Random Forests and Networks Analysis

D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a powerful tool in analyzing structures on networks and along this line of thinking, in recent works~\cite{AG1,AG2,ACGM1,ACGM2} we focused on applications of spanning rooted forests on finite graphs. The resulting main conclusions are reviewed in this paper by collecting related theorems, algorithms, heuristics and numerical experiments. A first foundational part on determinantal structures and efficient sampling procedures is followed by four main applications: 1) a random-walk-based notion of well-distributed points in a graph 2) how to describe metastable dynamics in finite settings by means of Markov intertwining dualities 3) coarse graining schemes for networks and associated processes 4) wavelets-like pyramidal algorithms for graph signals.Comment: Survey pape

Perspectives in Neutrino Physics: Monochromatic Neutrino Beams

In the last few years spectacular results have been achieved with the demonstration of non vanishing neutrino masses and flavour mixing. The ultimate goal is the understanding of the origin of these properties from new physics. In this road, the last unknown mixing $[U_{e3}]$ must be determined. If it is proved to be non-zero, the possibility is open for Charge Conjugation-Parity (CP) violation in the lepton sector. This will require precision experiments with a very intense neutrino source. Here a novel method to create a monochromatic neutrino beam, an old dream for neutrino physics, is proposed based on the recent discovery of nuclei that decay fast through electron capture. Such nuclei will generate a monochromatic directional neutrino beam when decaying at high energy in a storage ring with long straight sections. We also show that the capacity of such a facility to discover new physics is impressive, so that fine tuning of the boosted neutrino energy allows precision measurements of the oscillation parameters even for a $[U_{e3}]$ mixing as small as 1 degree. We can thus open a window to the discovery of CP violation in neutrino oscillations.Comment: 15 pages, 7 figures. Contribution to the proceedings of GUSTAVOFEST - Symposium in Honour of Gustavo C. Branco: CP Violation and the Flavour Puzzle, Lisbon, Portugal, 19-20 July 200

Physics Reach with a Monochromatic Neutrino Beam from Electron Capture

Neutrino oscillation experiments from different sources have demonstrated non-vanishing neutrino masses and flavour mixings. The next experiments have to address the determination of the connecting mixing U(e3) and the existence of the CP violating phase. Whereas U(e3) measures the strength of the oscillation probability in appearance experiments, the CP phase acts as a phase-shift in the interference pattern. Here we propose to separate these two parameters by energy dependence, using the novel idea of a monochromatic neutrino beam facility based on the acceleration of ions that decay fast through electron capture. Fine tuning of the boosted neutrino energy allows precision measurements able to open a window for the discovery of CP violation, even for a mixing as small as 1 degree.Comment: 4 pages, 1 figure. Talk given at the International Europhysics Conference on High Energy Physics, HEP-EPS 2005, Lisbon, Portugal, July 21-27, 200

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

Conformal Invariance and Electrodynamics: Applications and General Formalism

The role of the conformal group in electrodynamics in four space-time dimensions is re-examined. As a pedagogic example we use the application of conformal transformations to find the electromagnetic field for a charged particle moving with a constant relativistic acceleration from the Coulomb electric field for the particle at rest. We also re-consider the reformulation of Maxwell's equations on the projective cone, which is isomorphic to a conformal compactification on Minkowski space, so that conformal transformations, belonging to the group O(4,2), are realised linearly. The resulting equations are different from those postulated previously and respect additional gauge invariances which play an essential role in ensuring consistency with conventional electrodynamics on Minkowski space. The solution on the projective cone corresponding to a constantly accelerating charged particle is discussed.Comment: 24 pages, 1 figure, plain tex, uses harvmac, eps

A note about the t`Hooft`s ansatz for SU(N) real time guage theories

The t`Hooft's ansatz reduces the classical Yang--Mills theory to the $\lambda\phi^4$ one. It is shown that in the frame of this ansatz the real-time classical solutions for the arbitrary SU(N) gauge group is obtained by embedding $SU(2)\times SU(2)$ into SU(N). It is argued that this group structure is the only possibility in the frame of the considered ansatz. New explicit solutions for SU(3) and SU(5) gauge groups are shown

Neutrino-nucleus interaction rates at a low-energy beta-beam facility

We compute the neutrino detection rates to be expected at a low-energy beta-beam facility. We consider various nuclei as neutrino detectors and compare the case of a small versus large storage ring.Comment: 6 pages, 3 figure

Obstructive Sleep Apnoea Syndrome, Endothelial Function and Markers of Endothelialization. Changes after CPAP

STUDY OBJECTIVES: This study tries to assess the endothelial function in vivo using flow-mediated dilatation (FMD) and several biomarkers of endothelium formation/restoration and damage in patients with obstructive sleep apnoea (OSA) syndrome at baseline and after three months with CPAP therapy. DESIGN: Observational study, before and after CPAP therapy. SETTING AND PATIENTS: We studied 30 patients with apnoea/hypopnoea index (AHI) >15/h that were compared with themselves after three months of CPAP therapy. FMD was assessed non-invasively in vivo using the Laser-Doppler flowmetry. Circulating cell-free DNA (cf-DNA) and microparticles (MPs) were measured as markers of endothelial damage and the vascular endothelial growth factor (VEGF) was determined as a marker of endothelial restoration process. MEASUREMENTS AND RESULTS: After three month with CPAP, FMD significantly increased (1072.26 ± 483.21 vs. 1604.38 ± 915.69 PU, p< 0.005) cf-DNA and MPs significantly decreased (187.93 ± 115.81 vs. 121.28 ± 78.98 pg/ml, p<0.01, and 69.60 ± 62.60 vs. 39.82 ± 22.14 U/μL, p<0.05, respectively) and VEGF levels increased (585.02 ± 246.06 vs. 641.11 ± 212.69 pg/ml, p<0.05). These changes were higher in patients with more severe disease. There was a relationship between markers of damage (r = -0.53, p<0.005) but not between markers of damage and restoration, thus suggesting that both types of markers should be measured together. CONCLUSIONS: CPAP therapy improves FMD. This improvement may be related to an increase of endothelial restoration process and a decrease of endothelial damage

Physics Reach of Electron-Capture Neutrino Beams

To complete the picture of neutrino oscillations two fundamental parameters need to be measured, theta13 and delta. The next generation of long baseline neutrino oscillation experiments -superbeams, betabeams and neutrino factories- indeed take aim at measuring them. Here we explore the physics reach of a new candidate: an electron-capture neutrino beam. Emphasis is made on its feasibility thanks to the recent discovery of nuclei that decay fast through electron capture, and on the interplay with a betabeam (its closest relative).Comment: 5 pages, 3 png figures. Talk given at the 7th International Workshop on Neutrino Factories and Superbeams (NuFact 05), Frascati, Italy, June 200