arXiv research

A method to analyze maps into circles with singularities.

Derives energy-momentum tensor from Standard Model, examines energy conditions.

Traditional centralized energy systems have the disadvantages of difficult management and insufficient incentives. Blockchain is an emerging technology, which can be utilized in energy systems to enhance their management and control. Integrating token economy and blockchain technology, token economic systems in energy …

We derive gradient and energy estimates for critical points of the full supersymmetric sigma model and discuss several applications.

In this thesis I explore challenging discrete energy minimization problems that arise mainly in the context of computer vision tasks. This work motivates the use of such "hard-to-optimize" non-submodular functionals, and proposes methods and algorithms to cope with the NP-hardness of their optimization. Consequently, t…

The area of building energy management has received a significant amount of interest in recent years. This area is concerned with combining advancements in sensor technologies, communications and advanced control algorithms to optimize energy utilization. Reinforcement learning is one of the most prominent machine lear…

Competency questions help experts select best clustering for energy data.

We prove a bubble-neck decomposition together with an energy quantization result for sequences of Willmore surfaces into an arbitrary euclidian space with uniformly bounded energy and non-degenerating conformal type. We deduce the strong compactness of Willmore closed surfaces of a given genus modulo the Möbius group a…

The paper is devoted to study the Dirichelet energy of moving frames on 2-dimensional tori immersed in the euclidean $3\leq m$-dimensional space. This functional, called Frame energy, is naturally linked to the Willmore energy of the immersion and on the conformal structure of the abstract underlying surface. As first …

This work develops machine learning for micromagnetic energy minimization.

This paper applies Heath-Jarrow-Morton framework to energy markets for practical use.

Li-Yau inequality applied to curves in 2D space.

EB-RANSAC uses energy-based model for robust estimation without complex sampling.

Tree ensemble method tackles multi-objective constrained optimization in energy systems.

The paper proves $\Gamma$-convergence of discrete tangent-point energies to continuous energies and ropelength, with applications to biarc curves.

We consider in dimension four weakly convergent sequences of approximate biharmonic maps to a Riemannian manifold with bi-tension fields bounded in $L^p$ for $p>\frac43$. We prove an energy identity that accounts for the loss of hessian energies by the sum of hessian energies over finitely many nontrivial biharmonic ma…

New algorithm reduces costs in wind energy systems by minimizing decision changes.

The area renormalization procedure gives an invariant of even-dimensional closed submanifolds in a conformal manifold, which we call the Graham-Witten energy, and it is a generalization of the classical Willmore energy. In this paper, we obtain an explicit formula for the second variation of this energy at minimal subm…

Versatile model for High Energy Physics events.

A new method, based on the original theory of conservation of sum of kinetic and potential energy defined for prices is proposed and applied on Dow Jones Industrials Average (DJIA). The general trends averaged over months or years gave a roughly conserved total energy, with three different potential energies, i.e. posi…

Let $(X,ω)$ be a compact Kähler manifold and $\mathcal H$ the space of Kähler metrics cohomologous to $ω$. If a cscK metric exists in $\mathcal H$, we show that all finite energy minimizers of the extended K-energy are smooth cscK metrics, partially confirming a conjecture of Y.A. Rubinstein and the second author. As a…

In the present work, torsion energy is defined. Its law of conservation is given. It is shown that this type of energy gives rise to a repulsive force which can be used to interpret supernovae type Ia observations, and consequently the accelerating expansion of the Universe. This interpretation is a pure geometric one …

Extends denoising and score estimation to energy models via Tweedie's formula.

The article discusses conservation laws for polyharmonic maps and their applications.

Under a spectral assumption on the Laplacian of a Poincaré--Einstein manifold, we establish an energy inequality relating the energy of a fractional GJMS operator of order $2γ\in(0,2)$ or $2γ\in(2,4)$ and the energy of the weighted conformal Laplacian or weighted Paneitz operator, respectively. This spectral assumption…

We introduce and study the notion of the energy of a smooth metric measure space, which includes as special cases the Yamabe constant and Perelman's $ν$-entropy. We then investigate some properties the energy shares with these constants, in particular its relationship with the $κ$-noncollapsing property. Finally, we us…

New calibration energy measures deviation from calibrated geometry, enabling mean curvature flow in infinite volumes.

This paper reviews low voltage load forecasting methods and applications.

Based on the concept of self-decomposable random variables we discuss the application of a model for a pair of dependent Poisson processes to energy facilities. Due to the resulting structure of the jump events we can see the self-decomposability as a form of cointegration among jumps. In the context of energy faciliti…

The paper improves energy decay estimates for Dir-stationary Q-valued functions and applies them to Liouville-type theorems and continuity.

In this paper, we compute the derivatives of the line segment energy for a symmetric tensor field and apply them to obtain slightly more general log-concavity estimates for positive solutions of heat equations and first eigenfunctions on bounded strictly convex domains.

We introduce a combinatorial energy for maps of triangulated surfaces with simplicial metrics and analyze the existence and uniqueness properties of the corresponding harmonic maps. We show that some important applications of smooth harmonic maps can be obtained in this setting.

For a fixed smooth map $u_0$ between two Riemann surfaces $Σ$ and $S$ with non-zero degree, we consider the energy function on Teichmüller space $\mc{T}$ of $Σ$ that assigns to a complex structure $t\in \mc{T}$ on $Σ$ the energy of the harmonic map $u_t:Σ_t:=(Σ,t) \to S$ homotopic to $u_0$. We prove that the energy fun…

PIML enhances machine learning for subsurface energy systems.

RNE provides a flexible framework for diffusion models, enabling inference-time control and energy-based training.

For a sequence of coupled fields $\{(φ_n,ψ_n)\}$ from a compact Riemann surface $M$ with smooth boundary to a general compact Riemannian manifold with uniformly bounded energy and satisfying the Dirac-harmonic system up to some uniformly controlled error terms, we show that the energy identity holds during a blow-up pr…

In 1996, Shi generalized the epsilon-regularity theorem of Schoen and Uhlenbeck to energy-minimizing harmonic maps from a domain equipped with a bounded measurable Riemannian metric. In the present work we prove a compactness result for such energy-minimizing maps. As an application, we combine our result with Shi's th…

We introduce different Finsler metrics on the space of smooth Kähler potentials that will induce a natural geometry on various finite energy classes $\mathcal E_{\tilde χ}(X,ω)$. Motivated by questions raised by R. Berman, V. Guedj and Y. Rubinstein, we characterize the underlying topology of these spaces in terms of c…

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 ${\mathbb{R}}^n$. It turns out that due to a smoothing effect any seq…

A new functional for simplicial surfaces is suggested. It is invariant with respect to Moebius transformations and is a discrete analogue of the Willmore functional. Minima of this functional are investigated. as an application a bending energy for discrete thin-shells is derived.

Generalizes energy-momentum method for non-autonomous Hamiltonian systems.

New proof of harmonic map uniqueness with analytic targets.

The paper classifies biharmonic quadratic maps between spheres, proving their energy density properties.

The paper proves a reverse isoperimetric inequality and applies it to analyze surface flows.

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schrödinger equation is mapped onto a non-linear statistical regression problem of reduced complexity. Regression models a…

Energy distance measures feature heterogeneity in federated learning.

This paper introduces intermittent learning - the goal of which is to enable energy harvested computing platforms capable of executing certain classes of machine learning tasks effectively and efficiently. We identify unique challenges to intermittent learning relating to the data and application semantics of machine l…

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…