in deep learning models for IoT devices.
method Energy-aware early exiting policy to balance energy consumption and inference accuracy.
result Accuracy and service rate improved up to 25% and 35% respectively.
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.