Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet's splitting

We consider locally minimizing measures for the conservative twist maps of the $d$-dimensional annulus or for the Tonelli Hamiltonian flows defined on a cotangent bundle $T^*M$. For weakly hyperbolic such measures (i.e. measures with no zero Lyapunov exponents), we prove that the mean distance/angle between the stable and the unstable Oseledet's bundles gives an upper bound of the sum of the positive Lyapunov exponents and a lower bound of the smallest positive Lyapunov exponent. Some more precise results are proved too

Functionnectome as a framework to analyse the contribution of brain circuits to fMRI

In recent years, the field of functional neuroimaging has moved away from a pure localisationist approach of isolated functional brain regions to a more integrated view of these regions within functional networks. However, the methods used to investigate functional networks rely on local signals in grey matter and are limited in identifying anatomical circuitries supporting the interaction between brain regions. Mapping the brain circuits mediating the functional signal between brain regions would propel our understanding of the brain’s functional signatures and dysfunctions. We developed a method to unravel the relationship between brain circuits and functions: The Functionnectome. The Functionnectome combines the functional signal from fMRI with white matter circuits’ anatomy to unlock and chart the first maps of functional white matter. To showcase this method’s versatility, we provide the first functional white matter maps revealing the joint contribution of connected areas to motor, working memory, and language functions. The Functionnectome comes with an open-source companion software and opens new avenues into studying functional networks by applying the method to already existing datasets and beyond task fMRI

Density of a gas of spin polarized fermions in a magnetic field

For a fermion gas with equally spaced energy levels that is subjected to a magnetic field, the particle density is calculated. The derivation is based on the path integral approach for identical particles, in combination with the inversion techniques for the generating function of the static response functions. Explicit results are presented for the ground state density as a function of the magnetic field with a number of particles ranging from 1 to 45.Comment: 9 pages, 8 figures; To appear in Phys. Rev. E on December 1, 2000; e-mail addresses: [email protected], [email protected], [email protected], [email protected]

Aminopeptidase B, a glucagon-processing enzyme: site directed mutagenesis of the Zn2+-binding motif and molecular modelling

<p>Abstract</p> <p>Background</p> <p>Aminopeptidase B (Ap-B; EC 3.4.11.6) catalyzes the cleavage of basic residues at the N-terminus of peptides and processes glucagon into miniglucagon. The enzyme exhibits, <it>in vitro</it>, a residual ability to hydrolyze leukotriene A₄into the pro-inflammatory lipid mediator leukotriene B₄. The potential bi-functional nature of Ap-B is supported by close structural relationships with LTA₄hydrolase (LTA₄H ; EC 3.3.2.6). A structure-function analysis is necessary for the detailed understanding of the enzymatic mechanisms of Ap-B and to design inhibitors, which could be used to determine the complete <it>in vivo </it>functions of the enzyme.</p> <p>Results</p> <p>The rat Ap-B cDNA was expressed in <it>E. coli </it>and the purified recombinant enzyme was characterized. 18 mutants of the H³²⁵EXXHX₁₈E³⁴⁸Zn²⁺-binding motif were constructed and expressed. All mutations were found to abolish the aminopeptidase activity. A multiple alignment of 500 sequences of the M1 family of aminopeptidases was performed to identify 3 sub-families of exopeptidases and to build a structural model of Ap-B using the x-ray structure of LTA₄H as a template. Although the 3D structures of the two enzymes resemble each other, they differ in certain details. The role that a loop, delimiting the active center of Ap-B, plays in discriminating basic substrates, as well as the function of consensus motifs, such as RNP1 and Armadillo domain are discussed. Examination of electrostatic potentials and hydrophobic patches revealed important differences between Ap-B and LTA₄H and suggests that Ap-B is involved in protein-protein interactions.</p> <p>Conclusion</p> <p>Alignment of the primary structures of the M1 family members clearly demonstrates the existence of different sub-families and highlights crucial residues in the enzymatic activity of the whole family. <it>E. coli </it>recombinant enzyme and Ap-B structural model constitute powerful tools for investigating the importance and possible roles of these conserved residues in Ap-B, LTA₄H and M1 aminopeptidase catalytic sites and to gain new insight into their physiological functions. Analysis of Ap-B structural model indicates that several interactions between Ap-B and proteins can occur and suggests that endopeptidases might form a complex with Ap-B during hormone processing.</p

Remote Laboratory for E-Learning of Systems on Chip and Their Applications to Nuclear and Scientific Instrumentation

Configuring and setting up a remote access laboratory for an advanced online school on fully programmable System-on-Chip (SoC) proved to be an outstanding challenge. The school, jointly organized by the International Centre for Theoretical Physics (ICTP) and the International Atomic Energy Agency (IAEA), focused on SoC and its applications to nuclear and scientific instrumentation and was mainly addressed to physicists, computer scientists and engineers from developing countries. The use of e-learning tools, which some of them adopted and others developed, allowed the school participants to directly access both integrated development environment software and programmable SoC platforms. This facilitated the follow-up of all proposed exercises and the final project. During the four weeks of the training activity, we faced and overcame different technology and communication challenges, whose solutions we describe in detail together with dedicated tools and design methodology. We finally present a summary of the gained experience and an assessment of the results we achieved, addressed to those who foresee to organize similar initiatives using e-learning for advanced training with remote access to SoC platforms

A Mission to Explore the Pioneer Anomaly

The Pioneer 10 and 11 spacecraft yielded the most precise navigation in deep space to date. These spacecraft had exceptional acceleration sensitivity. However, analysis of their radio-metric tracking data has consistently indicated that at heliocentric distances of $\sim 20-70$ astronomical units, the orbit determinations indicated the presence of a small, anomalous, Doppler frequency drift. The drift is a blue-shift, uniformly changing with a rate of $\sim(5.99 \pm 0.01)\times 10^{-9}$ Hz/s, which can be interpreted as a constant sunward acceleration of each particular spacecraft of $a_P = (8.74 \pm 1.33)\times 10^{-10} {\rm m/s^2}$. This signal has become known as the Pioneer anomaly. The inability to explain the anomalous behavior of the Pioneers with conventional physics has contributed to growing discussion about its origin. There is now an increasing number of proposals that attempt to explain the anomaly outside conventional physics. This progress emphasizes the need for a new experiment to explore the detected signal. Furthermore, the recent extensive efforts led to the conclusion that only a dedicated experiment could ultimately determine the nature of the found signal. We discuss the Pioneer anomaly and present the next steps towards an understanding of its origin. We specifically focus on the development of a mission to explore the Pioneer Anomaly in a dedicated experiment conducted in deep space.Comment: 8 pages, 9 figures; invited talk given at the 2005 ESLAB Symposium "Trends in Space Science and Cosmic Vision 2020", 19-21 April 2005, ESTEC, Noordwijk, The Netherland

Fundamental Physics with the Laser Astrometric Test Of Relativity

The Laser Astrometric Test Of Relativity (LATOR) is a joint European-U.S. Michelson-Morley-type experiment designed to test the pure tensor metric nature of gravitation - a fundamental postulate of Einstein's theory of general relativity. By using a combination of independent time-series of highly accurate gravitational deflection of light in the immediate proximity to the Sun, along with measurements of the Shapiro time delay on interplanetary scales (to a precision respectively better than 0.1 picoradians and 1 cm), LATOR will significantly improve our knowledge of relativistic gravity. The primary mission objective is to i) measure the key post-Newtonian Eddington parameter \gamma with accuracy of a part in 10^9. (1-\gamma) is a direct measure for presence of a new interaction in gravitational theory, and, in its search, LATOR goes a factor 30,000 beyond the present best result, Cassini's 2003 test. The mission will also provide: ii) first measurement of gravity's non-linear effects on light to ~0.01% accuracy; including both the Eddington \beta parameter and also the spatial metric's 2nd order potential contribution (never measured before); iii) direct measurement of the solar quadrupole moment J2 (currently unavailable) to accuracy of a part in 200 of its expected size; iv) direct measurement of the "frame-dragging" effect on light by the Sun's gravitomagnetic field, to 1% accuracy. LATOR's primary measurement pushes to unprecedented accuracy the search for cosmologically relevant scalar-tensor theories of gravity by looking for a remnant scalar field in today's solar system. We discuss the mission design of this proposed experiment.Comment: 8 pages, 9 figures; invited talk given at the 2005 ESLAB Symposium "Trends in Space Science and Cosmic Vision 2020," 19-21 April 2005, ESTEC, Noodrwijk, The Netherland

Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds

Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property.Comment: 49 page