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

Associations of the metabolic syndrome and its components with cognitive impairment in older adults

BACKGROUND: The metabolic syndrome (MetS) is an established cardiovascular risk factor. Here, we investigated its role in cognitive impairment. METHODS: Baseline data from 202 participants (aged 65 to 87 years) of the BioCog study were used. All were free of clinical dementia (MMSE≥24/30). Cognitive impairment was defined as the lowest tertile of a cognitive summary score. Multiple logistic regression analyses examined associations of body mass index (BMI), triglycerides (TG), high-density lipoprotein (HDL-C), glucose and glycated hemoglobin A1c (HbA1c) levels with the odds of cognitive impairment. MetS was defined as ≥3 of its 5 components obesity (BMI ≥ 30 kg/m2), elevated TG (TG ≥1.7 mmol/L), reduced HDL-C (males:  0.05). Results for HDL-C were similar when HDL-C, glucose, BMI and TG were entered into a single model (OR 2.56 per 1 mmol/L reduction, 95% CI 1.09, 5.88, p = 0.031) and when cerebrovascular disease and coronary heart disease were additionally controlled for (OR 2.56 per 1 mmol/L reduction, 95% CI 1.06, 6.25, p = 0.036). Among the 5 MetS components, participants with elevated TG were at 2-fold increased odds of impairment (OR 2.09, 95% CI 1.08, 4.05, p = 0.028) including when the remaining 4 MetS components were entered (OR 2.23, 95% CI 1.07, 4.65, p = 0.033), but the finding was no longer statistically significant when cerebrovascular disease and coronary heart disease were additionally controlled for (p = 0.11). Presence of MetS and of obesity, reduced HDL-C, elevated glucose or elevated blood pressure were not significantly associated with impairment (all p > 0.05). CONCLUSION: Our findings support low HDL-C as an independent risk marker of cognitive impairment in older age. The need for research into mediatory and confounding factors, and re-evaluation of traditional cut-off points is highlighted. TRIAL REGISTRATION: The study was registered on 15th October 2014 at clinicaltrials.gov (NCT02265263)

Elemental analysis of contemporary dental materials regarding potential beryllium content

Exposure to beryllium (Be) can lead to lung pathologies, such as chronic beryllium disease (CBD). This occupational illness has been more prevalent among dental technicians compared to the non-exposed population. Although most manufacturers state that dental materials are Be-free, this prevalence raises the question of whether the materials are completely devoid of Be-traces. Thus, the objective of the present study was to analyze the elemental composition, with emphasis on Be, of a wide range of commercially available dental materials frequently used by dental laboratories. Samples of 32 different materials were collected and analyzed using inductively coupled plasma-optical emission spectrometry (ICP-OES) and X-ray fluorescence spectroscopy. The results showed that the Be content was below the limit of quantification in all included samples (< 0.00005 mass-%). Therefore, it can be concluded that possible traces of Be were below clinical relevance in dental materials. Exposure of dental technicians to alternative Be sources should be further evaluated

A Modified Approach to Induce Predictable Congestive Heart Failure by Volume Overload in Rats

The model of infrarenal aortocaval fistula (ACF) has recently gained new interest in its use to investigate cardiac pathophysiology. Since in previous investigations the development of congestive heart failure (CHF) was inconsistent and started to develop earliest 8-10 weeks after fistula induction using a 18G needle, this project aimed to induce a predictable degree of CHF within a definite time period using a modified approach. An aortocaval fistula was induced in male Wistar rats using a 16G needle as a modification of the former 18G needle-technique described by Garcia and Diebold. Results revealed within 28 +/- 2 days of ACF significantly increased heart and lung weight indices in the ACF group accompanied by elevated filling pressure. All hemodynamic parameters derived from a pressure-volume conductance-catheter in vivo were significantly altered in the ACF consistent with severe systolic and diastolic left ventricular dysfunction. This was accompanied by systemic neurohumoral activation as demonstrated by elevated rBNP-45 plasma concentrations in every rat of the ACF group. Furthermore, the restriction in overall cardiac function was associated with a beta 1- and beta 2-adrenoreceptor mRNA downregulation in the left ventricle. In contrast, beta 3-adrenoreceptor mRNA was upregulated. Finally, electron microscopy of the left ventricle of rats in the ACF group showed signs of progressive subcellular myocardial fragmentation. In conclusion, the morphometric, hemodynamic and neurohumoral characterization of the modified approach revealed predictable and consistent signs of congestive heart failure within 28 +/- 2 days. Therefore, this modified approach might facilitate the examination of various questions specific to CHF and allow for pharmacological interventions to determine pathophysiological pathways

Diabetes, but not hypertension and obesity, is associated with postoperative cognitive dysfunction

BACKGROUND/AIMS: Older people undergoing surgery are at risk of developing postoperative cognitive dysfunction (POCD), but little is known of risk factors predisposing patients to POCD. Our objective was to estimate the risk of POCD associated with exposure to preoperative diabetes, hypertension, and obesity. METHODS: Original data from 3 randomised controlled trials (OCTOPUS, DECS, SuDoCo) were obtained for secondary analysis on diabetes, hypertension, baseline blood pressure, obesity (BMI ≥30 kg/m(2)), and BMI as risk factors for POCD in multiple logistic regression models. Risk estimates were pooled across the 3 studies. RESULTS: Analyses totalled 1,034 patients. POCD occurred in 5.2% of patients in DECS, in 9.4% in SuDoCo, and in 32.1% of patients in OCTOPUS. After adjustment for age, sex, surgery type, randomisation, obesity, and hypertension, diabetes was associated with a 1.84-fold increased risk of POCD (OR 1.84; 95% CI 1.14, 2.97; p = 0.01). Obesity, BMI, hypertension, and baseline blood pressure were each not associated with POCD in fully adjusted models (all p > 0.05). CONCLUSION: Diabetes, but not obesity or hypertension, is associated with increased POCD risk. Consideration of diabetes status may be helpful for risk assessment of surgical patients

Characterizing the gamma-ray long-term variability of PKS 2155-304 with H.E.S.S. and Fermi-LAT

Studying the temporal variability of BL Lac objects at the highest energies provides unique insights into the extreme physical processes occurring in relativistic jets and in the vicinity of super-massive black holes. To this end, the long-term variability of the BL Lac object PKS 2155-304 is analyzed in the high (HE, 100 MeV 200 GeV) gamma-ray domain. Over the course of ~9 yr of H.E.S.S observations the VHE light curve in the quiescent state is consistent with a log-normal behavior. The VHE variability in this state is well described by flicker noise (power-spectral-density index {\ss}_VHE = 1.10 +0.10 -0.13) on time scales larger than one day. An analysis of 5.5 yr of HE Fermi LAT data gives consistent results ({\ss}_HE = 1.20 +0.21 -0.23, on time scales larger than 10 days) compatible with the VHE findings. The HE and VHE power spectral densities show a scale invariance across the probed time ranges. A direct linear correlation between the VHE and HE fluxes could neither be excluded nor firmly established. These long-term-variability properties are discussed and compared to the red noise behavior ({\ss} ~ 2) seen on shorter time scales during VHE-flaring states. The difference in power spectral noise behavior at VHE energies during quiescent and flaring states provides evidence that these states are influenced by different physical processes, while the compatibility of the HE and VHE long-term results is suggestive of a common physical link as it might be introduced by an underlying jet-disk connection.Comment: 11 pages, 16 figure

A First Search for coincident Gravitational Waves and High Energy Neutrinos using LIGO, Virgo and ANTARES data from 2007

We present the results of the first search for gravitational wave bursts associated with high energy neutrinos. Together, these messengers could reveal new, hidden sources that are not observed by conventional photon astronomy, particularly at high energy. Our search uses neutrinos detected by the underwater neutrino telescope ANTARES in its 5 line configuration during the period January - September 2007, which coincided with the fifth and first science runs of LIGO and Virgo, respectively. The LIGO-Virgo data were analysed for candidate gravitational-wave signals coincident in time and direction with the neutrino events. No significant coincident events were observed. We place limits on the density of joint high energy neutrino - gravitational wave emission events in the local universe, and compare them with densities of merger and core-collapse events.Comment: 19 pages, 8 figures, science summary page at http://www.ligo.org/science/Publication-S5LV_ANTARES/index.php. Public access area to figures, tables at https://dcc.ligo.org/cgi-bin/DocDB/ShowDocument?docid=p120000

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