Related papers: Normal and pseudonormal numbers
Many research works have concerned normality-preserving selection rules and operations on the sequence of digits of a given normal number that maintain or violate normality. This leads us to introduce rearrangement operations on finite…
We define some natural notions of strong and weak Borel Ramsey properties for countable Borel equivalence relations and show that they hold for a countable Borel equivalence relation if and only if the equivalence relation is smooth. We…
We consider sequences of polynomials that satisfy differential-difference recurrences. Polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete…
All the already known results on self descriptive numbers, together with the demonstration of the uniqueness for bases greater than 6, are here obtained through a systematic scheme of proof and not trial and error. The proof is also…
We formalize the idea of probability distributions that lead to reliable predictions about some, but not all aspects of a domain. The resulting notion of `safety' provides a fresh perspective on foundational issues in statistics, providing…
Separation logic is a substructural logic which has proved to have numerous and fruitful applications to the verification of programs working on dynamic data structures. Recently, Barthe, Hsu and Liao have proposed a new way of giving…
We establish a necessary condition for pseudoprimality and a sufficient condition for primality of Fermat numbers, based on a congruence involving the exponent $(F_n-1)/4$. Moreover, in connection with P\'epin's primality test, we obtain a…
In the present paper we extend Champernowne's construction of normal numbers to provide sequences which are generic for a given invariant probability measure, which need not be the maximal one. We present a construction together with…
A class of self-similar sets of entangled quantum states is introduced, for which a recursive definition is provided. These sets, the "Bell gems," are defined by the subsystem exchange symmetry characteristic of the Bell states. Each Bell…
Contrary to popular misconception, the question in the title is far from simple. It involves sets of numbers on the first level, sets of sets of numbers on the second level, and so on, endlessly. The infinite hierarchy of the levels…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
A stratified pseudomanifold is normal if its links are connected. A normalization of a stratified pseudomanifold $X$ is a normal stratified pseudomanifold $Y$ together with a finite-to-one projection $n:Y\to X$ satisfying a local condition…
We consider Bernoulli measures $\mu_p$ on the interval $[0,1]$. For the standard Lebesgue measure the digits $0$ and $1$ in the binary representation of real numbers appear with an equal probability $1/2$. For the Bernoulli measures, the…
Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…
Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future…
We study a natural measurable selection problem for which the standard uniformisation theorems do not seem to apply directly, yet a Borel selector exists. More precisely, we consider families of finite dimensional functions that admit…
We consider the problem of sensitivity of threshold risk, defined as the probability of a function of a random variable falling below a specified threshold level $\delta >0.$ We demonstrate that for polynomial and rational functions of that…
We show a Condition Number Theorem for the condition number of zero counting for real polynomial systems. That is, we show that this condition number equals the inverse of the normalized distance to the set of ill-posed systems (i.e., those…
We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on the parameter…
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a…