arXiv research

The calculation of minimum energy paths for transitions such as atomic and/or spin re-arrangements is an important task in many contexts and can often be used to determine the mechanism and rate of transitions. An important challenge is to reduce the computational effort in such calculations, especially when ab initio …

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 …

Paper proves existence of minimum energy solutions in 5D contact spin manifolds.

We study the misclassification error for community detection in general heterogeneous stochastic block models (SBM) with noisy or partial label information. We establish a connection between the misclassification rate and the notion of minimum energy on the local neighborhood of the SBM. We develop an optimally weighte…

We show that the surface energy introduced by Auckly and Sadun attains the minimum value at the Clifford torus among tori of revolution.

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 present a boundary version of a theorem about solenoidal unit vector fields with minimum energy on a spherical domain of an odd dimensional Euclidean sphere.

Researchers find a surface with minimum bending energy for any genus and isoperimetric ratio.

ECD algorithm speeds up non-convex optimization, offering quantum and stochastic enhancements.

Study rigidity of Hamiltonians near a minimum in symplectic and magnetic settings.

Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The co…

This work is about recognizing human activities occurring in videos at distinct semantic levels, including individual actions, interactions, and group activities. The recognition is realized using a two-level hierarchy of Long Short-Term Memory (LSTM) networks, forming a feed-forward deep architecture, which can be tra…

A physically natural potential energy for simple closed curves in $\bold R^3$ is shown to be invariant under Möbius transformations. This leads to the rapid resolution of several open problems: round circles are precisely the absolute minima for energy; there is a minimum energy threshold below which knotting cannot oc…

In this article, we study the small sphere limit of the Wang-Yau quasi-local energy defined in [18,19]. Given a point $p$ in a spacetime $N$, we consider a canonical family of surfaces approaching $p$ along its future null cone and evaluate the limit of the Wang-Yau quasi-local energy. The evaluation relies on solving …

Neural networks are a powerful class of nonlinear functions that can be trained end-to-end on various applications. While the over-parametrization nature in many neural networks renders the ability to fit complex functions and the strong representation power to handle challenging tasks, it also leads to highly correlat…

SGD with machine learning noise converges to global minimum exponentially fast.

We establish a fundamental connection between smooth and polygonal knot energies, showing that the Minimum Distance Energy for polygons inscribed in a smooth knot converges to the Moebius Energy of the smooth knot as the polygons converge to the smooth knot. However, the polygons must converge in a ``nice'' way, and th…

In a previous preprint we defined an energy associated to every embedding of a surface into $R^n$ or $S^n$. This energy is invariant under Moebius tranformations and the "round" sphere is its only absolute minimum. Here we sketch a proof of the compactness property for a variant of it. The details will appear elsewhere…

Researchers find optimal configurations of complex knots and links.

The ropelength of a knot is the quotient of its length by its thickness. We consider a family of energy functions for knots, depending on a power p, which approach ropelength as p increases. We describe a numerically computed trefoil knot which seems to be a local minimum for ropelength; there are nearby critical point…

We provide a new proof of a result of X.X.Chen and G.Tian : for a polarized extremal Kähler manifold, an extremal metric attains the minimum of the modified K-energy. The proof uses an idea of C.Li adapted to the extremal metrics using some weighted balanced metrics.

Minimum attention improves reinforcement learning performance in high-dimensional dynamics.

We give a unified statement and proof of a class of wellknown mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energ…

Paper studies Lagrangian submanifolds and their homological monodromy.

FEAT estimates free energy using adaptive transports.

The study examines the behavior of Gaussian processes' minimums and overshoots.

Inference problems in graphical models can be represented as a constrained optimization of a free energy function. It is known that when the Bethe free energy is used, the fixedpoints of the belief propagation (BP) algorithm correspond to the local minima of the free energy. However BP fails to converge in many cases o…

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…

Many recent models of trade dynamics use the simple idea of wealth exchanges among economic agents in order to obtain a stable or equilibrium distribution of wealth among the agents. In particular, a plain analogy compares the wealth in a society with the energy in a physical system, and the trade between agents to the…

We address the problem of banking system resilience by applying off-equilibrium statistical physics to a system of particles, representing the economic agents, modelled according to the theoretical foundation of the current banking regulation, the so called Merton-Vasicek model. Economic agents are attracted to each ot…

The article analyzes the stability of a curve shortening flow for planar networks.

In this paper, we define a certain "proportional volume property" for an unit vector field on a spherical domain in S3. We prove that the volume of these vector fields has an absolute minimum and this value is equal to the volume of the Hopf vector field. Some examples of such vector fields are given. We also study the…

Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered to be useful models for structural analysis of these molecules. One interested quantity is the minimum number of monomers necessary to realize a molecular knot. The minimum lattice length $\mbox{Len}(K)$ of a knot $K$ i…

In recent years, deep learning has surpassed traditional approaches to the problem of singing voice separation. The Wave-U-Net is a recent deep network architecture that operates directly on the time domain. The standard Wave-U-Net is trained with data augmentation and early stopping to prevent overfitting. Minimum hyp…

We analyse the definition of quasi-local energy in GR based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular the Hamiltonian constraint on the timelike boundary, neglected in previous studies, is emphasized here. We argue that a consis…

Method selects interpretable circular coordinates from data.

We use matricial free energy to regularize autoencoders, producing Gaussian-like codes.

A new loss function ED simplifies training energy-based models without scores.

Maximin UCB algorithm optimizes energy harvesting for sensor networks.

The paper analyzes how SGD visits different regions of a non-convex problem's state space.

A new AI optimization method uses energy-conserving dynamics inspired by Born-Infeld theory.

Residential homes constitute roughly one-fourth of the total energy usage worldwide. Providing appliance-level energy breakdown has been shown to induce positive behavioral changes that can reduce energy consumption by 15%. Existing approaches for energy breakdown either require hardware installation in every target ho…

In this paper, we prove the following theorem regarding the Wang-Yau quasi-local energy of a spacelike two-surface in a spacetime: Let $Σ$ be a boundary component of some compact, time-symmetric, spacelike hypersurface $Ω$ in a time-oriented spacetime $N$ satisfying the dominant energy condition. Suppose the induced me…

The paper analyzes risk spillovers between AI ETFs, AI tokens, and green markets.

Training neural networks involves finding minima of a high-dimensional non-convex loss function. Knowledge of the structure of this energy landscape is sparse. Relaxing from linear interpolations, we construct continuous paths between minima of recent neural network architectures on CIFAR10 and CIFAR100. Surprisingly, …

We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. As an extension of Welling and Teh (2001), we define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals and derive an …

In this paper we study Lagrangian tori in ${\mathbb C}P^2$. A two-dimensional periodic Schrödinger operator is associated with every Lagrangian torus in ${\mathbb C}P^2$. We introduce an energy functional for tori as an integral of the potential of the Schrödinger operators, which has a natural geometrical meaning. We …

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…