Towards a model-independent partial wave analysis for pseudoscalar meson photoproduction

Amplitude and partial wave analyses for pion, eta or kaon photoproduction are discussed in the context of `complete experiments'. It is shown that the model-independent helicity amplitudes obtained from at least 8 polarization observables including beam, target and recoil polarization can not be used to determine underlying resonance parameters. However, a truncated partial wave analysis, which theoretically requires only 5 observables will be possible with minimal model input.Comment: Proc. of NSTAR2011, 6 pages, 1 figur

Helicity Amplitudes and Sum Rules for Real and Virtual Photons

Results of the recently developed unitary isobar model (MAID) are presented for helicity amplitudes, spin asymmetries, structure functions and relevant sum rules for real and virtual photons in the resonance region. Our evaluation of the energy-weighted integrals is in good agreement for the proton but shows big discrepancies for the neutron.Comment: 10 pages LaTeX including 3 figures, Talk given at the GDH 2000 Conference, Mainz, June 14-17, 2000; to be published in World Scientifi

Distribution of Damages in Car Accidents throught the Use of Neural Networks

After a traffic accident the damage has to be fairly divided among the parties involved, and a ratio has to be determined. There are many precedents for this, and judges have developed catalogues suggesting ratios for common types of accidents. The problem that "every case is different," however, remains. Many cases have familiar aspects, but also unfamiliar ones. Even if a case is composed of several familiar aspects with established ratios, the question remains as to how these are to be figured into one ratio. The first thought would be to invent a mathematical formula, but such formulae are rigid and speculative. The body of law has grown organically and must not be forced into a sleek system. The distant consequences of using a mathematical formula cannot be foreseen; they might well be grossly unjust. I suggest using a neural network instead. Precedents may be fed into the network directly as learning patterns. This has the advantage that court rulings can be transferred directly and not via a formula. Future modifications in court rulings also can be adopted by the network. As far as the effect of the learning patterns on new cases is concerned, a relatively safe assumption is that they will fit in harmoniously with the precedents. This is due to the network's structure—a number of simple decisional units, which are interconnected, tune their activity to each other, thus achieving a state of equilibrium. When the conditions of such an equilibrium are translated back into the terms of the case, the solution can hardly be totally unjust

Modular forms and Donaldson invariants for 4-manifolds with b+=1b_+=1

We study the Donaldson invariants of simply connected $4$-manifolds with $b_+=1$, and in particular the change of the invariants under wall-crossing. We assume the conjecture of Kotschick and Morgan about the shape of the wall-crossing terms (which Oszva\'th and Morgan are now able to prove), and are determine a generating function for the wall-crossing terms in terms of modular forms. As an application we determine all the Donaldson invariants of the projective plane in terms of modular forms. The main tool are the blowup formulas, which are used to obtain recursive relations.Comment: I correct a number of missing attributions and citations. In particular this applies to the cited paper of Kotschick and Lisca "Instanton invariants via topology", which contains some ideas which have been important for this work. AMSLaTe