Related papers: New separation between $s(f)$ and $bs(f)$
An examination of leptons in ${\Upsilon (4S)}$ events tagged by reconstructed $B$ decays yields semileptonic branching fractions of $b_-=(10.1 \pm 1.8\pm 1.4)\%$ for charged and $b_0=(10.9 \pm 0.7\pm 1.1)\%$ for neutral $B$ mesons. This is…
One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required.…
In this paper, we propose the Fourier Discrepancy Function, a new discrepancy to compare discrete probability measures. We show that this discrepancy takes into account the geometry of the underlying space. We prove that the Fourier…
For a translation invariant convex density basis $B$ it is shown that its Busemann-Feller extension $B_{\mathrm{BF}}$ has close to $B$ properties, in particular, $B_{\mathrm{BF}}$ differentiates the same class of non-negative functions as…
Using 14M $\psi (2S)$ events collected at BESII, the branching fraction of $\psi (2S)\to \tau ^{+}\tau ^{-}$ is measured to be $Br_{\tau \tau}=(3.10\pm 0.21\pm 0.38)\times 10^{-3}$, where the first error is statistical and the second is…
Bourgain showed that any noise stable Boolean function $f$ can be well-approximated by a junta. In this note we give an exponential sharpening of the parameters of Bourgain's result under the additional assumption that $f$ is a halfspace.
Second-order Boolean logic is a generalization of QBF, whose constant alternation fragments are known to be complete for the levels of the exponential time hierarchy. We consider two types of restriction of this logic: 1) restrictions to…
We report the first observation of $B_s^0\to J/\psi\eta$ and evidence for $B_s^0\to J/\psi\eta'$. These results are obtained from $23.6 \mathrm{fb}^{-1}$ of data collected at the $\Upsilon(5S)$ resonance with the Belle detector at the KEKB…
A Boolean function $f$ on $n$ variables is said to be a bent function if the absolute value of all its Walsh coefficients is $2^{n/2}$. Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on…
Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testing PTFs has exploited structural and…
In this work we investigate into energy complexity, a Boolean function measure related to circuit complexity. Given a circuit $\mathcal{C}$ over the standard basis $\{\vee_2,\wedge_2,\neg\}$, the energy complexity of $\mathcal{C}$, denoted…
Given Boolean functions \( f, g : \mathbb{F}_2^n \to \{-1,+1\} \), we say they are {\em linearly isomorphic} if there exists \( A \in \mathrm{GL}_n(\mathbb{F}_2) \) such that \( f(x)=g(Ax) \) for all \( x \). We study this problem in the…
In a recent work with Kindler and Wimmer we proved an invariance principle for the slice for low-influence, low-degree functions. Here we provide an alternative proof for general low-degree functions, with no constraints on the influences.…
We discuss the physics case of a high luminosity B-Factory running at the Y(5S) resonance. We show that the coherence of the B meson pairs is preserved at this resonance, and that Bs can be well distinguished from Bd and charged B mesons.…
This paper develops upper and lower bounds for the probability of Boolean functions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. We call this approach dissociation and give an…
The decay $B_c^+ \to \psi(2S)\pi^+$ with $\psi(2S) \to \mu^+\mu^-$ is observed with a significance of $5.2\,\sigma$ using $pp$ collision data corresponding to an integrated luminosity of $1.0\,\invfb$ collected by the LHCb experiment. The…
Frequency Selective Bolometers (FSBs) are a new type of detector for millimeter and sub-millimeter wavelengths that are transparent to all but a narrow range of frequencies as set by characteristics of the absorber itself. Therefore, stacks…
We report a measurement of the $B^0\rightarrow\psi(2S)\pi^0$ branching fraction based on the full $\Upsilon(4S)$ data set of $772\times10^{6}$ $B\bar{B}$ pairs collected by the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.…
A sample of 3.95M $\psi(2S)$ decays registered in the BES detector are used to study final states containing pairs of octet and decuplet baryons. We report branching fractions for $\psi(2S)\to p\bar{p}$, $\Lambda\bar{\Lambda}$,…
Consider critical Bernoulli percolation in the plane. We give a new proof of the sharp noise sensitivity theorem shown by Garban, Pete and Schramm. Contrary to the previous approaches, we do not use any spectral tool. We rather study…