Regularization independent of the noise level: an analysis of quasi-optimality

The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always counterexamples with very poor performance. We propose an average case analysis of quasi-optimality for spectral cut-off estimators and we prove that the quasi-optimality criterion determines estimators which are rate-optimal {\em on average}. Its practical performance is illustrated with a calibration problem from mathematical finance.Comment: 18 pages, 3 figure

Reconstruction of multiplicative space- and time-dependent sources

This paper presents a numerical regularization approach to the simultaneous determination of multiplicative space- and time-dependent source functions in a nonlinear inverse heat conduction problem with homogeneous Neumann boundary conditions together with specified interior and final time temperature measurements. Under these conditions a unique solution is known to exist. However, the inverse prob- lem is still ill-posed since small errors in the input interior temperature data cause large errors in the output heat source solution. For the numerical discretisation, the boundary element method combined with a regularized nonlinear optimization are utilized. Results obtained from several numerical tests are provided in order to illustrate the efficiency of the adopted computational methodology

Development of Muon Drift-Tube Detectors for High-Luminosity Upgrades of the Large Hadron Collider

The muon detectors of the experiments at the Large Hadron Collider (LHC) have to cope with unprecedentedly high neutron and gamma ray background rates. In the forward regions of the muon spectrometer of the ATLAS detector, for instance, counting rates of 1.7 kHz/square cm are reached at the LHC design luminosity. For high-luminosity upgrades of the LHC, up to 10 times higher background rates are expected which require replacement of the muon chambers in the critical detector regions. Tests at the CERN Gamma Irradiation Facility showed that drift-tube detectors with 15 mm diameter aluminum tubes operated with Ar:CO2 (93:7) gas at 3 bar and a maximum drift time of about 200 ns provide efficient and high-resolution muon tracking up to the highest expected rates. For 15 mm tube diameter, space charge effects deteriorating the spatial resolution at high rates are strongly suppressed. The sense wires have to be positioned in the chamber with an accuracy of better than 50 ?micons in order to achieve the desired spatial resolution of a chamber of 50 ?microns up to the highest rates. We report about the design, construction and test of prototype detectors which fulfill these requirements

Ions in Fluctuating Channels: Transistors Alive

Ion channels are proteins with a hole down the middle embedded in cell membranes. Membranes form insulating structures and the channels through them allow and control the movement of charged particles, spherical ions, mostly Na+, K+, Ca++, and Cl-. Membranes contain hundreds or thousands of types of channels, fluctuating between open conducting, and closed insulating states. Channels control an enormous range of biological function by opening and closing in response to specific stimuli using mechanisms that are not yet understood in physical language. Open channels conduct current of charged particles following laws of Brownian movement of charged spheres rather like the laws of electrodiffusion of quasi-particles in semiconductors. Open channels select between similar ions using a combination of electrostatic and 'crowded charge' (Lennard-Jones) forces. The specific location of atoms and the exact atomic structure of the channel protein seems much less important than certain properties of the structure, namely the volume accessible to ions and the effective density of fixed and polarization charge. There is no sign of other chemical effects like delocalization of electron orbitals between ions and the channel protein. Channels play a role in biology as important as transistors in computers, and they use rather similar physics to perform part of that role. Understanding their fluctuations awaits physical insight into the source of the variance and mathematical analysis of the coupling of the fluctuations to the other components and forces of the system.Comment: Revised version of earlier submission, as invited, refereed, and published by journa

Parameter identification in a semilinear hyperbolic system

We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigte the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings

Elastic-Net Regularization: Error estimates and Active Set Methods

This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously l^1 and l^2 regularization. The stability of the minimizer and its consistency are studied, and convergence rates for both a priori and a posteriori parameter choice rules are established. Two iterative numerical algorithms of active set type are proposed, and their convergence properties are discussed. Numerical results are presented to illustrate the features of the functional and algorithms

CA 125 regression after two completed cycles of chemotherapy: lack of prediction for long-term survival in patients with advanced ovarian cancer

The prognostic influence of CA 125 regression between the time point before surgery and after two completed courses of chemotherapy was studied in 210 patients with advanced ovarian cancer, and was compared to other well established prognostic factors. CA 125 blood samples were collected preoperatively (CA 125 pre) and 3 months after surgery (CA 125 3 mo) (at the beginning of the 3rd cycle of chemotherapy). The parameter CA 125 regression defined as log10 (CA 125 3 mo/CA 125 pre) was used for statistical analysis. In a survival analysis using a Cox proportional hazards model, CA 125 regression (P = 0.0001), residual tumour (P = 0.0001), age (P = 0.0095) and grading (P = 0.044) were independent variables, whereas stage of disease, histology, ascites and type of surgery failed to retain significance. Using log10 (CA 125 3 mo/CA 125 pre) as simple covariate in a Cox model showed a hazard ratio of 1.70 (95% confidence interval 1.32–2.19, P = 0.0001). However, a detailed analysis of the interaction of time with the prognostic factor CA 125 regression on survival revealed a strong time-dependent effect with a hazard ratio of more than 6 immediately after two courses of chemotherapy, whereas within approximately 1 year the hazard ratio for the surviving patients dropped quickly to the neutral level of 1. In summary, CA 125 regression is an independent prognostic factor for survival of women with advanced ovarian cancer and allows an identification of a high-risk population among patients with advanced ovarian cancer. However, the discriminating power of serial CA 125 for long-term survival seems to be temporary and prediction of individual patients outcome is far less precise. © 1999 Cancer Research Campaig

Adaptive Covariance Estimation with model selection

We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud