¿Conocía Sherlock Holmes la teoría de grafos?

En este artículo se muestran las ventajas que ofrece la Teoría de Grafos a la hora de resolver determinados problemas clásicos de Matemáticas, que normalmente se suelen intentar probando una a una las diferentes posibilidades existentes, o bien por el conocido método de la “cuenta de la vieja”. Su principal objetivo es mostrar cómo esta Teoría facilita una gran cantidad de estrategias útiles para la resolución de estos problemas, de manera más rápida, elegante y sencilla de la habitual. Uno de estos problemas trata precisamente de cómo Sherlock Holmes pudo resolver un caso de asesinato, utilizando los grafos.In this paper, we show the advantages offered by Graph Theory to solve some classic mathematical problems, which are normally solved by using other non systematic techniques, such that to go one to one testing different possibilities or to use what in Spain is called “la cuenta de la vieja”. Its main goal is to show how Graph Theory allows to systematize and formalize a lot of useful strategies to find the solution of those problems in an easier, smarter and faster way than usual. One of these problems deals with the solution given by Sherlock Holmes to a case of murder by using graphs

Effectiveness of an intervention for improving drug prescription in primary care patients with multimorbidity and polypharmacy:Study protocol of a cluster randomized clinical trial (Multi-PAP project)

This study was funded by the Fondo de Investigaciones Sanitarias ISCIII (Grant Numbers PI15/00276, PI15/00572, PI15/00996), REDISSEC (Project Numbers RD12/0001/0012, RD16/0001/0005), and the European Regional Development Fund ("A way to build Europe").Background: Multimorbidity is associated with negative effects both on people's health and on healthcare systems. A key problem linked to multimorbidity is polypharmacy, which in turn is associated with increased risk of partly preventable adverse effects, including mortality. The Ariadne principles describe a model of care based on a thorough assessment of diseases, treatments (and potential interactions), clinical status, context and preferences of patients with multimorbidity, with the aim of prioritizing and sharing realistic treatment goals that guide an individualized management. The aim of this study is to evaluate the effectiveness of a complex intervention that implements the Ariadne principles in a population of young-old patients with multimorbidity and polypharmacy. The intervention seeks to improve the appropriateness of prescribing in primary care (PC), as measured by the medication appropriateness index (MAI) score at 6 and 12months, as compared with usual care. Methods/Design: Design:pragmatic cluster randomized clinical trial. Unit of randomization: family physician (FP). Unit of analysis: patient. Scope: PC health centres in three autonomous communities: Aragon, Madrid, and Andalusia (Spain). Population: patients aged 65-74years with multimorbidity (≥3 chronic diseases) and polypharmacy (≥5 drugs prescribed in ≥3months). Sample size: n=400 (200 per study arm). Intervention: complex intervention based on the implementation of the Ariadne principles with two components: (1) FP training and (2) FP-patient interview. Outcomes: MAI score, health services use, quality of life (Euroqol 5D-5L), pharmacotherapy and adherence to treatment (Morisky-Green, Haynes-Sackett), and clinical and socio-demographic variables. Statistical analysis: primary outcome is the difference in MAI score between T0 and T1 and corresponding 95% confidence interval. Adjustment for confounding factors will be performed by multilevel analysis. All analyses will be carried out in accordance with the intention-to-treat principle. Discussion: It is essential to provide evidence concerning interventions on PC patients with polypharmacy and multimorbidity, conducted in the context of routine clinical practice, and involving young-old patients with significant potential for preventing negative health outcomes. Trial registration: Clinicaltrials.gov, NCT02866799Publisher PDFPeer reviewe

Measurement of the (eta c)(1S) production cross-section in proton-proton collisions via the decay (eta c)(1S) -> p(p)over-bar

The production of the $\eta_c (1S)$ state in proton-proton collisions is probed via its decay to the $p \bar{p}$ final state with the LHCb detector, in the rapidity range $2.0 6.5$ GeV/c. The cross-section for prompt production of $\eta_c (1S)$ mesons relative to the prompt $J/\psi$ cross-section is measured, for the first time, to be $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.74 \pm 0.29 \pm 0.28 \pm 0.18 _{B}$ at a centre-of-mass energy $\sqrt{s} = 7$ TeV using data corresponding to an integrated luminosity of 0.7 fb$^{-1}$, and $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.60 \pm 0.29 \pm 0.25 \pm 0.17 _{B}$ at $\sqrt{s} = 8$ TeV using 2.0 fb$^{-1}$. The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the $\eta_c (1S)$ and $J/\psi$ decays to the $p \bar{p}$ final state. In addition, the inclusive branching fraction of $b$-hadron decays into $\eta_c (1S)$ mesons is measured, for the first time, to be $B ( b \rightarrow \eta_c X ) = (4.88 \pm 0.64 \pm 0.25 \pm 0.67 _{B}) \times 10^{-3}$, where the third uncertainty includes also the uncertainty on the $J/\psi$ inclusive branching fraction from $b$-hadron decays. The difference between the $J/\psi$ and $\eta_c (1S)$ meson masses is determined to be $114.7 \pm 1.5 \pm 0.1$ MeV/c$^2$.The production of the $\eta _c (1S)$ state in proton-proton collisions is probed via its decay to the $p\overline{p}$ final state with the LHCb detector, in the rapidity range $2.0 6.5 \mathrm{{\,GeV/}{ c}}$ . The cross-section for prompt production of $\eta _c (1S)$ mesons relative to the prompt ${{ J}}/{\psi }$ cross-section is measured, for the first time, to be $\sigma _{\eta _c (1S)}/\sigma _{{{{ J}}/{\psi }}} = 1.74\, \pm \,0.29\, \pm \, 0.28\, \pm \,0.18 _{{\mathcal{B}}}$ at a centre-of-mass energy ${\sqrt{s}} = 7 {~\mathrm{TeV}}$ using data corresponding to an integrated luminosity of 0.7 fb$^{-1}$ , and $\sigma _{\eta _c (1S)}/\sigma _{{{{ J}}/{\psi }}} = 1.60 \pm 0.29 \pm 0.25 \pm 0.17 _{{\mathcal{B}}}$ at ${\sqrt{s}} = 8 {~\mathrm{TeV}}$ using 2.0 fb$^{-1}$ . The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the $\eta _c (1S)$ and ${{ J}}/{\psi }$ decays to the $p\overline{p}$ final state. In addition, the inclusive branching fraction of ${b}$ -hadron decays into $\eta _c (1S)$ mesons is measured, for the first time, to be ${\mathcal{B}}( b {\rightarrow } \eta _c X ) = (4.88\, \pm \,0.64\, \pm \,0.29\, \pm \, 0.67 _{{\mathcal{B}}}) \times 10^{-3}$ , where the third uncertainty includes also the uncertainty on the ${{ J}}/{\psi }$ inclusive branching fraction from ${b}$ -hadron decays. The difference between the ${{ J}}/{\psi }$ and $\eta _c (1S)$ meson masses is determined to be $114.7 \pm 1.5 \pm 0.1 {\mathrm {\,MeV\!/}c^2}$ .The production of the $\eta_c (1S)$ state in proton-proton collisions is probed via its decay to the $p \bar{p}$ final state with the LHCb detector, in the rapidity range $2.0 6.5$ GeV/c. The cross-section for prompt production of $\eta_c (1S)$ mesons relative to the prompt $J/\psi$ cross-section is measured, for the first time, to be $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.74 \pm 0.29 \pm 0.28 \pm 0.18 _{B}$ at a centre-of-mass energy $\sqrt{s} = 7$ TeV using data corresponding to an integrated luminosity of 0.7 fb$^{-1}$, and $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.60 \pm 0.29 \pm 0.25 \pm 0.17 _{B}$ at $\sqrt{s} = 8$ TeV using 2.0 fb$^{-1}$. The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the $\eta_c (1S)$ and $J/\psi$ decays to the $p \bar{p}$ final state. In addition, the inclusive branching fraction of $b$-hadron decays into $\eta_c (1S)$ mesons is measured, for the first time, to be $B ( b \rightarrow \eta_c X ) = (4.88 \pm 0.64 \pm 0.29 \pm 0.67 _{B}) \times 10^{-3}$, where the third uncertainty includes also the uncertainty on the $J/\psi$ inclusive branching fraction from $b$-hadron decays. The difference between the $J/\psi$ and $\eta_c (1S)$ meson masses is determined to be $114.7 \pm 1.5 \pm 0.1$ MeV/c$^2$

Search for the lepton flavour violating decay tau(-) -> mu(-)mu(+)mu(-)

A search for the lepton flavour violating decay $\tau^-\rightarrow\mu^-\mu^+\mu^-$ is performed with the LHCb experiment. The data sample corresponds to an integrated luminosity of 1.0 fb$^{−1}$ of proton-proton collisions at a centre-of-mass energy of 7 TeV and 2.0 fb$^{−1}$ at 8 TeV. No evidence is found for a signal, and a limit is set at 90% confidence level on the branching fraction, $\mathcal{B}(\tau^-\rightarrow\mu^-\mu^+\mu^-)<4.6\times10^{−8}$.A search for the lepton flavour violating decay τ$^{−}$ → μ$^{−}$ μ$^{+}$ μ$^{−}$ is performed with the LHCb experiment. The data sample corresponds to an integrated luminosity of 1.0 fb$^{−1}$ of proton-proton collisions at a centre-of-mass energy of 7 TeV and 2.0 fb$^{−1}$ at 8 TeV. No evidence is found for a signal, and a limit is set at 90% confidence level on the branching fraction, $\mathrm{\mathcal{B}}\left({\tau}^{-}\to {\mu}^{-}{\mu}^{+}{\mu}^{-}\right)<4.6\times {10}^{-8}$ .A search for the lepton flavour violating decay $\tau^-\to \mu^-\mu^+\mu^-$ is performed with the LHCb experiment. The data sample corresponds to an integrated luminosity of $1.0\mathrm{\,fb}^{-1}$ of proton-proton collisions at a centre-of-mass energy of $7\mathrm{\,Te\kern -0.1em V}$ and $2.0\mathrm{\,fb}^{-1}$ at $8\mathrm{\,Te\kern -0.1em V}$. No evidence is found for a signal, and a limit is set at $90\%$ confidence level on the branching fraction, $\mathcal{B}(\tau^-\to \mu^-\mu^+\mu^-) < 4.6 \times 10^{-8}$

Search for CP violation using T-odd correlations in D-0 -&gt; K+K-pi(+)pi(-) decays

A search for $CP$ violation using $T$-odd correlations is performed using the four-body $D^0 \to K^+K^-\pi^+\pi^-$ decay, selected from semileptonic $B$ decays. The data sample corresponds to integrated luminosities of $1.0\,\text{fb}^{-1}$ and $2.0\,\text{fb}^{-1}$ recorded at the centre-of-mass energies of 7 TeV and 8 TeV, respectively. The $CP$-violating asymmetry $a_{CP}^{T\text{-odd}}$ is measured to be $(0.18\pm 0.29\text{(stat)}\pm 0.04\text{(syst)})\%$. Searches for $CP$ violation in different regions of phase space of the four-body decay, and as a function of the $D^0$ decay time, are also presented. No significant deviation from the $CP$ conservation hypothesis is found

Measurement of CP asymmetry in B-s(0) -&gt; D-s(-/+) K--/+ decays

We report on measurements of the time-dependent CP violating observables in $B^0_s\rightarrow D^{\mp}_s K^{\pm}$ decays using a dataset corresponding to 1.0 fb$^{-1}$ of pp collisions recorded with the LHCb detector. We find the CP violating observables $C_f=0.53\pm0.25\pm0.04$, $A^{\Delta\Gamma}_f=0.37\pm0.42\pm0.20$, $A^{\Delta\Gamma}_{\bar{f}}=0.20\pm0.41\pm0.20$, $S_f=-1.09\pm0.33\pm0.08$, $S_{\bar{f}}=-0.36\pm0.34\pm0.08$, where the uncertainties are statistical and systematic, respectively. We use these observables to make the first measurement of the CKM angle $\gamma$ in $B^0_s\rightarrow D^{\mp}_s K^{\pm}$ decays, finding $\gamma$ = (115$_{-43}^{+28}$)$^\circ$ modulo 180$^\circ$ at 68% CL, where the error contains both statistical and systematic uncertainties.We report on measurements of the time-dependent CP violating observables in B$_{s}^{0}$  → D$_{s}^{∓}$ K$^{±}$ decays using a dataset corresponding to 1.0 fb$^{−1}$ of pp collisions recorded with the LHCb detector. We find the CP violating observables C$_{f}$ = 0.53±0.25±0.04, A$_{f}^{ΔΓ}$  = 0.37 ± 0.42 ± 0.20, ${A}_{\overline{f}}^{\varDelta \varGamma }=0.20\pm 0.41\pm 0.20$ , S$_{f}$ = −1.09±0.33±0.08, ${S}_{\overline{f}}=-0.36\pm 0.34\pm 0.08$ , where the uncertainties are statistical and systematic, respectively. Using these observables together with a recent measurement of the B$_{s}^{0}$ mixing phase −2β$_{s}$ leads to the first extraction of the CKM angle γ from B$_{s}^{0}$  → D$_{s}^{∓}$ K$^{±}$ decays, finding γ = (115$_{− 43}^{+ 28}$ )° modulo 180° at 68% CL, where the error contains both statistical and systematic uncertainties.We report on measurements of the time-dependent CP violating observables in $B^0_s\rightarrow D^{\mp}_s K^{\pm}$ decays using a dataset corresponding to 1.0 fb$^{-1}$ of pp collisions recorded with the LHCb detector. We find the CP violating observables $C_f=0.53\pm0.25\pm0.04$, $A^{\Delta\Gamma}_f=0.37\pm0.42\pm0.20$, $A^{\Delta\Gamma}_{\bar{f}}=0.20\pm0.41\pm0.20$, $S_f=-1.09\pm0.33\pm0.08$, $S_{\bar{f}}=-0.36\pm0.34\pm0.08$, where the uncertainties are statistical and systematic, respectively. Using these observables together with a recent measurement of the $B^0_s$ mixing phase $-2\beta_s$ leads to the first extraction of the CKM angle $\gamma$ from $B^0_s \rightarrow D^{\mp}_s K^{\pm}$ decays, finding $\gamma$ = (115$_{-43}^{+28}$)$^\circ$ modulo 180$^\circ$ at 68% CL, where the error contains both statistical and systematic uncertainties

A study of CP violation in B-+/- -&gt; DK +/- and B-+/- -&gt; D pi(+/-) decays with D -&gt; (KSK +/-)-K-0 pi(-/+) final states

A first study of CP violation in the decay modes $B^\pm\to [K^0_{\rm S} K^\pm \pi^\mp]_D h^\pm$ and $B^\pm\to [K^0_{\rm S} K^\mp \pi^\pm]_D h^\pm$, where $h$ labels a $K$ or $\pi$ meson and $D$ labels a $D^0$ or $\overline{D}^0$ meson, is performed. The analysis uses the LHCb data set collected in $pp$ collisions, corresponding to an integrated luminosity of 3 fb$^{-1}$. The analysis is sensitive to the CP-violating CKM phase $\gamma$ through seven observables: one charge asymmetry in each of the four modes and three ratios of the charge-integrated yields. The results are consistent with measurements of $\gamma$ using other decay modes

Measurement of Upsilon production in collisions at root s=2.76 TeV

The production of $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ mesons decaying into the dimuon final state is studied with the LHCb detector using a data sample corresponding to an integrated luminosity of 3.3 $pb^{-1}$ collected in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=2.76$ TeV. The differential production cross-sections times dimuon branching fractions are measured as functions of the $\Upsilon$ transverse momentum and rapidity, over the ranges $p_{\rm T} Upsilon(1S) X) x B(Upsilon(1S) -> mu+mu-) = 1.111 +/- 0.043 +/- 0.044 nb, sigma(pp -> Upsilon(2S) X) x B(Upsilon(2S) -> mu+mu-) = 0.264 +/- 0.023 +/- 0.011 nb, sigma(pp -> Upsilon(3S) X) x B(Upsilon(3S) -> mu+mu-) = 0.159 +/- 0.020 +/- 0.007 nb, where the first uncertainty is statistical and the second systematic