Related papers: New separation between $s(f)$ and $bs(f)$
We prove that, to compute a Boolean function $f$ on $N$ variables with error probability $\epsilon$, any quantum black-box algorithm has to query at least $\frac{1 - 2\sqrt{\epsilon}}{2} \rho_f N = \frac{1 - 2\sqrt{\epsilon}}{2} \bar{S}_f$…
We report measurements of branching fractions for psi(2S) decays into omega pi pi, b1 pi,omega f2(1270),omega KK, omega p pbar, phi pi pi, phi f0(980),phi KK, and an upper limit for phi p pbar final states based on a data sample of 4 X 10^6…
The branching fraction of the psi(2S) decay into tau pair has been measured for the first time using the BES detector at the Beijing Electron-Positron Collider. The result is $B_{\tau\tau}=(2.71\pm 0.43 \pm 0.55) \times 10^{-3}$, where the…
We propose a new frequency standard based on a $4f^{14} 6s6p~ ^3\!P_0 - 4f^{13} 6s^2 5d ~(J=2)$ transition in neutral Yb. This transition has a potential for high stability and accuracy and the advantage of the highest sensitivity among…
In the first part of this talk I discuss two somewhat different supergravity approaches to calculating correlation functions in strongly coupled Yang-Mills theory. The older approach relates two-point functions to cross-sections for…
We report first observations of $B_s^0\to J/\psi\eta$ and $B_s^0\to J/\psi\eta'$. The results are obtained from 121.4 fb^{-1} of data collected at the $\Upsilon(5S)$ resonance with the Belle detector at the KEKB $e^+e^-$ collider. We obtain…
Suppose that f is a boolean function from F_2^n to {0,1} with spectral norm (that is the sum of the absolute values of its Fourier coefficients) at most M. We show that f may be expressed as +/- 1 combination of at most 2^(2^(O(M^4)))…
In this paper, we uncover a new uncertainty principle that governs the complexity of Boolean functions. This principle manifests as a fundamental trade-off between two central measures of complexity: a combinatorial complexity of its…
In this paper we consider some properties of a space B(X) of Borel functions on a set of reals X, with pointwise topology, that are stronger than separability.
In a recent result, Knop, Lovett, McGuire and Yuan (STOC 2021) proved the log-rank conjecture for communication complexity, up to log n factor, for any Boolean function composed with AND function as the inner gadget. One of the main tools…
We study the relationship between two measures of Boolean functions; \emph{algebraic thickness} and \emph{normality}. For a function $f$, the algebraic thickness is a variant of the \emph{sparsity}, the number of nonzero coefficients in the…
A subset $S$ of the Boolean hypercube $\mathbb{F}_2^n$ is a sumset if $S = \{a + b : a, b\in A\}$ for some $A \subseteq \mathbb{F}_2^n$. Sumsets are central objects of study in additive combinatorics, featuring in several influential…
This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the…
QED theory of the hyperfine splitting of the $1s$ and $2s$ state in hydrogen isotopes and helium-3 ion is considered. We develop an accurate theory of a specific difference 8E_{HFS}(2s)-E_{HFS}(1s). We take into account fourth order…
A new combined sub-filter scale turbulence and shock-capturing model is developed for high-order finite volume numerics, extending previous work to unstructured solvers. Block Spectral Stresses (BSS) method relies on the spectra of the…
We give a non-adaptive algorithm that makes $2^{\tilde{O}(\sqrt{k\log(1/\varepsilon_2 - \varepsilon_1)})}$ queries to a Boolean function $f:\{\pm 1\}^n \rightarrow \{\pm 1\}$ and distinguishes between $f$ being $\varepsilon_1$-close to some…
Dempster-Shafer theory is widely applied in uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. A distance between two basic probability assignments(BPAs) presents a measure of performance…
In a recent paper by Jonasson and Steif, definitions to describe the volatility of sequences of Boolean functions, \( f_n \colon \{ -1,1 \}^n \to \{ -1,1 \} \) were introduced. We continue their study of how these definitions relate to…
The Gap-Hamming distance problem is the promise problem of deciding if the Hamming distance $h$ between two strings of length $n$ is greater than $a$ or less than $b$, where the gap $g=|a-b|\geq 1$ and $a$ and $b$ could depend on $n$. In…
The decay branching fractions of the three narrow Upsilon resonances to mu+ mu- have been measured by analyzing about 4.3 1/fb e+e- data collected with the CLEO III detector. The branching fraction B(Y(1S) -> mu+ mu-) = (2.49 +- 0.02 +-…