相关论文: Sensitivity kernels for time-distance helioseismol…

Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…

Strongly lensed supernovae (glSNe) provide a powerful, independent method to measure the Hubble constant, $H_{0}$, through time delays between their multiple images. The accuracy of this measurement depends critically on both the precision…

The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…

Using a 3D global solver of the linearized Euler equations, we model acoustic oscillations over background velocity flow fields of single-cell meridional circulation with deep and shallow return flows as well as double-cell meridional…

Aims. The H-alpha emission of solar flare kernels and associated hard X-ray (HXR) emission often show similar time variations but their light curves are shifted in time by energy transfer mechanisms. We searched for fast radiative response…

Using the Zwanzig projection-operator formalism, we derive a causal two-point spatiotemporal kernel for heat conduction, defined microscopically as a space-resolved equilibrium heat-flux time-correlation function, that encodes temporal…

Supergranules create a peak in the spatial spectrum of photospheric velocity features. They have some properties of convection cells but their origin is still being debated in the literature. The time-distance helioseismology constitutes a…

The modeling of the heliosphere requires continuous three-dimensional solar wind data. The in-situ out-of-ecliptic measurements are very rare, so that other methods of solar wind detection are needed. We use the remote-sensing data of the…

Recent revisions of the determination of the solar composition have resulted in solar models in marked disagreement with helioseismic inferences. The effect of the composition change on the model is largely caused by the change in the…

As large--distance rays (say, 10\,-\,$24 ^\circ$) approach the solar surface approximately vertically, travel times measured from surface pairs for these large separations are mostly sensitive to vertical flows, at least for shallow flows…

This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…

The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…

Seismology of coronal loops using observations of damped transverse oscillations in combination with results from theoretical models is a tool to indirectly infer physical parameters in the solar atmospheric plasma. Existing seismology…

A crucial feature not widely accounted for in local helioseismology is that surface magnetic regions actually open a window from the interior into the solar atmosphere, and that the seismic waves leak through this window, reflect high in…

The quantum correlations of $N$ noninteracting spinless fermions in their ground state can be expressed in terms of a two-point function called the kernel. Here we develop a general and compact method for computing the kernel in a general…

Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…

A key component of solar interior dynamics is the meridional circulation (MC), whose poleward component in the surface layers has been well observed. Time-distance helioseismic studies of the deep structure of MC, however, have yielded…

We introduce the loss kernel, an interpretability method for measuring similarity between data points according to a trained neural network. The kernel is the covariance matrix of per-sample losses computed under a distribution of…

This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…

Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…