1,806 research outputs found
A remark on trace properties of K-cycles
In this paper we discuss trace properties of -summable -cycles
considered by A.Connes in [\rfr(Conn4)]. More precisely we give a proof of a
trace theorem on the algebra \A of a --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 -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 -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
Pyroxenites sow discord between parent mantle and daughter MORB
Mantle rocks and MORBs sampled along the 26 Ma
record of the Vema Lithospheric Section or VLS (Mid
Atlantic 11\ub0N) reveal a profound divergence between parent
and daughter rocks in their compositional evolution. Finding
the cause of this discordance requires comparing the
evolution through time of the extent of melting with the
produced crustal thickness and changes in the chemistry and
isotopic composition of the sampled rocks. Mantle rocks
show a progressive increase of their degree of melting during
time, as if the potential temperature had increased in the last
26 Ma. However, plate kinematics reveal a significant
decrease of the spreading rate that should sensibly lower the
average degree of melting. MORB inferred degree of melting
decreases through time while their isotopic fingerprint
becomes more depleted. The observed variations can be
reconciled by considering that a variable amount of lowmelting
lithologies entered the melting region. The observed
decoupling of the degree of melting of mantle and MORB is
attributed to the effect of undercooling exerted by lowmelting
heterogeneities due to heat diffusion before the host
mantle starts melting itself. The observed temporal evolution
is matched by a decreasing amount of low-melting,
isotopically enriched, lithologies (pyroxenites) dispersed in a
DMM-type host mantle. Approaching the present day setting,
the amount of pyroxenites has become negligible restoring
harmony between parent mantle and MORB daughters in
terms of degree of melting and integrated melt production.
This observation can be extended to the entire MOR
system revealing the sensitivity of the spreading system to the
amount of low-melting lithologies dispersed in the depleted
mantle host. At limit conditions of the mantle potential
temperature, heat diffusion into the low-solidus melting
lithology prevents the host mantle from reaching its solidus
Spectral triples for the Sierpinski Gasket
We construct a family of spectral triples for the Sierpinski Gasket . For
suitable values of the parameters, we determine the dimensional spectrum and
recover the Hausdorff measure of in terms of the residue of the volume
functional tr at its abscissa of convergence , which
coincides with the Hausdorff dimension of the fractal. We determine the
associated Connes' distance showing that it is bi-Lipschitz equivalent to the
distance on induced by the Euclidean metric of the plane, and show that the
pairing of the associated Fredholm module with (odd) -theory is non-trivial.
When the parameters belong to a suitable range, the abscissa of convergence
of the energy functional
tr takes the value
, which we call energy dimension, and the
corresponding residue gives the standard Dirichlet form on .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
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
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