arXiv research

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

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…

Study of energy conservation in fourth-order gravity theories.

Study quadratic one-forms on logarithmic Higgs bundles on pointed curves.

Study connects curvature to graph theory and reveals differences.

Quantitative stability for nearly minimizing Yamabe metrics.

A key issue in the estimation of energy hedges is the hedgers' attitude towards risk which is encapsulated in the form of the hedgers' utility function. However, the literature typically uses only one form of utility function such as the quadratic when estimating hedges. This paper addresses this issue by estimating an…

Optimizes quadratic bandits with tight Hessian-dependent sample complexity bounds.

New rigidity results for critical metrics of a quadratic curvature functional.

Study on finite energy SU(2) monopoles on AC 3-manifolds, proving integrality of charge and curvature decay.

We study some analytical and geometric properties of a two-dimensional nonlinear sigma model with gravitino which comes from supersymmetric string theory. When the action is critical w.r.t. variations of the various fields including the gravitino, there is a symmetric, traceless and divergence-free energy-momentum tens…

We describe the space of measured foliations induced on a compact Riemann surface by meromorphic quadratic differentials. We prove that any such foliation is realized by a unique such differential $q$ if we prescribe, in addition, the principal parts of $\sqrt q$ at the poles. This generalizes a theorem of Hubbard and …

We show that in the setting of proper metric spaces one obtains a solution of the classical two-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area (in the sense of convex geometry) has been chosen appropriately. We prove the quasi-convexity of this new definition o…

Paper proposes a novel optimization method for disaggregating smart meter data.

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…

The paper proves new rigidity results for critical metrics of quadratic curvature functionals.

Gradient descent recovers planted weights in shallow neural networks with quadratic activations.

We explore a new method for discrete-time control problems using randomization and entropy.

Reinforcement learning for continuous-time risk-sensitive asset allocation

Energy statistics was proposed by Sz\' ekely in the 80's inspired by Newton's gravitational potential in classical mechanics and it provides a model-free hypothesis test for equality of distributions. In its original form, energy statistics was formulated in Euclidean spaces. More recently, it was generalized to metric…

Improved HGF networks avoid negative precision errors in volatility updates.

Kuwert and Schätzle showed in 2001 that the Willmore flow converges to a standard round sphere, if the initial energy is small. In this situation, we prove stability estimates for the barycenter and the quadratic moment of the surface. Moreover, in codimension one we obtain stability bounds for the enclosed volume and …

Study the energy spectrum of metrics on surfaces and its relation to simple length spectrum.

New method accelerates energetic variational inference using particle dynamics.

A meromorphic quadratic differential with poles of order two, on a compact Riemann surface, induces a measured foliation on the surface, with a spiralling structure at any pole that is determined by the complex residue of the differential at the pole. We introduce the space of such measured foliations, and prove that f…

A new algebra for Frobenius manifolds solves PDEs and constraints.

Two non-local asymptotic invariants of magnetic fields for the ideal magnetohydrodynamics are introduced. The velocity of variation of the invariants for a non-ideal magnetohydrodynamics with a small magnetic dissipation is estimated. By means of the invariants the spectra of electromagnetic fields are investigated. A …

We show that the concept of $H^2$-gradient flow for the Willmore energy and other functionals that depend at most quadratically on the second fundamental form is well-defined in the space of immersions of Sobolev class $W^{2,p}$ from a compact, $n$-dimensional manifold into Euclidean space, provided that $p \geq 2$ and…

The paper finds a unique curve minimizing Loewner energy among piecewise geodesic Jordan curves.

MF-PID uses interacting samples to efficiently transport probability mass.

We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of power and gas. Volatility modulated Volterra processes are in general not semimart…

Model predicts BESS interactions and price impacts in energy markets.

Let $(Σ,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $Σ$ with a pole of order $(k+2)$ at $p$, having a connected critical graph and an induced metric composed of $k$ Euclidean half-planes. The parameters form a finite-…

The problem of the existence of an additional (independent on the energy) first integral, of a geodesic (or magnetic geodesic) flow, which is polynomial in momenta is studied. The relation of this problem to the existence of nontrivial solutions of stationary dispersionless limits of two-dimensional soliton equations i…

A new sampler for complex discrete distributions efficiently updates all variables in parallel.

CRBMs improve financial regime detection with PCD and free energy analysis.

Critical metrics on four-dimensional manifolds are either Einstein or product of two-dimensional manifolds.

Solves risk-sensitive investment via duality, entropic regularization, and RL.

In Lorentzian manifolds of any dimension the concept of causal tensors is introduced. Causal tensors have positivity properties analogous to the so-called ``dominant energy condition''. Further, it is shown how to build, from ANY given tensor $A$, a new tensor quadratic in $A$ and ``positive'', in the sense that it is …

Researchers confirm scalar-flatness for critical metrics in 5-9 dimensions.

D-LinOSS models learn to dissipate energy, improving performance on long-range tasks.

Modeling intraday dispatch for wind-battery assets to meet grid targets.

The Teichmüller harmonic map flow, introduced in [9], evolves both a map from a closed Riemann surface to an arbitrary compact Riemannian manifold, and a constant curvature metric on the domain, in order to reduce its harmonic map energy as quickly as possible. In this paper, we develop the geometric analysis of holomo…

CLuP achieves near optimal ground state energies for positive and negative Hopfield models.

Optimizes power systems with energy storage under uncertainty using scenario-based method.

The family of temporal difference (TD) methods span a spectrum from computationally frugal linear methods like TD(λ) to data efficient least squares methods. Least square methods make the best use of available data directly computing the TD solution and thus do not require tuning a typically highly sensitive learning r…

New algorithm nearly achieves ground state free energy of SK model.

We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties: not on…