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We study the renormalization group flow of higher derivative gravity, utilizing the functional renormalization group equation for the average action. Employing a recently proposed algorithm, termed the universal renormalization group…
This paper is the fourth and the last part of the series "Spherical higher order Fourier analysis over finite fields", aiming to develop the higher order Fourier analysis method along spheres over finite fields, and to solve the Geometric…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as…
A new two-parametric family of mass distribution for spherical stellar systems is considered. It generalizes families by Kuzmin, Veltmann (1972) and by An, Evans (2006). Steady velocity dispersions are found for these models by solving an…
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action $\Gamma_k$. The ordinary effective action $\Gamma_0$ can be obtained by integrating the flow equation from…
New type of tomographic probability distribution, which contains complete information on the density matrix (wave function) related to the Fresnel transform of the complex wave function, is introduced. Relation to symplectic tomographic…
We shall establish the convergence of an adaptive conforming finite element method for the reconstruction of the distributed flux in a diffusion system. The adaptive method is based on a posteriori error estimators for the distributed flux,…
In directional statistics, the von Mises-Fisher (vMF) distribution is one of the most basic and popular probability distributions for data on the unit hypersphere. Recently, the spherical normal (SN) distribution was proposed as an…
Diffusion magnetic resonance has been employed for determining the distribution of net displacements (ensemble average propagator), moments and correlations of net displacements, and the steady-state distribution of magnetized particles.…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design…
In this paper, we study how the mean shift algorithm can be used to denoise a dataset. We introduce a new framework to analyze the mean shift algorithm as a denoising approach by viewing the algorithm as an operator on a distribution…
We present a general theorem on the structure of bivariate generating functions which gives sufficient conditions such that the limiting probability distribution is a half-normal distribution. If $X$ is a normally distributed random…
Accurate representation of large-scale flow patterns in low-resolution ocean simulations is one of the most challenging problems in ocean modelling. The main difficulty is to correctly reproduce effects of unresolved small scales on the…
The incorporation of generative models as regularisers within variational formulations for inverse problems has proven effective across numerous image reconstruction tasks. However, the resulting optimisation problem is often non-convex and…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
A spatial signal is defined by its evaluations on the whole domain. In this paper, we consider stable reconstruction of real-valued signals with finite rate of innovations (FRI), up to a sign, from their magnitude measurements on the whole…