Persistence of Diophantine flows for quadratic nearly-integrable Hamiltonians under slowly decaying aperiodic time dependence

The aim of this paper is to prove a Kolmogorov-type result for a nearly-integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the forced system, provided that the perturbation is real-analytic and (exponentially) decaying with time. The advantage consists of the possibility to choose an arbitrarily small decaying coefficient, consistently with the perturbation size.Comment: Several corrections in the proof with respect to the previous version. Main statement unchange

Short-term effects of focal muscle vibration on motor recovery after acute stroke: a pilot randomized sham-controlled study

Repetitive focal muscle vibration (rMV) is known to promote neural plasticity and long-lasting motor recovery in chronic stroke patients. Those structural and functional changes within the motor network underlying motor recovery occur in the very first hours after stroke. Nonetheless, to our knowledge, no rMV-based studies have been carried out in acute stroke patients so far, and the clinical benefit of rMV in this phase of stroke is yet to be determined. The aim of this randomized double-blind sham-controlled study is to investigate the short-term effect of rMV on motor recovery in acute stroke patients. Out of 22 acute stroke patients, 10 were treated with the rMV (vibration group–VG), while 12 underwent the sham treatment (control group–CG). Both treatments were carried out for 3 consecutive days, starting within 72 h of stroke onset; each daily session consisted of three 10-min treatments (for each treated limb), interspersed with a 1-min interval. rMV was delivered using a specific device (Cro®System, NEMOCO srl, Italy). The transducer was applied perpendicular to the target muscle's belly, near its distal tendon insertion, generating a 0.2–0.5 mm peak-to-peak sinusoidal displacement at a frequency of 100 Hz. All participants also underwent a daily standard rehabilitation program. The study protocol underwent local ethics committee approval (ClinicalTrial.gov NCT03697525) and written informed consent was obtained from all of the participants. With regard to the different pre-treatment clinical statuses, VG patients showed significant clinical improvement with respect to CG-treated patients among the NIHSS (p < 0.001), Fugl-Meyer (p = 0.001), and Motricity Index (p < 0.001) scores. In addition, when the upper and lower limb scales scores were compared between the two groups, VG patients were found to have a better clinical improvement at all the clinical end points. This study provides the first evidence that rMV is able to improve the motor outcome in a cohort of acute stroke patients, regardless of the pretreatment clinical status. Being a safe and well-tolerated intervention, which is easy to perform at the bedside, rMV may represent a valid complementary non-pharmacological therapy to promote motor recovery in acute stroke patients

Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories

We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, that can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form, so as to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that is at basis of the analytic part of the Nekhoroshev's theorem, so as to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller.Comment: 31 pages, 2 figures. arXiv admin note: text overlap with arXiv:1010.260

Finding the complement of the invariant manifolds transverse to a given foliation for a 3D flow

A method is presented to establish regions of phase space for 3D vector fields through which pass no co-oriented invariant 2D submanifolds transverse to a given oriented 1D foliation. Refinements are given for the cases of volume-preserving or Cartan-Arnol’d Hamiltonian flows and for boundaryless submanifolds

Regularization of the circular restricted three-body problem using 'similar' coordinate systems

The regularization of a new problem, namely the three-body problem, using 'similar' coordinate system is proposed. For this purpose we use the relation of 'similarity', which has been introduced as an equivalence relation in a previous paper (see \cite{rom11}). First we write the Hamiltonian function, the equations of motion in canonical form, and then using a generating function, we obtain the transformed equations of motion. After the coordinates transformations, we introduce the fictitious time, to regularize the equations of motion. Explicit formulas are given for the regularization in the coordinate systems centered in the more massive and the less massive star of the binary system. The 'similar' polar angle's definition is introduced, in order to analyze the regularization's geometrical transformation. The effect of Levi-Civita's transformation is described in a geometrical manner. Using the resulted regularized equations, we analyze and compare these canonical equations numerically, for the Earth-Moon binary system.Comment: 24 pages, 7 figures; Accepted for publication in Astrophysics and Space Scienc

Physics of the Riemann Hypothesis

Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics. Here we choose a particular number theoretical function, the Riemann zeta function and examine its influence in the realm of physics and also how physics may be suggestive for the resolution of one of mathematics' most famous unconfirmed conjectures, the Riemann Hypothesis. Does physics hold an essential key to the solution for this more than hundred-year-old problem? In this work we examine numerous models from different branches of physics, from classical mechanics to statistical physics, where this function plays an integral role. We also see how this function is related to quantum chaos and how its pole-structure encodes when particles can undergo Bose-Einstein condensation at low temperature. Throughout these examinations we highlight how physics can perhaps shed light on the Riemann Hypothesis. Naturally, our aim could not be to be comprehensive, rather we focus on the major models and aim to give an informed starting point for the interested Reader.Comment: 27 pages, 9 figure

Educating a New Generation of Doctors to Improve the Health of Populations in Low- and Middle-Income Countries

Francesca Celletti and colleagues from WHO argue that a transformation in the scale-up of medical education in low- and middle-income countries is needed, and detail what this might look like

A silicon imaging calorimeter prototype for antimatter search in space: experimental results

Abstract This report presents the results obtained with a prototype silicon-tungsten (Si-W) electromagnetic calorimeter, conceived as a fine-grained imaging device to carry out studies of the antimatter component in primary cosmic radiation. The calorimeter prototype contains 20 x , y sampling layers interleaved with 19 showering material planes. One sensitive layer is obtained with two silicon strip detectors (Si-D) (60 × 60) mm 2 , each divided into 16 strips, 3.6 mm wide; the two detectors are assembled back to back with perpendicular strips. This allows the transverse distributions of the shower in both coordinates at each sampling (0.5 X 0 ) to be pictured. The basic characteristics of the design and the experimental results obtained on a test beam at the CERN proton synchrotron (PS) for electrons and pions are reported. The main results presented are the response of the calorimeter to the electron at various energies (1–7 GeV), and the transverse shower profiles at different calorimeter depths as well as the patterns of the electromagnetic shower and those of the interacting and non-interacting pions. The capability of the calorimeter in measuring the direction of the incoming electromagnetic particle from the pattern of the shower has been evaluated at different energies. These results are encouraging in view of the possible use of this detector to search for high-energy γ sources in space

Silicon calorimeter for cosmic antimatter search

Abstract The silicon sampling calorimeter presented is conceived as a fine grained imaging device to carry out studies of the anti-matter component in the primary cosmic radiation; it will be used in balloon payload program starting in 1993. The first sampling layer (48×48 cm2) of this silicon calorimeter has been completed and successfully tested. We report the first results form studies performed at the CERN PS t7 beam. The complete calorimeter contains 20 xy sampling layers (strip pitch 3.6 mm) interleaved with 19 showering material planes (tungsten 0.5 X0). This allows to picture the transverse distributions of the shower in both coordinates at each sampling. The outstanding imaging capabilities reflects in high particle identification power. Preliminary results from beam tests performed with antiprotons at 3.5 GeV on a tower prototype of the calorimeter are reported