Algebraic structure of stochastic expansions and efficient simulation

We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems.Our motivation is to construct efficient integrators. These are approximations that generate strong numerical integration schemes that are more accurate than the corresponding stochastic Taylor approximation, independent of the governing vector fields and to all orders. The sinhlog integrator introduced by Malham & Wiese (2009) is one example. Herein we: show that the natural context to study stochastic integrators and their properties is the convolution shuffle algebra of endomorphisms; establish a new whole class of efficient integrators; and then prove that, within this class, the sinhlog integrator generates the optimal efficient stochastic integrator at all orders.Comment: 19 page

CP, T and CPT violation in future long baseline experiments

I give a short overview about the possibilities and problems related to the measurement of CP violation in long baseline experiments. Special attention is paid to the issue of degeneracies and a method for their resolution is quantitatively discussed. The CP violation reach for different experiments is compared in dependence of $\sin^22\theta_{13}$ and \dm{21}. Furthermore a short comment about the possible effects of matter induced T violation is made. Finally the limits on CPT violation obtainable at a neutrino factory are shown.Comment: Talk presented at NUFACT02, London, 1-6 July, 2002. 3 pages, 2 figure

Optimal β\beta-beam at the CERN-SPS

A $\beta$-beam with maximum $\gamma=150$ (for \helio ions) or $\gamma=250$ (for \neon) could be achieved at the CERN-SPS. We study the sensitivity to $\theta_{13}$ and $\delta$ of such a beam as function of $\gamma$, optimizing with the baseline constrained to CERN-Frejus (130 km), and also with simultaneous variation of the baseline. These results are compared to the {\it standard} scenario previously considered, with lower $\gamma=60/100$, and also with a higher $\gamma\sim 350$ option that requires a more powerful accelerator. Although higher $\gamma$ is better, loss of sensitivity to $\theta _{13}$ and $\delta$ is most pronounced for $\gamma$ below 100.Comment: 22 page

Physics Potential of the SPL Super Beam

Performances of a neutrino beam generated by the CERN SPL proton driver are computed considering a 440 kton water Cerenkov detector at 130 km from the target. $\theta_{13}$ sensitivity down to $1.2^\circ$ and a $\delta$ sensitivity comparable to a Neutrino Factory, for $\theta_{13} \geq 3^\circ$, are within the reach of such a project.Comment: Invited talk at the Nufact02 Workshop, Imperial College of Science, Technology and Medicine, London, July 200

Flows driven by Banach space-valued rough paths

We show in this note how the machinery of C^1-approximate flows devised in the work "Flows driven by rough paths", and applied there to reprove and extend most of the results on Banach space-valued rough differential equations driven by a finite dimensional rough path, can be used to deal with rough differential equations driven by an infinite dimensional Banach space-valued weak geometric Holder p-rough paths, for any p>2, giving back Lyons' theory in its full force in a simple way.Comment: 8 page

Neutrino oscillation physics with a higher γ\gamma β\beta-beam

The precision measurement and discovery potential of a neutrino factory based on a storage ring of boosted radioactive ions ($\beta$-beam) is re-examined. In contrast with past designs, which assume ion $\gamma$ factors of $\sim 100$ and baselines of L=130 km, we emphasize the advantages of boosting the ions to higher $\gamma$ and increasing the baseline proportionally. In particular, we consider a medium-$\gamma$ scenario ($\gamma \sim 500$, L=730 km) and a high-$\gamma$ scenario ($\gamma \sim 2000$, L = 3000 km).The increase in statistics, which grow linearly with the average beam energy, the ability to exploit the energy dependence of the signal and the sizable matter effects at this longer baseline all increase the discovery potential of such a machine very significantly.Comment: An error corrected, conclusions unchanged. Revised version to appear in Nuclear Physics

Physics Potential of Very Intense Conventional Neutrino Beams

The physics potential of high intensity conventional beams is explored. We consider a low energy super beam which could be produced by a proposed new accelerator at CERN, the Super Proton Linac. Water Cherenkov and liquid oil scintillator detectors are studied as possible candidates for a neutrino oscillation experiment which could improve our current knowledge of the atmospheric parameters and measure or severely constrain the parameter connecting the atmospheric and solar realms. It is also shown that a very large water detector could eventually observe leptonic CP violation. The reach of such an experiment to the neutrino mixing parameters would lie in-between the next generation of neutrino experiments (MINOS, OPERA, etc) and a future neutrino factory.Comment: Talk given at the Venice Conference on Neutrino Telescopes, Venice, March, 200

Swallowing Activity Assessed by Ambulatory Impedance-pH Monitoring Predicts Awake and Asleep Periods at Night

Introduction: Voluntary muscle activity, including swallowing, decreases during the night. The association between nocturnal awakenings and swallowing activity is under-researched with limited information on the frequency of swallows during awake and asleep periods. Aim: The aim of this study was to assess nocturnal swallowing activity and identify a cut-off predicting awake and asleep periods. Methods: Patients undergoing impedance-pH monitoring as part of GERD work-up were asked to wear a wrist activity detecting device (Actigraph®) at night. Swallowing activity was quantified by analysing impedance changes in the proximal esophagus. Awake and asleep periods were determined using a validated scoring system (Sadeh algorithm). Receiver operating characteristics (ROC) analyses were performed to determine sensitivity, specificity and accuracy of swallowing frequency to identify awake and asleep periods. Results: Data from 76 patients (28male, 48 female; mean age 56±15years) were included in the analysis. The ROC analysis found that 0.33sw/min (i.e. one swallow every 3min) had the optimal sensitivity (78%) and specificity (76%) to differentiate awake from asleep periods. A swallowing frequency of 0.25sw/min (i.e. one swallow every 4min) was 93% sensitive and 57% specific to identify awake periods. A swallowing frequency of 1sw/min was 20% sensitive but 96% specific in identifying awake periods. Summary and Conclusion: Impedance-pH monitoring detects differences in swallowing activity during awake and asleep periods. Swallowing frequency noticed during ambulatory impedance-pH monitoring can predict the state of consciousness during nocturnal period

Unveiling Neutrino Mixing and Leptonic CP Violation

We review the present understanding of neutrino masses and mixings, discussing what are the unknowns in the three family oscillation scenario. Despite the anticipated success coming from the planned long baseline neutrino experiments in unraveling the leptonic mixing sector, there are two important unknowns which may remain obscure: the mixing angle $\theta_{13}$ and the CP-phase $\delta$. The measurement of these two parameters has led us to consider the combination of superbeams and neutrino factories as the key to unveil the neutrino oscillation picture.Comment: Invited brief review, 18 pages, 6 figure

νμ\nu_\mu disappearance at the SPL, T2K-I, NOν\nuA and the Neutrino Factory

We study the measurement of the atmospheric neutrino oscillation parameters, $\theta_{23}$ and $\Delta m^2_{23}$, at the $\nu_\mu$ disappearance channel at three conventional beam facilities, the SPL, T2K-phase I and NO$\nu$A. These two parameters have been shown to be of crucial importance in the measurement of two of the unknowns of the PMNS mixing matrix, $\theta_{13}$ and the leptonic CP-violating phase $\delta$. In our analyis, the effect of the two discrete ambiguities, ${\rm sign}(\Delta m^2_{23})$ and ${\rm sign}(\tan 2 \theta_{23})$, is explicitly taken into account. We analyse also the $\nu_\mu$ disappearance channel at the Neutrino Factory, and combine it with the ``golden'' $\nu_e \to \nu_\mu$ and ``silver'' $\nu_e \to \nu_\tau$ appearance channels to study its impact on the measurement of $\theta_{13}$ and $\delta$. Eventually, we present the sensitivity of the four facilities to different observables: $\theta_{13}$, $\delta$, maximal $\theta_{23}$, the sign of the atmospheric mass difference, $s_{atm}$, and the $\theta_{23}$-octant, $s_{oct}$.Comment: 40 pages using epsfig; bibliography modifie