Article provides Bernstein gradient estimates for heat equations with potential terms.
problem Gradient estimates for heat equations with potential terms on weighted Riemannian manifolds.
method Derived Bernstein type gradient estimates for two systems of heat equations with linear, exponential, and combined potentials.
result Resolves part of the problem raised by Bhattacharyya et al. in \cite{SB-1}.
We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator with a nonconvex potential in terms of a distance associated with the potential. The results here can be applied to the double well potential.
Characterizes potential function of almost conformal Ricci solitons on Sasakian manifolds.
problem Characterizing potential functions of almost conformal Ricci solitons on Sasakian manifolds.
method Characterization through the potential function f and non-dynamical scalar field p. result Established a sufficient condition for an almost conformal Ricci soliton to be an almost conformal gradient Ricci soliton.
Study the limit of Calabi-Yau metrics with degenerate skeletons.
problem Understanding the behavior of Calabi-Yau metrics with degenerate skeletons.
method Using polarised degenerations and optimal transport problems.
result Describe the limiting behaviour of the Calabi-Yau potential.
The paper describes flat Hessian metrics on surfaces and their potentials.
problem Understanding Hessian metrics on surfaces.
method Theoretical description and explicit construction using integrable systems.
result Explicit construction of potentials for flat Hessian metrics on surfaces.
We study the influence of an additional scalar potential on various geometric and analytic properties of Dirac-harmonic maps. We will create a mathematical wish list of the possible benefits from inducing the potential term and point out that the latter cannot be achieved in general. Finally, we focus on several potent…
We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth term and multiple stochastic nonsmooth terms. In each iteration, our splitting t…
We consider several diffeomorphism invariant field theories of 2- and 3-forms in six dimensions. They all share the same kinetic term BdC, but differ in the potential term that is added. The theory BdC with no potential term is topological - it describes no propagating degrees of freedom. We show that the theory co…
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.
We give upper bounds for the Bergman kernels associated to tensor powers of a smooth positive line bundle in terms of the rate of growth of the Taylor coefficients of the Kähler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevr…
A generalization of Callias' index theorem for self adjoint Dirac operators with skew adjoint potentials on asymptotically conic manifolds is presented in which the potential term may have constant rank nullspace at infinity. The index obtained depends on the choice of a family of Fredholm extensions, though as in the …
Recovering matrix valued potentials from wave equation data on stationary spacetimes.
problem Recovering a time-dependent matrix valued potential from wave equation data.
method Reduction to non-Abelian light ray transform and study of the transform.
result Sufficient conditions for solving the inverse problem on stationary spacetimes.
A kinematics of the motion of a car is reformulated in terms of the theory of gauge potentials (connection on principal bundle). E(2)-connection originates in the no-slipping contact of the car with a road.
In this article we discuss the distribution of asset price movements by the market potential function. From the principle of free energy minimization we analyze two different kinds of market potentials. We obtain a U-shaped potential when market reversion (i.e. contrarian investors) is dominant. On the other hand, if t…
In the present work, it is shown that, the application of the Bazanski approach to Lagrangians, written in AP-geometry and including the basic vector of the space, gives rise to a new class of path equations. The general equation representing this class contains four extra terms, whose vanishing reduces this equation t…
We study the implicit bias of generic optimization methods, such as mirror descent, natural gradient descent, and steepest descent with respect to different potentials and norms, when optimizing underdetermined linear regression or separable linear classification problems. We explore the question of whether the specifi…
Symmetry operators of twistor spinors and harmonic spinors can be constructed from conformal Killing-Yano forms. Transformation operators relating twistors to harmonic spinors are found in terms of potential forms. These constructions are generalized to gauged twistor spinors and gauged harmonic spinors. The operators …
Study shows conditions for nonexistence of solutions in Riemannian geometry.
problem Nonexistence of global solutions for quasilinear parabolic problems.
method Test function argument to identify parameter ranges for nonexistence.
result Explicit parameter ranges where nonexistence holds.
Study classifies static potentials on 3-manifolds, proving one-dimensionality under specific conditions.
problem Classifying the dimension of static potentials on 3-manifolds.
method Analysis of relative zero sets of static potentials, using Miao and Tam's technique.
result Proves one-dimensionality of static potentials under specific conditions.
The paper connects Schrödinger equations to geodesics on a 2-surface.
problem Understanding the relationship between Schrödinger equations and geodesics.
method Analyzes the geodesic equation of a specific metric on a 2-surface.
result Explicit solutions for the metric and geodesics in terms of the Baker--Akhiezer function for finite-gap potentials.
We point out a duality between steady incompressible Euler flows and solutions of the strongly coupled Faddeev-Skyrme sigma model with potential (mass) term. We supplement this result with various applications and several explicit examples.
We adapt Thistlethwaite's alternating tangle decomposition of a knot diagram to identify the potential extreme terms in its bracket polynomial, and give a simple combinatorial calculation for their coefficients, based on the intersection graph of certain chord diagrams.
Researchers compute the heterotic moduli-space metric up to α′2.
problem Computing the heterotic moduli-space metric up to a specific order.
method Using α′2 for backgrounds with a smooth α′o0 limit, focusing on the Kaehler potential and metric corrections. result Metric corrections from the deformation of the Hull connection are identified.
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the τ function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete …
We prove the Fundamental Gap Conjecture, which states that the difference between the first two Dirichlet eigenvalues (the spectral gap) of a Schrödinger operator with convex potential and Dirichlet boundary data on a convex domain is bounded below by the spectral gap on an interval of the same diameter with zero poten…
We study the geometric flow of a planar curve driven by its curvature and the normal derivative of its capacity potential. Under a convexity condition that is natural to our problem, we establish long term existence and large time asymptotics of this flow.
Potential theory extended to Gromov hyperbolic spaces.
problem Extending potential theory to a new class of spaces.
method Unified framework for Gromov hyperbolic metric measure spaces.
result Boundary Harnack inequalities and complete classification of positive harmonic functions.
The bias potential model explains how generative models can generalize or memorize samples.
problem Understanding and achieving generalization in generative models like GANs.
method Introducing the bias potential model to analyze the behavior of generative models.
result Dimension-independent generalization accuracy can be achieved with early stopping in the bias potential model.
The paper extends Weyl formulae for Schrödinger operators with singular potentials.
problem Analyzing the spectral behavior of Schrödinger operators with critically singular potentials.
method Generalizations of classical Weyl formulae, extending results by Avakumović, Levitan, and Hörmander.
result Obtained O(λn−1) bounds for the error term in the Weyl formula under minimal assumptions. 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 …
This paper analyzes how kinetic terms in stock market equations can affect symmetry breaking.
problem Spontaneous symmetry breaking in quantum finance and its impact on stock market dynamics.
method Analyzes the role of kinetic terms in the context of the martingale condition in stock market equations.
result Kinetic terms can shift the effective location of the vacuum state, affecting symmetry breaking patterns.
We construct a toric generalised Kähler structure on CP2 and show that the various structures such as the complex structure, metric etc are expressed in terms of certain elliptic functions. We also compute the generalised Kähler potential in terms of integrals of elliptic functions.
Paper analyzes complexity of PSGLA for sampling log-concave distributions.
problem Sampling from log-concave distributions with composite potentials.
method Uses primal-dual interpretation and duality gap to analyze PSGLA complexity.
result Complexity of PSGLA is O(1/ε2) for strongly convex potentials. Bitcoin has emerged as a fascinating phenomenon of the financial markets. Without any central authority issuing the currency, it has been associated with controversy ever since its popularity and public interest reached high levels. Here, we contribute to the discussion by examining potential drivers of Bitcoin prices …
We prove that the solution of a Wess-Zumino-Witten type equation from a domain D in Cm to the space of Kähler potentials can be approximated uniformly by Hermitian-Yang-Mills metrics on certain vector bundles. The key is a new version of Berndtsson's theorem on the positivity of direct image bundles.
The classification problem for holonomy of pseudo-Riemannian manifolds is actual and open. In the present paper, holonomy algebras of Lorentz-Kähler manifolds are classified. A simple construction of a metric for each holonomy algebra is given. Complex Walker coordinates are introduced and described using the potential…
LMC algorithm achieves efficient sampling from complex distributions with specific tail behaviors.
problem Sampling from distributions with specific tail behaviors and Hölder continuous gradients.
method Unadjusted Langevin Monte Carlo (LMC) algorithm with analysis of potential function tail growth and smoothness.
result LMC achieves efficient sampling with a rate independent of tail growth for linearly growing tails.
Proves bounds on spanning two-forests and random cut sizes.
problem Counting spanning two-forests and estimating random cut sizes.
method Uses pairwise effective resistances and potential theory.
result Establishes bounds on the number of spanning two-forests and average cut size.
Genetic algorithms are a well-known method for tackling the problem of variable selection. As they are non-parametric and can use a large variety of fitness functions, they are well-suited as a variable selection wrapper that can be applied to many different models. In almost all cases, the chromosome formulation used …
We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eige…
We analyze wealth condensation for a wide class of stochastic economy models on the basis of the economic analog of thermodynamic potentials, termed transfer potentials. The economy model is based on three common transfers modes of wealth: random transfer, profit proportional to wealth and motivation of poor agents to …
New method estimates Schrödinger bridge potentials via empirical risk minimization.
problem Estimating Schrödinger bridge potentials from samples.
method Rewriting Schrödinger system as a fixed-point equation and estimating the potential via empirical risk minimization.
result Uniform concentration of empirical risk around population counterpart under sub-Gaussian assumptions.
Improved sensitivity to Higgs potential through neural simulation-based inference for di-Higgs events.
problem Improving sensitivity to physics beyond the Standard Model through di-Higgs events.
method Simulation-based inference using neural networks to estimate per-event likelihood ratios.
result Adding kinematic observables improves experimental sensitivity to Higgs self-coupling.
We examine the fixed points to first-order RG flow of a non-linear sigma model with background metric, dilaton and tachyon fields. We show that on compact target spaces, the existence of fixed points with non-zero tachyon is linked to the sign of the second derivative of the tachyon potential V′′(T) (this is the anal…
A classical result by Cheng in 1976, improved later by Besson and Nadirashvili, says that the multiplicities of the eigenvalues of the Schrodinger operator with a smooth potential on a compact Riemannian surface M are bounded in terms of the eigenvalue index and the genus of M. We prove that these multiplicity bounds h…
We use the DPW method to obtain the associate family of Delaunay surfaces and derive a formula for the neck size of the surface in terms of the entries of the holomorphic potential.
This paper describes the data collection effort that is part of the project Sprekend Nederland (The Netherlands Talking), and discusses its potential use in Automatic Accent Location. We define Automatic Accent Location as the task to describe the accent of a speaker in terms of the location of the speaker and its hist…
We compute the equivariant elliptic genera of several classes of ALE and ALF manifolds using localization in gauged linear sigma models. In the sigma model computation the equivariant action corresponds to chemical potentials for U(1) currents and the elliptic genera exhibit interesting pole structure as a function of …