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

Simulator study of the low-speed handling qualities of a supersonic cruise arrow-wing transport configuration during approach and landing

A fixed-based simulator study was conducted to determine the low-speed flight characteristics of an advanced supersonic cruise transport having an arrow wing, a horizontal tail, and four dry turbojets with variable geometry turbines. The primary piloting task was the approach and landing. The statically unstable (longitudinally) subject configuration has unacceptable low-speed handling qualities with no augmentation. Therefore, a hardened stability augmentation system is required to achieve acceptable handling qualities, should the normal operational stability and control augmentation system fail. In order to achieve satisfactory handling qualities, considerable augmentation was required

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

Thermodynamic reaction control of nucleoside phosphorolysis

Nucleoside analogs represent a class of important drugs for cancer and antiviral treatments. Nucleoside phosphorylases (NPases) catalyze the phosphorolysis of nucleosides and are widely employed for the synthesis of pentose‐1‐phosphates and nucleoside analogs, which are difficult to access via conventional synthetic methods. However, for the vast majority of nucleosides, it has been observed that either no or incomplete conversion of the starting materials is achieved in NPase‐catalyzed reactions. For some substrates, it has been shown that these reactions are reversible equilibrium reactions that adhere to the law of mass action. In this contribution, we broadly demonstrate that nucleoside phosphorolysis is a thermodynamically controlled endothermic reaction that proceeds to a reaction equilibrium dictated by the substrate‐specific equilibrium constant of phosphorolysis, irrespective of the type or amount of NPase used, as shown by several examples. Furthermore, we explored the temperature‐dependency of nucleoside phosphorolysis equilibrium states and provide the apparent transformed reaction enthalpy and apparent transformed reaction entropy for 24 nucleosides, confirming that these conversions are thermodynamically controlled endothermic reactions. This data allows calculation of the Gibbs free energy and, consequently, the equilibrium constant of phosphorolysis at any given reaction temperature. Overall, our investigations revealed that pyrimidine nucleosides are generally more susceptible to phosphorolysis than purine nucleosides. The data disclosed in this work allow the accurate prediction of phosphorolysis or transglycosylation yields for a range of pyrimidine and purine nucleosides and thus serve to empower further research in the field of nucleoside biocatalysis.DFG, 390540038, EXC 2008: UniSysCatTU Berlin, Open-Access-Mittel - 201

Efficient Biocatalytic Synthesis of Dihalogenated Purine Nucleoside Analogues Applying Thermodynamic Calculations

The enzymatic synthesis of nucleoside analogues has been shown to be a sustainable and efficient alternative to chemical synthesis routes. In this study, dihalogenated nucleoside analogues were produced by thermostable nucleoside phosphorylases in transglycosylation reactions using uridine or thymidine as sugar donors. Prior to the enzymatic process, ideal maximum product yields were calculated after the determination of equilibrium constants through monitoring the equilibrium conversion in analytical-scale reactions. Equilibrium constants for dihalogenated nucleosides were comparable to known purine nucleosides, ranging between 0.071 and 0.081. To achieve 90% product yield in the enzymatic process, an approximately five-fold excess of sugar donor was needed. Nucleoside analogues were purified by semi-preparative HPLC, and yields of purified product were approximately 50% for all target compounds. To evaluate the impact of halogen atoms in positions 2 and 6 on the antiproliferative activity in leukemic cell lines, the cytotoxic potential of dihalogenated nucleoside analogues was studied in the leukemic cell line HL-60. Interestingly, the inhibition of HL-60 cells with dihalogenated nucleoside analogues was substantially lower than with monohalogenated cladribine, which is known to show high antiproliferative activity. Taken together, we demonstrate that thermodynamic calculations and small-scale experiments can be used to produce nucleoside analogues with high yields and purity on larger scales. The procedure can be used for the generation of new libraries of nucleoside analogues for screening experiments or to replace the chemical synthesis routes of marketed nucleoside drugs by enzymatic processes.DFG, 390540038, EXC 2008: UniSysCatDFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli

The multifocal pattern electroretinogram in chloroquine retinopathy

Purpose: Optimal screening for ocular toxicity caused by chloroquine and hydroxychloroquine is still controversial. With the multifocal pattern electroretinogram (mfPERG), a new electrophysiological technique has recently become available to detect early changes of ganglion cells. In this study this new technique is applied to a series of 10 patients seen consecutively receiving long-term chloroquine medication. Methods: In 10 patients receiving chloroquine medication, clinical examination, Amsler visual field testing and computerized color vision testing were performed. If toxicity was suspected, automated perimetry was carried out. In addition, in all patients conventional pattern electroretinogram (PERG) and mfPERG testing were performed. Results: On clinical examination 8 patients showed no chloroquine-associated maculopathy, while 2 patients did. Of these 2, only 1 reported abnormalities when viewing the Amsler chart, while automated perimetry showed typical, ring-like paracentral scotomas in both affected patients and color vision was significantly abnormal. In the normal patients, 4 of 8 had a mild color vision disturbance, which correlated to age-related macular changes. The amplitudes of the PERG and the central (approximately 10degrees) responses of the mfPERG were markedly reduced in chloroquine maculopathy, while the latencies were unchanged. The peripheral rings of mfPERG (ranging to 48degrees) were not affected by chloroquine toxicity. Both PERG and mfPERG were less affected by age-related macular changes. Conclusions: The reduction of PERG and central mfPERG responses in chloroquine maculopathy may help with the early detection of toxicity. Copyright (C) 2004 S. Karger AG, Basel

Quality of Heusler Single Crystals Examined by Depth Dependent Positron Annihilation Techniques

Heusler compounds exhibit a wide range of different electronic ground states and are hence expected to be applicable as functional materials in novel electronic and spintronic devices. Since the growth of large and defect-free Heusler crystals is still challenging, single crystals of Fe2TiSn and Cu2MnAl were grown by the optical floating zone technique. Two positron annihilation techniques -Angular Correlation of Annihilation Radiation (ACAR) and Doppler Broadening Spectroscopy (DBS)- were applied in order to study both, the electronic structure and lattice defects. Recently, we succeeded to observe clearly the anisotropy of the Fermi surface of Cu2MnAl, whereas the spectra of Fe2TiSn were disturbed by foreign phases. In order to estimate the defect concentration in different samples of Heusler compounds the positron diffusion length was determined by DBS using a monoenergetic positron beam

Long-range crystalline nature of the skyrmion lattice in MnSi

We report small angle neutron scattering of the skyrmion lattice in MnSi using an experimental set-up that minimizes the effects of demagnetizing fields and double scattering. Under these conditions the skyrmion lattice displays resolution-limited Gaussian rocking scans that correspond to a magnetic correlation length in excess of several hundred {\mu}m. This is consistent with exceptionally well-defined long-range order. We further establish the existence of higher-order scattering, discriminating parasitic double-scattering with Renninger scans. The field and temperature dependence of the higher-order scattering arises from an interference effect. It is characteristic for the long-range crystalline nature of the skyrmion lattice as shown by simple mean field calculations.Comment: 4 page

Australopithecus afarensis endocasts suggest ape-like brain organization and prolonged brain growth

Human brains are three times larger, are organized differently, and mature for a longer period of time than those of our closest living relatives, the chimpanzees. Together, these characteristics are important for human cognition and social behavior, but their evolutionary origins remain unclear. To study brain growth and organization in the hominin species Australopithecus afarensis more than 3 million years ago, we scanned eight fossil crania using conventional and synchrotron computed tomography. We inferred key features of brain organization from endocranial imprints and explored the pattern of brain growth by combining new endocranial volume estimates with narrow age at death estimates for two infants. Contrary to previous claims, sulcal imprints reveal an ape-like brain organization and no features derived toward humans. A comparison of infant to adult endocranial volumes indicates protracted brain growth in A. afarensis, likely critical for the evolution of a long period of childhood learning in hominins

Ground-based and in-flight simulator studies of low-speed handling characteristics of two supersonic cruise transport concepts

Conventional and powered lift concepts for supersonic approach and landing tasks are considered. Results indicated that the transport concepts had unacceptable low-speed handling qualities with no augmentation, and that in order to achieve satisfactory handling qualities, considerable augmentation was required. The available roll-control power was acceptable for the powered-lift concept