High performance parallel numerical methods for Volterra equations with weakly singular kernels

Non-stationary discrete time waveform relaxation methods for Abel systems of Volterra integral equations using fractional linear multistep formulae are introduced. Fully parallel discrete waveform relaxation methods having an optimal convergence rate are constructed. A significant expression of the error is proved, which allows us to estimate the number of iterations needed to satisfy a prescribed tolerance and allows us to identify the problems where the optimal methods offer the best performance. The numerical experiments confirm the theoretical expectations

GaAs hetero-epitaxial layers grown by MOVPE on exactly-oriented and off-cut (1 1 1)Si: Lattice tilt, mosaicity and defects content

Integration of III-V devices with Si-photonics and fabrication of monolithic III-V/Si tandem solar cells require the heteroepitaxy of III-V compounds on Si. We report on the lattice tilt, mosaicity and defects content of relaxed GaAs grown by MOVPE on exactly-oriented and 4°-offcut (1 1 1)Si. Thin GaAs single-layers grown at 400 °C and annealed at 700 °C show ∼ 3×10^8 cm−2 density of surface pinholes. Double-layer samples were obtained by GaAs overgrowth at 700 °C. GaAs epilayers are tilted by (0.05–0.14)° with respect to Si. Rotational twins were observed in X-ray diffraction (XRD) pole figures: the most abundant ones originate from 60°-rotation of GaAs around the [1 ̄1 ̄1 ̄] growth direction and are identified as micro-twins along the GaAs/Si hetero-interface. Twins obtained by rotations around the [1 ̄1 ̄1], [11 ̄1 ̄], and [1 ̄11 ̄] directions or by combined rotations around the growth direction and one of the former, were also observed. The GaAs mosaicity and block size were studied through high-resolution XRD intensity mapping: for single-layer samples crystal blocks are ascribed to 3–5 nm thin micro-twins, whose size does not change upon annealing. In double-layer samples thicker (32–35 nm) micro-twins occur. GaAs samples grown on offcut (1 1 1)Si show less rotational twins but a reduced mosaic block size with respect to exactly-oriented Si

Replica symmetric evaluation of the information transfer in a two-layer network in presence of continuous+discrete stimuli

In a previous report we have evaluated analytically the mutual information between the firing rates of N independent units and a set of multi-dimensional continuous+discrete stimuli, for a finite population size and in the limit of large noise. Here, we extend the analysis to the case of two interconnected populations, where input units activate output ones via gaussian weights and a threshold linear transfer function. We evaluate the information carried by a population of M output units, again about continuous+discrete correlates. The mutual information is evaluated solving saddle point equations under the assumption of replica symmetry, a method which, by taking into account only the term linear in N of the input information, is equivalent to assuming the noise to be large. Within this limitation, we analyze the dependence of the information on the ratio M/N, on the selectivity of the input units and on the level of the output noise. We show analytically, and confirm numerically, that in the limit of a linear transfer function and of a small ratio between output and input noise, the output information approaches asymptotically the information carried in input. Finally, we show that the information loss in output does not depend much on the structure of the stimulus, whether purely continuous, purely discrete or mixed, but only on the position of the threshold nonlinearity, and on the ratio between input and output noise.Comment: 19 pages, 4 figure

Balancing exploration and exploitation in public management: Proposal for an organizational model

Over the last 30 years, a wave of reforms has reshaped the panorama of public administrations around the world, which have also stimulated debates on the subject reform in public sector relations. Much research has focused on discussing the validity of New Public Management (NPM) as a paradigm, including the recognition of regional versions of a number of universal problems in the Public Governance, NPM, and Public Value areas. This debate is focused on the need to give concrete answers to the new management needs of policy makers and to the growing demands of citizens. Increasingly public administration is based on meeting two needs: society requires creative, flexible, and innovation-oriented approaches, whilst economic pressures and budget cuts are forcing uses and models oriented toward efficiency, competitiveness, and cost savings. As regard the changing requirements of the public government, the new organizational system needs to incorporate the creativity, innovation capacity, and flexibility necessary to achieve sustainability and public value. The purpose of this research is to offer an organizational model, which balances exploration activities with those of exploitation, thus being able to meet the changing needs within the Administration, and the actions envisaged for its operations. This article also introduces the requirements for a decision support system to measure regional performance and service quality. It is hoped that we add to our knowledge and understanding of coordinated public policy and good governance that is effective even in these radically demanding Covid-19 times

A PMT-Block test bench

The front-end electronics of the ATLAS hadronic calorimeter (Tile Cal) is housed in a unit, called {\it PMT-Block}. The PMT-Block is a compact instrument comprising a light mixer, a PMT together with its divider and a {\it 3-in-1} card, which provides shaping, amplification and integration for the signals. This instrument needs to be qualified before being assembled on the detector. A PMT-Block test bench has been developed for this purpose. This test bench is a system which allows fast, albeit accurate enough, measurements of the main properties of a complete PMT-Block. The system, both hardware and software, and the protocol used for the PMT-Blocks characterisation are described in detail in this report. The results obtained in the test of about 10000 PMT-Blocks needed for the instrumentation of the ATLAS (LHC-CERN) hadronic Tile Calorimeter are also reported.Comment: 23 pages, 10 figure

A theoretical model of neuronal population coding of stimuli with both continuous and discrete dimensions

In a recent study the initial rise of the mutual information between the firing rates of N neurons and a set of p discrete stimuli has been analytically evaluated, under the assumption that neurons fire independently of one another to each stimulus and that each conditional distribution of firing rates is gaussian. Yet real stimuli or behavioural correlates are high-dimensional, with both discrete and continuously varying features.Moreover, the gaussian approximation implies negative firing rates, which is biologically implausible. Here, we generalize the analysis to the case where the stimulus or behavioural correlate has both a discrete and a continuous dimension. In the case of large noise we evaluate the mutual information up to the quadratic approximation as a function of population size. Then we consider a more realistic distribution of firing rates, truncated at zero, and we prove that the resulting correction, with respect to the gaussian firing rates, can be expressed simply as a renormalization of the noise parameter. Finally, we demonstrate the effect of averaging the distribution across the discrete dimension, evaluating the mutual information only with respect to the continuously varying correlate.Comment: 20 pages, 10 figure