Discrete Spacings

Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring units have length less than $k$. When centered and scaled by $n^{-1/2}$ the resulting numbers of spacings of length $1, 2,..., k-1$ have simultaneously a limiting normal distribution as $n\to\infty$. This is proved by the classical method of moments.Comment: 14 page

The Politics of Pension Reform under Ageing

In this paper we address the question whether in case of population ageing a transition from an unfunded to a more funded pension scheme is politically feasible in a representative democracy. We consider two parties: a right-wing party which is willing to trade off intragenerational equity against efficiency gains in intergenerational redistribution, and a left-wing party which does not want to adjust the level of intragenerational distribution. We show that, in an economy with an exogenously given interest rate, only a thus defined right-wing government will propose a social-security reform. Moreover, we demonstrate that such a policy proposal may lead to electoral success if it entails an appropriate mix of distributional efficiency and equity.Ageing, overlapping generations, pensions

Time-optimal Control Strategies for Electric Race Cars with Different Transmission Technologies

This paper presents models and optimization methods to rapidly compute the achievable lap time of a race car equipped with a battery electric powertrain. Specifically, we first derive a quasi-convex model of the electric powertrain, including the battery, the electric machine, and two transmission technologies: a single-speed fixed gear and a continuously variable transmission (CVT). Second, assuming an expert driver, we formulate the time-optimal control problem for a given driving path and solve it using an iterative convex optimization algorithm. Finally, we showcase our framework by comparing the performance achievable with a single-speed transmission and a CVT on the Le Mans track. Our results show that a CVT can balance its lower efficiency and higher weight with a higher-efficiency and more aggressive motor operation, and significantly outperform a fixed single-gear transmission.Comment: 5 pages, 4 figures, submitted to the 2020 IEEE Vehicle Power and Propulsion Conferenc

Search for quasi-periodic signals in magnetar giant flares

Quasi-periodic oscillations (QPOs) discovered in the decaying tails of giant flares of magnetars are believed to be torsional oscillations of neutron stars. These QPOs have a high potential to constrain properties of high-density matter. In search for quasi-periodic signals, we study the light curves of the giant flares of SGR 1806-20 and SGR 1900+14, with a non-parametric Bayesian signal inference method called D$^3$PO. The D$^3$PO algorithm models the raw photon counts as a continuous flux and takes the Poissonian shot noise as well as all instrument effects into account. It reconstructs the logarithmic flux and its power spectrum from the data. Using this fully noise-aware method, we do not confirm previously reported frequency lines at $\nu\gtrsim17\,$Hz because they fall into the noise-dominated regime. However, we find two new potential candidates for oscillations at $9.2\,$Hz (SGR 1806-20) and $7.7\,$Hz (SGR 1900+14). If these are real and the fundamental magneto-elastic oscillations of the magnetars, current theoretical models would favour relatively weak magnetic fields $\bar B\sim 6\times10^{13} - 3\times10^{14}\,$G (SGR 1806-20) and a relatively low shear velocity inside the crust compared to previous findings

Strategy for control of muscle force using a 3D multi electrode array in intraneural stimulation

A control algorithm for regulation of the force produced by the rat EDL muscle is presented, using a 128-electrodes intraneural stimulation device. The algorithm is based on force regulation in nature; its task is basically to find a combination of rate coding and recruitment to produce a required force, keeping fatigue minimized. The algorithm was tested in a simulated environment, with satisfactory result

Control electronics for a neuro-electronic interface implemented in a gate array

Presents a Gate Array for implementing electronic circuitry to control multi-electrode arrays, which consist of 128 microelectrodes. The chip contains multiplexers, current sources and buffer amplifiers in CMOS technolog