arXiv research

Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.

Automated design using neural networks and gradient descent.

The paper explores how sinks and diagonal patterns prevent attention oversmoothing.

This work explains the structural origins of attention sinks in LLMs.

New approach identifies offshore financial centers in global corporate network.

New proof of injectivity for broken non-abelian X-ray transform in Minkowski space.

FlowGN tackles graph representation learning by tracing information flow paths.

This paper surveys various methods for dimensionality reduction and nearest neighbor search.

A new method reduces the computational cost of Sinkhorn algorithm for OT and UOT problems.

An efficient method to price bonds with optional sinking feature is presented. Such instruments equip their issuer with the option (but not the obligation) to redeem parts of the notional prior to maturity, therefore the future cash flows are random. In a one-factor model for the issuer's default intensity we show that…

We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after eliminating trivial bubbles in the branched surface). The first three conditions are…

Proves analyticity of quasinormal modes in Kerr and Kerr-de Sitter spacetimes.

Randomly initialized transformers show extreme token preferences.

Gradient flow in softmax models tends to produce low-entropy outputs.

McKernel speeds up kernel approximations for large-scale learning.

This study analyzes information flow networks in Chinese stock sectors using transfer entropy.

A graph (digraph) $G=(V,E)$ with a set $T\subseteq V$ of terminals is called inner Eulerian if each nonterminal node $v$ has even degree (resp. the numbers of edges entering and leaving $v$ are equal). Cherkassky and Lovász showed that the maximum number of pairwise edge-disjoint $T$-paths in an inner Eulerian graph $G…

Data-driven method clusters and analyzes heat load patterns in district heating networks.

Study Kleinian groups using orbital functions and heat kernels.

The Poincare-Hopf theorem tells us that given a smooth, structurally stable vector field on a surface of genus g, the number of saddles is 2-2g less than the number of sinks and sources. We generalize this result by introducing a more complex combinatorial invariant. Using this tool, we demonstrate that many such struc…

Quantum heat traces study new invariants from elliptic operators.

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…

The paper proves recurrence relations for heat kernels on hyperbolic and spherical spaces.

Despite their successes, what makes kernel methods difficult to use in many large scale problems is the fact that storing and computing the decision function is typically expensive, especially at prediction time. In this paper, we overcome this difficulty by proposing Fastfood, an approximation that accelerates such co…

Study on biharmonic map heat flow with monotonicity formula.

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…

New entropy formulae for heat equation on manifolds.

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…

New Alexander polynomial defined for transverse graphs.

Geometric symbols help compute heat invariants.

The paper studies heat kernel asymptotics and proves Morse inequalities.

Derives gradient estimates for CR heat equation on pseudo-Hermitian manifolds.

New method predicts heat load in thermal grids using latent variables.

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…

Paper studies heat flow for maps on manifolds, avoiding singularities.

SEA model predicts heat demand combining neural network and ARIMA.

New heat equation method solves intertwining problems in CR geometry.

Proves upper bounds for heat kernels evolving on manifolds.

Formulae connect heat kernels on glued manifolds.

Study the heat kernel on quaternionic anti-de Sitter spaces and related spaces.

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.

The study examines heat kernel bounds for manifolds with Ricci curvature in the Kato class.

Study spectral invariants for polygons and orbisurfaces.