Intrinsic Taylor formula for Kolmogorov-type homogeneous groups

We consider a class of ultra-parabolic Kolmogorov-type operators satisfying the Hormander's condition. We prove an intrinsic Taylor formula with global and local bounds for the remainder given in terms of the norm in the homogeneous Lie group naturally associated to the differential operator

Taylor formula for Kolmogorov equations

After briefly discuss the natural homogeneous Lie group structure induced by Kolmogorov equations in chapter one, we define an intrinsic version of Taylor polynomials and Holder spaces in chapter two. We also compare our definition with others yet known in literature. In chapter three we prove an analogue of Taylor formula, that is an estimate of the remainder in terms of the homogeneous metric

Averaged stochastic processes and Kolmogorov operators

In this thesis we study a class of multidimensional stochastic processes in which a component is the time integral of another. Our interest stems both from the great variety of applications and the challenging structure of the related Kolmogorov backward operators. In fact, while such processes are widely used in physics and finance, the natural geometric framework to study them is considerably far from the standard Euclidean one and still vague. We wish to clarify it developing a new notion of Hölder spaces of any order and proving a Taylor type formula for functions on them. As applications, we prove an error estimate for an asymptotic expansion arising in studying Asian financial options and we also present and analytically investigate a new model for mine valuation

Measurements of the Higgs boson production and decay rates and coupling strengths using pp collision data at √S=7 and 8 TeV in the ATLAS experiment

Combined analyses of the Higgs boson production and decay rates as well as its coupling strengths to vector bosons and fermions are presented. The combinations include the results of the analyses of the H -> gamma gamma, ZZ*, WW*, Z gamma, b (b) over bar, tau tau and mu mu decay modes, and the constraints on the associated production with a pair of top quarks and on the off-shell coupling strengths of the Higgs boson. The results are based on the LHC proton-proton collision datasets, with integrated luminosities of up to 4.7 fb(-1) at root s = 7 TeV and 20.3 fb(-1) at root s = 8 TeV, recorded by the ATLAS detector in 2011 and 2012. Combining all production modes and decay channels, the measured signal yield, normalised to the Standard Model expectation, is 1.18(-0.14)(+0.15). The observed Higgs boson production and decay rates are interpreted in a leading-order coupling framework, exploring a wide range of benchmark coupling models both with and without assumptions on the Higgs boson width and on the Standard Model particle content in loop processes. The data are found to be compatible with the Standard Model expectations for a Higgs boson at a mass of 125.36 GeV for all models considered

The impact of COVID-19 pandemic on surgical neuro-oncology: A survey from the Italian society of neurosurgery (SINch)

Background: The COVID-19 pandemic and its impact on hospitals' activity and organization has imposed a vast change in standard neurosurgical oncology practice to accommodate for shifting resources. Aims: This investigation aims to analyse the nationwide capability in reorganizing the surgical neuro-oncological activity during the COVID-19 pandemic to evaluate whether COVID-19-pandemic influenced the surgical management in these patients. Method: A web-based dataset model organized by the Italian Neurosurgical Society (SINCh) was sent to all the Italian neurosurgical departments in May 2021, requesting to report the types and numbers of surgical procedures performed in the pre-pandemic period (from March 9th 2019 to March 9th 2020) compared to the pandemic period (from March 10th 2020 to March 10th 2021). Results: This multicentre investigation included the surgical activity of 35 Italian Neurosurgical Departments in a pre-pandemic year versus a pandemic year. During the COVID period, 699 fewer neuro-oncological patients were operated on than in the pre-COVID period. We noted a slight increase in urgency and a more severe decrease in elective and benign pathology. None of these differences was statistically significant. Surgically treated patients who tested positive for SARS-CoV-2 were 36, of which 11 died. Death was found to be COVID-related only in 2 cases. Conclusion: The reorganization of the Italian Neurosurgical Departments was able to guarantee a redistribution of the CNS tumors during the inter-pandemic periods, demonstrating that patients even in the pandemic era could be treated without compromising the efficacy and safety of the surgical procedure

Measurements of the Total and Differential Higgs Boson Production Cross Sections Combining the H??????? and H???ZZ*???4??? Decay Channels at s\sqrt{s}=8??????TeV with the ATLAS Detector

Measurements of the total and differential cross sections of Higgs boson production are performed using 20.3~fb$^{-1}$ of $pp$ collisions produced by the Large Hadron Collider at a center-of-mass energy of $\sqrt{s} = 8$ TeV and recorded by the ATLAS detector. Cross sections are obtained from measured $H \rightarrow \gamma \gamma$ and $H \rightarrow ZZ ^{*}\rightarrow 4\ell$ event yields, which are combined accounting for detector efficiencies, fiducial acceptances and branching fractions. Differential cross sections are reported as a function of Higgs boson transverse momentum, Higgs boson rapidity, number of jets in the event, and transverse momentum of the leading jet. The total production cross section is determined to be $\sigma_{pp \to H} = 33.0 \pm 5.3 \, ({\rm stat}) \pm 1.6 \, ({\rm sys}) \mathrm{pb}$. The measurements are compared to state-of-the-art predictions.Measurements of the total and differential cross sections of Higgs boson production are performed using 20.3  fb-1 of pp collisions produced by the Large Hadron Collider at a center-of-mass energy of s=8  TeV and recorded by the ATLAS detector. Cross sections are obtained from measured H→γγ and H→ZZ*→4ℓ event yields, which are combined accounting for detector efficiencies, fiducial acceptances, and branching fractions. Differential cross sections are reported as a function of Higgs boson transverse momentum, Higgs boson rapidity, number of jets in the event, and transverse momentum of the leading jet. The total production cross section is determined to be σpp→H=33.0±5.3 (stat)±1.6 (syst)  pb. The measurements are compared to state-of-the-art predictions.Measurements of the total and differential cross sections of Higgs boson production are performed using 20.3 fb$^{-1}$ of $pp$ collisions produced by the Large Hadron Collider at a center-of-mass energy of $\sqrt{s} = 8$ TeV and recorded by the ATLAS detector. Cross sections are obtained from measured $H \rightarrow \gamma \gamma$ and $H \rightarrow ZZ ^{*}\rightarrow 4\ell$ event yields, which are combined accounting for detector efficiencies, fiducial acceptances and branching fractions. Differential cross sections are reported as a function of Higgs boson transverse momentum, Higgs boson rapidity, number of jets in the event, and transverse momentum of the leading jet. The total production cross section is determined to be $\sigma_{pp \to H} = 33.0 \pm 5.3 \, ({\rm stat}) \pm 1.6 \, ({\rm sys}) \mathrm{pb}$. The measurements are compared to state-of-the-art predictions