Improved solution of the lidar equation utilizing particle counter measurements

The extraction of particle backscattering from incoherent lidar measurements poses some problems. In the case of measurements of the stratospheric aerosol layer the solution of the lidar equation is based on two assumptions which are necessary to normalize the measured signal and to correct it with the two-way transmission of the laser pulse. Normalization and transmission are tackled by adding the information contained in aerosol particle counter measurements of the University of Wyoming to the ruby lidar measurements at Garmisch-Partenkirchen. Calculated backscattering from height levels above 25 km for the El Chichon period will be compared with lidar measurements and necessary corrections. The calculated backscatter-to-extinction ratios are compared to those, which were derived from a comparison of published extinction values to measured lidar backscattering at Garmisch. These ratios were used to calculate the Garmisch lidar returns. For the period 4 to 12 months after the El Chichon eruption a backscater-to-extinction ratio of 0.026 1/sr was applied with smaller values before and after that time

Metastability of a granular surface in a spinning bucket

The surface shape of a spinning bucket of granular material is studied using a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. An experimentally observed central subcritical region is reproduced by the model. The subcritical region occurs when a metastable surface becomes unstable via a nonlinear instability mechanism. The nonlinear instability mechanism destabilizes the surface in large systems while a linear instability mechanism is relevant for smaller systems. The range of angles in which the granular surface is metastable vanishes with increasing system size.Comment: 8 pages with postscript figures, RevTex, to appear in Phys. Rev.

Thermal convection in mono-disperse and bi-disperse granular gases: A simulation study

We present results of a simulation study of inelastic hard-disks vibrated in a vertical container. An Event-Driven Molecular Dynamics method is developed for studying the onset of convection. Varying the relevant parameters (inelasticity, number of layers at rest, intensity of the gravity) we are able to obtain a qualitative agreement of our results with recent hydrodynamical predictions. Increasing the inelasticity, a first continuous transition from the absence of convection to one convective roll is observed, followed by a discontinuous transition to two convective rolls, with hysteretic behavior. At fixed inelasticity and increasing gravity, a transition from no convection to one roll can be evidenced. If the gravity is further increased, the roll is eventually suppressed. Increasing the number of monolayers the system eventually localizes mostly at the bottom of the box: in this case multiple convective rolls as well as surface waves appear. We analyze the density and temperature fields and study the existence of symmetry breaking in these fields in the direction perpendicular to the injection of energy. We also study a binary mixture of grains with different properties (inelasticity or diameters). The effect of changing the properties of one of the components is analyzed, together with density, temperature and temperature ratio fields. Finally, the presence of a low-fraction of quasi-elastic impurities is shown to determine a sharp transition between convective and non-convective steady states.Comment: 11 pages, 12 figures, accepted for publication on Physical Review

Hierarchical Temporal Representation in Linear Reservoir Computing

Recently, studies on deep Reservoir Computing (RC) highlighted the role of layering in deep recurrent neural networks (RNNs). In this paper, the use of linear recurrent units allows us to bring more evidence on the intrinsic hierarchical temporal representation in deep RNNs through frequency analysis applied to the state signals. The potentiality of our approach is assessed on the class of Multiple Superimposed Oscillator tasks. Furthermore, our investigation provides useful insights to open a discussion on the main aspects that characterize the deep learning framework in the temporal domain.Comment: This is a pre-print of the paper submitted to the 27th Italian Workshop on Neural Networks, WIRN 201

Sleep deprivation (SD) on focal brain ischemia in the rat : effects of different SD protocols

Sleep-wake disturbances are frequently observed in stroke patients and are associated with poorer functional outcome. Until now the effects of sleep on stroke evolution are unknown. The purpose of the present study was to evaluate the effects of three sleep deprivation (SD) protocols on brain damages after focal cerebral ischemia in a rat model. Permanent occlusion of distal branches of the middle cerebral artery was induced in adult rats. The animals were then subjected to 6h SD, 12h SD or sleep disturbances (SDis) in which 3 x 12h sleep deprivation were performed by gentle handling. Infarct size and brain swelling were assessed by Cresyl violet staining, and the number of damaged cells was measured by terminal deoxynucleotidyl transferase mediated dUTP nick end labeling (TUNEL) staining. Behavioral tests, namely tape removal and cylinder tests, were performed for assessing sensorimotor function. In the 6h SD protocol, no significant difference (P > 0.05) was found either in infarct size (42.5 ± 30.4 mm3 in sleep deprived animals vs. 44.5 ± 20.5 mm3 in controls, mean ± s.d.), in brain swelling (10.2 ± 3.8 % in sleep deprived animals vs. 11.3 ± 2.0 % in controls) or in number of TUNEL-positive cells (21.7 ± 2.0/mm2 in sleep deprived animals vs. 23.0 ± 1.1/mm2 in controls). In contrast, 12h sleep deprivation increased infarct size by 40 % (82.8 ± 10.9 mm3 in SD group vs. 59.2 ± 13.9 mm3 in control group, P = 0.008) and number of TUNEL-positive cells by 137 % (46.8 ± 15/mm in SD group vs. 19.7 ± 7.7/mm2 in control group, P = 0.003). There was no significant difference (P > 0.05) in brain swelling (12.9 ± 6.3 % in sleep deprived animals vs. 11.6 ± 6.0 % in controls). The SDis protocol also increased infarct size by 76 % (3 x 12h SD 58.8 ± 20.4 mm3 vs. no SD 33.8 ± 6.3 mm3, P = 0.017) and number of TUNEL-positive cells by 219 % (32.9 ± 13.2/mm2 vs. 10.3 ± 2.5/mm2, P = 0.008). Brain swelling did not show any difference between the two groups (24.5 ± 8.4 % in SD group vs. 16.7 ± 8.9 % in control group, p > 0.05). Both behavioral tests did not show any concluding results. In summary, we demonstrate that sleep deprivation aggravates brain damages in a rat model of stroke. Further experiments are needed to unveil the mechanisms underlying these effects

A study in the mathematical theory of the conduction of heat

This work represents a study in the application of the Laplace Trans format! on method to the Theory of Conduction of Heat; with a few exceptions indicated in footnotes, the derivation by this method of all the results is new. In Chapters II, VI, VIII, and X which contain collections of results, some of these are classical and given for completeness, and some are new* Almost all the results of Chapters I, III, IV, VII, and IX are believed to be new# None of this work has been submitted for any degree, and it is entirely my own with the exception of Chapters I and X, which have been written for publication in collaboration with Professor Carslaw. These are included here since they form an essential part of the whole scheme; the problems considered were solved independently and published jointly. The parts of this thesis which the referee may deem suitable will be published as soon as possible. Chapters I, VII, and X, and portion of Chapter I1/ have already been published, and Chapter III, and portions of Chapters VIII and IX are in the press# It is my pleasure to adknowledge my great indebtedness to Professor Carslaw who not only aroused my interest in the subject, but in the course of a frequent correspondence extending over several years has been most generous with advice and criticism# I am also indebted to Miss M. E. Clarke for her assistance with the computations of Chapter V and for the preparation of the typescript