2,334 research outputs found

    Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

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    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

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    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

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    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

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    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

    Recognition of cognitive impairment and depressive symptoms in older patients with heart failure

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    INTRODUCTION: Cognitive impairment and depression in patients with heart failure (HF) are common comorbidities and are associated with increased morbidity, readmissions and mortality. Timely recognition of cognitive impairment and depression is important for providing optimal care. The aim of our study was to determine if these disorders were recognised by clinicians and, secondly, if they were associated with hospital admissions and mortality within 6 months’ follow-up. METHODS: Patients (aged ≥65 years) diagnosed with HF were included from the cardiology outpatient clinic of Gelre Hospitals. Cognitive status was evaluated with the Montreal Cognitive Assessment test (score ≤22). Depressive symptoms were assessed with the Geriatric Depression Scale (score >5). Patient characteristics were collected from electronic patient files. The clinician was blinded to the tests and asked to assess cognitive status and mood. RESULTS: We included 157 patients. Their median age was 79 years (65–92); 98 (62%) were male. The majority had New York Heart Association functional class II. Cognitive impairment was present in 56 (36%) patients. Depressive symptoms were present in 21 (13%) patients. In 27 of 56 patients (48%) cognitive impairment was not recognised by clinicians. Depressive symptoms were not recognised in 11 of 21 patients (52%). During 6 months’ follow-up 24 (15%) patients were readmitted for HF-related reasons and 18 (11%) patients died. There was no difference in readmission and mortality rate between patients with or without cognitive impairment and patients with or without depressive symptoms. CONCLUSION: Cognitive impairment and depressive symptoms were infrequently recognised during outpatient clinic visits

    Cellulose lattice strains and stress transfer in native and delignified wood

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    Small specimens of spruce wood with different degrees of delignification were studied using in-situ tensile tests and simultaneous synchrotron X-ray diffraction to reveal the effect of delignification and densification on their tensile properties at relative humidity of 70–80 %. In addition to mechanical properties, these analyses yield the ratio of strains in the cellulose crystals and in the bulk, which reflects the stress-transfer to crystalline cellulose. While the specific modulus of elasticity slightly increases from native wood by partial or complete delignification, the lattice strain ratio does not show a significant change. This could indicate a compensatory effect from the decomposition of the amorphous matrix by delignification and from a tighter packing of cellulose crystals that would increase the stress transfer. The reduced strain to failure and maximum lattice strain of delignified specimens suggests that the removal of lignin affects the stress-strain behavior with fracture at lower strain levels