arXiv research

In this paper we study potential function of gradient steady Ricci solitons. We prove that infimum of potential function decays linearly; in particular, potential function of rectifiable gradient steady Ricci solitons decays linearly. As a consequence, we show that a gradient steady Ricci soliton with bounded potential…

We show two results about the Conway potential function which is known as the normalized multivariable Alexander polynomial. We first show that the Conway potential function introduced by Kauffman in "Formal Knot Theory" is indeed a link invariant. Next we show that Kauffman's potential function equals Hartley's potent…

Paper connects AJ conjecture and colored Jones polynomial potential function.

New method constructs potential functions for Kähler-Einstein metrics.

We consider the Frobenius algebra of functions on the critical set of the master function of a weighted arrangement of hyperplanes in $\C^k$ with normal crossings. We construct two potential functions (of first and second kind) of variables labeled by hyperplanes of the arrangement and prove that the matrix coefficient…

Characterizes potential function of almost conformal Ricci solitons on Sasakian manifolds.

The paper characterizes potential functions whose level sets are orbits in mechanical systems.

New method trains normalizing flows using entropy-regularized transport.

The study of potential functions on noncompact quasi-Einstein manifolds, focusing on dimensions and flatness.

Characterizes gradient Yamabe solitons with specific conditions.

We interpret the variational inference of the Stochastic Gradient Descent (SGD) as minimizing a new potential function named the \textit{quasi-potential}. We analytically construct the quasi-potential function in the case when the loss function is convex and admits only one global minimum point. We show in this case th…

Unified approach for estimating quantiles of potential outcomes using inverse estimating equations.

In this article, we introduce and study the notion of a complete special holonomy manifold $(X,ω)$ which is given by a global perturbation potential function, i.e., there is a function $f$ on $X$ such that $ω'=ω-\mathcal{L}_{\nabla f}ω$ is sufficiently small in $L^{\infty}$-norm. We establish some vanishing theorems on…

Study on gradient Ricci solitons with isoparametric potential functions.

A new logit model derived from the Weibull manifold.

Estimates classical potential from stock price data using quantum mechanics.

The classical Kaehler potential is a real-valued function (KP) such that one can determine a Kaehler (symplectic) structure by differentiating KP. We define a mirror Kaehler potential on Calabi-Yau 3-folds, a real-valued function (MKP) such that one can determine a complex structure by differentiating MKP.

We explain how to construct certain potential functions for the hyperbolic structures of a knot complement, which are closely related to the analytic functions on the deformation space of hyperbolic structures.

Study of metrics on positive-definite matrices from power potential, linking to power means.

Bayesian inference reconstructs external potentials in DFT for many-particle systems.

Mirror flow optimizes separable data problems, converging to a maximum margin classifier.

A weight system is defined from the (multivariable) Conway potential function. We also show that it can be calculated recursively by using five axioms.

The study extends GBM to include stable nonzero prices and finds a pronounced potential well.

We give a closed formula for the multivariable Conway potential function of any graph link in a homology sphere. As corollaries, we answer three questions by Walter Neumann about graph links.

The paper studies $m$-quasi Einstein manifolds with convex potential and finds constant scalar curvature.

For an oriented diagram of a link $L$ in the 3-sphere, Cho and Murakami defined the potential function whose critical point, slightly different from the usual sense, corresponds to a boundary parabolic $\mathrm{PSL}(2,\mathbb{C})$-representation of $π_1(S^3 \setminus L)$. They also showed that the volume and Chern-Simo…

The article derives some novel independence measures and contrast functions for Blind Source Separation (BSS) application. For the $k^{th}$ order differentiable multivariate functions with equal hyper-volumes (region bounded by hyper-surfaces) and with a constraint of bounded support for $k>1$, it proves that equality …

Study Kähler-Einstein potentials on stable varieties near singularities

We investigate a potential obtained as the convolution of a radially symmetric function and the characteristic function of a body (the closure of a bonded open set) with exterior cones. In order to restrict the location of a maximizer of the potential into a smaller closed region contained in the interior of the body, …

Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank four and find a negative answer. We study this from the perspective of solving t…

Mirror flows converge to a limiting flow with a convex potential.

The paper proves the existence of a complete holomorphic vector field on a complex manifold with a Kähler-Einstein metric.

We give a geometric construction of the multivariable Conway potential function for colored links. In the case of a single color, it is Kauffman's definition of the Conway polynomial in terms of a Seifert matrix.

The paper proves inequalities and growth rates for Schouten solitons.

We characterize Ricci almost solitons on semi-Riemannian warped products, considering the potential function to depend on the fiber or not. We show that the fiber is necessarily an Einstein manifold. As a consequence of our characterization we prove that when the potential function depends on the fiber, if the gradient…

The paper describes flat Hessian metrics on surfaces and their potentials.

We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target distribution, and therefore does not perform its full power on truncated distribu…

We show how Conway's multivariable potential function can be constructed using braids and the reduced Gassner representation. The resulting formula is a multivariable generalization of a construction, due to Kassel-Turaev, of the Alexander-Conway polynomial in terms of the Burau representation. Apart from providing an …

A hyperKähler potential is a function rho that is a Kähler potential for each complex structure compatible with the hyperKähler structure. Nilpotent orbits in a complex simple Lie algebra are known to carry hyperKähler metrics admitting such potentials. In this paper, we explicitly calculate the hyperKähler potential w…

Develops a framework for potentials on Lauritzen manifolds using bi-forms.

This paper introduces a new potential function using Tsallis entropy for neural network optimization.

We consider self-similar solutions to mean curvature evolution of entire Lagrangian graphs. When the Hessian of the potential function $u$ has eigenvalues strictly uniformly between -1 and 1, we show that on the potential level all the shrinking solitons are quadratic polynomials while the expanding solitons are in one…

In this paper we prove the infinitesimal uniqueness theorem for the Newton potential of non simply connected bodies using the singularity theory approach. We consider the Newtonian potentials of the domains in ${\bf R}^n$ boundaries of which are the vanishing cycles on the level hypersurface of a holomorphic function w…

Study on the spectrum of drift Laplacian on Ricci expanders.

An LCK manifold with potential is a compact quotient M of a Kahler manifold X equipped with a positive plurisubharmonic function f, such that the monodromy group acts on $X$ by holomorphic homotheties and maps f to a function proportional to f. It is known that M admits an LCK potential if and only if it can be holomor…

The paper connects Schrödinger equations to geodesics on a 2-surface.

Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the cost is given by minimizing a Lagrangian action.

Improved reinforcement learning with deep learning.