Electrocardiogram of the Mixmaster Universe

The Mixmaster dynamics is revisited in a new light as revealing a series of transitions in the complex scale invariant scalar invariant of the Weyl curvature tensor best represented by the speciality index $\mathcal{S}$, which gives a 4-dimensional measure of the evolution of the spacetime independent of all the 3-dimensional gauge-dependent variables except for the time used to parametrize it. Its graph versus time characterized by correlated isolated pulses in its real and imaginary parts corresponding to curvature wall collisions serves as a sort of electrocardiogram of the Mixmaster universe, with each such pulse pair arising from a single circuit or ``complex pulse'' around the origin in the complex plane. These pulses in the speciality index and their limiting points on the real axis seem to invariantly characterize some of the so called spike solutions in inhomogeneous cosmology and should play an important role as a gauge invariant lens through which to view current investigations of inhomogeneous Mixmaster dynamics.Comment: version 3: 20 pages iopart style, 19 eps figure files for 8 latex figures; added example of a transient true spike to contrast with the permanent true spike example from the Lim family of true spike solutions; remarks in introduction and conclusion adjusted and toned down; minor adjustments to the remaining tex

Excised acoustic black holes: the scattering problem in the time domain

The scattering process of a dynamic perturbation impinging on a draining-tub model of an acoustic black hole is numerically solved in the time domain. Analogies with real black holes of General Relativity are explored by using recently developed mathematical tools involving finite elements methods, excision techniques, and constrained evolution schemes for strongly hyperbolic systems. In particular it is shown that superradiant scattering of a quasi-monochromatic wavepacket can produce strong amplification of the signal, offering the possibility of a significant extraction of rotational energy at suitable values of the angular frequency of the vortex and of the central frequency of the wavepacket. The results show that theoretical tools recently developed for gravitational waves can be brought to fruition in the study of other problems in which strong anisotropies are present.Comment: 8 pages, 9 figure

Neutrino current in a gravitational plane wave collision background

The behaviour of a massless Dirac field on a general spacetime background representing two colliding gravitational plane waves is discussed in the Newman-Penrose formalism. The geometrical properties of the neutrino current are analysed and explicit results are given for the special Ferrari-Ibanez solution.Comment: 17 pages, 6 Postscript figures, accepted by International Journal of Modern Physics

Use of the Natural Circulation Flow Map for Natural Circulation Systems Evaluation

The aim of this paper is to collect and resume the work done to build and develop, at the University of Pisa, an engineering tool related to the natural circulation. After a brief description of the different loop flow regimes in single phase and two phase, the derivation of a suitable tool to judge the NC performance in a generic system is presented. Finally, an extensive comparison among the NC performance of various nuclear power plants having different design is done to show a practical application of the NC flow map

development of a deep convolutional neural network to predict grading of canine meningiomas from magnetic resonance images

Abstract An established deep neural network (DNN) based on transfer learning and a newly designed DNN were tested to predict the grade of meningiomas from magnetic resonance (MR) images in dogs and to determine the accuracy of classification of using pre- and post-contrast T1-weighted (T1W), and T2-weighted (T2W) MR images. The images were randomly assigned to a training set, a validation set and a test set, comprising 60%, 10% and 30% of images, respectively. The combination of DNN and MR sequence displaying the highest discriminating accuracy was used to develop an image classifier to predict the grading of new cases. The algorithm based on transfer learning using the established DNN did not provide satisfactory results, whereas the newly designed DNN had high classification accuracy. On the basis of classification accuracy, an image classifier built on the newly designed DNN using post-contrast T1W images was developed. This image classifier correctly predicted the grading of 8 out of 10 images not included in the data set

The Speciality Index as invariant indicator in the BKL Mixmaster Dynamics

The speciality index, which has been mainly used in Numerical Relativity for studying gravitational waves phenomena as an indicator of the special or non-special Petrov type character of a spacetime, is applied here in the context of Mixmaster cosmology, using the Belinski-Khalatnikov-Lifshitz map. Possible applications for the associated chaotic dynamics are discussed