Parsability approaches of several grammar formalisms generating also non-context-free languages are explored. Chomsky grammars, Lindenmayer systems, grammars with controlled derivations, and grammar systems are treated. Formal properties of these mechanisms are investigated, when they are used as language acceptors. Furthermore, cooperating distributed grammar systems are restricted so that efficient deterministic parsing without backtracking becomes possible. For this class of grammar systems, the parsing algorithm is presented and the feature of leftmost derivations is investigated in detail. / Ansätze zum Parsing verschiedener Grammatikformalismen, die auch nicht-kontextfreie Sprachen erzeugen können, werden diskutiert. Chomsky-Grammatiken, Lindenmayer-Systeme, Grammatiken mit gesteuerten Ersetzungen und Grammatiksysteme werden behandelt. Formale Eigenschaften dieser Mechanismen als Akzeptoren von Sprachen werden untersucht. Weiterhin werden kooperierende verteilte (CD) Grammatiksysteme derart beschränkt, dass effizientes deterministisches Parsing ohne Backtracking möglich ist. Für diese Klasse von Grammatiksystemen wird der Parsingalgorithmus vorgestellt und die Rolle von Linksableitungen wird detailliert betrachtet.

Der entorhinale Cortex (EC) nimmt eine zentrale Stellung im limbischem System ein und ist darüber hinaus eine Verbindungsstelle zwischen Hippocampus und Cortex. Um die Eigenschaften der Projektionszellen im EC genauer zu charakterisieren, führten wir intrazelluläre Ableitungen an den Neuronen der oberflächlichen (Schicht II und III) und der tiefen (Schicht IV-VI) Schichten durch, von denen etwa ein Viertel während der Ableitung mit dem Farbstoff Biozytin gefärbt werden konnten. In Schicht III des medialen EC fanden wir vier unterschiedliche Zelltypen, von denen zwei als Projektionsneurone (Typ 1 und Typ 2) charakterisiert wurden. Die Projektionszellen der Schicht III besitzen eine niedrige Schwelle zur Auslösung synaptisch evozierter Aktionspotentiale. Daneben konnten wir zwei weitere Typen von Zellen (Typ 3 und Typ 4) bestimmen, deren Somata in der Schicht III lagen, die aber nicht in den Hippocampus projizierten, sondern lokal im EC verschaltet waren. In den tiefen Schichten des EC fanden sich zur Area Dentata (AD) projezierende bipolare und multipolare Neurone, die trotz der morphologischen Ähnlichkeit mit GABAergen Interneuronen die typischen elektrophysiologischen und neurochemischen Eigenschaften von Prinzipalzellen des EC besitzen. Diese Neurone können vermutlich Funktionen von sowohl Lokal- als auch Projektionszellen übernehmen und dementsprechend die schnelle Informationsübertragung zwischen den tiefen und oberflächlichen Schichten einerseits und zwischen EC und AD andererseits ausüben. Um der Frage nachzugehen, unter welchen Bedingungen die Schicht II- und III-Projektionszellen aktiviert werden, führten wir repetitive synaptische Reizungen im EC durch. Hochfrequente repetitive synaptische Reizung (> 10 Hz) führt zu einer bevorzugten Aktivierung der Schicht II-Zellen. Hingegen werden die Schicht III-Zellen bei niedrigeren Reizfrequenzen (< 6 Hz) bevorzugt aktiviert und Schicht II-Zellen gleichzeitig gehemmt. Dies läßt vermuten, daß der Informationstransfer zwischen EC und Hippocampus frequenzabhängig gesteuert wird. / The entorhinal cortex (EC) occupies a key position in the limbic system because it functions as a relay station between the hippocampus and cortex. To analyze the properties of the projection cells of the EC we used intracellular recordings from superficial (layers II and III) and deep layers (layers IV-VI). Intracellular electrodes contained the marker biocytin and the labeled neurons were processed for posthoc anatomical identification. We can classify medial EC layer III cells into four different types. Type 1 and 2 cells were projection cells. These cells exhibited a low threshold of action potential generation upon synaptic stimulation. We identified the two other, presumed local circuit type 3 and type 4 cells, whose axons remained within the EC. In deep EC layers we described bipolar and multipolar neurons which form projections from the deep layers of the EC to the dentate gyrus (DG). Despite the morphological similarity of these cells to those of GABAergic interneurons in the EC, their electrophysiological characteristics were similar to those of principal neurons. We conclude that neurons of the deep layers of the EC that project to the DG may function both as local circuit and projection neurons thereby providing a rapid transfer of information from deep layers of the EC to the DG and superficial layers of the EC. We next studied how the separate pathways from layers II and III of the EC to the hippocampus are preferentially effective as a function of stimulation frequency. High frequency (>10 Hz) synaptic activation of the EC was more effective at eliciting action potentials from layer II EC neurons. In contrast, during low frequency (

In dieser Arbeit werden Techniken beschrieben, die es erlauben (höhere) Ableitungen und Taylorapproximationen solcher Computerprogramme effizient zu berechnen. Auch inbesondere dann, wenn die Programme Algorithmen der numerischen linearen Algebra (NLA) enthalten. Im Gegensatz zur traditionellen algorithmischen Differentiation (AD), bei der die zugrunde liegenden Algorithmen um zusätzliche Befehlere erweitert werden, sind in dieser Arbeit die Zerlegungen durch definierende Gleichungen charakterisiert. Basierend auf den definierenden Gleichungen werden Strukturausnutzende Algorithmen hergeleitet. Genauer, neuartige Algorithmen für die Propagation von Taylorpolynomen durch die QR, Cholesky und reell-symmetrischen Eigenwertzerlegung werden präsentiert. Desweiteren werden Algorithmen für den Rückwärtsmodus der AD hergeleitet, welche im Wesentlichen nur die Faktoren der Zerlegungen benötigen. Im Vergleich zum traditionellen Ansatz, bei dem alle Zwischenergebnisse gespeichert werden, ist dies eine Reduktion von O(N^3) zu O(N^2) für Algorithmen mit O(N^3) Komplexität. N ist hier die Größe der Matrix. Zusätzlich kann bestehende, hoch-optimierte Software verwendet werden. Ein Laufzeitvergleich zeigt, dass dies im Vergleich zum traditionellen Ansatz zu einer Beschleunigung in der Größenordnung 100 führen kann. Da die NLA Funktionen als Black Box betrachtet werden, ist desweiteren auch der Berechnungsgraph um Größenordnungen kleiner. Dies bedeutet, dass Software, welche Operator Overloading benutzt, weniger Overhead hervorruft und auch weniger Speicher benötigt. / This thesis provides a framework for the evaluation of first and higher-order derivatives and Taylor series expansions through large computer programs that contain numerical linear algebra (NLA) functions. It is a generalization of traditional algorithmic differentiation (AD) techniques in that NLA functions are regarded as black boxes where the inputs and outputs are related by defining equations. Based on the defining equations, structure-exploiting algorithms are derived. More precisely, novel algorithms for the propagation of Taylor polynomials through the QR, Cholesky,- and real-symmetric eigenvalue decomposition are shown. Recurrences for the reverse mode of AD, which require essentially only the returned factors of the decomposition, are also derived. Compared to the traditional approach where all intermediates of an algorithm are stored, this is a reduction from O(N^3) to O(N^2) for algorithms with O( N^3) complexity. N denotes the matrix size. The derived algorithms make it possible to use existing high-performance implementations. A runtime comparison shows that the treatment of NLA functions as atomic can be more than one order of magnitude faster than an automatic differentiation of the underlying algorithm. Furthermore, the computational graph is orders of magnitudes smaller. This reduces the additional memory requirements, as well as the overhead, of operator overloading techniques to a fraction.

The bifunctional formalism presents an alternative how to obtain the functional value from its functional derivative by exploiting homogeneous density scaling. In the bifunctional formalism the density dependence of the functional derivative is suppressed. Consequently, those derivatives have to be treated as formal functional derivatives. For a pointwise correspondence between the true and the formal functional derivative, the bifunctional expression yields the same value as the density functional. Within the bifunctional formalismthe functional value can directly be obtained fromits derivative (while the functional itself remains unknown). Since functional derivatives are up to a constant uniquely defined, this approach allows for a pointwise comparison between approximate potentials and reference potentials. This aspect is especially important in the field of orbital-free density functional theory, where the burden is to approximate the kinetic energy. Since in the bifunctional approach the potential is approximated directly, full control is given over the latter, and consequently over the final electron densities obtained from variational procedure. Besides the bifunctional formalismitself another concept is introduced, dividing the total non-interacting kinetic energy into a known functional part and a remainder, called Pauli kinetic energy. Only the remainder requires further approximations. For practical purposes sufficiently accurate Pauli potentials for application on atoms, molecular and solid-state systems are presented.

The three dimensional Monte Carlo radiation transport model McArtim is extended to account for the simulation of the propagation of polarized radiation and the inelastic rotational Raman scattering which is the cause of the so called Ring effect. From the achieved and now sufficient precision of the calculated Ring effect new opportunities in optical absorption spectroscopy arise. In the calculation the method of importance sampling (IS) is applied. Thereby one obtains from an ensemble of Monte Carlo photon trajectories an intensity accounting for the elastic aerosol particle-, Cabannes- and the inelastic rotational Raman scattering (RRS) and simultaneously an intensity, for which Rayleigh scattering is treated as an elastic scattering process. By combining both intensities one obtains the so called filling-in (FI, which quantifies the filling-in of Fraunhofer lines) as a measure for the strength of the Ring effect with the same relative precision as the intensities. The validation of the polarized radiometric quantities and the Ring effect is made by comparison with partially published results of other radiation transport models. Furthermore the concept of discretisation of the optical domain into grid cells is extended by making grid cells arbitrarily joining into so called clusters, i.e. grid cell aggregates. Therewith the program is able to calculate derivatives of radiometrically or spectroscopically accessible quantities, namely the intensities at certain locations in the atmospheric radiation field and the light path integrals of trace gas concentrations associated thereto, i.e. the product of the DOAS (differential optical absorption spectroscopy) method, with respect to optical properties of aerosols and gases in connected spatial regions. The first and second order derivatives are validated through so called self-consistency tests. These derivatives allow the inversion of three dimensional tracegas and aerosol concentration profiles and pave the way down to 3D optical scattered light tomography. If such tomographic inversion scheme is based solely on spectral intensitites the available second order derivatives allows the consideration of the curvature in the cost function and therefore allows implementation of efficient optimisation algorithms. The influence of the instrument function on the spectra is analysed in order to mathematically assess the potential of DOAS to a sufficient degree. It turns out that the detailed knowledge of the instrument function is required for an advanced spectral analysis. Concludingly the mathematical separability of narrow band signatures of absorption and the Ring effect from the relatively broad band influence of the elastic scattering processes on the spectra is demonstrated which corresponds exactly to the DOAS principle. In that procedure the differential signal is obtained by approximately 4 orders of magnitude faster then by the separate modelling with and without narrow band structures. Thereby the fusion of the separated steps DOAS spectral analysis and subsequent radiation transport modeling becomes computationally feasible.

The three dimensional Monte Carlo radiation transport model McArtim is extended to account for the simulation of the propagation of polarized radiation and the inelastic rotational Raman scattering which is the cause of the so called Ring effect. From the achieved and now sufficient precision of the calculated Ring effect new opportunities in optical absorption spectroscopy arise. In the calculation the method of importance sampling (IS) is applied. Thereby one obtains from an ensemble of Monte Carlo photon trajectories an intensity accounting for the elastic aerosol particle-, Cabannes- and the inelastic rotational Raman scattering (RRS) and simultaneously an intensity, for which Rayleigh scattering is treated as an elastic scattering process. By combining both intensities one obtains the so called filling-in (FI, which quantifies the filling-in of Fraunhofer lines) as a measure for the strength of the Ring effect with the same relative precision as the intensities. The validation of the polarized radiometric quantities and the Ring effect is made by comparison with partially published results of other radiation transport models. Furthermore the concept of discretisation of the optical domain into grid cells is extended by making grid cells arbitrarily joining into so called clusters, i.e. grid cell aggregates. Therewith the program is able to calculate derivatives of radiometrically or spectroscopically accessible quantities, namely the intensities at certain locations in the atmospheric radiation field and the light path integrals of trace gas concentrations associated thereto, i.e. the product of the DOAS (differential optical absorption spectroscopy) method, with respect to optical properties of aerosols and gases in connected spatial regions. The first and second order derivatives are validated through so called self-consistency tests. These derivatives allow the inversion of three dimensional tracegas and aerosol concentration profiles and pave the way down to 3D optical scattered light tomography. If such tomographic inversion scheme is based solely on spectral intensitites the available second order derivatives allows the consideration of the curvature in the cost function and therefore allows implementation of efficient optimisation algorithms. The influence of the instrument function on the spectra is analysed in order to mathematically assess the potential of DOAS to a sufficient degree. It turns out that the detailed knowledge of the instrument function is required for an advanced spectral analysis. Concludingly the mathematical separability of narrow band signatures of absorption and the Ring effect from the relatively broad band influence of the elastic scattering processes on the spectra is demonstrated which corresponds exactly to the DOAS principle. In that procedure the differential signal is obtained by approximately 4 orders of magnitude faster then by the separate modelling with and without narrow band structures. Thereby the fusion of the separated steps DOAS spectral analysis and subsequent radiation transport modeling becomes computationally feasible.:1.1. Radiation Transport Modeling and Atmospheric State Inversion 1.2. Vector RTE Solution Methods 1.3. Scope of the Thesis 1.4. Outline of the Thesis 2.1. General Structure 2.1.1. Chemical Composition of the Gas Phase 2.1.2. The Troposphere, Temperature and Pressure Vertical Structure 2.1.3. The Stratosphere 2.2. Aerosols and Clouds 2.2.1. Classification and Morphology 2.2.2. Water Related Particle Growth and Shrinking Processes 2.2.3. Size Spectra and Modes 3.1. Electromagnetic Waves 3.1.1. Maxwell\''s Equations 3.1.2. Measurement of Electromagnetic Waves 3.1.3. Polarization State of EM Waves 3.1.4. Stokes Vectors 3.2. Scattering and Absorption of EM Waves by Molecules and Particles 3.2.1. General Description of Scattering and Coordinate Systems 3.2.2. Molecular Scattering 3.2.3. Molecular Absorption Processes and Electronic Molecular States 3.2.4. Scattering On Spherical Particles - Mie Theory 3.3. Mathematical Description of Radiation Transport 3.3.1. Radiance and Irradiance 3.3.2. Absorption, Scattering and Extinction Coefficients 3.3.3. Optical Thickness and Transmission 3.3.4. Scattering 3.3.5. Incident (Ir)Radiance 3.3.6. The Black Surface Single Scattering Approximation 3.3.7. Radiative Transfer Equations 4.1. General Monte Carlo Methods 4.1.1. Numerical Integration 4.1.2. Importance Sampling and Zero Variance Estimates 4.1.3. Optimal Sampling 4.1.4. Sampling from Arbitrary Distributions 4.2. Path Generation or Collision Density Estimation 4.2.1. Discretization of the Optical Domain into Cells and Clusters 4.2.2. RTE Integral Form 4.2.3. Formal Solution of the IRTE 4.2.4. Overview on Monte Carlo RTE Solution Algorithms 4.2.5. Crude Monte Carlo 4.2.6. Sequential Importance Sampling (SIS) or Path Generation 4.3. Importance Sampling in Monte Carlo SIS Radiative Transfer 4.3.1. Weights for Alternate Kernels 4.3.2. Weights in the Calculation of RTE Functional Estimates 4.3.3. Application of IS to Mie Phase Functions Scatter Angle Sampling 5.1. Radiances, Intensities and the Reciprocity Theorem 5.1.1. Scalar Radiance Estimates 5.1.2. Backward Monte Carlo Scalar Radiance 5.1.3. Vector Radiances 5.2. Radiance Derivatives 5.2.1. Variables for Radiance Derivatives 5.3. Validation of Functionals 5.3.1. Validation of Vector Radiances 5.3.2. Validation of Radiance Derivatives 6.1. A Simply Structured Instrument Forward Model 6.2. Pure Atmospheric Spectra and Absorption 6.2.1. Direct Light Spectra 6.2.2. Scattered Sun Light Spectra 6.3. (D)OAS from the Perspective of Radiative Transfer Modeling 6.3.1. (Rest) Signatures of Weakly Absorbing Gases 6.3.2. Spectroscopic Measurements and Standard DOAS 6.4. DOAS Analysis Summary 6.4.1. DSCD Retrieval 6.4.2. Inversion 7.1. RRS-Modified RTE 7.1.1. RRS Cross Sections for Scattering out and into a Wavelength 7.1.2. Modification of the RTE Loss and Source Terms 7.2. Intensity Estimates Considering Rotational Raman Scattering 7.2.1. RRS in the Path Sampling Procedure 7.2.2. Adjoint RRS Correction Weights 7.2.3. Local Estimates of Intensities with RRS 7.2.4. Intensity Estimates 7.3. Ring Spectra 7.3.1. Elastic Biasing of the Local Estimates 7.3.2. Cumulative Weights and Local Estimates 7.3.3. Test of the Elastic Biasing 7.4. Validation 7.4.1. Comparison to an Analytic Single Scattering Code 7.4.2. Single Scattering Model Including Rotational Raman Scattering 7.4.3. Multiple Scattering Model Comparison 7.4.4. Comparison with A Measurement 7.4.5. Validation of Approximate Methods For Ring Effect Modeling 7.5. Summary and Discussion 8.1. Status and Summary 8.1.1. Ring-Effect and Absorption Corrected Radiances 8.1.2. Derivatives of Radiometric Quantities Accessible Through Spectroscopy 8.1.3. Polarization 8.1.4. Time Integrated Sensitivities for 3D UV/vis/NIR Remote Sensing 8.2. Outlook A.1. Zero Variance Estimates A.2. Free Path Length Sampling in a Homogeneous Medium A.3. Cumulative Differential Scatter Cross Sections A.3.1. Cardanic formulas A.3.2. Rayleigh and Raman Phase Functions A.3.3. Henyey-Greenstein Model A.3.4. Legendre Polynomial Phase Function Model A.3.5. Table Methods A.4. Greens Function in the Derivation of the IRTE A.5. Source Code For Stokes Vector Transformation Plot B.1. 1st Order Derivatives B.2. 2nd Order Derivatives B.3. Hessian of Integrals Depending on Many Variables C.1. Slit Function f Derivatives C.2. Signal Sn Derivatives C.3. Chi Square Spline Fitting C.3.1. Constrained Non-Linear Least Square Problem C.3.2. Spline Fitting C.3.3. Jacobians and Hessian

In der vorliegenden Arbeit wird die Entwicklung eines effizienten Verfahrens zur parametrischen Finite Elemente Simulation von Mikrosystemen und zum Export dieser Modelle in Elektronik- und Systemsimulationswerkzeuge vorgestellt. Parametrische FE-Modelle beschreiben den Einfluss von geometrischen Abmessungen, Schwankungen von Materialeigenschaften und veränderten Umgebungsbedingungen auf das Funktionsverhalten von Sensoren und Aktuatoren. Parametrische FE-Modelle werden für die Auswahl geeigneter Formelemente und deren Dimensionierung während des Entwurfsprozesses in der Mikrosystemtechnik benötigt. Weiterhin ermöglichen parametrische Modelle Sensitivitätsanalysen zur Bewertung des Einflusses von Toleranzen und Prozessschwankungen auf die Qualität von Fertigungsprozessen. In Gegensatz zu üblichen Sample- und Fitverfahren wird in dieser Arbeit eine Methode entwickelt, welche die Taylorkoeffizienten höherer Ordnung zur Beschreibung des Einflusses von Designparametern direkt aus der Finite-Elemente- Formulierung, durch Ableitungen der Systemmatrizen, ermittelt. Durch Ordnungsreduktionsverfahren werden die parametrischen FE-Modelle in verschiedene Beschreibungssprachen für einen nachfolgenden Elektronik- und Schaltungsentwurf überführt. Dadurch wird es möglich, neben dem Sensor- und Aktuatorentwurf auch das Zusammenwirken von Mikrosystemen mit elektronischen Schaltungen in einer einheitlichen Simulationsumgebung zu analysieren und zu optimieren. / The thesis deals with advanced parametric modeling technologies based on differentiation of the finite element equations which account for parameter variations in a single FE run. The key idea of the new approach is to compute not only the governing system matrices of the FE problem but also high order partial derivatives with regard to design parameters by means of automatic differentiation. As result, Taylor vectors of the system’s response can be expanded in the vicinity of the initial position capturing dimensions and physical parameter. A novel approaches for the parametric MEMS simulation have been investigated for mechanical, electrostatic and fluidic domains in order to improve the computational efficiency. Objective of reduced order modeling is to construct a simplified model which approximates the original system with reasonable accuracy for system level design of MEMS. The modal superposition technique is most suitable for system with flexible mechanical components because the deformation state of any flexible system can be accurately described by a linear combination of its lowest eigenvectors. The developed simulation approach using parametric FE analyses to extract basis functions have been applied for parametric reduced order modeling. The successful implementation of a derivatives based technique for parameterization of macromodel by the example of microbeam and for exporting this macromodel into MATLAB/Similink to simulate dynamical behavior has been reported.

No description available.

In der vorliegenden Arbeit wird die Entwicklung eines effizienten Verfahrens zur parametrischen Finite Elemente Simulation von Mikrosystemen und zum Export dieser Modelle in Elektronik- und Systemsimulationswerkzeuge vorgestellt. Parametrische FE-Modelle beschreiben den Einfluss von geometrischen Abmessungen, Schwankungen von Materialeigenschaften und veränderten Umgebungsbedingungen auf das Funktionsverhalten von Sensoren und Aktuatoren. Parametrische FE-Modelle werden für die Auswahl geeigneter Formelemente und deren Dimensionierung während des Entwurfsprozesses in der Mikrosystemtechnik benötigt. Weiterhin ermöglichen parametrische Modelle Sensitivitätsanalysen zur Bewertung des Einflusses von Toleranzen und Prozessschwankungen auf die Qualität von Fertigungsprozessen. In Gegensatz zu üblichen Sample- und Fitverfahren wird in dieser Arbeit eine Methode entwickelt, welche die Taylorkoeffizienten höherer Ordnung zur Beschreibung des Einflusses von Designparametern direkt aus der Finite-Elemente- Formulierung, durch Ableitungen der Systemmatrizen, ermittelt. Durch Ordnungsreduktionsverfahren werden die parametrischen FE-Modelle in verschiedene Beschreibungssprachen für einen nachfolgenden Elektronik- und Schaltungsentwurf überführt. Dadurch wird es möglich, neben dem Sensor- und Aktuatorentwurf auch das Zusammenwirken von Mikrosystemen mit elektronischen Schaltungen in einer einheitlichen Simulationsumgebung zu analysieren und zu optimieren. / The thesis deals with advanced parametric modeling technologies based on differentiation of the finite element equations which account for parameter variations in a single FE run. The key idea of the new approach is to compute not only the governing system matrices of the FE problem but also high order partial derivatives with regard to design parameters by means of automatic differentiation. As result, Taylor vectors of the system’s response can be expanded in the vicinity of the initial position capturing dimensions and physical parameter. A novel approaches for the parametric MEMS simulation have been investigated for mechanical, electrostatic and fluidic domains in order to improve the computational efficiency. Objective of reduced order modeling is to construct a simplified model which approximates the original system with reasonable accuracy for system level design of MEMS. The modal superposition technique is most suitable for system with flexible mechanical components because the deformation state of any flexible system can be accurately described by a linear combination of its lowest eigenvectors. The developed simulation approach using parametric FE analyses to extract basis functions have been applied for parametric reduced order modeling. The successful implementation of a derivatives based technique for parameterization of macromodel by the example of microbeam and for exporting this macromodel into MATLAB/Similink to simulate dynamical behavior has been reported.

No description available.