Related papers: New separation between $s(f)$ and $bs(f)$

The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in…

About 90% of Bs-bar Bs pairs produced at the Upsilon(5s) resonance are initially Bs*-bar Bs* pairs which decay radiatively to Bs-bar Bs. This implies that the Bs pair will then be in an eigenstate of charge conjugation (i.e. C=-1) and…

Sensitivity is an important complexity measure of Boolean functions. In this paper we present properties of the minimal and maximal sensitivity of the simplified weighted sum function. A simple close formula of the minimal sensitivity of…

Let $\Lambda_s$ denote the Lipschitz space of order $s\in(0,\infty)$ on $\mathbb{R}^n$, which consists of all $f\in\mathfrak{C}\cap L^\infty$ such that, for some constant $L\in(0,\infty)$ and some integer $r\in(s,\infty)$, \begin{equation*}…

We establish sensitivity analysis on the sphere. We present formulas that allow us to decompose a function $f\colon \mathbb S^d\rightarrow \mathbb R$ into a sum of terms $f_{\boldsymbol u,\boldsymbol \xi}$. The index $\boldsymbol u$ is a…

Rare leptonic decays of $B_{(s)}^0$ mesons are sensitive probes of New Physics effects. A combination of the CMS and LHCb analyses on the search of the rare decays $B_{s}^0 \rightarrow \mu^+\mu^-$ and $B^0 \rightarrow \mu^+\mu^-$ is…

We have made the first observation of Bs->Ds(*)+Ds(*)- decays using 23.6 fb-1 of data recorded by the Belle experiment running on the Upsilon(5S) resonance. The branching fractions are measured to be B(B^0_s\ra D^+_s D^-_s) =…

Using $pp$ collision data collected by LHCb at center-of-mass energies $\sqrt{s}$ = 7 TeV and 8 TeV, corresponding to an integrated luminosity of 3 fb$^{-1}$, the ratio of the branching fraction of the $B_c^+ \rightarrow \psi(2S)\pi^+$…

In discriminating between objects from different classes, the more separable these classes are the less computationally expensive and complex a classifier can be used. One thus seeks a measure that can quickly capture this separability…

The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…

In this paper we compute the Fourier spectra of some recently discovered binomial APN functions. One consequence of this is the determination of the nonlinearity of the functions, which measures their resistance to linear cryptanalysis.…

Bose proved the inequality $b\geq v+r-1$ for resolvable balanced incomplete block designs (RBIBDs) and Kageyama improved it for RBIBDs which are not affine resolvable. In this note we prove a new lower bound on the number of blocks $b$ that…

The ratio of the $B^0_s$ and $B^0$ fragmentation fractions, $f_s/f_d$, in proton-proton collisions at the LHC, is obtained as a function of $B$-meson transverse momentum and collision centre-of-mass energy from the combined analysis of…

In this paper we prove results regarding Boolean functions with small spectral norm (the spectral norm of f is $\|\hat{f}\|_1=\sum_{\alpha}|\hat{f}(\alpha)|$). Specifically, we prove the following results for functions $f:\{0,1\}^n \to…

We determine the order of magnitude of the variance of the Fibonacci partition function. The answer is different to the most naive guess. The proof involves a diophantine system and an inhomogeneous linear recurrence.

Boolean automata networks (aka Boolean networks) are space-time discrete dynamical systems, studied as a model of computation and as a representative model of natural phenomena. A collection of simple entities (the automata) update their…

The decay psi(2S)-->K_S K_L is observed for the first time using psi(2S) data collected with the Beijing Spectrometer (BESII) at the Beijing Electron Positron Collider (BEPC); the branching ratio is determined to be B(psi(2S)-->K_S K_L) =…

In this investigation, we have suggested a special two-slit experiment which can distinguish between the standard and the Bohmian quantum mechanics. At the first step, we have shown that observable individual predictions obtained from these…

The study of the hyperfine (hfs) anomaly in neutron rich nuclei can give a very specific and unique way to study the neutron distribution and the clustering structure. We study the sensitivity of the hfs anomaly to the clustering effects in…

We present a new method for proving Correa-Jofr\'e-Thibault theorem that monotonicity of subdifferential implies convexity of the function. This new method is based on barrier functions. Barrier functions help overcome some of the main…