Unbounded Fredholm Operators and Spectral Flow

We study the gap (= "projection norm" = "graph distance") topology of the space of (not necessarily bounded) self--adjoint Fredholm operators in a separable Hilbert space by the Cayley transform and direct methods. In particular, we show that the space is connected contrary to the bounded case. Moreover, we present a rigorous definition of spectral flow of a path of such operators (actually alternative but mutually equivalent definitions) and prove the homotopy invariance. As an example, we discuss operator curves on manifolds with boundary.Comment: 23 pages, 2 figures; 09/10/2001 minor corrections, Proposition characterizing the range of the Riesz transformation added; 02/12/2004 very final version 1.0.2, minor correction

Local Retrodiction Models for Photon-Noise-Limited Images

Imaging technologies working at very low light levels acquire data by attempting to count the number of photons impinging on each pixel. Especially in cases with, on average, less than one photocount per pixel the resulting images are heavily corrupted by Poissonian noise and a host of successful algorithms trying to reconstruct the original image from this noisy data have been developed. Here we review a recently proposed scheme that complements these algorithms by calculating the full probability distribution for the local intensity distribution behind the noisy photocount measurements. Such a probabilistic treatment opens the way to hypothesis testing and confidence levels for conclusions drawn from image analysis

Travelling-wave analysis of a model describing tissue degradation by bacteria

We study travelling-wave solutions for a reaction-diffusion system arising as a model for host-tissue degradation by bacteria. This system consists of a parabolic equation coupled with an ordinary differential equation. For large values of the `degradation-rate parameter' solutions are well approximated by solutions of a Stefan-like free boundary problem, for which travelling-wave solutions can be found explicitly. Our aim is to prove the existence of travelling waves for all sufficiently large wave-speeds for the original reaction-diffusion system and to determine the minimal speed. We prove that for all sufficiently large degradation rates the minimal speed is identical to the minimal speed of the limit problem. In particular, in this parameter range, nonlinear selection of the minimal speed occurs.Comment: 15 pages, 3 figure

Killing them with Kindness: Negative Distributional Externalities of Increasing UI Benefits

Of the many labour market Hartz IV reforms that have been implemented in Germany since 2005, the role of short-term unemployment insurance has not received much attention. In this paper we examine distributional effects of labour earnings and unemployment benefits using simulated increases in unemployment insurance replacement rates or equivalently, increases in the net present value of benefit duration. Starting around an 18%-point increase in the replacement rate, there are significant negative labour supply effects, drawing those employed into unemployment shifting the mass of the earnings distribution to the left. At around a 25%-point increase in the replacement rate, the mass of the distribution shifts right again, as those receiving unemployment benefits simply enjoy an increased transfer. Thus, due to the substantial negative labour supply effects, German economic policy should avoid potentially increasing the UI benefit replacement rate (or equivalently, increasing the benefit duration) in the near future as a response to the worldwide economic crisis.Unemployment, income distribution, labour supply

Blood Money: Incentives for Violence in NHL Hockey

The level of violence in the National Hockey League (NHL) reached its highest point in 1987 and has reduced somewhat since then, although to levels much larger than before the first team expansions in 1967. Using publicly available information from several databases 1996–2007, the incentives for violence in North American ice hockey are analyzed.We examine the role of penalty minutes and more specifically, fighting, during the regular season in determining wages for professional hockey players and team-level success indicators. There are substantial returns paid not only to goal scoring skills but also to fighting ability, helping teams move higher in the playoffs and showing up as positive wage premia for otherwise observed low-skill wing players. These estimated per-fight premia, depending on fight success ($10,000 to$18,000), are even higher than those for an additional point made. By introducing a “fight fine” of twice the maximum potential gain ($36,000) and adding this amount to salaries paid for the team salary cap (fines would be 6.7% of the team salary cap or the average wage of 2 players), then all involved would have either little or no incentives to allow fighting to continue.Compensating wage differentials, health risk, violence, subjective indicators