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This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's method as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods are investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.
Carbohydrate recognition is a ubiquitous principle underlying many fundamental biological processes like fertilization, embryogenesis and viral infections. But how carbohydrate specificity and affinity induce a molecular event is not well understood. One of these examples is bacteriophage P22 that binds and infects three distinct Salmonella enterica (S.) hosts. It recognizes and depolymerizes repetitive carbohydrate structures of O antigen in its host´s outer membrane lipopolysaccharide molecule. This is mediated by tailspikes, mainly β helical appendages on phage P22 short non contractile tail apparatus (podovirus). The O antigen of all three Salmonella enterica hosts is built from tetrasaccharide repeating units consisting of an identical main chain with a distinguished 3,6 dideoxyhexose substituent that is crucial for P22 tailspike recognition: tyvelose in S. Enteritidis, abequose in S. Typhimurium and paratose in S. Paratyphi. In the first study the complexes of P22 tailspike with its host’s O antigen octasaccharide were characterized. S. Paratyphi octasaccharide binds less tightly (ΔΔG≈7 kJ/mol) to the tailspike than the other two hosts. Crystal structure analysis of P22 tailspike co crystallized with S. Paratyphi octasaccharides revealed different interactions than those observed before in tailspike complexes with S. Enteritidis and S. Typhimurium octasaccharides. These different interactions occur due to a structural rearrangement in the S. Paratyphi octasaccharide. It results in an unfavorable glycosidic bond Φ/Ψ angle combination that also had occurred when the S. Paratyphi octasaccharide conformation was analyzed in an aprotic environment. Contributions of individual protein surface contacts to binding affinity were analyzed showing that conserved structural waters mediate specific recognition of all three different Salmonella host O antigens. Although different O antigen structures possess distinct binding behavior on the tailspike surface, all are recognized and infected by phage P22. Hence, in a second study, binding measurements revealed that multivalent O antigen was able to bind with high avidity to P22 tailspike. Dissociation rates of the polymer were three times slower than for an octasaccharide fragment pointing towards high affinity for O antigen polysaccharide. Furthermore, when phage P22 was incubated with lipopolysaccharide aggregates before plating on S. Typhimurium cells, P22 infectivity became significantly reduced. Therefore, in a third study, the function of carbohydrate recognition on the infection process was characterized. It was shown that large S. Typhimurium lipopolysaccharide aggregates triggered DNA release from the phage capsid in vitro. This provides evidence that phage P22 does not use a second receptor on the Salmonella surface for infection. P22 tailspike binding and cleavage activity modulate DNA egress from the phage capsid. DNA release occurred more slowly when the phage possessed mutant tailspikes with less hydrolytic activity and was not induced if lipopolysaccharides contained tailspike shortened O antigen polymer. Furthermore, the onset of DNA release was delayed by tailspikes with reduced binding affinity. The results suggest a model for P22 infection induced by carbohydrate recognition: tailspikes position the phage on Salmonella enterica and their hydrolytic activity forces a central structural protein of the phage assembly, the plug protein, onto the host´s membrane surface. Upon membrane contact, a conformational change has to occur in the assembly to eject DNA and pilot proteins from the phage to establish infection. Earlier studies had investigated DNA ejection in vitro solely for viruses with long non contractile tails (siphovirus) recognizing protein receptors. Podovirus P22 in this work was therefore the first example for a short tailed phage with an LPS recognition organelle that can trigger DNA ejection in vitro. However, O antigen binding and cleaving tailspikes are widely distributed in the phage biosphere, for example in siphovirus 9NA. Crystal structure analysis of 9NA tailspike revealed a complete similar fold to P22 tailspike although they only share 36 % sequence identity. Moreover, 9NA tailspike possesses similar enzyme activity towards S. Typhimurium O antigen within conserved amino acids. These are responsible for a DNA ejection process from siphovirus 9NA triggered by lipopolysaccharide aggregates. 9NA expelled its DNA 30 times faster than podovirus P22 although the associated conformational change is controlled with a similar high activation barrier. The difference in DNA ejection velocity mirrors different tail morphologies and their efficiency to translate a carbohydrate recognition signal into action.
In continuation of a successful series of events, the 4th Many-core Applications Research Community (MARC) symposium took place at the HPI in Potsdam on December 8th and 9th 2011. Over 60 researchers from different fields presented their work on many-core hardware architectures, their programming models, and the resulting research questions for the upcoming generation of heterogeneous parallel systems.
This thesis aims at a better mechanistic understanding of animal communities. Therefore, an allometry- and individual-based model has been developed which was used to simulate mammal and bird communities in heterogeneous landscapes, and to to better understand their response to landscape changes (habitat loss and fragmentation).
Structuring process models
(2012)
One can fairly adopt the ideas of Donald E. Knuth to conclude that process modeling is both a science and an art. Process modeling does have an aesthetic sense. Similar to composing an opera or writing a novel, process modeling is carried out by humans who undergo creative practices when engineering a process model. Therefore, the very same process can be modeled in a myriad number of ways. Once modeled, processes can be analyzed by employing scientific methods. Usually, process models are formalized as directed graphs, with nodes representing tasks and decisions, and directed arcs describing temporal constraints between the nodes. Common process definition languages, such as Business Process Model and Notation (BPMN) and Event-driven Process Chain (EPC) allow process analysts to define models with arbitrary complex topologies. The absence of structural constraints supports creativity and productivity, as there is no need to force ideas into a limited amount of available structural patterns. Nevertheless, it is often preferable that models follow certain structural rules. A well-known structural property of process models is (well-)structuredness. A process model is (well-)structured if and only if every node with multiple outgoing arcs (a split) has a corresponding node with multiple incoming arcs (a join), and vice versa, such that the set of nodes between the split and the join induces a single-entry-single-exit (SESE) region; otherwise the process model is unstructured. The motivations for well-structured process models are manifold: (i) Well-structured process models are easier to layout for visual representation as their formalizations are planar graphs. (ii) Well-structured process models are easier to comprehend by humans. (iii) Well-structured process models tend to have fewer errors than unstructured ones and it is less probable to introduce new errors when modifying a well-structured process model. (iv) Well-structured process models are better suited for analysis with many existing formal techniques applicable only for well-structured process models. (v) Well-structured process models are better suited for efficient execution and optimization, e.g., when discovering independent regions of a process model that can be executed concurrently. Consequently, there are process modeling languages that encourage well-structured modeling, e.g., Business Process Execution Language (BPEL) and ADEPT. However, the well-structured process modeling implies some limitations: (i) There exist processes that cannot be formalized as well-structured process models. (ii) There exist processes that when formalized as well-structured process models require a considerable duplication of modeling constructs. Rather than expecting well-structured modeling from start, we advocate for the absence of structural constraints when modeling. Afterwards, automated methods can suggest, upon request and whenever possible, alternative formalizations that are "better" structured, preferably well-structured. In this thesis, we study the problem of automatically transforming process models into equivalent well-structured models. The developed transformations are performed under a strong notion of behavioral equivalence which preserves concurrency. The findings are implemented in a tool, which is publicly available.
In this thesis, different aspects within the research field of protein spectro- and electro-chemistry on nanostructured materials are addressed. On the one hand, this work is related to the investigation of nanostructured transparent and conductive metal oxides as platform for the immobilization of electroactive enzymes. On the other hand the second part of this work is related to the immobilization of sulfite oxidase on gold nanoparticles modified electrode. Finally direct and mediated spectroelectrochemistry protein with high structure complexity such as the xanthine dehydrogenase from Rhodobacter capsulatus and its high homologues the mouse aldehyde oxidase homolog 1. Stable immobilization and reversible electrochemistry of cytochrome c in a transparent and conductive tin-doped and tin-rich indium oxide film with a well-defined mesoporosity is reported. The transparency and good conductivity, in combination with the large surface area of these materials, allow the incorporation of a high amount of electroactive biomolecules (between 250 and 2500 pmol cm-2) and their electrochemical and spectroscopic investigation. Both, the electrochemical behavior and the immobilization of proteins are influenced by the geometric parameters of the porous material, such as the structure and pore shape, the surface chemistry, as well as the protein size and charge. UV-Vis and resonance Raman spectroscopy, in combination with direct protein voltammetry, are employed for the characterization of cytochrome c immobilized in the mesoporous indium tin oxide and reveal no perturbation of the structural integrity of the redox protein. A long term protein immobilization is reached using these unmodified mesoporous indium oxide based materials, i.e. more than two weeks even at high ionic strength. The potential of this modified material as an amperometric biosensor for the detection of superoxide anions is demonstrated. A sensitivity of about 100 A M-1 m-2, in a linear measuring range of the superoxide concentration between 0.13 and 0.67 μM, is estimated. In addition an electrochemical switchable protein-based optical device is designed with the core part composed of cytochrome c immobilized on a mesoporous indium tin oxide film. A color developing redox sensitive dye is used as switchable component of the system. The cytochrome c-catalyzed oxidation of the dye by hydrogen peroxide is spectroscopically investigated. When the dye is co-immobilized with the protein, its redox state is easily controlled by application of an electrical potential at the supporting material. This enables to electrochemical reset the system to the initial state and repetitive signal generation. The case of negative charged proteins, which does not have a good interaction with the negative charged indium oxide based films, is also explored. The modification of an indium tin oxide film with a positive charged polymer and the employment of a antimony doped tin oxide film were investigated in this work in order to overcome the repulsion induced by similar charges of the protein and electrode. Human sulfite oxidase and its separated heme-containing domain are able to direct exchange electrons with the supporting material. A study of a new approach for sulfite biosensing, based on enhanced direct electron transfer of a human sulfite oxidase immobilized on a gold nanoparticles modified electrode is reported. The spherical gold nanoparticles were prepared via a novel method by reduction of HAuCl4 with branched poly(ethyleneimine) in an ionic liquid resulting in particles of about 10 nm in hydrodynamic diameter. These nanoparticles were covalently attached to a mercaptoundecanoic acid modified Au-electrode and act as platform where human sulfite oxidase is adsorbed. An enhanced interfacial electron transfer and electrocatalysis is therefore achieved. UV-Vis and resonance Raman spectroscopy, in combination with direct protein voltammetry, were employed for the characterization of the system and reveal no perturbation of the structural integrity of the redox protein. The proposed biosensor exhibited a quick steady-state current response, within 2 s and a linear detection range between 0.5 and 5.4 μM with high sensitivity (1.85 nA μM-1). The investigated system provides remarkable advantages, since it works at low applied potential and at very high ionic strength. Therefore these properties could make the proposed system useful in the development of bioelectronic devices and its application in real samples. Finally protein with high structure complexity such as the xanthine dehydrogenase from Rhodobacter capsulatus and the mouse aldehyde oxidase homolog 1 were spectroelectrochemically studied. It could be demonstrated that different cofactors present in the protein structure, like the FAD and the molybdenum cofactor, are able to directly exchange electrons with an electrode and are displayed as a single peak in a square wave voltammogram. Protein mutants bearing a serine substituted to the cysteines, bounding to the most exposed iron sulfur cluster additionally showed direct electron transfer which can be attributable to this cluster. On the other hand a mediated spectroelectrochemical titration of the protein bound FAD cofactor was performed in presence of transparent iron and cobalt complex mediators. The results showed the formation of the stable semiquinone and the fully reduced flavin. Two formal potentials for each single electron exchange step were then determined.
In the context of cosmological structure formation sheets, filaments and eventually halos form due to gravitational instabilities. It is noteworthy, that at all times, the majority of the baryons in the universe does not reside in the dense halos but in the filaments and the sheets of the intergalactic medium. While at higher redshifts of z > 2, these baryons can be detected via the absorption of light (originating from more distant sources) by neutral hydrogen at temperatures of T ~ 10^4 K (the Lyman-alpha forest), at lower redshifts only about 20 % can be found in this state. The remain (about 50 to 70 % of the total baryons mass) is unaccounted for by observational means. Numerical simulations predict that these missing baryons could reside in the filaments and sheets of the cosmic web at high temperatures of T = 10^4.5 - 10^7 K, but only at low to intermediate densities, and constitutes the warm-hot intergalactic medium (WHIM). The high temperatures of the WHIM are caused by the formation of shocks and the subsequent shock-heating of the gas. This results in a high degree of ionization and renders the reliable detection of the WHIM a challenging task. Recent high-resolution hydrodynamical simulations indicate that, at redshifts of z ~ 2, filaments are able to provide very massive galaxies with a significant amount of cool gas at temperatures of T ~ 10^4 K. This could have an important impact on the star-formation in those galaxies. It is therefore of principle importance to investigate the particular hydro- and thermodynamical conditions of these large filament structures. Density and temperature profiles, and velocity fields, are expected to leave their special imprint on spectroscopic observations. A potential multiphase structure may act as tracer in observational studies of the WHIM. In the context of cold streams, it is important to explore the processes, which regulate the amount of gas transported by the streams. This includes the time evolution of filaments, as well as possible quenching mechanisms. In this context, the halo mass range in which cold stream accretion occurs is of particular interest. In order to address these questions, we perform particular hydrodynamical simulations of very high resolution, and investigate the formation and evolution of prototype structures representing the typical filaments and sheets of the WHIM. We start with a comprehensive study of the one-dimensional collapse of a sinusoidal density perturbation (pancake formation) and examine the influence of radiative cooling, heating due to an UV background, thermal conduction, and the effect of small-scale perturbations given by the cosmological power spectrum. We use a set of simulations, parametrized by the wave length of the initial perturbation L. For L ~ 2 Mpc/h the collapse leads to shock-confined structures. As a result of radiative cooling and of heating due to an UV background, a relatively cold and dense core forms. With increasing L the core becomes denser and more concentrated. Thermal conduction enhances this trend and may lead to an evaporation of the core at very large L ~ 30 Mpc/h. When extending our simulations into three dimensions, instead of a pancake structure, we obtain a configuration consisting of well-defined sheets, filaments, and a gaseous halo. For L > 4 Mpc/h filaments form, which are fully confined by an accretion shock. As with the one-dimensional pancakes, they exhibit an isothermal core. Thus, our results confirm a multiphase structure, which may generate particular spectral tracers. We find that, after its formation, the core becomes shielded against further infall of gas onto the filament, and its mass content decreases with time. In the vicinity of the halo, the filament's core can be attributed to the cold streams found in other studies. We show, that the basic structure of these cold streams exists from the very beginning of the collapse process. Further on, the cross section of the streams is constricted by the outwards moving accretion shock of the halo. Thermal conduction leads to a complete evaporation of the cold stream for L > 6 Mpc/h. This corresponds to halos with a total mass higher than M_halo = 10^13 M_sun, and predicts that in more massive halos star-formation can not be sustained by cold streams. Far away from the gaseous halo, the temperature gradients in the filament are not sufficiently strong for thermal conduction to be effective.
Duplicate detection is the task of identifying all groups of records within a data set that represent the same real-world entity, respectively. This task is difficult, because (i) representations might differ slightly, so some similarity measure must be defined to compare pairs of records and (ii) data sets might have a high volume making a pair-wise comparison of all records infeasible. To tackle the second problem, many algorithms have been suggested that partition the data set and compare all record pairs only within each partition. One well-known such approach is the Sorted Neighborhood Method (SNM), which sorts the data according to some key and then advances a window over the data comparing only records that appear within the same window. We propose several variations of SNM that have in common a varying window size and advancement. The general intuition of such adaptive windows is that there might be regions of high similarity suggesting a larger window size and regions of lower similarity suggesting a smaller window size. We propose and thoroughly evaluate several adaption strategies, some of which are provably better than the original SNM in terms of efficiency (same results with fewer comparisons).
The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments.
On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators
(2012)
We consider a Sturm-Liouville boundary value problem in a bounded domain D of R^n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on bD. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact self-adjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types.
We consider the Dirichlet, Neumann and Zaremba problems for harmonic functions in a bounded plane domain with nonsmooth boundary. The boundary curve belongs to one of the following three classes: sectorial curves, logarithmic spirals and spirals of power type. To study the problem we apply a familiar method of Vekua-Muskhelishvili which consists in using a conformal mapping of the unit disk onto the domain to pull back the problem to a boundary problem for harmonic functions in the disk. This latter is reduced in turn to a Toeplitz operator equation on the unit circle with symbol bearing discontinuities of second kind. We develop a constructive invertibility theory for Toeplitz operators and thus derive solvability conditions as well as explicit formulas for solutions.
We study maximal subsemigroups of the monoid T(X) of all full transformations on the set X = N of natural numbers containing a given subsemigroup W of T(X), where each element of a given set U is a generator of T(X) modulo W. This note continues the study of maximal subsemigroups of the monoid of all full transformations on an infinite set.
The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which takes into account both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration this modification is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.
In the limit we analyze the generators of families of reversible jump processes in the n-dimensional space associated with a class of symmetric non-local Dirichlet forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of certain eikonal equation. Fine results are sensitive to the rate functions being twice differentiable or just Lipschitz. Our estimates are similar to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice.
We analyze a general class of difference operators containing a multi-well potential and a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we treat the eigenvalue problem as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix similar to the analysis for the Schrödinger operator, and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.
We say that (weak/strong) time duality holds for continuous time quasi-birth-and-death-processes if, starting from a fixed level, the first hitting time of the next upper level and the first hitting time of the next lower level have the same distribution. We present here a criterion for time duality in the case where transitions from one level to another have to pass through a given single state, the so-called bottleneck property. We also prove that a weaker form of reversibility called balanced under permutation is sufficient for the time duality to hold. We then discuss the general case.
For a sequence of Hilbert spaces and continuous linear operators the curvature is defined to be the composition of any two consecutive operators. This is modeled on the de Rham resolution of a connection on a module over an algebra. Of particular interest are those sequences for which the curvature is "small" at each step, e.g., belongs to a fixed operator ideal. In this context we elaborate the theory of Fredholm sequences and show how to introduce the Lefschetz number.
We introduce a theoretical framework for performing statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses. This extends the standard statistical setting for multiple hypotheses testing, which is restricted to a finite set. This work is motivated by numerous modern applications where the observed signal is modeled by a stochastic process over a continuum. As a measure of type I error, we extend the concept of false discovery rate (FDR) to this setting. The FDR is defined as the average ratio of the measure of two random sets, so that its study presents some challenge and is of some intrinsic mathematical interest. Our main result shows how to use the p-value process to control the FDR at a nominal level, either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting, the latter one leading to a less conservative procedure. The interest of this approach is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables. Conceptually, an interesting feature of the setting advocated here is that it focuses directly on the intrinsic hypothesis space associated with a testing model on a random process, without referring to an arbitrary discretization.