Open billiards : cantor sets, invariant and conditionally invariant probabilities

A b stract - Billiards are the simplest models fur nudcrstanding statistical properties of thc dynamics of a gas in a closed compartment. vVc analyze the dynamics of a class of billiards (the open billiard on the plane) in terms of iuva.riant and conditionally inva.riant proba.bilities. The dynamical system has a horse-shoe structure. The stable and unstable manifolds are analytically described. The natural probability J.L is invariant and has support in a Cantor set. This probability is the conditiona.l limit of a conditiona.l probability J.LF that has a Holder continuous density with respcct to the Lebesgue measure. A formula relating entropy, Liapunov exponent and Hausdorff dimcnsion of a natural probability J.L for the system is presented. The natural probability fl is a Gibbs state of a potcntial 'lj; ( cohomologous to the potential associated to the positive Liapunov exponent, see formula (0.1 )), and we show that for a dense set of such billiards the potential 'lj; is not lattice. As the system has a horse-shoe structure one can compute the asymptotic growth rate of n(1·), the number of closed trajectories with the largest eigcuvalue of the derivative smaller tKru1 .r

Explicit bivariate rate functions for large deviations in AR(1) and MA(1) processes with Gaussian innovations

We investigate the large deviations properties for centered stationary AR(1) and MA(1) processes with independent Gaussian innovations, by giving the explicit bivariate rate functions for the sequence of two-dimensional random vectors [...]. Via the Contraction Principle, we provide the explicit rate functions for the sample mean and the sample second moment. In the AR(1) case, we also give the explicit rate function for the sequence of two-dimensional random vectors [...], but we obtain an analytic rate function that gives different values for the upper and lower bounds, depending on the evaluated set and its intersection with the respective set of exposed points. A careful analysis of the properties of a certain family of Toeplitz matrices is necessary. The large deviations properties of three particular sequences of one-dimensional random variables will follow after we show how to apply a weaker version of the Contraction Principle for our setting, providing new proofs for two already known results on the explicit deviation function for the sample second moment and Yule-Walker estimators. We exhibit the properties of the large deviations of the first-order empirical autocovariance, its explicit deviation function and this is also a new result

Invariant measures for gauss maps associated with interval exchange maps

An explidt formula for an ergodic cr-finite measure inva.ria.nt by the Gauss map associated to a new induction on the interval exchange maps is given. The techniques devcloped allow another proof of Keane's conjecture which was first shown to be true by Veech and Mazur

Parameter estimation in Manneville–Pomeau processes

In this paper, we study a class of stochastic processes [...], where[...] is obtained from the iterations of the transformation , invariant for an ergodic probability[...] on [...] and a certain constant by partial function [...]. We consider here the family of transformations[...] indexed by a parameter , known as the Manneville–Pomeau family of transformations. The autocorrelation function of the resulting process decays hyperbolically (or polynomially) and we obtain efficient methods to estimate the parameter[...] from a finite time series. As a consequence, we also estimate the rate of convergence of the autocorrelation decay of these processes. We compare different estimation methods based on the periodogram function, the smoothed periodogram function, the variance of the partial sum, and the wavelet theory. To obtain our results we analyzed the properties of the spectral density function and the associated Fourier series

The calculus of thermodynamical formalism

Given an onto map T acting on a metric space and an appropriate Banach space of functions X./, one classically constructs for each potential A 2 X a transfer operator LA acting on X./. Under suitable hypotheses, it is well-known that LA has a maximal eigenvalue A, has a spectral gap and defines a unique Gibbs measure A. Moreover there is a unique normalized potential of the form B D ACf f T Cc acting as a representative of the class of all potentials defining the same Gibbs measure. The goal of the present article is to study the geometry of the set N of normalized potentials, of the normalization map A 7! B, and of the Gibbs map A 7! A. We give an easy proof of the fact that N is an analytic submanifold of X and that the normalization map is analytic; we compute the derivative of the Gibbs map; and we endow N with a natural weak Riemannian metric (derived from the asymptotic variance) with respect to which we compute the gradient flow induced by the pressure with respect to a given potential, e.g. the metric entropy functional. We also apply these ideas to recover in a wide setting existence and uniqueness of equilibrium states, possibly under constraints

Microbiome analyses of the Uraim River in the Amazon and georeferencing analyses to establish correlation with anthropogenic impacts of land use

One of the primary challenges in the spread of infectious diseases is the consumption of poorly or untreated water, which is increasingly being used due to the growth of different human activities and the effect of urbanization on freshwater sources, which are often used for consumption purposes. The determination of pathogenic bacteria in freshwater rivers influenced by anthropogenic activities allows for the assessment of the impact these factors have on water quality. Thus, the purpose of this study was to identify the diversity of pathogenic bacteria and virulence genes in the Uraim River in the northern region of Brazil. For this purpose, surface water was collected from five points with varying degrees of anthropogenic impact along the Uraim River. In situ measurements of physicochemical components were conducted, and metagenomic analysis was used for the identification of pathogenic bacteria and virulence genes. Regarding the physicochemical parameters, variability was observed among the different analysis points, as well as diversity among bacteria and virulence genes. Notably, enterobacteria and the ESKAPE group were highlighted among the bacteria, with significant negative associations found between dissolved oxygen and the diversity of virulence genes and between deforestation and population density with the presence of ESKAPE group bacteria

Multidifferential study of identified charged hadron distributions in ZZ-tagged jets in proton-proton collisions at s=\sqrt{s}=13 TeV

Jet fragmentation functions are measured for the first time in proton-proton collisions for charged pions, kaons, and protons within jets recoiling against a $Z$ boson. The charged-hadron distributions are studied longitudinally and transversely to the jet direction for jets with transverse momentum 20 $< p_{\textrm{T}} < 100$ GeV and in the pseudorapidity range $2.5 < \eta < 4$. The data sample was collected with the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 1.64 fb$^{-1}$. Triple differential distributions as a function of the hadron longitudinal momentum fraction, hadron transverse momentum, and jet transverse momentum are also measured for the first time. This helps constrain transverse-momentum-dependent fragmentation functions. Differences in the shapes and magnitudes of the measured distributions for the different hadron species provide insights into the hadronization process for jets predominantly initiated by light quarks.Comment: All figures and tables, along with machine-readable versions and any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-013.html (LHCb public pages

Study of the B−→Λc+Λˉc−K−B^{-} \to \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-} K^{-} decay

The decay $B^{-} \to \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-} K^{-}$ is studied in proton-proton collisions at a center-of-mass energy of $\sqrt{s}=13$ TeV using data corresponding to an integrated luminosity of 5 $\mathrm{fb}^{-1}$ collected by the LHCb experiment. In the $\Lambda_{c}^+ K^{-}$ system, the $\Xi_{c}(2930)^{0}$ state observed at the BaBar and Belle experiments is resolved into two narrower states, $\Xi_{c}(2923)^{0}$ and $\Xi_{c}(2939)^{0}$, whose masses and widths are measured to be $$m(\Xi_{c}(2923)^{0}) = 2924.5 \pm 0.4 \pm 1.1 \,\mathrm{MeV}, \\ m(\Xi_{c}(2939)^{0}) = 2938.5 \pm 0.9 \pm 2.3 \,\mathrm{MeV}, \\ \Gamma(\Xi_{c}(2923)^{0}) = \phantom{000}4.8 \pm 0.9 \pm 1.5 \,\mathrm{MeV},\\ \Gamma(\Xi_{c}(2939)^{0}) = \phantom{00}11.0 \pm 1.9 \pm 7.5 \,\mathrm{MeV},$$ where the first uncertainties are statistical and the second systematic. The results are consistent with a previous LHCb measurement using a prompt $\Lambda_{c}^{+} K^{-}$ sample. Evidence of a new $\Xi_{c}(2880)^{0}$ state is found with a local significance of $3.8\,\sigma$, whose mass and width are measured to be $2881.8 \pm 3.1 \pm 8.5\,\mathrm{MeV}$ and $12.4 \pm 5.3 \pm 5.8 \,\mathrm{MeV}$, respectively. In addition, evidence of a new decay mode $\Xi_{c}(2790)^{0} \to \Lambda_{c}^{+} K^{-}$ is found with a significance of $3.7\,\sigma$. The relative branching fraction of $B^{-} \to \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-} K^{-}$ with respect to the $B^{-} \to D^{+} D^{-} K^{-}$ decay is measured to be $2.36 \pm 0.11 \pm 0.22 \pm 0.25$, where the first uncertainty is statistical, the second systematic and the third originates from the branching fractions of charm hadron decays.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-028.html (LHCb public pages

Measurement of the ratios of branching fractions R(D∗)\mathcal{R}(D^{*}) and R(D0)\mathcal{R}(D^{0})

The ratios of branching fractions $\mathcal{R}(D^{*})\equiv\mathcal{B}(\bar{B}\to D^{*}\tau^{-}\bar{\nu}_{\tau})/\mathcal{B}(\bar{B}\to D^{*}\mu^{-}\bar{\nu}_{\mu})$ and $\mathcal{R}(D^{0})\equiv\mathcal{B}(B^{-}\to D^{0}\tau^{-}\bar{\nu}_{\tau})/\mathcal{B}(B^{-}\to D^{0}\mu^{-}\bar{\nu}_{\mu})$ 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 $\tau^{-}\to\mu^{-}\nu_{\tau}\bar{\nu}_{\mu}$. The measured values are $\mathcal{R}(D^{*})=0.281\pm0.018\pm0.024$ and $\mathcal{R}(D^{0})=0.441\pm0.060\pm0.066$, where the first uncertainty is statistical and the second is systematic. The correlation between these measurements is $\rho=-0.43$. 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.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-039.html (LHCb public pages

Physics case for an LHCb Upgrade II - Opportunities in flavour physics, and beyond, in the HL-LHC era

The LHCb Upgrade II will fully exploit the flavour-physics opportunities of the HL-LHC, and study additional physics topics that take advantage of the forward acceptance of the LHCb spectrometer. The LHCb Upgrade I will begin operation in 2020. Consolidation will occur, and modest enhancements of the Upgrade I detector will be installed, in Long Shutdown 3 of the LHC (2025) and these are discussed here. The main Upgrade II detector will be installed in long shutdown 4 of the LHC (2030) and will build on the strengths of the current LHCb experiment and the Upgrade I. It will operate at a luminosity up to 2×1034 cm−2s−1, ten times that of the Upgrade I detector. New detector components will improve the intrinsic performance of the experiment in certain key areas. An Expression Of Interest proposing Upgrade II was submitted in February 2017. The physics case for the Upgrade II is presented here in more depth. CP-violating phases will be measured with precisions unattainable at any other envisaged facility. The experiment will probe b → sl+l−and b → dl+l− transitions in both muon and electron decays in modes not accessible at Upgrade I. Minimal flavour violation will be tested with a precision measurement of the ratio of B(B0 → μ+μ−)/B(Bs → μ+μ−). Probing charm CP violation at the 10−5 level may result in its long sought discovery. Major advances in hadron spectroscopy will be possible, which will be powerful probes of low energy QCD. Upgrade II potentially will have the highest sensitivity of all the LHC experiments on the Higgs to charm-quark couplings. Generically, the new physics mass scale probed, for fixed couplings, will almost double compared with the pre-HL-LHC era; this extended reach for flavour physics is similar to that which would be achieved by the HE-LHC proposal for the energy frontier