Coupling Poisson and Jacobi structures on foliated manifolds

Let M be a differentiable manifold endowed with a foliation F. A Poisson structure P on M is F-coupling if the image of the annihilator of TF by the sharp-morphism defined by P is a normal bundle of the foliation F. This notion extends Sternberg's coupling symplectic form of a particle in a Yang-Mills field. In the present paper we extend Vorobiev's theory of coupling Poisson structures from fiber bundles to foliations and give simpler proofs of Vorobiev's existence and equivalence theorems of coupling Poisson structures on duals of kernels of transitive Lie algebroids over symplectic manifolds. Then we discuss the extension of the coupling condition to Jacobi structures on foliated manifolds.Comment: LateX, 38 page

Arithmetic of split Kummer surfaces: Montgomery endomorphism of Edwards products

International audienceLet $E$ be an elliptic curve, $\mathcal{K}_1$ its Kummer curve $E/\{\pm1\}$, $E^2$ its square product, and $\mathcal{K}_2$ the split Kummer surface $E^2/\{\pm1\}$. The addition law on $E^2$ gives a large endomorphism ring, which induce endomorphisms of $\mathcal{K}_2$. With a view to the practical applications to scalar multiplication on $\mathcal{K}_1$, we study the explicit arithmetic of $\mathcal{K}_2$

Observation of Multi-Tev Diffuse Gamma Rays from the Galactic Plane with the Tibet Air Shower Array

Data from the Tibet-III air shower array (with energies around 3 TeV) and from the Tibet-II array (with energies around 10 TeV) have been searched for diffuse gamma rays from the Galactic plane. These arrays have an angular resolution of about 0.9 degrees. The sky regions searched are the inner Galaxy, 20 degrees <= l <= 55 degrees, and outer Galaxy, 140 degrees <= l <= 225 degrees, and |b| <= 2 degrees or <= 5 degrees. No significant Galactic plane gamma-ray excess was observed. The 99% confidence level upper limits for gamma-ray intensity obtained are (for |b| <= 2 degrees) 1.1 times 10^{-15} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 3 TeV and 4.1 times 10^{-17} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 10 TeV for the inner Galaxy, and 3.6 times 10^{-16} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 3 TeV and 1.3 times 10^{-17} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 10 TeV for the outer Galaxy, assuming a differential spectral index of 2.4. The upper limits are significant in the multi-TeV region when compared to those from Cherenkov telescopes in the lower energy region and other air shower arrays in the higher energy region; however, the results are not sufficient to rule out the inverse Compton model with a source electron spectral index of 2.0.Comment: 22 pages, 8 figures, Accepted for publication in Ap

Observation of Multi-Tev Gamma Rays from the Crab Nebula Using the Tibet Air Shower Array

The Tibet experiment, operating at Yangbajing (4,300 m above sea level), is the lowest energy air shower array and the new high density array constructed in 1996 has sensitivity to $\gamma$-ray air showers at energies as low as 3 TeV. With this new array, the Crab Nebula was observed in multi-TeV $\gamma$-rays and a signal was detected at the 5.5 $\sigma$ level. We also obtained the energy spectrum of $\gamma$-rays in the energy region above 3 TeV which partially overlaps those observed with imaging atmospheric Cherenkov telescopes. This is the first observation of $\gamma$-ray signals from point sources with a conventional air shower array using scintillation detectors.Comment: 9 pages, 4 figures, Accepted for publication in ApJ Letter

Detection of Multi-TeV Gamma Rays from Markarian 501 during an Unforeseen Flaring State in 1997 with the Tibet Air Shower Array

In 1997, the BL Lac Object Mrk 501 entered a very active phase and was the brightest source in the sky at TeV energies, showing strong and frequent flaring. Using the data obtained with a high density air shower array that has been operating successfully at Yangbajing in Tibet since 1996, we searched for gamma-ray signals from this source during the period from February through August in 1997. Our observation detected multi-TeV $\gamma$-ray signals at the 3.7-Sigma level during this period. The most rapid increase of the excess counts was observed between April 7 and June 16 and the statistical significance of the excess counts in this period was 4.7-Sigma. Among several observations of flaring TeV gamma-rays from Mrk 501 in 1997, this is the only observation using a conventional air shower array. We present the energy spectrum of gamma-rays which will be worthy to compare with those obtained by imaging atmospheric Cerenkov telescopes.Comment: 9 pages, 7 figures, To appear in Ap

Primary proton spectrum between 200 TeV and 1000 TeV observed with the Tibet burst detector and air shower array

Since 1996, a hybrid experiment consisting of the emulsion chamber and burst detector array and the Tibet-II air-shower array has been operated at Yangbajing (4300 m above sea level, 606 g/cm^2) in Tibet. This experiment can detect air-shower cores, called as burst events, accompanied by air showers in excess of about 100 TeV. We observed about 4300 burst events accompanied by air showers during 690 days of operation and selected 820 proton-induced events with its primary energy above 200 TeV using a neural network method. Using this data set, we obtained the energy spectrum of primary protons in the energy range from 200 to 1000 TeV. The differential energy spectrum obtained in this energy region can be fitted by a power law with the index of -2.97 $\pm$ 0.06, which is steeper than that obtained by direct measurements at lower energies. We also obtained the energy spectrum of helium nuclei at particle energies around 1000 TeV.Comment: 25 pages, 22 figures, Accepted for publication in Phys. Rev.

Examination of the Effects of Heterogeneous Organization of RyR Clusters, Myofibrils and Mitochondria on Ca2+ Release Patterns in Cardiomyocytes

Spatio-temporal dynamics of intracellular calcium, [Ca2+]i, regulate the contractile function of cardiac muscle cells. Measuring [Ca2+]i flux is central to the study of mechanisms that underlie both normal cardiac function and calcium-dependent etiologies in heart disease. However, current imaging techniques are limited in the spatial resolution to which changes in [Ca2+]i can be detected. Using spatial point process statistics techniques we developed a novel method to simulate the spatial distribution of RyR clusters, which act as the major mediators of contractile Ca2+ release, upon a physiologically-realistic cellular landscape composed of tightly-packed mitochondria and myofibrils.We applied this method to computationally combine confocal-scale (~ 200 nm) data of RyR clusters with 3D electron microscopy data (~ 30 nm) of myofibrils and mitochondria, both collected from adult rat left ventricular myocytes. Using this hybrid-scale spatial model, we simulated reaction-diffusion of [Ca2+]i during the rising phase of the transient (first 30 ms after initiation). At 30 ms, the average peak of the simulated [Ca2+]i transient and of the simulated fluorescence intensity signal, F/F0, reached values similar to that found in the literature ([Ca2+]i 1 μM; F/F0 5.5). However, our model predicted the variation in [Ca2+]i to be between 0.3 and 12.7 μM (~3 to 100 fold from resting value of 0.1 μM) and the corresponding F/F0 signal ranging from 3 to 9.5. We demonstrate in this study that: (i) heterogeneities in the [Ca2+]i transient are due not only to heterogeneous distribution and clustering of mitochondria; (ii) but also to heterogeneous local densities of RyR clusters. Further, we show that: (iii) these structureinduced heterogeneities in [Ca2+]i can appear in line scan data. Finally, using our unique method for generating RyR cluster distributions, we demonstrate the robustness in the [Ca2+]i transient to differences in RyR cluster distributions measured between rat and human cardiomyocytes

The Dopamine D3 Receptor Knockout Mouse Mimics Aging-Related Changes in Autonomic Function and Cardiac Fibrosis

Blood pressure increases with age, and dysfunction of the dopamine D3 receptor has been implicated in the pathogenesis of hypertension. To evaluate the role of the D3 receptor in aging-related hypertension, we assessed cardiac structure and function in differently aged (2 mo, 1 yr, 2 yr) wild type (WT) and young (2 mo) D3 receptor knockout mice (D3KO). In WT, systolic and diastolic blood pressures and rate-pressure product (RPP) significantly increased with age, while heart rate significantly decreased. Blood pressure values, heart rate and RPP of young D3KO were significantly elevated over age-matched WT, but similar to those of the 2 yr old WT. Echocardiography revealed that the functional measurements of ejection fraction and fractional shortening decreased significantly with age in WT and that they were significantly smaller in D3KO compared to young WT. Despite this functional change however, cardiac morphology remained similar between the age-matched WT and D3KO. Additional morphometric analyses confirmed an aging-related increase in left ventricle (LV) and myocyte cross-sectional areas in WT, but found no difference between age-matched young WT and D3KO. In contrast, interstitial fibrosis, which increased with age in WT, was significantly elevated in the D3KO over age-matched WT, and similar to 2 yr old WT. Western analyses of myocardial homogenates revealed significantly increased levels of pro- and mature collagen type I in young D3KO. Column zymography revealed that activities of myocardial MMP-2 and MMP-9 increased with age in WTs, but in D3KO, only MMP-9 activity was significantly increased over age-matched WTs. Our data provide evidence that the dopamine D3 receptor has a critical role in the emergence of aging-related cardiac fibrosis, remodeling, and dysfunction