Heuristic parameter-choice rules for convex variational regularization based on error estimates

In this paper, we are interested in heuristic parameter choice rules for general convex variational regularization which are based on error estimates. Two such rules are derived and generalize those from quadratic regularization, namely the Hanke-Raus rule and quasi-optimality criterion. A posteriori error estimates are shown for the Hanke-Raus rule, and convergence for both rules is also discussed. Numerical results for both rules are presented to illustrate their applicability

A normal form for excitable media

We present a normal form for travelling waves in one-dimensional excitable media in form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite wavelength effects are captured by a delay. The normal form describes the behaviour of single pulses in a periodic domain and also the richer behaviour of wave trains. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with the saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We verify the existence of these bifurcations in numerical simulations. The parameters of the normal form are determined and its predictions are tested against numerical simulations of partial differential equation models of excitable media with good agreement.Comment: 22 pages, accepted for publication in Chao

Some Remarks on the Model Theory of Epistemic Plausibility Models

Classical logics of knowledge and belief are usually interpreted on Kripke models, for which a mathematically well-developed model theory is available. However, such models are inadequate to capture dynamic phenomena. Therefore, epistemic plausibility models have been introduced. Because these are much richer structures than Kripke models, they do not straightforwardly inherit the model-theoretical results of modal logic. Therefore, while epistemic plausibility structures are well-suited for modeling purposes, an extensive investigation of their model theory has been lacking so far. The aim of the present paper is to fill exactly this gap, by initiating a systematic exploration of the model theory of epistemic plausibility models. Like in 'ordinary' modal logic, the focus will be on the notion of bisimulation. We define various notions of bisimulations (parametrized by a language L) and show that L-bisimilarity implies L-equivalence. We prove a Hennesy-Milner type result, and also two undefinability results. However, our main point is a negative one, viz. that bisimulations cannot straightforwardly be generalized to epistemic plausibility models if conditional belief is taken into account. We present two ways of coping with this issue: (i) adding a modality to the language, and (ii) putting extra constraints on the models. Finally, we make some remarks about the interaction between bisimulation and dynamic model changes.Comment: 19 pages, 3 figure

The Active Mirror Control of the MAGIC Telescope

One of the main design goals of the MAGIC telescopes is the very fast repositioning in case of Gamma Ray Burst (GRB) alarms, implying a low weight of the telescope dish. This is accomplished by using a space frame made of carbon fiber epoxy tubes, resulting in a strong but not very rigid support structure. Therefore it is necessary to readjust the individual mirror tiles to correct for deformations of the dish under varying gravitational load while tracking an object. We present the concept of the Active Mirror Control (AMC) as implemented in the MAGIC telescopes and the actual performance reached. Additionally we show that also telescopes using a stiff structure can benefit from using an AMC.Comment: Contribution to the 30th ICRC, Merida, Mexico, July 2007 on behalf of the MAGIC Collaboratio

Driver-pressure-impact and response-recovery chains in European rivers: observed and predicted effects on BQEs

The report presented in the following is part of the outcome of WISER’s river Workpackage WP5.1 and as such part of the module on aquatic ecosystem management and restoration. The ultimate goal of WP5.1 is to provide guidance on best practice restoration and management to the practitioners in River Basin Management. Therefore, a series of analyses was undertaken, each of which used a part of the WP5.1 database in order to track two major pathways of biological response: 1) the response of riverine biota to environmental pressures (degradation) and 2) the response of biota to the reduction of these impacts (restoration). This report attempts to provide empirical evidence on the environment-biota relationships for both pathways

A one-compartment, direct glucose fuel cell for powering long-term medical implants

We present the operational concept, microfabrication, and electrical performance of an enzyme-less direct glucose fuel cell for harvesting the chemical energy of glucose from body fluids. The spatial concentrations of glucose and oxygen at the electrodes of the one-compartment setup are established by self-organization, governed by the balance of electro-chemical depletion and membrane diffusion. Compared to less stable enzymatic and immunogenic microbial fuel cells, this robust approach excels with an extended life time, the amenability to sterilization and biocompatibility, showing up a clear route towards an autonomous power supply for long-term medical implants without the need of surgical replacement and external refueling. Operating in physiological phosphate buffer solution containing 0.1 wt% glucose and having a geometrical cathode area of 10 cm2, our prototype already delivers 20 µ W peak power over a period of 7 days

A test for a conjecture on the nature of attractors for smooth dynamical systems

Dynamics arising persistently in smooth dynamical systems ranges from regular dynamics (periodic, quasiperiodic) to strongly chaotic dynamics (Anosov, uniformly hyperbolic, nonuniformly hyperbolic modelled by Young towers). The latter include many classical examples such as Lorenz and H\'enon-like attractors and enjoy strong statistical properties. It is natural to conjecture (or at least hope) that most dynamical systems fall into these two extreme situations. We describe a numerical test for such a conjecture/hope and apply this to the logistic map where the conjecture holds by a theorem of Lyubich, and to the Lorenz-96 system in 40 dimensions where there is no rigorous theory. The numerical outcome is almost identical for both (except for the amount of data required) and provides evidence for the validity of the conjecture.Comment: Accepted version. Minor modifications from previous versio

Spectral density in resonance region and analytic confinement

We study the role of finite widths of resonances in a nonlocal version of the Wick-Cutkosky model. The spectrum of bound states is known analytically in this model and forms linear Regge tragectories. We compute the widths of resonances, calculate the spectral density in an extension of the Breit-Wigner {\it ansatz} and discuss a mechanism for the damping of unphysical exponential growth of observables at high energy due to finite widths of resonances.Comment: 13 pages, RevTeX, 6 figures. Revised version with typographical corrections and additional comments in conclusion