A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper proposes an unsupervised learning method to solve heat equations on chips.
Methane is considered being a good choice as a propellant for future reusable launch systems. However, the heat transfer prediction for supercritical methane flowing in cooling channels of a regeneratively cooled combustion chamber is challenging. Because accurate heat transfer predictions are essential to design relia…
LGAC enhances heat transfer in turbulent boundary layers using slot jets.
Estimates heat equation on shrinking Ricci solitons with uniform bounds.
Introduce a thermodynamically informed, temperature-transferable MLCG framework for proteins.
Proposes learning manifold implicitly via heat kernel.
Physics-based framework improves building energy forecasting.
CTS machines improve screen development in printing industries, reducing costs and increasing profitability.
A new method trains physics-constrained neural networks more efficiently.
We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L^2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of …
This paper discusses the existence of gradient estimates for second order hypoelliptic heat kernels on manifolds. It is now standard that such inequalities, in the elliptic case, are equivalent to a lower bound on the Ricci tensor of the Riemannian metric. For hypoelliptic operators, the associated "Ricci curvature" ta…
We show that in dimension 4 and above, the lifespan of Ricci flows depends on the relative smallness of the Ricci curvature compared to the Riemann curvature on the initial manifold. We can generalize this lifespan estimate to the local Ricci flow, using which we prove the short-time existence of Ricci flow solutions o…
Develops kernels for matchings, overcoming computational challenges.
In this paper, we quantify the statistical coherence between financial time series by means of the Renyi entropy. With the help of Campbell's coding theorem we show that the Renyi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly suppressing others. This accentu…
The paper compares heat kernels on manifolds with Robin boundary conditions.
We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this…
Study on biharmonic map heat flow with monotonicity formula.
Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.
Understanding the heat usage of customers is crucial for effective district heating operations and management. Unfortunately, existing knowledge about customers and their heat load behaviors is quite scarce. Most previous studies are limited to small-scale analyses that are not representative enough to understand the b…
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We show explicitly that the obtaine…
The heat kernel for the Cauchy-Riemann subLaplacian on S(2n+1) is derived in a manner which is completely analogous to the classical derivation of elliptic heat kernels. This suggests that the classical hamiltonian construction of elliptic heat kernels, with appropriate modifications, does yield heat kernels for subell…
The paper studies heat kernel asymptotics and proves Morse inequalities.
Derives gradient estimates for CR heat equation on pseudo-Hermitian manifolds.
New heat equation method solves intertwining problems in CR geometry.
The Liouville theorem is proven for V T-harmonic map heat flow.
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal s…
New method predicts heat load in thermal grids using latent variables.
Paper studies heat flow for maps on manifolds, avoiding singularities.
In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres. Finally, as an application, we compute the diagonal of heat kernels for odd dimensional…
Formulae connect heat kernels on glued manifolds.
Proves upper bounds for heat kernels evolving on manifolds.
This paper describes results characterizing the range of the time-t heat operator on various manifolds, including Euclidean spaces, spheres, and hyperbolic spaces. The guiding principle behind these results is this: The functions in the range of the heat operator should be, roughly, those functions having an analytic c…
Study on biharmonic heat equation on manifolds with curvature constraints.
Derives properties of heat kernel for Rumin complex on Heisenberg groups.
The paper studies heat kernels on weighted Riemannian manifolds with curvature bounds.
In this paper we give Hamilton's Laplacian estimates for the heat equation on complete noncompact manifolds with nonnegative Ricci curvature. As an application, combining Li-Yau's lower and upper bounds of the heat kernel, we give an estimate on Laplacian form of the heat kernel on complete manifolds with nonnegative R…
Paper studies smoothness of bi-conformal heat flow on 4-manifolds.
Study heat content in sub-Riemannian manifolds, obtaining asymptotic expansion.
In this paper, we study two kind of L^2 norm preserved non-local heat flows on closed manifolds. We first study the global existence, stability and asymptotic behavior to such non-local heat flows. Next we give the gradient estimates of positive solutions to these heat flows.
The paper develops heat kernel comparison theorems and applies them to spectral geometry.
Heat flow fails to preserve concavity in curved spaces.
We develop a new method for the calculation of the heat trace asymptotics of the Laplacian on symmetric spaces that is based on a representation of the heat semigroup in form of an average over the Lie group of isometries and obtain a generating function for the whole sequence of all heat invariants.
Bounds on Hessian of heat equation coupled with Ricci flow.
We study new invariants of elliptic partial differential operators acting on sections of a vector bundle over a closed Riemannian manifold that we call the relativistic heat trace and the quantum heat traces. We obtain some reduction formulas expressing these new invariants in terms of some integral transforms of the u…
Exponential rate of convergence for harmonic heat flow maps.
From the uniformization theorem, we know that every Riemann surface has a simply-connected covering space. Moreover, there are only three simply-connected Riemann surfaces: the sphere, the Euclidean plane, and the hyperbolic plane. In this paper, we collect the known heat kernels, or Green's functions, for these three …
In a 1991 paper by Buttig and Eichhorn, the existence and uniqueness of a differential forms heat kernel on open manifolds of bounded geometry was proven. In that paper, it was shown that the heat kernel obeyed certain properties, one of which was a relationship between the derivative of heat kernel of different degree…
New heat semigroup characterizes Sobolev and BV spaces in Carnot groups.