A remark on trace properties of K-cycles

In this paper we discuss trace properties of $d^+$-summable $K$-cycles considered by A.Connes in [\rfr(Conn4)]. More precisely we give a proof of a trace theorem on the algebra \A of a $K$--cycle stated in [\rfr(Conn4)], namely we show that a natural functional on \A is a trace functional. Then we discuss whether this functional gives a trace on the whole universal graded differential algebra \Q(\A). On the one hand we prove that the regularity conditions on $K$-cycles considered in [\rfr(Conn4)] imply the trace property on \Q(\A). On the other hand, by constructing an explicit counterexample, we remark that the sole $K$-cycle assumption is not sufficient for such a property to hold.Comment: 11 pages, plain Te

Integrals and Potentials of Differential 1-forms on the Sierpinski Gasket

We provide a definition of integral, along paths in the Sierpinski gasket K, for differential smooth 1-forms associated to the standard Dirichlet form K. We show how this tool can be used to study the potential theory on K. In particular, we prove: i) a de Rham reconstruction of a 1-form from its periods around lacunas in K; ii) a Hodge decomposition of 1-forms with respect to the Hilbertian energy norm; iii) the existence of potentials of smooth 1-forms on a suitable covering space of K. We finally show that this framework provides versions of the de Rham duality theorem for the fractal K.Comment: Some proofs have been clarified, reference to previous literature is now more accurate, 33 pages, 6 figure

Mantle-Crust Isotopic Relationships along Mid Ocean Ridges: Constraints from the Analysis of Time Series

Isotopic relationships between parent mantle and daughter MORBs have been used to reveal the composite nature of the source tracking the missing components in their isotopic fingerprints. An opportunity to address this issue is given by temporal sections of single ridge segments where MORB and residual parent mantle peridotites can be assessed together. The possibility has been offered by the flexured and uplifted lithospheric slab that exposes, on the sea floor along a seafloor spreading flow line, a zero to 26 Ma relatively undisturbed lithospheric section (Vema Lithospheric Section or VLS) generated at the 80 km long Mid Atlantic ridge segment (EMAR) at 11°N. Temporal variations of the Nd isotopic composition of crustal basalts and parental mantle along the VLS reveal a large dispersion of residual isotopic composition with respect to the melt products. Equilibration with partially mixed melts can account for the observed relationships in the mantle rocks. The mean MORB isotopic composition and the average composition of the residues do not match because of the preferential extraction of the low-melting component. The compositional difference in both isotopic and elemental distribution is a function of the average degree of melting of the mantle. This observation can only be justified by progressive melting of composite lithologies where mantle potential temperature and amount of dispersed low-melting lithologies control the relative extent of melting of the mantle host and that of the dispersed heterogeneities resulting in differential fractions of mixed melts in the final products. This observation is confirmed by global correlations in Nd isotopes and chemical indicators of degree of melting from other portions of the mid ocean ridge system

Spectral triples for the Sierpinski Gasket

We construct a family of spectral triples for the Sierpinski Gasket $K$. For suitable values of the parameters, we determine the dimensional spectrum and recover the Hausdorff measure of $K$ in terms of the residue of the volume functional $a\to$ tr$(a\,|D|^{-s})$ at its abscissa of convergence $d_D$, which coincides with the Hausdorff dimension $d_H$ of the fractal. We determine the associated Connes' distance showing that it is bi-Lipschitz equivalent to the distance on $K$ induced by the Euclidean metric of the plane, and show that the pairing of the associated Fredholm module with (odd) $K$-theory is non-trivial. When the parameters belong to a suitable range, the abscissa of convergence $\delta_D$ of the energy functional $a\to$ tr$(|D|^{-s/2}|[D,a]|^2\,|D|^{-s/2})$ takes the value $d_E=\frac{\log(12/5)}{\log 2}$, which we call energy dimension, and the corresponding residue gives the standard Dirichlet form on $K$.Comment: 48 pages, 9 figures. Final version, to appear in J.Funct.Ana

OGTA: Open gaze tracker and analyzer a remote low cost system based on off-the-shelf components and open source modular software

Several academic and commercial eye tracking systems have evolved to the point that they can operate without contact with the user. In addition, they also permit free head movement (within reasonable limits) without losing tracking and maintaining a good accuracy (errors below 1 degree). However, there are still several aspects which require further improvement before these systems can be extensively used. These include price, accuracy, robustness, and ease of set-up and use. This work proposes a preliminary version of a remote eye tracking system which starts to deal with some of those critical points. To drastically reduce the costs, the system has been built by assembling low cost off-the-shelf components, and the cross-platform software has been developed based on an open source philosophy. Second, the accuracy in gaze detection has been improved through the Starburst algorithm. Last and importantly, the plug-in organization of the software architecture, which crucially distinguishes the proposed system from similar ones previously proposed in literature. This facilitates the addition of dedicated software modules designed to improve specific features according to the particular application at hand. Here we present the architecture of the system and preliminary results on the functioning and accuracy of the system

Optical interferometry in the presence of large phase diffusion

Phase diffusion represents a crucial obstacle towards the implementation of high precision interferometric measurements and phase shift based communication channels. Here we present a nearly optimal interferometric scheme based on homodyne detection and coherent signals for the detection of a phase shift in the presence of large phase diffusion. In our scheme the ultimate bound to interferometric sensitivity is achieved already for a small number of measurements, of the order of hundreds, without using nonclassical light

Water in Mid Ocean Ridge Basalts: Some Like it Hot, Some Like it Cold.

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The neuron-astrocyte-microglia triad in a rat model of chronic cerebral hypoperfusion: Protective effect of dipyridamole

Chronic cerebral hypoperfusion during aging may cause progressive neurodegeneration as ischemic conditions persist. Proper functioning of the interplay between neurons and glia is fundamental for the functional organization of the brain. The aim of our research was to study the pathophysiological mechanisms, and particularly the derangement of the interplay between neurons and astrocytes-microglia with the formation of triads, in a model of chronic cerebral hypoperfusion induced by the 2-vessel occlusion (2VO) in adult Wistar rats (n=15). The protective effect of dipyridamole given during the early phases after 2VO (4 mg/kg/day i.v., the first 7 days after 2VO) was verified (n=15). Sham-operated rats (n=15) were used as controls. Immunofluorescent triple staining of neurons (NeuN), astrocytes (GFAP) and microglia (IBA1) was performed 90 days after 2VO. We found significantly higher amount of ectopic neurons, neuronal debris and apoptotic neurons in CA1 Str. Radiatum and Str. Pyramidale of 2VO rats. In CA1 Str. Radiatum of 2VO rats the amount of astrocytes (cells/mm2) did not increase. In some instances several astrocytes surrounded ectopic neurons and formed a micro scar around them. Astrocyte branches could infiltrate the cell body of ectopic neurons, and, together with activated microglia cells formed the triads. In the triad, significantly more numerous in CA1 Str. Radiatum of 2VO than in sham rats, astrocytes and microglia cooperated in the phagocytosis of ectopic neurons. These events might be common mechanisms underlying many neurodegenerative processes. The frequency to which they appear might depend upon, or might be the cause of, the burden and severity of neurodegeneration. Dypiridamole significantly reverted all the above described events. The protective effect of chronic administration of dipyridamole might be a consequence of its vasodilatory, antioxidant and anti-inflammatory role during the early phases after 2VO