Related papers: New separation between $s(f)$ and $bs(f)$
In the SU(3) symmetry limit, semileptonic $D^+\to Sl^+\nu$ and $B^-\to Sl^-\bar\nu$ decays, with $S=a_0(980)$, $f_0(980)$ and $f_0(600)$, are found to obey different sum rules in the $\bar qq$ and the tetra-quark descriptions for scalar…
We prove two main results on how arbitrary linear threshold functions $f(x) = \sign(w\cdot x - \theta)$ over the $n$-dimensional Boolean hypercube can be approximated by simple threshold functions. Our first result shows that every…
Atoms and molecules can serve as sensitive probes of a possible variation of the fine structure constant $\alpha$ and electron-to-proton mass ratio $\mu$. Two types of sensitivity coefficients are often used to quantify and compare the…
A natural measure of smoothness of a Boolean function is its sensitivity (the largest number of Hamming neighbors of a point which differ from it in function value). The structure of smooth or equivalently low-sensitivity functions is still…
The approximate degree of a Boolean function $f: \{-1, 1\}^n \to \{-1, 1\}$ is the minimum degree of a real polynomial that approximates $f$ to within error $1/3$ in the $\ell_\infty$ norm. In an influential result, Aaronson and Shi (J. ACM…
A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$ and parameters $k$ and $d$, we prove a strong upper bound on the…
We have measured the branching fractions of the colour suppressed decays B^{+} --> \psi(2S) K^{*+}(892) and B^{0} --> psi(2S)K^{*0}(892) using a data sample of 84 million B\bar{B} events recorded by the Belle detector on the Upsilon(4S)…
In this paper, we first study a new sensitivity index that is based on higher moments and generalizes the so-called Sobol one. Further, following an idea of Borgonovo ([3]), we define and study a new sensitivity index based on the…
The observation of new suppressed Bs decays, Bs-> J/Psi K* (892)0 and Bs->J/Psi Ks, and the measurement of their branching ratios are presented. This measurement is based on an integrated luminosity of 5.9 fb-1 of CDF data collected by a…
We combine all the available experimental information on Bs mixing, including the very recent tagged analyses of Bs to J/Psi phi by the CDF and D0 collaborations. We find that the phase of the Bs mixing amplitude deviates more than 3 sigma…
In this work, we consider a new type of Fourier-like representation of Boolean function $f\colon\{+1,-1\}^n\to\{+1,-1\}$ \[ f(x) = \cos\left(\pi\sum_{S\subseteq[n]}\phi_S \prod_{i\in S} x_i\right). \] This representation, which we call the…
We show an equivalence between 1-query quantum algorithms and representations by degree-2 polynomials. Namely, a partial Boolean function $f$ is computable by a 1-query quantum algorithm with error bounded by $\epsilon<1/2$ iff $f$ can be…
The relative rates of B-meson decays into $J/\psi$ and $\psi(2S)$ mesons are measured for the three decay modes in pp collisions recorded with the LHCb detector. The ratios of branching fractions ($\mathcal{B}$) are measured to be…
Recently the study of noise sensitivity and noise stability of Boolean functions has received considerable attention. The purpose of this paper is to extend these notions in a natural way to a different class of perturbations, namely those…
In this paper, we establish a new bound tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a…
Reversible Boolean function is a one-to-one function which maps $n$-bit input to $n$-bit output. Reversible logic synthesis has been widely studied due to its relationship with low-energy computation as well as quantum computation. In this…
For a real function $f:[0,1]\to\mathbb{R}$, the difference quotient of $f$ is the function of two real variables $\operatorname{DQ}_f(a,b)=\dfrac{f(b)-f(a)}{b-a}$, which we view as defined on the triangle $\mathcal{T}=\{(a,b):0\leq…
A Boolean function $f:\{0,1\}^n \mapsto \{0,1\}$ is said to be $\eps$-far from monotone if $f$ needs to be modified in at least $\eps$-fraction of the points to make it monotone. We design a randomized tester that is given oracle access to…
In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and…
A function $f : \mathbb{F}_2^n \to \mathbb{R}$ is $s$-sparse if it has at most $s$ non-zero Fourier coefficients. Motivated by applications to fast sparse Fourier transforms over $\mathbb{F}_2^n$, we study efficient algorithms for the…