Discrete Symmetry and Stability in Hamiltonian Dynamics

In this tutorial we address the existence and stability of periodic and quasiperiodic orbits in N degree of freedom Hamiltonian systems and their connection with discrete symmetries. Of primary importance in our study are the nonlinear normal modes (NNMs), i.e periodic solutions which represent continuations of the system's linear normal modes in the nonlinear regime. We examine the existence of such solutions and discuss different methods for constructing them and studying their stability under fixed and periodic boundary conditions. In the periodic case, we employ group theoretical concepts to identify a special type of NNMs called one-dimensional "bushes". We describe how to use linear combinations such NNMs to construct s(>1)-dimensional bushes of quasiperiodic orbits, for a wide variety of Hamiltonian systems and exploit the symmetries of the linearized equations to simplify the study of their destabilization. Applying this theory to the Fermi Pasta Ulam (FPU) chain, we review a number of interesting results, which have appeared in the recent literature. We then turn to an analytical and numerical construction of quasiperiodic orbits, which does not depend on the symmetries or boundary conditions. We demonstrate that the well-known "paradox" of FPU recurrences may be explained in terms of the exponential localization of the energies Eq of NNM's excited at the low part of the frequency spectrum, i.e. q=1,2,3,.... Thus, we show that the stability of these low-dimensional manifolds called q-tori is related to the persistence or FPU recurrences at low energies. Finally, we discuss a novel approach to the stability of orbits of conservative systems, the GALIk, k=2,...,2N, by means of which one can determine accurately and efficiently the destabilization of q-tori, leading to the breakdown of recurrences and the equipartition of energy, at high values of the total energy E.Comment: 50 pages, 13 figure

Ki-67 expression predicts locoregional recurrence in stage I oral tongue carcinoma

Oral tongue squamous cell carcinoma (OTSCC) is an aggressive cancer associated with poor prognosis. Methods for determining the aggressiveness of OTSCC from analysis of the primary tumour specimen are thus highly desirable. We investigated whether genomic instability and proliferative activity (by means of Ki-67 activity) could be of clinical use for prediction of locoregional recurrence in 76 pretreatment OTSCC paraffin samples (stage I, n=22; stage II, n=33; stage III, n=8; stage IV, n=13). Eleven surgical tumour specimens were also analysed for remnants of proliferative activity after preoperative radiotherapy. Ninety-seven percent of cases (n=72) were characterised as being aneuploid as measured by means of image cytometry. Preoperative radiotherapy (50–68 Gy) resulted in significant reduction of proliferative activity in all patients for which post-treatment biopsies were available (P-value=0.001). Proliferative activity was not associated with response to radiation in stage II patients. However, we report a significant correlation between high proliferation rates and locoregional recurrences in stage I OTSCC patients (P-value=0.028). High-proliferative activity is thus related to an elevated risk of recurrence after surgery alone. We therefore conclude that Ki-67 expression level is a potentially useful clinical marker for predicting recurrence in surgically treated stage I OTSCC

Competitive Tendering In The Netherlands: Central Planning Or Functional Specifications?

Institute of Transport and Logistics Studies. Faculty of Economics and Business. The University of Sydne

Test of lepton universality in b→sℓ+ℓ−b \rightarrow s \ell^+ \ell^- decays

The first simultaneous test of muon-electron universality using $B^{+}\rightarrow K^{+}\ell^{+}\ell^{-}$ and $B^{0}\rightarrow K^{*0}\ell^{+}\ell^{-}$ decays is performed, in two ranges of the dilepton invariant-mass squared, $q^{2}$. The analysis uses beauty mesons produced in proton-proton collisions collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 $\mathrm{fb}^{-1}$. Each of the four lepton universality measurements reported is either the first in the given $q^{2}$ interval or supersedes previous LHCb measurements. The results are compatible with the predictions of the Standard Model.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-046.html (LHCb public pages

Measurement of the Λb0→Λ(1520)μ+μ−\Lambda_{b}^{0}\to \Lambda(1520) \mu^{+}\mu^{-} differential branching fraction

The branching fraction of the rare decay $\Lambda_{b}^{0}\to \Lambda(1520) \mu^{+}\mu^{-}$ is measured for the first time, in the squared dimuon mass intervals, $q^2$, excluding the $J/\psi$ and $\psi(2S)$ regions. The data sample analyzed was collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of $9\ \mathrm{fb}^{-1}$. The result in the highest$q^{2}$interval,$q^{2} >15.0\ \mathrm{GeV}^2/c^4$, where theoretical predictions have the smallest model dependence, agrees with the predictions.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-050.html (LHCb public pages

Non-AIDS defining cancers in the D:A:D Study-time trends and predictors of survival : a cohort study

BACKGROUND:Non-AIDS defining cancers (NADC) are an important cause of morbidity and mortality in HIV-positive individuals. Using data from a large international cohort of HIV-positive individuals, we described the incidence of NADC from 2004-2010, and described subsequent mortality and predictors of these.METHODS:Individuals were followed from 1st January 2004/enrolment in study, until the earliest of a new NADC, 1st February 2010, death or six months after the patient's last visit. Incidence rates were estimated for each year of follow-up, overall and stratified by gender, age and mode of HIV acquisition. Cumulative risk of mortality following NADC diagnosis was summarised using Kaplan-Meier methods, with follow-up for these analyses from the date of NADC diagnosis until the patient's death, 1st February 2010 or 6 months after the patient's last visit. Factors associated with mortality following NADC diagnosis were identified using multivariable Cox proportional hazards regression.RESULTS:Over 176,775 person-years (PY), 880 (2.1%) patients developed a new NADC (incidence: 4.98/1000PY [95% confidence interval 4.65, 5.31]). Over a third of these patients (327, 37.2%) had died by 1st February 2010. Time trends for lung cancer, anal cancer and Hodgkin's lymphoma were broadly consistent. Kaplan-Meier cumulative mortality estimates at 1, 3 and 5 years after NADC diagnosis were 28.2% [95% CI 25.1-31.2], 42.0% [38.2-45.8] and 47.3% [42.4-52.2], respectively. Significant predictors of poorer survival after diagnosis of NADC were lung cancer (compared to other cancer types), male gender, non-white ethnicity, and smoking status. Later year of diagnosis and higher CD4 count at NADC diagnosis were associated with improved survival. The incidence of NADC remained stable over the period 2004-2010 in this large observational cohort.CONCLUSIONS:The prognosis after diagnosis of NADC, in particular lung cancer and disseminated cancer, is poor but has improved somewhat over time. Modifiable risk factors, such as smoking and low CD4 counts, were associated with mortality following a diagnosis of NADC

Measurement of the ratios of branching fractions R(D*) and R(D0)

The ratios of branching fractions R ( D ∗ ) ≡ B ( ¯ B → D ∗ τ − ¯ ν τ ) / B ( ¯ B → D ∗ μ − ¯ ν μ ) and R ( D 0 ) ≡ B ( B − → D 0 τ − ¯ ν τ ) / B ( B − → D 0 μ − ¯ ν μ ) are measured, assuming isospin symmetry, using a sample of proton-proton collision data corresponding to 3.0     fb − 1 of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode τ − → μ − ν τ ¯ ν μ . The measured values are R ( D ∗ ) = 0.281 ± 0.018 ± 0.024 and R ( D 0 ) = 0.441 ± 0.060 ± 0.066 , where the first uncertainty is statistical and the second is systematic. The correlation between these measurements is ρ = − 0.43 . The results are consistent with the current average of these quantities and are at a combined 1.9 standard deviations from the predictions based on lepton flavor universality in the standard model

Test of lepton universality in b→sℓ+ℓ− decays

The first simultaneous test of muon-electron universality using B + → K + ℓ + ℓ − and B 0 → K * 0 ℓ + ℓ − decays is performed, in two ranges of the dilepton invariant-mass squared, q 2 . The analysis uses beauty mesons produced in proton-proton collisions collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9     fb − 1 . Each of the four lepton universality measurements reported is either the first in the given q 2 interval or supersedes previous LHCb measurements. The results are compatible with the predictions of the Standard Model