Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by A. Neubauer in 1994. Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in two senses, namely as optimal order of convergence over a certain set which at the same time, must be optimal (in a very precise sense) with respect to the error. Finally, two converse results are proved and the theory is applied to find sufficient conditions which ensure the existence of global saturation for spectral methods with classical qualification of finite positive order and for methods with maximal qualification. Finally, several examples of regularization methods possessing global saturation are shown.Comment: 29 page

Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur

The analysis of spectra of novae taken near maximum

A project to analyze ultraviolet spectra of novae obtained at or near maximum optical light is presented. These spectra are characterized by a relatively cool continuum with superimposed permitted emission lines from ions such as Fe II, Mg II, and Si II. Spectra obtained late in the outburst show only emission lines from highly ionized species and in many cases these are forbidden lines. The ultraviolet data will be used with calculations of spherical, expanding, stellar atmospheres for novae to determine elemental abundances by spectral line synthesis. This method is extremely sensitive to the abundances and completely independent of the nebular analyses usually used to obtain novae abundances

Computable randomness is about more than probabilities

We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense that we consider lower expectations (or sets of probabilities) instead of classical 'precise' probabilities. Secondly, instead of binary sequences, we consider sequences whose elements take values in some finite sample space. Interestingly, we find that every sequence is computably random with respect to at least one lower expectation, and that lower expectations that are more informative have fewer computably random sequences. This leads to the intriguing question whether every sequence is computably random with respect to a unique most informative lower expectation. We study this question in some detail and provide a partial answer

Structures of technetium and rhenium complexes

Investigations in the 99mTc chemistry are stimulated by the search for new radiopharmaceuticals for nuclear medical applications. To understand the coordination mode of Tc with various complexing agents, macroscopic studies of technetium coordination chemistry are often performed using the low energy ß-emitting radionuclide 99Tc, which has a much longer half life (t1/2 = 2.12 x 105 years) than 99mTc, in the mg level. Investigations of Re coordination chemistry are done in conjunction with Tc studies because Re possesses chemical properties similar to those of Tc. For some chemical tasks, Re provides a non-radioactive alternative to work with Tc radioisotopes. In addition, 186Re and 188Re are of great interest to nuclear medicine as they possess nuclear properties favorable for use in therapeutic radiopharmaceuticals. Our investigations of Tc and Re coordination chemistry are toward this goal. A large series of technetium and rhenium complexes resulted from this studies have been characterized by X-ray crystal structure determinations. This survey covers the structural investigations performed by P.Leibnitz and G.Reck (BAM) from 1992 till now. It summarizes results obtained in the Rossendorf technetium group and is not intended to compete with the well-written reviews published so far

Basal forebrain cholinergic system volume is associated with general cognitive ability in the elderly

OBJECTIVE: At the present, it is unclear whether association of basal forebrain cholinergic system (BFCS) volume with cognitive performance exists in healthy as well as in cognitively impaired elderly subjects. Whereas one small study reported an association of BFCS volume with general cognitive ability 'g' in healthy ageing, effects on specific cognitive domains have only been found in subjects with cognitive decline. Here we aim to clarify whether an association of BFCS volume and 'g' is present in a larger sample of elderly subjects without obvious symptoms of dementia and whether similar associations can also be observed in specific cognitive domains. METHODS: 282 pre-surgical patients from the BioCog study (aged 72.7±4.9 years with a range of 65-87 years, 110 women) with a median MMSE score of 29 points (range 24-30) were investigated. BFCS and brain volume as well as brain parenchymal fraction were assessed in T1-weighted MR images using SPM12 and a probabilistic map of the BFCS. Neuropsychological assessment comprised the CANTAB cognitive battery and paper-and-pencil based tests. For data analysis, generalised linear models and quantile regression were applied. RESULTS: Significant associations of BFCS volume with 'g' and several cognitive domains were found, with the strongest association found for 'g'. BFCS volume explained less variance in cognitive performance than brain volume. The association was not confounded by brain parenchymal fraction. Furthermore, the association of BFCS volume and 'g' was similar in high- and low-performers. CONCLUSION: Our results extend previous study findings on BFCS volume associations with cognition in elderly subjects. Despite the observed associations of BFCS volume and cognitive performance, this association seems to reflect a more general association of brain volume and cognition. Accordingly, a specific association of BFCS volume and cognition in non-demented elderly subjects is questionable

Are there valid proxy measures of clinical behaviour?

Background: Accurate measures of health professionals' clinical practice are critically important to guide health policy decisions, as well as for professional self-evaluation and for research-based investigation of clinical practice and process of care. It is often not feasible or ethical to measure behaviour through direct observation, and rigorous behavioural measures are difficult and costly to use. The aim of this review was to identify the current evidence relating to the relationships between proxy measures and direct measures of clinical behaviour. In particular, the accuracy of medical record review, clinician self-reported and patient-reported behaviour was assessed relative to directly observed behaviour. Methods: We searched: PsycINFO; MEDLINE; EMBASE; CINAHL; Cochrane Central Register of Controlled Trials; science/social science citation index; Current contents (social & behavioural med/clinical med); ISI conference proceedings; and Index to Theses. Inclusion criteria: empirical, quantitative studies; and examining clinical behaviours. An independent, direct measure of behaviour (by standardised patient, other trained observer or by video/audio recording) was considered the 'gold standard' for comparison. Proxy measures of behaviour included: retrospective self-report; patient-report; or chart-review. All titles, abstracts, and full text articles retrieved by electronic searching were screened for inclusion and abstracted independently by two reviewers. Disagreements were resolved by discussion with a third reviewer where necessary. Results: Fifteen reports originating from 11 studies met the inclusion criteria. The method of direct measurement was by standardised patient in six reports, trained observer in three reports, and audio/video recording in six reports. Multiple proxy measures of behaviour were compared in five of 15 reports. Only four of 15 reports used appropriate statistical methods to compare measures. Some direct measures failed to meet our validity criteria. The accuracy of patient report and chart review as proxy measures varied considerably across a wide range of clinical actions. The evidence for clinician self-report was inconclusive. Conclusion: Valid measures of clinical behaviour are of fundamental importance to accurately identify gaps in care delivery, improve quality of care, and ultimately to improve patient care. However, the evidence base for three commonly used proxy measures of clinicians' behaviour is very limited. Further research is needed to better establish the methods of development, application, and analysis for a range of both direct and proxy measures of behaviour

Status and Recent Results of the Acoustic Neutrino Detection Test System AMADEUS

The AMADEUS system is an integral part of the ANTARES neutrino telescope in the Mediterranean Sea. The project aims at the investigation of techniques for acoustic neutrino detection in the deep sea. Installed at a depth of more than 2000m, the acoustic sensors of AMADEUS are based on piezo-ceramics elements for the broad-band recording of signals with frequencies ranging up to 125kHz. AMADEUS was completed in May 2008 and comprises six "acoustic clusters", each one holding six acoustic sensors that are arranged at distances of roughly 1m from each other. The clusters are installed with inter-spacings ranging from 15m to 340m. Acoustic data are continuously acquired and processed at a computer cluster where online filter algorithms are applied to select a high-purity sample of neutrino-like signals. 1.6 TB of data were recorded in 2008 and 3.2 TB in 2009. In order to assess the background of neutrino-like signals in the deep sea, the characteristics of ambient noise and transient signals have been investigated. In this article, the AMADEUS system will be described and recent results will be presented.Comment: 7 pages, 8 figures. Proceedings of ARENA 2010, the 4th International Workshop on Acoustic and Radio EeV Neutrino Detection Activitie

Electrodiagnostic assessment of the autonomic nervous system: A consensus statement endorsed by the American Autonomic Society, American Academy of Neurology, and the International Federation of Clinical Neurophysiology

Evaluation of disorders of the autonomic nervous system is both an art and a science, calling upon the physician's most astute clinical skills as well as knowledge of autonomic neurology and physiology. Over the last three decades, the development of noninvasive clinical tests that assess the function of autonomic nerves, the validation and standardization of these tests, and the growth of a large body of literature characterizing test results in patients with autonomic disorders have equipped clinical practice further with a valuable set of objective tools to assist diagnosis and prognosis. This review, based on current evidence, outlines an international expert consensus set of recommendations to guide clinical electrodiagnostic autonomic testing. Grading and localization of autonomic deficits incorporates scores from sympathetic cardiovascular adrenergic, parasympathetic cardiovagal, and sudomotor testing, as no single test alone is sufficient to diagnose the degree or distribution of autonomic failure. The composite autonomic severity score (CASS) is a useful score of autonomic failure that is normalized for age and gender. Valid indications for autonomic testing include generalized autonomic failure, regional or selective system syndromes of autonomic impairment, peripheral autonomic neuropathy and ganglionopathy, small fiber neuropathy, orthostatic hypotension, orthostatic intolerance, syncope, neurodegenerative disorders, autonomic hyperactivity, and anhidrosis

Contribution of IQ in young adulthood to the associations of education and occupation with cognitive ability in older age

BACKGROUND: Studies suggest that a higher education and occupation are each associated with a higher late-life cognitive ability, but their inter-relationships in their association with cognitive ability and the contribution of peak IQ in young adulthood ('pre-morbid IQ') often remain unclear. METHODS: Cross-sectional analysis of 623 participants aged ≥65 years of the BioCog study. Education was coded according to the International Standard Classification of Education (ISCED; range 1 to 6). Occupation was coded as 'semi/unskilled', 'skilled manual', 'skilled non-manual', 'managerial', 'professional'. A summary score of global ability (‘g’) was constructed from six cognitive tests. Pre-morbid IQ was estimated from vocabulary. The Geriatric Depression Scale assessed symptoms of depression. Age- and sex-adjusted analyses of covariance were performed. RESULTS: Education (partial eta2 0.076; p < 0.001) and occupation (partial eta2 = 0.037; p < 0.001) were each significantly associated with g. For education, the association was attenuated but remained statistically significant when pre-morbid IQ was controlled for (partial eta2 0.036; p < 0.001) and was unchanged with additional adjustment for depression (partial eta2 0.037; p < 0.001). For occupation, the association with g was no longer significant when pre-morbid IQ (partial eta2 = 0.015; p = 0.06) and depression (partial eta2 = 0.011; p = 0.18) were entered as covariates in separate steps. When education and occupation were entered concurrently into the fully adjusted model, only education was independently associated with g (partial eta2 0.030; p < 0.001; occupation, p = 0.93). CONCLUSION: While a higher education and a higher occupation were each associated with a higher late-life cognitive ability, only for education some unique contribution to cognitive ability remained over and above its relationship with pre-morbid IQ, depression, and occupation. Further research is needed to address whether a longer time spent in education may promote late-life cognitive ability