über die Definition von effektiven Zufallstests

Summary We continue the discussion on the definition of random sequences from Part I. We will show that the idea of Kolmogoroff to characterize random sequences by their program complexity can be formulated in such a way as to let this definition coÏncide with the others given in Part I. Another equivalent definition of random sequences can be derived from the games of chance. A sequence is random, if and only if no player who calculates his pool by effective methods can raise his fortune indefinitely when playing on this sequence. Finally we will study transformations which preserve the random property of a sequence. We will prove that the original concept of v. Mises can also be modified in such a manner as to coÏncide with all our other definitions. A sequence is random, if and only if it satisfies the strong law of large numbers and if every sequence obtained from it by a constructive measure-preserving transformation is random, too.

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Die Arbeit stellt einen Teil der Habilitationsschrift dar, die der Mathematisch-Naturwissenschaftlichen FakultÄt der UniversitÄt des Saarlandes vom Verfasser vorgelegt wurde.     

Physical Dimensions/Units and Universal Constants: Their Invariance in Special and General Relativity

The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing mechanics and electrodynamics, it naturally leads one, besides the dimensions of length and time, to the fundamental units of action $\mathfrak{h}$, electric charge q, and magnetic flux ?. Also, $q\times ?=\text{action}$ and $q/?=1/\text{resistance}$ are known. These results of classical physics suggests to look into the corresponding quantum aspects of q and ? (and also of $\mathfrak{h}$): The electric charge occurs exclusively in elementary charges e, whereas the magnetic flux can have any value; in specific situations, however, in superconductors of type II at very low temperatures, ? appears quantized in the form of fluxons (Abrikosov vortices). And $\mathfrak{h}$ leads, of course, to the Planck quantum h. Thus, one is directed to superconductivity and, because of the resistance, to the quantum Hall effect. In this way, the Josephson and the quantum Hall effects come into focus quite naturally. One goal is to determine the behavior of the fundamental constants in special and in general relativity.     

The Memetic Tree-based Genetic Algorithm and its application to Portfolio Optimization

We introduce a Memetic system to solve the application problem of Financial Portfolio Optimization. This problem consists of selecting a number of assets from a market and their relative weights to form an investment strategy. These weights must be optimized against a utility function that considers the expected return of each asset, and their co-variance; which means that as the number of available assets increases, the search space increases exponentially. Our method introduces two new concepts that set it apart from previous evolutionary based approaches. The first is the Tree-based Genetic Algorithm (GA), a recursive representation for individuals which allows the genome to learn information regarding relationships between the assets, and the evaluation of intermediate nodes. The second is the hybridization with local search, which allows the system to fine-tune the weights of assets after the tree structure has been decided. These two innovations make our system superior than other representations used for multi-weight assignment of portfolios.     

Structure and dynamics of alpha-lactalbumin adsorbed at a charged brush interface

We have studied the adsorption of alpha-lactalbumin at a planar poly(acrylic acid) (PAA) brush using neutron reflectometry (NR) and total internal reflection fluorescence (TIRF) spectroscopy. The PAA brush has been prepared by spin-coating silicon or quartz plates with a hydrophobic poly(styrene) film and by transferring the copolymer poly(styrene)-poly(acrylic acid) onto the modified surface. In the case of NR, the poly(styrene) film and the poly(styrene) chain ends of the copolymer were perdeuterated in order to generate a high contrast to the non-deuterated PAA brush. alpha-Lactalbumin was chosen as the model protein because it is a relatively small globular protein with a negative net charge at neutral pH-values, as chosen in the experiments. Thus, it is interacting with the PAA brush on the 'wrong' side of its isoelectric point. In addition, the effects of temperature on the volume fraction profile and the reorientational mobility of the protein within the PAA brush were determined. From the analysis of the NR data, it has been found that despite of its negative net charge, alpha-lactalbumin is penetrating into the PAA brush. Its volume fraction profile parallels that of the PAA brush, indicating an exclusive interaction between the protein and the PAA. No protein accumulation is found at the inner poly(styrene) or the outer solution interface of the PAA brush. When increasing the temperature from 20 to 40 degrees C, less protein is adsorbed, suggesting the presence of enthalpic interaction contributions. From the analysis of the TIRF data, a high degree of reorientational mobility of alpha-lactalbumin within a PAA brush can be inferred. The reorientational correlation time of alpha-lactalbumin labeled with the Alexa Fluor 488 dye was found to increase from 5.5 to 32 ns upon adsorption, which can well be explained by the higher viscosity inside the PAA brush. Overall, the results of this study quantify for the first time the molecular details of the unique interaction of a protein on the 'wrong' side of its isoelectric point with a planar charged brush interface. It is concluded that the high mobility of alpha-lactalbumin within a PAA brush can partially be understood by the presence of repulsive electrostatic interactions. There is no 'freezing' of the protein dynamics, which is a precondition for biological activity.     

Biomimetic membrane arrays on cast hydrogel supports

Lipid bilayers are intrinsically fragile and require mechanical support in technical applications based on biomimetic membranes. Tethering the lipid bilayer membranes to solid substrates, either directly through covalent or ionic substrate-lipid links or indirectly on substrate-supported cushions, provides mechanical support but at the cost of small molecule transport through the membrane-support sandwich. To stabilize biomimetic membranes while allowing transport through a membrane-support sandwich, we have investigated the feasibility of using an ethylene tetrafluoroethylene (ETFE)/hydrogel sandwich as the support. The sandwich is realized as a perforated surface-treated ETFE film onto which a hydrogel composite support structure is cast. We report a simple method to prepare arrays of lipid bilayer membranes with low intrinsic electrical conductance on the highly permeable, self-supporting ETFE/hydrogel sandwiches. We demonstrate how the ETFE/hydrogel sandwich support promotes rapid self-thinning of lipid bilayers suitable for hosting membrane-spanning proteins.     

A simple and rapid chemical method for the determination of cephalosporins

A simple and rapid chemical assay for cephalosporins is described. It is a simple modification of the colorimetric determination of penicillins in which the narrow spectrum beta-lactamase (penicillinase) is replaced by a broad spectrum beta-lactamase (cephalosporinase) produced by Enterobacter cloacae. The method can be used for assay of fermentation broths as well as for pure cephalosporins.