Related papers: Normal numbers and normality measure

The normal sequences NS(n) and near-normal sequences NN(n) play an important role in the construction of orthogonal designs and Hadamard matrices. They can be identified with certain base sequences (A;B;C;D), where A and B have length n+1…

The consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maximization of expected utility. It enables the decider to assign…

Likelihood is a standard estimate for outlier detection. The specific role of the normalization constraint is to ensure that the out-of-distribution (OOD) regime has a small likelihood when samples are learned using maximum likelihood.…

This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…

This is the fourth in a series of articles devoted to showing that a typical covering map of large degree to a fixed, regular graph has its new adjacency eigenvalues within the bound conjectured by Alon for random regular graphs. In this…

We prove the chain rule in the more general framework of the Wiener-Poisson space, allowing us to obtain the so-called Nourdin-Peccati bound. From this bound we obtain a second-order Poincare-type inequality that is useful in terms of…

The particle number $N$ can be used as a quantitative gauge of non-Gaussianity. This idea extends to systems that are not literally finite by assigning them a notional $N$ that captures the same deviation. For an ideal gas with $N$…

Let K be a finite Galois extension of Q. The normal basis theorem provides an element of K whose conjugates form a Q-basis of K. Here we obtain such an element with controlled size. This improves a recent result by Fukshansky and Jeong. By…

A few years ago new quantitative measures of pseudorandomness of binary sequences have been introduced. Since that these measures have been studied in many papers and many constructions have been given along these lines. In this paper the…

A great challenge in the analysis of the discrepancy function D_N is to obtain universal lower bounds on the L-infty norm of D_N in dimensions d \geq 3. It follows from the average case bound of Klaus Roth that the L-infty norm of D_N is at…

In this paper, we obtain the upper bounds for the Hausdorff measures of nodal sets of eigenfunctions with the Robin boundary conditions, i.e., \begin{equation*} {\left\{\begin{array}{l} \triangle u+\lambda u=0,\quad in\quad \Omega,\\…

The nonparametric problem of detecting existence of an anomalous interval over a one dimensional line network is studied. Nodes corresponding to an anomalous interval (if exists) receive samples generated by a distribution q, which is…

We investigate the minimal error in approximating a general probability measure $\mu$ on $\mathbb{R}^d$ by the uniform measure on a finite set with prescribed cardinality $n$. The error is measured in the $p$-Wasserstein distance. In…

This paper is concerned with the following logarithmic Schr\"{o}dinger system: $$\left\{\begin{align} \ &\ -\Delta u_1+\omega_1u_1=\mu_1 u_1\log u_1^2+\frac{2p}{p+q}|u_2|^{q}|u_1|^{p-2}u_1,\\ \ &\ -\Delta u_2+\omega_2u_2=\mu_2 u_2\log…

We prove independence of normality to different bases We show that the set of real numbers that are normal to some base is Sigma^0_4 complete in the Borel hierarchy of subsets of real numbers. This was an open problem, initiated by…

A quantitative regularity theory is developed for weak solutions to the parabolic system $$ \partial_t u-\mathrm{div}\,{\boldsymbol{\mathsf A}}(x,t,Du)=0 \quad\text{in }E_T\subset \mathbb{R}^N\times\mathbb{R}, $$ which features the…

A.A. Suslin proved a normality theorem for an elementary linear group, which says that an elementary linear group of size bigger than or equal to 3 over a commutative ring with unity is normal in the general linear group of same size.…

We establish some new non-asymptotical lower bounds for deviation of regular unbiased estimation of unknown parameter from its true value in different norms, alike the classical Rao-Kramer's inequality. We show that if the new norm is…

We study sequential multiple testing with independent data streams, where the goal is to identify an unknown subset of signals while controlling commonly used error metrics, including generalized familywise rates and false discovery and…

Using the notion of higher-order Fourier dimension introduced in \cite{M2} (which was a sort of psuedorandomness condition stemming from the Gowers norms of Additive Combinatorics), we prove a maximal theorem and corresponding…