Convergence Rates for Inverse Problems with Impulsive Noise

We study inverse problems F(f) = g with perturbed right hand side g^{obs} corrupted by so-called impulsive noise, i.e. noise which is concentrated on a small subset of the domain of definition of g. It is well known that Tikhonov-type regularization with an L^1 data fidelity term yields significantly more accurate results than Tikhonov regularization with classical L^2 data fidelity terms for this type of noise. The purpose of this paper is to provide a convergence analysis explaining this remarkable difference in accuracy. Our error estimates significantly improve previous error estimates for Tikhonov regularization with L^1-fidelity term in the case of impulsive noise. We present numerical results which are in good agreement with the predictions of our analysis

The role of Japanese local governments in stabilisation policy

Local governments in Japan account for about 80 per cent of general government spending when excluding social security expenditures. Therefore, for the implementation of fiscal policy it is important how local governments will behave. On the basis of the economic theories on fiscal federalism it is generally rational for local government entities, especially smaller ones, not to participate in the stabilisation policy of the central government and to take a free rider position. Such a behaviour would imply a substantial reduction or even an offsetting of the effects of a stabilisation policy of the central government. As for empirical evidence, a procyclical behaviour of local entities was observed in several countries, among them Germany. We show that in Japan this was not the case and that so far local governments do participate in the stabilisation efforts of the central government. In a second step we show the institutional arrangements that have enabled the central government to influence the fiscal behaviour of the local governments accordingly. Will recent regulatory changes and the enourmous debt level have a significant impact? We argue that although from April 2000 some legal changes in the direction of decentralisation were enforced, many influence mechanisms remained intact and thus the changes weaken the established system, but did not break it up altogether. --local government borrowing,intergovernmental fiscal relations,Japan,federalism,fiscal equalisation,fiscal policy,government debt,local allocation tax,local autonomy,public finance,stabilisation policy

Improving local search heuristics for some scheduling problems - I

Local search techniques like simulated annealing and tabu search are based on a neighborhood structure defined on a set of feasible solutions of a discrete optimization problem. For the scheduling problems $P2||C_{max}, 1|prec|\sum C_i$ and $1||\sum T_i$ we replace a simple neighborhood by a neighborhood on the set of all locally optimal solutions. This allows local search on the set of solutions that are locally optimal

Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise

This paper is concerned with exponentially ill-posed operator equations with additive impulsive noise on the right hand side, i.e. the noise is large on a small part of the domain and small or zero outside. It is well known that Tikhonov regularization with an $L^1$ data fidelity term outperforms Tikhonov regularization with an $L^2$ fidelity term in this case. This effect has recently been explained and quantified for the case of finitely smoothing operators. Here we extend this analysis to the case of infinitely smoothing forward operators under standard Sobolev smoothness assumptions on the solution, i.e. exponentially ill-posed inverse problems. It turns out that high order polynomial rates of convergence in the size of the support of large noise can be achieved rather than the poor logarithmic convergence rates typical for exponentially ill-posed problems. The main tools of our analysis are Banach spaces of analytic functions and interpolation-type inequalities for such spaces. We discuss two examples, the (periodic) backwards heat equation and an inverse problem in gradiometry.Comment: to appear in SIAM J. Numer. Ana

Uphill Motion of Active Brownian Particles in Piecewise Linear Potentials

We consider Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion. Provided a supercritical supply of energy, these particles are able to move in a ``high velocity'' or active mode, which allows them to move also against the gradient of an external potential. We investigate the critical energetic conditions of this self-driven motion for the case of a linear potential and a ratchet potential. In the latter case, we are able to find two different critical conversion rates for the internal energy, which describe the onset of a directed net current into the two different directions. The results of computer simulations are confirmed by analytical expressions for the critical parameters and the average velocity of the net current. Further, we investigate the influence of the asymmetry of the ratchet potential on the net current and estimate a critical value for the asymmetry in order to obtain a positive or negative net current.Comment: accepted for publication in European Journal of Physics B (1999), for related work see http://summa.physik.hu-berlin.de/~frank/active.htm

Two Mezzogiornos

The analogy between the economic problems of the Mezzogiorno region and East Germany has been initially contested by many authors. This paper argues that there are striking similarities in the two regions, in terms of the causes of their economic predicament. With an aggregate labour productivity of 55% relative to the rest of the country, both are true transfer economies, whose consumption exceeds production by far. Beyond locational disadvantages, the present paper identifies overdrawn wages, high social security spending and the Dutch disease problem as core reasons for the poor economic performance and discusses possible cures.