Representation and Characterization of Non-Stationary Processes by Dilation Operators and Induced Shape Space Manifolds

We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a condensed way. Particularly interesting is the fact that the obtention of dilation matrices is regardless of the stationarity of the underlying process. When the process is stationary, it coincides with the Naimark Dilation and only one rotation matrix is computed, when the process is non-stationary, a set of rotation matrices are computed. In particular, the periodicity of the correlation function that may appear in some classes of signal is transmitted to the set of dilation matrices. These rotation matrices, which can be arbitrarily close to each other depending on the sampling or the rescaling of the signal are seen as a distinctive feature of the signal. In order to study this sequence of matrices, and guided by the possibility to rescale the signal, the correct geometrical framework to use with the dilation's theoretic results is the space of curves on manifolds, that is the set of all curve that lies on a base manifold. To give a complete sight about the space of curve, a metric and the derived geodesic equation are provided. The general results are adapted to the more specific case where the base manifold is the Lie group of rotation matrices. The notion of the shape of a curve can be formalized as the set of equivalence classes of curves given by the quotient space of the space of curves and the increasing diffeomorphisms. The metric in the space of curve naturally extent to the space of shapes and enable comparison between shapes.Comment: 19 pages, draft pape

The Abuse of Power: A Theological Problem

Reviewed Book: Poling, James N. (James Newton). The Abuse of Power: A Theological Problem. Nashville: Abingdon Press, 1991

Dynamic Security-aware Routing for Zone-based data Protection in Multi-Processor System-on-Chips

In this work, we propose a NoC which enforces the encapsulation of sensitive traffic inside the asymmetrical security zones while using minimal and non-minimal paths. The NoC routes guarantee that the sensitive traffic is communicated only through the trusted nodes which belong to the security zone. As the shape of the zones may change during operation, the sensitive traffic must be routed through low-risk paths. We test our proposal and we show that our solution can be an efficient and scalable alternative for enforce the data protection inside the MPSoC

Vortex state microwave resistivity in Tl-2212 thin films

We present measurements of the field induced changes in the 47 GHz complex resistivity, $\Delta \tilde \rho(H,T)$, in Tl$_{2}$Ba$_{2}$CaCu$_{2}$O$_{8+x}$ (TBCCO) thin films with $T_{c}\simeq$ 105 K, prepared on CeO$_{2}$ buffered sapphire substrates. At low fields ($\mu_{0}H<$10 mT) a very small irreversible feature is present, suggesting a little role of intergranular phenomena. Above that level $\Delta \tilde \rho(H,T)$ exhibits a superlinear dependence with the field, as opposed to the expected (at high frequencies) quasilinear behaviour. We observe a crossover between predominantly imaginary to predominantly real (dissipative) response with increasing temperature and/or field. In addition, we find the clear scaling property $\Delta \tilde \rho(H,T)=\Delta \tilde \rho[H/H^{*}(T)]$, where the scaling field $H^{*}(T)$ maps closely the melting field measured in single crystals. We discuss our microwave results in terms of loss of flux lines rigidity.Comment: 8 pages, 3 figures, proceedings of 9th HTSHFF, accepted for publication on J. Supercon