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.
Study predicts configurational energy of high entropy alloys using Bayesian methods.
problem Accurately predict the configurational energy of high entropy alloys with limited data.
method Robust data-driven framework based on Bayesian approaches, including effective pair interaction (EPI) model and ensemble sampling.
result Effective prediction of configurational energy with small data, demonstrating robust performance.
With the advent of the Internet of Things (IoT), an increasing number of energy harvesting methods are being used to supplement or supplant battery based sensors. Energy harvesting sensors need to be configured according to the application, hardware, and environmental conditions to maximize their usefulness. As of toda…
Study on Yang-Mills equation near instanton-anti-instanton configurations with energy constraints.
problem Understanding Yang-Mills connections near instanton-anti-instanton configurations.
method Analyzing the Uhlenbeck limit and bubble configurations, determining obstructions and proving solutions.
result Instantons are the only solutions with energy less than $4π^2 \left( |κ| + 2
ight) + \varepsilon_κ$.
Classifies low energy maps from curved surfaces into spheres.
problem Classifying maps from surfaces of constant curvature into spheres.
method Analyzes maps with low energy and degree ±1, focusing on bubble configurations.
result Maps are quantitively close to a bubble configuration with specific radii.
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.
Introduces non-Archimedean metrics for pseudoeffective classes on Kähler manifolds.
problem Characterizing and approximating non-Archimedean metrics on pseudoeffective classes.
method Extending Ross-Witt Nyström correspondence to relative case, introducing flag configurations.
result Non-Archimedean finite energy metrics are approximable by flag configurations, and very general Ding energies are continuous.
Researchers introduce new energies to study constant scalar curvature metrics.
problem Understanding constant scalar curvature metrics on compact Kähler manifolds.
method Introduced a family of Kβ energies using Berman's quantization and intersection theory. Combined with non-Archimedean techniques, provided a uniform Yau-Tian-Donaldson correspondence. result Uniform Yau-Tian-Donaldson correspondence characterizes the existence of a unique constant scalar curvature Kähler metric.
Study spider mechanism configuration spaces using squared distance function.
problem Understand configuration spaces of spider mechanisms.
method Use Morse theory of squared distance function from body to fixed point.
result List and describe critical manifolds of squared distance function as products of polygon spaces.
We propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds derived from the extended musculo-skeletal configuration manifold. The …
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.
The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the case of two-dimensional nematic liquid crystals coating a toroidal particle. Our…
Study on surface configurations with curvature and elasticity.
problem Equilibrium configurations of surfaces with curvature and elasticity.
method Investigates the Euler-Helfrich functional, focusing on axially symmetric surfaces and their variational problems.
result Critical surfaces for the Euler-Helfrich functional, if axially symmetric, satisfy a simpler second order variational problem.
In this article we study point configurations minimizing the discrete energy on a compact Riemannian manifold, where the energy kernel is taken to be the Green's function for the Laplacian. We show that every point in a minimizing configuration lies inside an open set called harmonic ball where no other point can enter…
We identify higher-charge configurations that satisfy Euler-Lagrange equations for the (strong coupling limit of) Faddeev-Hopf model, by means of adequate changes of the domain metric and a reduction technique based on α-Hopf construction. In the last case it is proved that the solutions are local minima for the redu…
Study identifies stable configurations of intertwined threads with repulsive interactions.
problem Stable configurations of entangled systems with repulsive interactions.
method Analysis of steepest descent flow of an energy functional.
result Existence and uniqueness of stable configuration of two layers drifting apart at t1/3 rate. This paper details a series of experiments in searching for minimal energy configurations for knots and links using the computer program KnotPlot. The most interesting phenomena found in these experiments is the dependence of the trajectories of energy descent upon the initial geometric conditions of the knotted embedd…
Characterizes closures of test configurations and algebraic singularity types.
problem Understanding closures of test configurations and algebraic singularity types.
method Analyzes metric spaces of L1 geodesic rays and characterizes closures of singularity types. result Arithmetic and non-pluripolar volumes coincide for algebraic singularity types, and equality holds on their closure.
The paper analyzes the emergence of almost-honeycomb structures in low-energy planar clusters.
problem Understanding the formation of shapes resembling honeycombs in low-energy configurations.
method Detailed quantitative estimates and a revision of the global isoperimetric principle for honeycomb clusters.
result The majority of chambers in low-energy planar clusters are generalized hexagons, closely resembling regular hexagons.
Training energy-based probabilistic models is confronted with apparently intractable sums, whose Monte Carlo estimation requires sampling from the estimated probability distribution in the inner loop of training. This can be approximately achieved by Markov chain Monte Carlo methods, but may still face a formidable obs…
In the present paper we introduce Mobius energy for the embedded graphs and formulate its main properties. This energy is invariant under the action of the group generated by all inversions in three-dimensional real space. We study critical configurations for the angles at vertices of degree less than five, and discuss…
Machine learning for entropy calculation from binary signals.
problem Calculating entropy from binary configurations/signals.
method Transformed entropy calculation into supervised classification tasks using machine learning.
result Reproduced entropy and free energy of the 2D Ising model.
This review reports some theoretical results on the Geometry of membranes. The governing equations to describe equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are derived from the variation of free energies of these structures. Some analytic solutions to these e…
Defines volume and Monge-Ampère energy on polarized affine varieties.
problem Volume and Monge-Ampère energy on polarized affine varieties.
method Definition of volume using asymptotics of jumping numbers, Monge-Ampère energy using forms and currents on Berkovich spaces.
result Monge-Ampère energy agrees with volume of filtrations and recovers known functionals.
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.
Mathematical framework for field theories on Finsler spacetimes.
problem Developing a consistent calculus for field theories on Finsler spacetimes.
method Constructing configuration bundles and applying coordinate-free calculus of variations.
result Averaged energy-momentum conservation law for Finsler field theories.
In this paper, we give a new version of the modified Futaki invariant for a test configuration associated to the soliton action on a Fano manifold. Our version will naturally come from toric test configurations defined by Donaldson for toric manifolds. As an application, we show that the modified K-energy is proper f…
The paper disproves compactness for high-energy Willmore immersions and finds minimal bubbles on Willmore surfaces.
problem Compactness for high-energy Willmore immersions of Willmore energy above 16π. method Explicit construction of minimal bubbles and analysis of limit sequences of Willmore immersions.
result Compactness for immersed Willmore tori of energy below 12π is proven. Study on surfaces minimizing elastic energy with boundary constraints.
problem Finding stable configurations of surfaces with elastic boundaries and surface energy.
method Investigation of critical surfaces with mean curvature and spontaneous curvature, coupled to boundary elastic energy.
result Characterization and minimization of surface energy for specific topological shapes.
Let X be a compact Kähler manifold with a given ample line bundle L. In \cite{Don05}, Donaldson proved that the Calabi energy of a Kähler metric in c1(L) is bounded from below by the supremum of a normalized version of the minus Donaldson--Futaki invariants of test configurations of (X,L). He also conjectured …
Approximate computing is being considered as a promising design paradigm to overcome the energy and performance challenges in computationally demanding applications. If the case where the accuracy can be configured, the quality level versus energy efficiency or delay also may be traded-off. For this technique to be use…
This review reports some key results in theoretical investigations on configurations of lipid membranes and presents several challenges in this field which involve (i) exact solutions to the shape equation of lipid vesicles; (ii) exact solutions to the governing equations of open lipid membranes; (iii) neck condition o…
Defines renormalised energies for singular harmonic maps into compact manifolds.
problem Analyzing harmonic maps with singularities in planar domains.
method Introduces renormalised energies and synharmony to study singularities and minimising configurations.
result Renormalised energies are coercive and Lipschitz-continuous, and associated with minimising singular harmonic maps.
This article provides some estimates for the relative sizes of the electric and magnetic contributions to the energy functional for the minimum energy configuration of an SU(2) gauge field on R^3 in the presence of an source in a fixed ball. The surprising fact is that the contribution to both energies from the free fi…
CNN detects phase transitions in Potts models without prior knowledge.
problem Detecting phase transitions in q-state Potts models using deep learning. method Trained a deep CNN on Ising model spin configurations and temperatures, then tested on Potts model images.
result Deep CNN accurately detects phase transitions in Potts models, including high- and low-temperature regions.
We consider planar networks of three curves that meet at two junctions with prescribed equal angles, minimizing a combination of the elastic energy and the length functional. We prove existence and regularity of minimizers, and we show some properties of the minimal configurations.
We apply the integral formula of volumes to the family of graded linear series constructed from any test configuration. This solves the conjecture raised by Witt--Nyström so that the sequence of spectral measures for the induced C∗-action on the central fiber converges to the canonical Duistermatt--Heckman …
Equivariant flows sample symmetric multi-body systems like proteins.
problem Sampling symmetric multi-body systems like proteins with strong interactions.
method Developed equivariant flows that respect the symmetries of the energy function.
result Equivariant flows can sample new configurations not possible with non-equivariant flows.
Case study shows impact of co-optimizing energy and reserve for wind energy.
problem Impact of lack of co-optimization of energy and reserve in high wind penetration scenarios.
method Developed two models with and without co-optimization, calibrated with Spanish market parameters.
result Models show significant differences in energy and reserve management.
Tripod spiders' energy control analyzed for Hooke and Coulomb potentials.
problem Control of tripod spiders' energy configurations.
method Morse theory for Hooke potential, stationary charges for Coulomb energy.
result For positive charges in a regular triangle, the domain of robust control is non-void.
The paper proposes a thermodynamic potential to guide training of generative models, breaking ergodicity to improve functionality.
problem Improving generative model functionality while limiting access to underrepresented patterns.
method Constructing a thermodynamic potential that guides training, leading to multiple minima in the free energy.
result Training a generative model breaks ergodicity, preventing escape into the high-temperature phase.
Resonant machine learning uses electrical network dynamics to optimize learning efficiently.
problem Traditional energy-based learning models are dissipative and inefficient.
method Proposes a new learning framework with two energy components (active and reactive) to ensure active-power dissipation during learning.
result Support vectors in resonant SVMs correspond to self-sustained oscillations in an LC network.
Deep neural networks improve free energy calculations for peptide conformations.
problem Challenges in developing suitable mappings for free energy perturbation.
method Adapted machine learning approach to train deep neural networks for mapping between Boltzmann distributions.
result Accurate free energy differences calculated between thermodynamic states with spring centers separated by 1 Å and sometimes 2 Å.
The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology (i) emerges even in zero strain configurations, and (ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key…
Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.
problem Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.
method Numerical simulations of static solutions to a particular class of problems in hyperelastic mechanics.
result Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.
Consider a polarized complex manifold (X,L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X,L). For most of the common functionals in Kähler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as…
Extremal Kahler metrics and Sasaki-Einstein metrics characterized via coercive energy.
problem Characterizing extremal Kahler and Sasaki metrics using energy coercivity.
method Maximal complex torus, coercive weighted Mabuchi energy, K-polystability.
result Coercive weighted Mabuchi energy implies strict positivity of Donaldson-Futaki invariant and existence of extremal metrics.
New model predicts grain boundary migration in metals.
problem Anisotropic grain boundary migration in polycrystals.
method Level set-finite element formulation based on thermodynamics and mechanics.
result First analytical solution for anisotropic grain boundary configurations.