Related papers: Matching for generalised $\beta$-transformations

We put forward an adaptive alpha (Type I Error) that decreases as the information grows, for hypothesis tests in which nested linear models are compared. A less elaborate adaptation was already presented in \citet{PP2014} for comparing…

We show that if $B \subset \mathbb{R}^n$ and $E \subset A(n,k)$ is a nonempty collection of $k$-dimensional affine subspaces of $\mathbb{R}^n$ such that every $P \in E$ intersects $B$ in a set of Hausdorff dimension at least $\alpha$ with…

A family of permutations $A \subset S_n$ is said to be \emph{$t$-set-intersecting} if for any two permutations $\sigma, \pi \in A$, there exists a $t$-set $x$ whose image is the same under both permutations, i.e. $\sigma(x)=\pi(x)$. We…

We show that sequences of the form $\alpha n^{\theta} \pmod{1}$ with $\alpha > 0$ and $0 < \theta < \tfrac{43}{117} = \tfrac{1}{3} + 0.0341 \ldots$ have Poissonian pair correlation. This improves upon the previous result by Lutsko,…

We consider the tensor product $\pi_{\alpha}\otimes \pi_{\beta}$ of complementary series representations $\pi_{\alpha}$ and $\pi_{\beta}$ of classical rank one groups $SO_0(n, 1)$, $SU(n, 1)$ and $Sp(n, 1)$. We prove that there is a…

We introduce and develop a class of \textit{Cantor-winning} sets that share the same amenable properties as the classical winning sets associated to Schmidt's $(\alpha,\beta)$-game: these include maximal Hausdorff dimension, invariance…

In this letter, we generalize the convolutional NMF by taking the $\beta$-divergence as the contrast function and present the correct multiplicative updates for its factors in closed form. The new updates unify the $\beta$-NMF and the…

Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…

The dynamics of the second order rational difference equation $\displaystyle{z_{n+1}=\frac{\alpha + \alpha z_{n}+\beta z_{n-1}}{1+z_{n}}}$ with complex parameters $\alpha$, $\beta$ and arbitrary complex initial conditions is investigated.…

In this article, we consider $\beta$-ensembles, i.e. collections of particles with random positions on the real line having joint distribution $$\frac{1}{Z_N(\beta)}|\Delta(\lambda)|^\beta e^{- \frac{N\beta}{4}\sum_{i=1}^N\lambda_i^2}d…

We study the combination of two o-minimal extensions of the theory of real closed fields: one by a T-convex subring and the other by a T-derivation. Let T be a complete, model complete o-minimal extension of RCF. We show that the combined…

Given $\beta\in(1,2)$, a $\beta$-expansion of a real $x$ is a power series in base $\beta$ with coefficients 0 and 1 whose sum equals $x$. The aim of this note is to study certain problems related to the universality and combinatorics of…

We prove that the critical point and the point $1$ have dense orbits for Lebesgue-a.e., parameter pairs in the two-parameter skew-tent family and generalised $\beta$-transformations. As an application, we show that for the generalised…

Let $x \in [0,1)$ be an irrational number with continued fraction expansion $[a_1(x),a_2(x), \cdots,a_n(x),\cdots]$ and $q_n(x)$ be the denominator of its $n$-th convergent. We establish, for any $\alpha,\beta$ in $[0,+\infty]$, the…

We establish that the set of pairs $(\alpha, \beta)$ of real numbers such that $$ \liminf_{q \to + \infty} q \cdot (\log q)^2 \cdot \Vert q \alpha \Vert \cdot \Vert q \beta \Vert > 0, $$ where $\Vert \cdot \Vert$ denotes the distance to the…

In 2024, Garvan, Sellers and Smoot discovered a remarkable symmetry in the families of congruences for generalized Frobenius partitions $c\psi_{2,0}$ and $c\psi_{2,1}$. They also emphasized that the considerations for the general case of…

Let $T\colon\mathbb{T}^d\to \mathbb{T}^d$, defined by $T x=Ax(\bmod 1)$, where $A$ is a $d\times d$ integer matrix with eigenvalues $1<|\lambda_1|\le|\lambda_2|\le\dots\le|\lambda_d|$. We investigate the Hausdorff dimension of the…

Let $(X,d)$ be a compact metric space, $f:X \mapsto X$ be a continuous map satisfying a property we call almost specification (which is slightly weaker than the $g$-almost product property of Pfister and Sullivan), and $\phi$ be a…

The procedure underlying the matching of 1-form (tetrad) fields in theories possessing absolute parallelism -- f(T) gravity being within this category -- is addressed and exemplified. We show that the remnant symmetries of the intervening…

We propose formulas for the large $N$ expansion of the generating function of connected correlators of the $\beta$-deformed Gaussian and Wishart-Laguerre matrix models. We show that our proposal satisfies the known transformation properties…