Computing cube roots when a fast square root is available

AbstractWhen a fast square root is available, it may be advantageous to use it to assist in the evaluation of cube roots. Several iteration methods are developed for computing cube roots, some of which should be superior to the conventional Newton's method in certain situations

Ramsey numbers of graphs with long tails

AbstractThe ramsey number of a connected nonbipartite graph G with a sufficiently long path emanating from one of its points is found to be (n−1)(χ−1)+s, where n is the number of points of G, χ is the chromatic number of G, and s is the minimum possible number of points in a color class in a χ-coloring of the points of G

Outcome measures for children with speech sound disorder : an umbrella review protocol

Introduction: Speech sound disorder (SSD) describes a ‘persistent difficulty with speech sound production that interferes with speech intelligibility or prevents verbal communication’. There is a need to establish which care pathways are most effective and efficient for children with SSD. Comparison of care pathways requires clearly defined, evidence-based, interventions and agreement on how to measure the outcomes. At present no list of assessments, interventions or outcomes exists. The objective of this paper is to provide a rigorous and detailed protocol for an umbrella review of assessments, interventions, and outcomes which target SSD in children. The protocol details the development of a search strategy, and trial of an extraction tool. Methods and Analyses: The umbrella review has been registered with PROSPERO (CRD42022316284). Papers included can use a review methodology of any sort, but must include children of any age, with a SSD of unknown origin. In accordance with the Joanna Briggs institute scoping review methods guidelines, an initial search of the Ovid Emcare and Ovid Medline databases was conducted. Following this a final search strategy for these databases were produced. A draft extraction form was developed. Ethics and Dissemination: Ethical approval is not needed for an umbrella review protocol. Following the systematic development of an initial search strategy and extraction form, an umbrella review of this topic can take place. Dissemination of findings will be through peer-reviewed publications, social media, and patient and public engagement

Short proofs of some extremal results III

We prove a selection of results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are reasonably short

Lines, Circles, Planes and Spheres

Let $S$ be a set of $n$ points in $\mathbb{R}^3$, no three collinear and not all coplanar. If at most $n-k$ are coplanar and $n$ is sufficiently large, the total number of planes determined is at least $1 + k \binom{n-k}{2}-\binom{k}{2}(\frac{n-k}{2})$. For similar conditions and sufficiently large $n$, (inspired by the work of P. D. T. A. Elliott in \cite{Ell67}) we also show that the number of spheres determined by $n$ points is at least $1+\binom{n-1}{3}-t_3^{orchard}(n-1)$, and this bound is best possible under its hypothesis. (By $t_3^{orchard}(n)$, we are denoting the maximum number of three-point lines attainable by a configuration of $n$ points, no four collinear, in the plane, i.e., the classic Orchard Problem.) New lower bounds are also given for both lines and circles.Comment: 37 page

Measurements of long-range near-side angular correlations in sNN=5\sqrt{s_{\text{NN}}}=5TeV proton-lead collisions in the forward region

Two-particle angular correlations are studied in proton-lead collisions at a nucleon-nucleon centre-of-mass energy of $\sqrt{s_{\text{NN}}}=5$TeV, collected with the LHCb detector at the LHC. The analysis is based on data recorded in two beam configurations, in which either the direction of the proton or that of the lead ion is analysed. The correlations are measured in the laboratory system as a function of relative pseudorapidity, $\Delta\eta$, and relative azimuthal angle, $\Delta\phi$, for events in different classes of event activity and for different bins of particle transverse momentum. In high-activity events a long-range correlation on the near side, $\Delta\phi \approx 0$, is observed in the pseudorapidity range $2.0<\eta<4.9$. This measurement of long-range correlations on the near side in proton-lead collisions extends previous observations into the forward region up to $\eta=4.9$. The correlation increases with growing event activity and is found to be more pronounced in the direction of the lead beam. However, the correlation in the direction of the lead and proton beams are found to be compatible when comparing events with similar absolute activity in the direction analysed.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-040.htm

Evidence for the strangeness-changing weak decay Ξb−→Λb0π−\Xi_b^-\to\Lambda_b^0\pi^-

Using a $pp$ collision data sample corresponding to an integrated luminosity of 3.0~fb$^{-1}$, collected by the LHCb detector, we present the first search for the strangeness-changing weak decay $\Xi_b^-\to\Lambda_b^0\pi^-$. No $b$ hadron decay of this type has been seen before. A signal for this decay, corresponding to a significance of 3.2 standard deviations, is reported. The relative rate is measured to be ${{f_{\Xi_b^-}}\over{f_{\Lambda_b^0}}}{\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-) = (5.7\pm1.8^{+0.8}_{-0.9})\times10^{-4}$, where $f_{\Xi_b^-}$ and $f_{\Lambda_b^0}$ are the $b\to\Xi_b^-$ and $b\to\Lambda_b^0$ fragmentation fractions, and ${\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-)$ is the branching fraction. Assuming $f_{\Xi_b^-}/f_{\Lambda_b^0}$ is bounded between 0.1 and 0.3, the branching fraction ${\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-)$ would lie in the range from $(0.57\pm0.21)\%$ to $(0.19\pm0.07)\%$.Comment: 7 pages, 2 figures, All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-047.htm

BB flavour tagging using charm decays at the LHCb experiment

An algorithm is described for tagging the flavour content at production of neutral $B$ mesons in the LHCb experiment. The algorithm exploits the correlation of the flavour of a $B$ meson with the charge of a reconstructed secondary charm hadron from the decay of the other $b$ hadron produced in the proton-proton collision. Charm hadron candidates are identified in a number of fully or partially reconstructed Cabibbo-favoured decay modes. The algorithm is calibrated on the self-tagged decay modes $B^+ \to J/\psi \, K^+$ and $B^0 \to J/\psi \, K^{*0}$ using $3.0\mathrm{\,fb}^{-1}$ of data collected by the LHCb experiment at $pp$ centre-of-mass energies of $7\mathrm{\,TeV}$ and $8\mathrm{\,TeV}$. Its tagging power on these samples of $B \to J/\psi \, X$ decays is $(0.30 \pm 0.01 \pm 0.01) \%$.Comment: All figures and tables, along with any supplementary material and additional information, are available at http://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-027.htm

Identification of beauty and charm quark jets at LHCb

Identification of jets originating from beauty and charm quarks is important for measuring Standard Model processes and for searching for new physics. The performance of algorithms developed to select $b$- and $c$-quark jets is measured using data recorded by LHCb from proton-proton collisions at $\sqrt{s}=7$ TeV in 2011 and at $\sqrt{s}=8$ TeV in 2012. The efficiency for identifying a $b(c)$ jet is about 65%(25%) with a probability for misidentifying a light-parton jet of 0.3% for jets with transverse momentum $p_{\rm T} > 20$ GeV and pseudorapidity $2.2 < \eta < 4.2$. The dependence of the performance on the $p_{\rm T}$ and $\eta$ of the jet is also measured

Search for B⁺c decays to the pp‾π⁺ final state

A search for the decays of the B + c meson to pp-π + is performed for the first time using a data sample corresponding to an integrated luminosity of 3.0 fb -1 collected by the LHCb experiment in pp collisions at centre-of-mass energies of 7 and 8 TeV. No signal is found and an upper limit, at 95% confidence level, is set, fcfu×B(B + c →ppπ + ) < 3.6×10-8 in the kinematic region m(pp) < 2.85 GeV/c2, p T (B) < 20 GeV/c and 2.0 < y(B) < 4.5, where B is the branching fraction and f c (f u ) is the fragmentation fraction of the b quark into a B c + (B + ) meson