arXiv research

Study on heat content for submanifolds in sub-Riemannian geometry.

Study heat content in sub-Riemannian manifolds, obtaining asymptotic expansion.

Study on heat content for domains with fractal boundaries.

Study heat content on RCD(K,N) spaces with specific boundary conditions.

Classifies domains critical for heat content and exit-time moments.

We obtain upper bounds on the heat content and on the torsional rigidity of a complete Riemannian manifold M, assuming a generalized Hardy inequality for the Dirichlet Laplacian on M.

Study spectral properties of sub-Laplacians in Carnot groups.

Study shows how heat leaks from material sets in low diffusivity scenarios.

Study heat content in sub-Riemannian structures, proving asymptotic series existence and coefficients.

Let $M$ be a Riemannian manifold and $Ω$ a compact domain of $M$ with smooth boundary. We study the solution of the heat equation on $Ω$ having constant unit initial conditions and Dirichlet boundary conditions. The purpose of this paper is to study the geometry of domains for which, at any fixed value of time, the nor…

This monograph develops the theory of covariant Schrödinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch. Contents: I. Sobolev spaces on vector bundles II. Smooth heat kernels on vector bundles III. Basis differential operators in Riemannian manifolds IV. Some specif…

The paper applies Gaussianization to analyze Earth data, simplifying complex multivariate distributions.

Study shows online learning algorithms incentivize low-quality content, proposing new algorithms to improve quality.

Proposes a model to optimize feedback for content creators on social media.

Proposes a VAE variant for ordinal content factors.

Sensory data are often comprised of independent content and transformation factors. For example, face images may have shapes as content and poses as transformation. To infer separately these factors from given data, various ``disentangling'' models have been proposed. However, many of these are supervised or semi-super…

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.

In the industry of video content providers such as VOD and IPTV, predicting the popularity of video contents in advance is critical not only from a marketing perspective but also from a network optimization perspective. By predicting whether the content will be successful or not in advance, the content file, which is l…

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…

Many businesses are using recommender systems for marketing outreach. Recommendation algorithms can be either based on content or driven by collaborative filtering. We study different ways to incorporate content information directly into the matrix factorization approach of collaborative filtering. These content-booste…

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…

Spotify improves content mix using contextual bandits.

The paper studies heat kernel asymptotics and proves Morse inequalities.

A new model considers fatigue in online content recommendation systems.

New PCGML approach generates novel game content across multiple platformer domains.

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…

We consider visual domains in which a class label specifies the content of an image, and class-irrelevant properties that differentiate instances constitute the style. We present a domain-independent method that permits the open-ended recombination of style of one image with the content of another. Open ended simply me…

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…

New study shows personalized content recommendations can lead to polarization of user preferences.

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.

Text style transfer aims to modify the style of a sentence while keeping its content unchanged. Recent style transfer systems often fail to faithfully preserve the content after changing the style. This paper proposes a structured content preserving model that leverages linguistic information in the structured fine-gra…

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…

With rapid development of the Internet, web contents become huge. Most of the websites are publicly available, and anyone can access the contents from anywhere such as workplace, home and even schools. Nevertheless, not all the web contents are appropriate for all users, especially children. An example of these content…

Paper studies smoothness of bi-conformal heat flow on 4-manifolds.

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.