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This work is concerned with two topics at the intersection of convex algebraic geometry and optimization.
We develop a new method for the optimization of polynomials over polytopes. From the point of view of convex algebraic geometry the most common method for the approximation of polynomial optimization problems is to solve semidefinite programming relaxations coming from the application of Positivstellensätze. In optimization, non-linear programming problems are often solved using branch and bound methods. We propose a fused method that uses Positivstellensatz-relaxations as lower bounding methods in a branch and bound scheme. By deriving a new error bound for Handelman's Positivstellensatz, we show convergence of the resulting branch and bound method. Through the application of Positivstellensätze, semidefinite programming has gained importance in polynomial optimization in recent years. While it arises to be a powerful tool, the underlying geometry of the feasibility regions (spectrahedra) is not yet well understood. In this work, we study polyhedral and spectrahedral containment problems, in particular we classify their complexity and introduce sufficient criteria to certify the containment of one spectrahedron in another one.
Tympanal hearing organs of insects emit distortion-product otoacoustic emissions (DPOAEs) which are indicative of nonlinear mechanical sound processing. General characteristics of insect DPOAEs are comparable to those measured in vertebrates, despite distinct differences in ear anatomy. DPOAEs appear during simultaneous stimulation with two pure tones (f1<f2) as additional spectral peaks at frequencies of nf1-(n-1)f2 and nf2-(n-1)f1, with the 2f1-f2 emission being the most prominent one. Insect DPOAEs are highly vulnerable to manipulations that interfere with the animal's physiological state and disappear after death. First evidence from locusts suggested that scolopidial mechanoreceptors might play a role in frequency-specific DPOAE generation (Möckel et al. 2007). The overall aim of this thesis was to determine the source of sensitive, nonlinear hearing at high frequencies and of DPOAE generation in tympanal organs of insects.
The first project of the present thesis involved general characteristics of DPOAE generation in the bushcricket Mecopoda elongata and the selective exclusion of the scolopidial mechanoreceptors using the neuroactive insectizide pymetrozine (Möckel et al. 2011). Pymetrozin appears to act highly effective and selectively on chordotonal organs, without affecting other sensory organs that lack scolopidial receptors. Pymetrozine solutions were applied as closely as possible to the scolopidia via a cuticle opening in the tibia, distally to the organ. Applications at concentrations between 10-3 and 10-7 M led to a pronounced and irreversible decrease of DPOAE amplitudes. Both this study on bushcrickets (Möckel et al. 2011) and an earlier one on locusts (Möckel et al. 2007) hence indicate the involvement of scolopidia in DPOAE generation in insects, by using complementary methods (pharmacological versus mechanical manipulation) and different animal models.
The second project of the present thesis investigated the temperature-dependence of DPOAEs in the locust Locusta migratoria (Möckel et al. 2012). The suggested biological origin of acoustic two-tone distortions in insects should involve metabolic processes, whose temperature-dependence would directly affect the DPOAE generation. Body temperature shifts resulted in reversible, level- and frequency-dependent effects on the 2f1–f2 emission. Using low f2 frequencies of up to 10 kHz, a body temperature increase (median +8–9°C) led to an upward shift of DPOAE amplitudes of approximately +10 dB, whereas a temperature decrease (median –7°C) was followed by a reduction of DPOAE amplitudes by 3 to 5 dB. Both effects were only present in the range of the low-level component of DPOAE growth functions below f2 stimulus levels of approximately 30-40 dB SPL. Emissions induced by higher stimulus levels and frequencies (e.g. 12 and 18 kHz) remained unaffected by any temperature shifts. The Arrhenius activation energy of the underlying cellular component amounted to 34 and 41 kJmol-1 (for growth functions measured with 8 and 10 kHz as f2, respectively). Such activation energy values provide a hint that an intact dynein-tubulin system within the scolopidial receptors could play an essential part in the DPOAE generation in tympanal organs.
The third project of this thesis demonstrated mechanical DPOAE analogs in the tympanum's vibration pattern during two-tone stimulation in the locust Schistocerca gregaria, using laser Doppler vibrometry (Möckel et al. 2014). DPOAE generation crucially relies on the integrity of the scolopidial mechanoreceptors (Möckel et al. 2007, 2011), which in locusts, directly attach to the tympanal membrane. During two-tone stimulation, DPOAEs were shown to mechanically emerge at the tympanum region where the auditory mechanoreceptors are attached. Those emission-coupled vibrations differed remarkably from tympanum waves evoked by external pure tones of the same frequency, in terms of wave propagation, energy distribution, and location of amplitude maxima. In contrast to traveling wave-like characteristics of externally evoked vibrations, intrinsically generated waves were locally restricted to the region around the high frequency receptors’ attachment position. The mechanical gradient of the tympanal membrane that leads to direction-dependent properties probably avoids the spreading of these locally evoked waves, which are then reflected and occur only in restricted areas as standing waves. Selective inactivation of mechanoreceptors by mechanical lesions did not affect the tympanum's response to external pure tones, but abolished the emission's displacement amplitude peak. These findings provide evidence that tympanal auditory receptors, comparable to the situation in mammals, comprise the required nonlinear response characteristics, which during two-tone stimulation lead to additional, highly localized deflections of the tympanum.
This thesis is structured into 7 chapters:
• Chapter 2 gives an overview of the ultrashort high intensity laser interaction with matter. The laser interaction with an induced plasma is described, starting from the kinematics of single electron motion, followed by collective electron effects and the ponderamotive motion in the laser focus and the plasma transparency for the laser beam. The three different mechanisms prepared to accelerate and propagate electrons through matter are discussed. The following indirect acceleration of protons is explained by the Target Normal Sheath Acceleration (TNSA) mechanism. Finally some possible applications of laser accelerated protons are explained briefly.
• Chapter 3 deals with the modeling of geometry and field mapping of magnetic lens. Initial proton and electron distributions, fitted to PHELIX measured data are generated, a brief description of employed codes and used techniques in simulation is given, and the aberrations at the solenoid focal spot is studied.
• Chapter 4 presents a simulation study for suggested corrections to optimize the proton beam as a later beam source. Two tools have been employed in these suggested corrections, an aperture placed at the solenoid focal spot as energy selection tool, and a scattering foil placed in the proton beam to smooth the radial energy beam profile correlation at the focal spot due to chromatic aberrations. Another suggested correction has been investigated, to optimize the beam radius at the focal spot by lens geometry controlling.
• Chapter 5 presents a simulation study for the de-neutralization problem in TNSA caused by the fringing fields of pulsed magnetic solenoid and quadrupole. In this simulation, we followed an electrostatic model, wherethe evolution of both, self and mutual fields through the pulsed magnetic solenoid could be found, which is not the case in the quadrupole and only the growth of self fields could be found. The field mapping of magnetic elements is generated by the Matlab program, while the TraceWin code is employed to study the tracking through magnetic elements.
• Chapter 6 describes the PHELIX laser parameters at GSI with chirp pulse amplification technique (CPA), and Gafchromic Radiochromic film RCF) as a spatial energy resolver film detector. The results of experiments with laser proton acceleration, which were performed in two experimental areas at GSI (Z6 area and PHELIX Laser Hall (PLH)), are presented in section 6.3.
• Chapter 7 includes the main results of this work, conclusions and gives a perspective for future experimental activities.
A multiple filter test for the detection of rate changes in renewal processes with varying variance
(2014)
The thesis provides novel procedures in the statistical field of change point detection in time series.
Motivated by a variety of neuronal spike train patterns, a broad stochastic point process model is introduced. This model features points in time (change points), where the associated event rate changes. For purposes of change point detection, filtered derivative processes (MOSUM) are studied. Functional limit theorems for the filtered derivative processes are derived. These results are used to support novel procedures for change point detection; in particular, multiple filters (bandwidths) are applied simultaneously in oder to detect change points in different time scales.
The work presented in this thesis is devoted to two classes of mathematical population genetics models, namely the Kingman-coalescent and the Beta-coalescents. Chapters 2, 3 and 4 of the thesis include results concerned with the first model, whereas Chapter 5 presents contributions to the second class of models.
Natural products (NPs) have been a rich source for pharmaceutically used anti-infectives and other drugs. However, the application of anti-infectives inevitably causes the development of resistant and multiresistant pathogens, which have to be treated with novel anti-infectives. The industrial research for novel anti-infectives has been concentrating on members of the bacterial Actinomycetales for a long time. Due to several reasons, e.g. the rediscovery of already known NPs, pharmaceutical companies abandoned their NP-research and focused on drug development based on combinatorial chemistry. However, the limited structural diversity of merely synthetic compound libraries has not been a fruitful source for bioactive compounds. Hence the discovery of novel bioactive NPs as a source for anti-infectives is still of economical and humanitarian interest and will remain to be an important branch of research in the future. One strategy to circumvent the rediscovery of bioactive NPs is the analysis of yet unexplored bacterial taxa. Based on this assumption, this work aimed at the discovery of novel NPs from the entomopathogenic bacterial genera Xenorhabdus and Photorhabdus and other promising taxa, as well as the investigation of their biosynthesis. ...
Acceleration of Biomedical Image Processing and Reconstruction with FPGAs
Increasing chip sizes and better programming tools have made it possible to increase the boundaries of application acceleration with reconfigurable computer chips. In this thesis the potential of acceleration with Field Programmable Gate Arrays (FPGAs) is examined for applications that perform biomedical image processing and reconstruction. The dataflow paradigm was used to port the analysis of image data for localization microscopy and for 3D electron tomography from an imperative description towards the FPGA for the first time.
After the primitives of image processing on FPGAs are presented, a general workflow is given for analyzing imperative source code and converting it to a hardware pipeline where every node processes image data in parallel. The theoretical foundation is then used to accelerate both example applications. For localization microscopy, an acceleration of 185 compared to an Intel i5 450 CPU was achieved, and electron tomography could be sped up by a factor of 5 over an Nvidia Tesla C1060 graphics card while maintaining full accuracy in both cases.
This thesis presents experimental studies of proton capture and fragmentation reactions with heavy-ion storage rings. In one experiment, the 96Ru(p, γ)97Rh cross sections near the Gamow window have been measured at the ESR of GSI. In the other experiment, the measurement of the fragmentation yields has been carried out at the CSRe of IMP.
It is essential to determine the cross sections of (γ, p) or (p, γ) reactions for p-process network calculations. However, only very few of the required cross sections have been measured and thus most of them rely solely on Hauser-Feshbach model predictions. The predictions of the model have always very large uncertainties because of the not well-known input parameters. These parameters can be constrained by experiments. Compared to the traditional activation technique, a novel method using a storage ring has been developed to measure the cross sections of (p, γ) reactions in inverse kinematics.
This proton capture experiment has been performed at the ESR, where the circulating 96Ru44+ ions interacted with a hydrogen gas target at 9, 10 and 11 MeV/u. The nuclear reaction products of (p, p), (p, α), (p, n) and (p, γ) reactions were registered by position sensitive detectors. A Geant4 simulation code has been developed to distinguish the (p, γ) reaction products unambiguously from the background reactions. In this work, a relative normalization method has been utilized to accurately determine the cross sections of the (p, γ) reaction. The 96Ru(p, γ)97Rh cross section in the Gamow window of the p process is sensitive to two parameters, i.e., the γ-ray strength function and the optical model potential, while it is mainly sensitive to the γ-ray strength function in the energy region of our experiment. Therefore, our experimental (p, γ) cross sections near 10 MeV/u have been used to directly constrain the γ-ray strength function used in the model. Furthermore, the proton potential has also been constrained by combining our results with additional experimental data for this reaction in the lower energy region. The constrained model has been used to calculate the reaction rate over a wide temperature range, which is an extremely important input for astrophysical calculations.
The yields of fragments produced by 78Kr fragmentation reactions have been measured at the CSRe for the Tz = −1/2 and Tz = 1/2 nuclei along or close to the paths of αp- and rp-processes. The measured yields present a significant odd-even staggering effect for Tz = −1/2 nuclides but they are small for Tz = 1/2 nuclides.
The magnitude of this effect for four consecutive yields has been quantified using a third-order difference formula. It is found that the largest odd-even staggering is reached near the closed shells Z = 20 and Z = 28. Our experimental results could also compared with the data from other experiments with different projectile-target combinations. All these experimental data strongly support the closed shells Z = 20 and Z = 28 for the Tz = −1/2 nuclei.
This thesis serves two main purposes:
1. The introduction of a novel experimental method to investigate phase change dynamics of supercooled liquids
2. First-time measurements for the crystallization behaviour for hydrogen isotopes under various conditions
1) The new method is established by the synergy of a liquid microjet of ~ 5 µm diameter and a scattering technique with high spatial resolution, here linear Raman spectroscopy. Due to the high directional stability and the known velocity of the liquid filament, its traveling axis corresponds to a time axis static in space. Utilizing evaporative cooling in a vacuum environment, the propagating liquid cools down rapidly and eventually experiences a phase transition to the crystalline state. This temporal evolution is probed along the filament axis, ultimately resulting in a time resolution of 10 ns. The feasibility of this approach is proven successfully within the following experiments.
2) A main object of study are para-hydrogen liquid filaments. Raman spectra reveal a temperature gradient of the liquid across the filament. This behaviour can quantitatively be reconstructed by numerical simulations using a layered model and is rooted in the effectiveness of evaporative cooling on the surface and a finite thermal conductivity. The deepest supercoolings achieved are ~ 30% below the melting point, at which the filament starts to solidify from the surface towards the core. With a crystal growth velocity extracted from the data the appropriate growth mechanism is identified. The crystal structure that initially forms is metastable and probably the result of Ostwald’s rule of stages. Indications for a transition within the solid towards the stable equilibrium phase support this interpretation.
The analog isotope ortho-deuterium is evidenced to behave qualitatively similar with quantitative differences being mass related.
In further measurements, isotopic mixtures of para-hydrogen and ortho-deuterium are investigated. It is found that the crystallization process starts earlier and lasts significantly longer compared to the pure substances with the maximum values between 20-50% ortho-deuterium content. A solely temperature based explanation for this effect can be excluded. The difference in the quantum character and hence effective size of the isotopes suggests a strong influence of the progressing liquid-solid-interface. Small dilutions of each para-hydrogen and ortho-deuterium with neon show an even more extended crystallization process compared to above isotopic mixtures. Additionally, the crystal is strongly altered in favor of the equilibrium lattice structure of neon.