Algebraic aspects and coherence conditions for conjunctions among conditional events

We deepen the study of a notion of conjunction among conditional events, introduced in previous papers in theframework of coherence. This notion of conjunction, differently from other approaches, is given in the setting ofconditional random quantities. We show that some well known properties which are satisfied by conjunctionsof unconditional events are also satisfied by conjunctions of conditional events. In particular we examine anadditive property and a decomposition formula, by also obtaining a generalized inclusion-exclusion formula. Then,by exploiting the notion of conjunction, we introduce the set of constituents generated bynconditional events.Moreover, under logical independence, we give a necessary and sufficient condition of coherence for the previsionassessments on a familyFconstituted bynconditional events and all possible conjunctions among some of them.This condition of coherence has a simple geometrical characterization in terms of a suitable convex hull. Such acharacterization amounts to the solvability of a linear system as in the case of unconditional events. Then, weillustrate the set of all coherent assessments on the familyFby a list of linear inequalities on the componentsof the prevision assessment. Finally, given a coherent assessmentMonF, we show that every possible value ofthe random vector associated withFis itself a particular coherent assessment onF

L'incertezza inSegna

Traendo spunto dalla manifestazione scientifica Esperienza inSegna, dal titolo Certo \ue8. . . probabile, svoltasi a Palermo nel 2014, in questo lavoro dapprima sono richiamati alcuni problemi che diedero la nascita al calcolo delle probabilit\ue0 e successivamente vengono analizzati due problemi popolari di probabilit\ue0 che normalmente sono oggetto di dibattito soprattutto tra i non addetti al settore: \u201cMonty Hall\u201d e il \u201cGratta e Vinci\u201d. Nel primo si mostra l\u2019importanza di tradurre correttamente, in termini di evento condizionante, l\u2019informazione acquisita quando si vogliono \u201caggiornare\u201d le probabilit\ue0; nel secondo si mette in guardia il lettore di fronte agli spot televisivi che annunciano vincite facili nelle lotterie a premi

Electromagnetic and strong isospin-breaking corrections to the muon g−2g - 2 from Lattice QCD+QED

We present a lattice calculation of the leading-order electromagnetic and strong isospin-breaking corrections to the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses between $\simeq 210$ and $\simeq 450$ MeV. The results are obtained adopting the RM123 approach in the quenched-QED approximation, which neglects the charges of the sea quarks. Quark disconnected diagrams are not included. After the extrapolations to the physical pion mass and to the continuum and infinite-volume limits the contributions of the light, strange and charm quarks are respectively equal to $\delta a_\mu^{\rm HVP}(ud) = 7.1 ~ (2.5) \cdot 10^{-10}$, $\delta a_\mu^{\rm HVP}(s) = -0.0053 ~ (33) \cdot 10^{-10}$ and $\delta a_\mu^{\rm HVP}(c) = 0.0182 ~ (36) \cdot 10^{-10}$. At leading order in $\alpha_{em}$ and $(m_d - m_u) / \Lambda_{QCD}$ we obtain $\delta a_\mu^{\rm HVP}(udsc) = 7.1 ~ (2.9) \cdot 10^{-10}$, which is currently the most accurate determination of the isospin-breaking corrections to $a_\mu^{\rm HVP}$.Comment: 23 pages, 7 figures, 5 tables. Version to appear in PRD. A bug in the update of the strange and charm contributions is removed and an extended discussion on the identification of the ground-state is included. arXiv admin note: text overlap with arXiv:1808.00887, arXiv:1707.0301

A probabilistic analysis of selected notions of iterated conditioning under coherence

It is well known that basic conditionals satisfy some desirable basic logical and probabilistic properties, such as the compound probability theorem. However checking the validity of these becomes trickier when we switch to compound and iterated conditionals. Herein we consider de Finetti's notion of conditional both in terms of a three-valued object and as a conditional random quantity in the betting framework. We begin by recalling the notions of conjunction and disjunction among conditionals in selected trivalent logics. Then we analyze the notions of iterated conditioning in the frameworks of the specific three-valued logics introduced by Cooper-Calabrese, by de Finetti, and by Farrel. By computing some probability propagation rules we show that the compound probability theorem and other important properties are not always preserved by these formulations. Then, for each trivalent logic we introduce an iterated conditional as a suitable random quantity which satisfies the compound prevision theorem as well as some other desirable properties. We also check the validity of two generalized versions of Bayes' Rule for iterated conditionals. We study the p-validity of generalized versions of Modus Ponens and two-premise centering for iterated conditionals. Finally, we observe that all the basic properties are satisfied within the framework of iterated conditioning followed in recent papers by Gilio and Sanfilippo in the setting of conditional random quantities

Finite-Volume QED Corrections to Decay Amplitudes in Lattice QCD

We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(\alpha)$ are universal, i.e. they are independent of the structure of the meson. This is analogous to a similar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading non-universal, structure-dependent terms are of $O(1/L^2)$ (compared to the $O(1/L^3)$ leading non-universal corrections in the spectrum). We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final state lepton). The result can be included in the strategy proposed in Ref.\,\cite{Carrasco:2015xwa} for using lattice simulations to compute the decay widths at $O(\alpha)$, with the remaining finite-volume effects starting at order $O(1/L^2)$. The methods developed in this paper can be generalised to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavour physics

Electromagnetic corrections to leptonic decay rates of charged pseudoscalar mesons: finite-volume effects

In Carrasco et al. we have recently proposed a method to calculate $O(e^2)$ electromagnetic corrections to leptonic decay widths of pseudoscalar mesons. The method is based on the observation that the infrared divergent contributions (that appear at intermediate stages of the calculation and that cancel in physical quantities thanks to the Bloch-Nordsieck mechanism) are universal, i.e. depend on the charge and the mass of the meson but not on its internal structure. In this talk we perform a detailed analysis of the finite-volume effects associated with our method. In particular we show that also the leading $1/L$ finite-volume effects are universal and perform an analytical calculation of the finite-volume leptonic decay rate for a point-like meson

Leading isospin-breaking corrections to pion, kaon and charmed-meson masses with Twisted-Mass fermions

We present a lattice computation of the isospin-breaking corrections to pseudoscalar meson masses using the gauge configurations produced by the European Twisted Mass collaboration with $N_f = 2 + 1 + 1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082$ and $0.089$ fm) with pion masses in the range $M_\pi \simeq 210 - 450$ MeV. The strange and charm quark masses are tuned at their physical values. We adopt the RM123 method based on the combined expansion of the path integral in powers of the $d$- and $u$-quark mass difference ($\widehat{m}_d - \widehat{m}_u$) and of the electromagnetic coupling $\alpha_{em}$. Within the quenched QED approximation, which neglects the effects of the sea-quark charges, and after the extrapolations to the physical pion mass and to the continuum and infinite volume limits, we provide results for the pion, kaon and (for the first time) charmed-meson mass splittings, for the prescription-dependent parameters $\epsilon_{\pi^0}$, \epsilon_\gamma(\overline{MS}, 2~\mbox{GeV}), \epsilon_{K^0}(\overline{MS}, 2~\mbox{GeV}), related to the violations of the Dashen's theorem, and for the light quark mass difference (\widehat{m}_d - \widehat{m}_u)(\overline{MS}, 2~\mbox{GeV}).Comment: 47 pages, 20 figures, 4 tables; comments on QED and QCD splitting prescriptions added; version to appear in PR

Strange and charm HVP contributions to the muon (g−2)g - 2) including QED corrections with twisted-mass fermions

We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon including leading-order electromagnetic corrections. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range $M_\pi \simeq 210 - 450$ MeV. The strange and charm quark masses are tuned at their physical values. Neglecting disconnected diagrams and after the extrapolations to the physical pion mass and to the continuum limit we obtain: $a_\mu^s(\alpha_{em}^2) = (53.1 \pm 2.5) \cdot 10^{-10}$, $a_\mu^s(\alpha_{em}^3) = (-0.018 \pm 0.011) \cdot 10^{-10}$ and $a_\mu^c(\alpha_{em}^2) = (14.75 \pm 0.56) \cdot 10^{-10}$, $a_\mu^c(\alpha_{em}^3) = (-0.030 \pm 0.013) \cdot 10^{-10}$ for the strange and charm contributions, respectively.Comment: 34 pages, 10 figures, 5 tables; version to appear in JHE

A probabilistic approach to stormwater runoff control through permeable pavements beneath urban trees

: One of the most current and urgent challenges is making cities sustainable and resilient to climate change. From this perspective, Nature-Based Solutions (NBSs) are well-recognized strategies for stormwater control and water cycle restoration. Urban trees are an example of NBS. However, the high degree of soil sealing typically found in urban environments limits natural processes such as infiltration and hinders the water and nutrient supply for proper root development, which weakens tree stability. Permeable pavements at the base of urban trees, on the one hand, facilitate infiltration, which helps runoff control, and on the other hand, improve stormwater retention and soil humidity, which enhance root feeding. This paper proposes an analytical-probabilistic approach to estimate the contribution of permeable pavements to stormwater management. The equations developed in this study relate the runoff probability to the storage volume, the infiltration rate into the underlying soil, and the average values of the hydrological variables in the input. The model allows us to select different runoff thresholds and considers the possibility that residual volume from previous rainfall events prefills the storage capacity. An application to a case study in Sao Paulo (Brazil) has been presented. It investigates the influence of the different parameters used in the model on the results. The comparison of the outcomes obtained using the developed equations with those obtained from the continuous simulation of measured data confirmed the effectiveness of the proposed analytical-probabilistic approach and the suitability of using permeable pavements at the base of urban trees for improving stormwater retention

The effectiveness of intra-articular injectionc of Hyalubrix combined with exercise therapy in the tratment of hip osteoarthritis

Purpose. Osteoarthritis (OA) is the most common joint disorder in the elderly, causing significant pain which negatively affects mobility and quality ol liie. The aim of the study was to assess the effectiveness of ultrasound \ucdmage-guided intra-articular injections of Hyalubrix@ combined with exercise therapy in the treatment of hip osteoarthritis. Methods. This was a single site, prosp\ue8ctive, open-fabel, Investigator-initiated study. Forty patients rilere enrolled and received three ultrasound image.guided injections of Hyalubrix@, 45 days apart, combined with three sessions a week of phys\uedcal therapy (proprioceptive rehabilitation of the lower limbs; gait training; balance training) up to a total of 30 sessions (10 weeks), starting from one week after the first injection. Results. The primary obiective was to achieve a lasting reduction in OA symptoms related to pain during activity. During the course of the study the pain perceived by the patient during activity dropped from a mean value of 6.94 cm to a mean value of 1.46 cm and showed a statistically significant decrease from visit 1 compared to baseline (p < 0.05) which was confirmed at all the subsequent time points. Significant improvements were also observed in the evaluation of the secondary objectives: hip disability; OA-related pain at rest; daily functioning and NSAIDs intake. Conclusions. Results from this study including 40 patients for a total of 65 treated hips demonstrate a significant improvement in OA-related pain, hip disability, and patient's daily functioning as well as a reduction in NSAIDS intake. Patients suffering from hip OA s\ue8em to benefil from the treatment wiih Hyalubrix@ injections plus exercise therapy