Paper calculates second variation of Graham-Witten energy for spheres.
problem Calculating the second variation of Graham-Witten energy.
method Explicit formula for second variation at minimal submanifolds in Einstein manifolds.
result Totally geodesic spheres in unit sphere are critical points with non-negative second variation.
The paper finds the explicit expression of Graham-Witten's invariant for 4D submanifolds.
problem Finding conformal invariants of submanifolds.
method Volume renormalization of minimal surfaces in conformally compact Einstein manifolds.
result Explicit expression of Graham-Witten's conformal invariant for 4D submanifolds.
The paper studies residues of manifolds and their applications in geometry.
problem Understanding the residues of manifolds and their geometric implications.
method Analytic continuation and Möbius invariance of residues, introduction of relative and weighted residues.
result Scalar curvature, mean curvature, and Euler characteristic can be expressed in terms of residues.
Paper derives a formula for renormalized area of minimal hypersurfaces in 5D Poincaré-Einstein spaces.
problem Calculating the renormalized area of minimal hypersurfaces in 5D Poincaré-Einstein spaces.
method Derives a Gauss-Bonnet formula for renormalized area in terms of scalar invariants and characterizes minimal hypersurfaces in terms of conformal geometry.
result Derives a formula expressing renormalized area in terms of integrals of scalar Riemannian invariants.
Study on relative entropy for hypersurfaces in hyperbolic space.
problem Understanding relative entropy for hypersurfaces in hyperbolic space.
method Relate relative entropy to renormalized area and apply monotonicity formula to mean curvature flows.
result Obtained a monotonicity formula for relative entropy in hyperbolic space.
The paper proves weighted monotonicity theorems in various spaces and applies them to minimal surfaces.
problem Proving weighted monotonicity theorems in different spaces.
method Proving weighted monotonicity theorems for functions proportional to the metric tensor in Riemannian manifolds.
result Weighted monotonicity theorems in hyperbolic space imply unweighted theorems, leading to bounds on minimal surface areas.
Defines renormalized volume for bounded regions in asymptotically hyperbolic Einstein spaces.
problem Calculating the volume of bounded regions in complex geometries.
method Defines renormalized volume, proves Gauss-Bonnet theorem, computes derivative under variations.
result Derives a Gauss-Bonnet theorem for the renormalized volume.
Extended Möbius energy formula for generalized O'Hara's energies.
problem Maintaining Möbius invariance in O'Hara's energies.
method Extended cosine formula for generalized O'Hara's energies.
result Condition for right circle minimization under length-constraint.
Holographic energy equals Hamiltonian energy.
problem Equating holographic and Hamiltonian energies.
method Relative holographic and Hamiltonian energy comparison.
result Holographic energy is identical to Hamiltonian energy.
Token economics improves energy systems with incentives and efficiency.
problem Traditional energy systems have inefficiencies and lack incentives.
method Integrating token economy and blockchain technology.
result Token economic systems enhance energy efficiency and reduce emissions.
Optimizes energy efficiency in wireless sensor networks with limited information.
problem Maximizing energy efficiency in energy harvesting wireless sensor networks with limited channel state information.
method Modeling as a Multi-Armed Bandits problem and developing an Upper Confidence Bound algorithm.
result Significant gains in energy efficiency compared to benchmark schemes.
Reduces energy for 4D submanifolds in R^n.
problem Energy reduction for 4D submanifolds in R^n.
method Connected sum energy reduction for fourth-order Willmore energy.
result Established a connected sum energy reduction for the fourth-order Willmore energy.
Paper tackles energy sharing in ZECs using DRL.
problem Improving energy status of ZECs through agent-based energy sharing.
method Modelled as a multi-agent environment, solved with DRL.
result Agents learn to collaborate and improve ZEC's energy status over time.
Let Ef be the energy of some knot τ for any f from certain class of functions. The problem is to find knots with extremal values of energy. We discuss the notion of the locally perturbed knot. The knot circle minimizes some energies Ef and maximizes some others. So, is there any energy such that the circle ne…
The paper develops a regularity theory for O'hara knot energies, focusing on Möbius energy.
problem Developing a regularity theory for extremal knots of scale invariant knot energies defined by J. O'hara.
method Reinterpreting O'hara knot energies as a nonlinear, nonlocal Lp-energy acting on the unit tangent of the knot parametrization, drawing a connection to the theory of (fractional) harmonic maps into spheres. result Proves regularity for minimizers and critical knots of the scale-invariant O'hara knot energies.
The positive energy theorem is proven for certain spacetimes with irregular curvature.
problem Proving the positive energy theorem for spacetimes with irregular curvature.
method Weak asymptotically anti-de Sitter initial data sets with distributional curvature under weak dominant energy condition.
result Positive energy theorem established for weakly irregular spacetimes.
New formula connects Loewner energy to moving frames' renormalised energy.
problem Calculating Loewner energy of Jordan curves.
method Using renormalised energy of moving frames.
result Loewner energy as Kähler potential for Weil-Petersson space.
The hyperbolic positive energy theorem links causal properties to energy-momentum vectors in asymptotically hyperbolic spaces.
problem Establishing the causal-future-directed character of energy-momentum vectors in hyperbolic spaces.
method Analyzing n-dimensional asymptotically hyperbolic Riemannian manifolds with spherical conformal infinity, focusing on the dominant energy condition. result The causal-future-directed character of the energy-momentum vector can be traced back to that of asymptotically Euclidean initial data sets.
The paper proves Γ-convergence of discrete tangent-point energies to continuous energies and ropelength, with applications to biarc curves.
problem Proving convergence of discrete tangent-point energies to continuous energies and ropelength.
method Using biarc curves and interpolation, the paper proves Γ-convergence of discretized tangent-point energies to the continuous tangent-point energies and ropelength functional. result Discrete almost minimizing biarc curves converge to ropelength minimizers and minimizers of continuous tangent-point energies.
Paper finds relations between Willmore-type energies, weighted areas, and vertical potential energies for cylindrical critical points.
problem Tackles relations between three types of energy functions for cylindrical critical points.
method Uses differential equations and critical point analysis for Willmore-type energies and weighted areas.
result Generating curves coincide for Willmore-type energies and weighted areas, and similar results hold for Willmore-type energies and vertical potential energies.
Quantizes Willmore energy in Riemannian manifolds with bounded energy and area.
problem Quantization of Willmore energy in bounded energy and area conditions.
method Uniform boundedness of Willmore energy and area, weak convergence of maps, and conformal structures in compact domain.
result Quantization of Willmore energy holds under specified conditions.
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.
Enhanced tabular benchmarks for energy-efficient neural architecture search.
problem Energy consumption in deep learning models.
method Introducing EC-NAS, an enhanced tabular benchmark with energy consumption data.
result EC-NAS reveals a balance between energy usage and accuracy in neural architecture search.
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.
This paper decomposes generalized O'Hara's energies into components.
problem Decomposing generalized O'Hara's energies to understand their components.
method Using an analogue of Doyle-Schramm's cosine formula, the paper derives a decomposition for generalized O'Hara energies.
result Derives a decomposition for generalized O'Hara energies into three components.
Discrete geometry model approximates Willmore energy.
problem Approximating the Willmore energy for triangulated surfaces.
method A discrete energy defined in the spirit of discrete differential geometry converges to the Willmore energy.
result The discrete energy converges to the Willmore energy in the sense of Γ-convergence. Investigates a new four-dimensional energy related to Willmore energy.
problem Exploring a new conformally invariant energy in four dimensions.
method Computed first variation, applied Noether's theorem, investigated other generalizations.
result Critical points of the new energy are smooth and do not include minimal hypersurfaces.
A new Möbius invariant discretization and decomposition of the Möbius energy is proposed.
problem Lack of Möbius invariant discretization and decomposition in existing discrete Möbius energy.
method Proposed a new discretization of Möbius energy that is Möbius invariant and can be decomposed into Möbius invariant components.
result The proposed discretization and decomposition maintain Möbius invariance and converge to the original components in the continuum limit.
Abstract reviews hyperbolic positive energy theorems.
problem Analyzing positive energy theorems for hyperbolic spaces.
method Review of existing literature on asymptotically hyperbolic manifolds.
result Summarizes positive energy theorems for hyperbolic spaces.
Derives energy-momentum tensor from Standard Model, examines energy conditions.
problem Validating energy conditions in the context of the Standard Model.
method Geometric variational problem on globally hyperbolic manifold, deriving energy-momentum tensor.
result Validates various energy conditions in general relativity.
Study of critical tori for mean curvature energies in Killing submersions.
problem Analyzing surface energies in Killing submersions.
method Symmetry reduction and binormal evolution of critical curves.
result Construction of vertical tori critical for mean curvature energies.
Study on infinite energy maps from surfaces to CAT(0) spaces.
problem Harmonic maps with infinite energy from Riemann surfaces to CAT(0) spaces.
method Estimates of energy growth near punctures, proof of uniqueness.
result Precise estimates of energy growth near punctures and proof of uniqueness of harmonic maps.
Proposes linking energy and force uncertainty in deep learning potentials.
problem Uncertainty in predicted energies and forces in machine learning models.
method Introduces a spatially correlated noise process to link energy and force uncertainty.
result Demonstrates the approach on molecular datasets, linking energy and force uncertainties.
Versatile model for High Energy Physics events.
problem Modeling complex interactions in high-energy physics data.
method Energy-based probabilistic model with multi-purpose architecture.
result Achieves success in diverse applications like simulation, anomaly detection, and particle identification.
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.
This paper prioritizes experience replay in robotics using energy-based principles.
problem Randomly replaying experience in HER leads to inefficient learning.
method Developed an energy-based framework to prioritize hindsight experience in robotic manipulation tasks.
result EBP outperforms state-of-the-art approaches in robotic manipulation tasks.
Derives stress-energy tensor for polyharmonic maps.
problem Characterizing polyharmonic maps between Riemannian manifolds.
method Derives stress-energy tensor and uses it to characterize polyharmonic maps.
result Characterizes polyharmonic maps, focusing on triharmonic maps.
New invariant for 4D hypersurfaces ensures smooth critical points.
problem Understanding smoothness of curvature energies on 4D hypersurfaces.
method Developed a new conformally invariant energy.
result Critical points of new energy are smooth.
Improved diffusion models using energy distillation and sequential Monte Carlo.
problem Training instability and inferior performance in energy parameterized diffusion models.
method Introduced a novel training regime for energy functions through distillation of pre-trained diffusion models, and cast the sampling procedure as a Feynman Kac model.
result Demonstrated improved performance and new sampling techniques.
Paper proposes energy-efficient DNN training methods.
problem Energy-constrained deployment of deep neural networks.
method Weighted sparse projection and layer input masking integrated into DNN training.
result Framework provides higher accuracy with same or lower energy budgets.
Stability of a new map derived from the equator map is analyzed.
problem Stability of a new map derived from the equator map.
method Detailed stability analysis of the generalized equator map as a critical point of the extrinsic k-energy and p-energy.
result Established generalizations of classical (in)stability results.
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.
Researchers establish bounds and continuity of decomposed Möbius energies using cosine formula.
problem Estimating the bounds and continuity of decomposed Möbius energies.
method Using the cosine formula to evaluate upper and lower bounds and modulus of continuity of decomposed energies.
result Affirmative answer to the question of estimating decomposed energies using the cosine formula.
Study of quasi-local energy limit near anti de-Sitter space for spacetimes with negative cosmological constant.
problem Evaluate the quasi-local energy near anti de-Sitter space for spacetimes with negative cosmological constant.
method Introduced a new quasi-local energy for spacetimes with a negative cosmological constant. Studied the small sphere limit using a canonical family of surfaces and solved the optimal embedding equation.
result The limit of the quasi-local energy recovers the stress-energy tensor of the matter field at a point in the spacetime.
Triangulates surfaces with bounded energy using diffeomorphisms.
problem Triangulating surfaces with bounded Kolasinski--Menger energy.
method Uses bounded distortion diffeomorphisms of subsets of a plane.
result Triangulation with bounded number of triangles.
Paper proves positivity of energy function on Riemannian manifolds.
problem Investigating positivity of energy function on Riemannian manifolds.
method Using energy function to prove positivity of initial energy.
result Simple method to obtain growth of eigen-solutions.
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.
Study on bending knots and energy changes in 3D space.
problem Understanding energy changes in knots under small deformations.
method Analyzes infinitesimal bending of knots and energy changes using Willmore and Mobius energies.
result Changes in energy under small deformations of knots have been quantified.