Investigates physical properties on surfaces of rotation using Clairaut's theorem.
problem Understanding specific energy and angular momentum on surfaces of rotation.
method Used Clairaut's theorem with geodesic conditions to derive specific energy and angular momentum.
result Physical expressions for specific energy and angular momentum on surfaces of rotation were derived.
Study quantizes energy for a specific fourth-order system in 4D.
problem Energy quantization for a fourth-order inhomogeneous system in 4D.
method Establishes angular energy quantization for the given system.
result Angular energy quantization proven for the system.
Study p-Willmore disks with boundary energies, finding equilibrium configurations.
problem Finding equilibrium configurations for p-Willmore disks with boundary energies.
method Model boundary as Kirchhoff elastic rod, interior term dependent on mean and Gaussian curvatures. Study among topological disks and p-Willmore examples.
result Equilibrium configurations for p-Willmore disks with boundary energies.
Signals are submanifolds; bounds on energy calculated.
problem Abstract theory of signal propagation.
method Energy inequalities and bounds calculated for specific signal spaces.
result Upper and lower bounds on energy derived for various signal configurations.
We investigate the low-energy behavior of the gradient flow of the L2 norm of the Riemannian curvature on four-manifolds. Specifically, we show long time existence and exponential convergence to a metric of constant sectional curvature when the initial metric has positive Yamabe constant and small initial energy.
Proves positive energy conjecture for a specific metric class.
problem Proving the positive energy conjecture for a class of AHM metrics.
method Analyzes asymptotically Horowitz-Myers (AHM) metrics on R2imesTn−2. result Generalizes previous results on positive energy conjecture.
Paper proves various types of varieties minimize a specific energy.
problem Minimizing a specific energy in various types of varieties.
method Analyzes various polarized varieties over Q. result Various types of varieties minimize the Arakelov K-energy.
The paper extends energy identities and neck existence for ε-harmonic maps.
problem Understanding the energy identity and neck formation for ε-harmonic maps.
method Finding analogues of energy identities and neck existence results for ε-harmonic maps.
result Specific quantities determine energy identity and neck formation for ε-harmonic maps.
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.
In the spirit of recent work of Lamm, Malchiodi and Micallef in the setting of harmonic maps, we identify Yang-Mills connections obtained by approximations with respect to the Yang-Mills α-energy. More specifically, we show that for the SU(2) Hopf fibration over the four sphere, for sufficiently small α values the SO(4…
Competency questions help experts select best clustering for energy data.
problem Ad hoc and subjective selection of clustering structures by domain experts.
method Formalize expert knowledge and requirements with competency questions.
result Competency questions improve reproducibility and evaluation of clustering applications.
Proves rigidity for specific initial data sets under the dominant energy condition.
problem Rigidity of initial data sets with boundary and convex polytopes.
method Solution of boundary value problems for Dirac operators and approximations by manifolds with smooth boundary.
result Proves rigidity for compact smooth spin manifolds and convex polytopes under the dominant energy condition.
In this thesis a connection between the worlds of discrete and continuous conformal geometry is explored. Specifically, a disk pattern production theroem is proved using an energy which measures how ``uniform'' the angle data of a triangulation is, see also math.DG/0002150. Then this energy is averaged over all the Del…
Stable solutions to a specific equation are one-dimensional.
problem Stability and dimensionality of solutions to the Allen-Cahn equation.
method Analysis of stable solutions with bounded energy density.
result Stable solutions to the Allen-Cahn equation are one-dimensional.
Energy Transformer integrates attention, energy models, and associative memory.
problem Lack of clear theoretical foundations in attention mechanisms and straightforward design of energy functions in energy-based models.
method Proposes Energy Transformer, a sequence of attention layers with a specifically engineered energy function.
result Obtained strong results on graph anomaly detection and classification tasks.
New method learns latent energy models using particle algorithms.
problem Learning latent variable models with energy priors.
method Continuous-time SDEs for MMLE, particle-based discretization.
result Practical algorithm converges to solve MMLE problem.
Proves existence of Yang-Mills fields for specific curvature conditions.
problem Yang-Mills theory with specific curvature constraints.
method Proof of existence for non-degenerate traceless Ricci curvature.
result Locally exists SO(3) Yang-Mills field matching curvature. We prove that capillary surfaces converge to a specific energy density as the angle approaches zero.
problem Understanding the limiting behavior of capillary surfaces as the angle approaches zero.
method Rigorous limiting analysis and application to curvature estimates.
result Capillary area-density converges to the Weiss energy density as the angle tends to zero.
Formula derived for ALH manifolds, showing existence of specific 3D manifolds.
problem Energy calculation and existence of specific 3D conformally compact ALH manifolds.
method Derivation of energy formula and application to manifold existence.
result Existence of 3D conformally compact ALH manifolds with specific properties.
This study proves energy bounds in specific AdS spacetimes.
problem Proving positive energy theorems in asymptotically locally AdS spacetimes.
method Derived positive energy theorem for spacetimes with compact, Einstein cross-sections.
result First complete proofs of BPS inequalities in AdS and locally AdS spacetimes.
EDCompress optimizes energy efficiency of CNN models on edge devices.
problem Low energy consumption for edge devices with diverse dataflow types.
method Energy-aware model compression using reinforcement learning.
result Improves energy efficiency by 20X, 17X, 37X in various networks.
The paper proves energy theorems for specific initial data sets in 3D spacetime.
problem Establishing energy theorems for specific initial data sets in 3D spacetime.
method Analysis of level sets of spacetime harmonic functions.
result Rigidity results showing vanishing total energy imply isometric manifolds.
Paper proves stability of positive mass theorem for specific types of manifolds.
problem Stability of positive mass theorem for compact graphical manifolds.
method Used Federer--Fleming flat distance and static quasi-local Brown-York energy.
result Proved stability of positive mass theorem for compact (locally) hyperbolic graphical manifolds.
We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in R3 equipped with a director field. The energies strongly penalize the deviation of the director from the surface unit normal and control the derivatives of the director. Such type of energies for example arise…
The paper studies how curves evolve under area constraints and converges to a critical point.
problem Evolution of plane curves with fixed area under elastic energy gradient.
method Local and global existence of the flow, simplicity assumption, Łojasiewicz--Simon inequality.
result The evolving curve's length remains bounded and converges to a critical point.
Optimal energy trading strategy for intraday markets using Hawkes processes.
problem Optimal execution in intraday energy markets with specific trading patterns.
method Calibrated Hawkes process model with transient price impact.
result Substantial cost reductions in TWAP and VWAP benchmarks.
Sustainability became the most important component of world development, as countries worldwide fight the battle against the climate change. To understand the effects of climate change, the ecological footprint, along with the biocapacity should be observed. The big part of the ecological footprint, the carbon footprin…
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.
Bayesian models' singular fluctuation is shown to be akin to specific heat, influencing model complexity and generalization.
problem Understanding the thermodynamic interpretation of singular fluctuation in Bayesian models.
method Showed singular fluctuation as the curvature of Bayesian free energy and variance of log-likelihood observable under a Gibbs posterior.
result Singular fluctuation is the statistical analogue of specific heat, controlling model complexity and generalization.
Energy-efficient detection of natural errors in deep networks.
problem Deep networks lack error detection capability without additional energy costs.
method Append RACs at hidden layers to detect natural errors with early classification termination.
result Early classification termination reduces energy consumption.
Paper benchmarks and customizes energy forecasting methods.
problem Energy forecasting challenges and differences from traditional time series.
method Collected large-scale load datasets and renewable energy datasets. Developed feature engineering and customized loss functions.
result Comprehensive evaluation of 21 forecasting methods in energy datasets.
Develops a PDE approach to constructing nontrivial anisotropic surfaces.
problem Min-max construction of anisotropic surfaces.
method PDE-based approach to anisotropic surface energies.
result Construction of an anisotropic min-max hypersurface.
Bio-oil molecule assessment is essential for the sustainable development of chemicals and transportation fuels. These oxygenated molecules have adequate carbon, hydrogen, and oxygen atoms that can be used for developing new value-added molecules (chemicals or transportation fuels). One motivation for our study stems fr…
A new AI optimization method uses energy-conserving dynamics inspired by Born-Infeld theory.
problem Optimization challenges in non-convex loss functions and machine learning tasks.
method Discretization of Born-Infeld dynamics for energy-conserving Hamiltonian optimization.
result The method avoids high local minima and outperforms traditional methods in shallow valleys.
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.
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.
This study optimizes energy storage scheduling under price uncertainty, balancing risk and reward.
problem Optimizing energy storage operation under price uncertainty and risk.
method Two-stage stochastic risk-constrained approach using conditional value-at-risk.
result Increasing risk aversion leads to substantial benefits in terms of risk reduction and expected reward.
New result on critical points of Bethe free energy under deformation retracts.
problem Characterizing critical points of Bethe free energy for complex graphs.
method Analyzing homotopy types and deformation retracts of factor graphs.
result Critical points of Bethe free energy are invariant under deformation retracts.
Paper uses autoencoders for time series clustering with energy data.
problem Challenges in time series clustering, especially with outliers.
method Combines convolutional autoencoder and k-medoids for clustering.
result Improves clustering robustness to outliers and finer clusters.
Based on forward curves modelled as Hilbert-space valued processes, we analyse the pricing of various options relevant in energy markets. In particular, we connect empirical evidence about energy forward prices known from the literature to propose stochastic models. Forward prices can be represented as linear functions…
Optimizes BESS for cross-market energy arbitrage to boost revenues.
problem Charging and discharging BESS at optimal times to maximize profits.
method Developed a generic framework, backtest engine, and optimization strategy.
result Boosted revenues by 10% through strategic BESS operation.
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…
Defines weak geodesics on specific subsets of manifolds.
problem Characterizing geodesics on prox-regular subsets of Riemannian manifolds.
method Defining weak geodesics as continuous curves with weak regularities, and characterizing them as viscosity critical points of the energy functional.
result Characterizes weak geodesics on prox-regular subsets of Riemannian manifolds.
Novel ML model predicts solvation free energies from atom interactions.
problem Predicting solvation free energies from atomistic interactions.
method Two encoding functions extract atomic feature vectors, interactions calculated by inner product.
result Outstanding performance and transferability on 6,493 experimental measurements.
This paper analyzes energy and carbon footprints in distributed and federated learning.
problem High energy costs and carbon emissions in centralized AI methods.
method A novel framework quantifying energy and carbon footprints in vanilla and consensus-based FL methods.
result Optimal bounds and operational points for green FL designs and sustainability assessment.
Paper improves DNN accelerator robustness against bit errors with energy savings.
problem Bit errors in quantized DNN weights reduce energy efficiency.
method Combines robust fixed-point quantization, weight clipping, and random bit error training.
result Significantly improves robustness against random bit errors with high energy savings.
L-GATr transforms high-energy physics data using geometric algebra and Lorentz symmetry.
problem Extracting scientific understanding from particle-physics experiments with high precision and efficiency.
method L-GATr, a geometric algebra Transformer, representing data in 4D space-time and being equivariant under Lorentz transformations.
result L-GATr achieves performance comparable to or better than domain-specific baselines on regression, classification, and generative tasks.
Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab-initio calculations) and at speeds suitable for molecular dynam- ics simulation. Best performance is achieved when the known physical constraints are encoded in the mac…