During neuronal development, the axonal and dendritic projections are polarized and oriented along specific body axis. To further explore the molecular basis of neuritogenesis in vivo, we used the nematode Caenorhabditis elegans as a developmental model and performed a forward genetic screen to identify genes that specify the polarity of neurite outgrowth. We examined the VC4 and VC5 neurons, members of the six VC motor neurons using the Pcat-1

In this thesis we present a method for detecting planar targets in real-time on power-constrained, or low-powered, hand-held devices such as mobile phones. We adopt the feature recognition (also referred to as feature matching) approach and employ fast-to-compute local feature descriptors to establish point correspondences. To obtain a satisfactory localization accuracy, most local feature descriptors seek a transformation of the input intensity patch that is invariant to various geometric and photometric deformations. Generally, such transformations are computationally intensive, hence are not ideal for real-time applications on limited hardware platforms. On the other hand, descriptors which are fast to compute are typically limited in their ability to provide invariance to a vast range of deformations. To address these shortcomings, we have developed a learning-based approach which can be applied to any local feature descriptor to increase the system’s robustness to both affine and perspective deformations. The motivation behind applying a learning-based approach is to transfer as much of the computational burden (as possible) onto an offline training phase, allowing a reduction in cost during online matching. The approach comprises of identifying keypoints which remain stable under artificially induced perspective transformations, extracting the corresponding feature vectors, and finally aggregating the feature vectors of coincident keypoints to obtain the final descriptors. We strictly focus on objects which are planar, thus allowing us to synthesize images of the object in order to capture the appearance of keypoint patches under several perspectives.

Cette thèse s'inscrit dans la théorie des cartes planaires aléatoires, active depuis une quizaine d'années, et plus précisément dans l'étude de modèles de nature hyperbolique.Dans un premier temps, nous nous intéressons à un modèle de triangulations aléatoires dynamiques basé sur les flips d'arêtes, et nous montrons une borne inférieure sur le temps de mélange de ce modèle.Dans la suite, l'objet d'étude principal est une famille de triangulations aléatoires hyperboliques, appelées PSHT. Il s'agit de variantes de la triangulation uniforme du plan (UIPT), qui ont été introduites en 2014 par Nicolas Curien. Nous commençons par établir un résultat de limite d'échelle quasi-critique : si on renormalise les distances tout en faisant tendre le paramètre d'hyperbolicité vers sa valeur critique, les triangulations étudiées convergent vers un espace métrique aléatoire appelé plan brownien hyperbolique. Nous étudions également des propriétés métriques fines des PSHT et du plan brownien hyperbolique, et notamment la structure de leurs géodésiques infinies. Nous présentons aussi de nouvelles propriétés de la frontière de Poisson des PSHT.Enfin, nous nous intéressons à un autre modèle naturel de cartes aléatoires hyperboliques : les cartes causales surcritiques, qui sont construites à partir d'arbres de Galton--Watson surcritiques, en ajoutant des arêtes entre sommets de même hauteur. Nous établissons des résultats d'hyperbolicité métrique, ainsi que des propriétés de la marche aléatoire sur ces cartes, dont un résultat de vitesse positive. Certaines des propriétés obtenues sont robustes, et peuvent se généraliser à n'importe quelle carte planaire contenant un arbre de Galton--Watson surcritique. / This thesis falls into the theory of random planar maps, which has been active in the last fifteen years, and more precisely into the study of hyperbolic models.We are first interested in a model of dynamical random triangulations based on edge-flips, where we prove a lower bound on the mixing time.In the rest of this thesis, the main objects that we study are the random hyperbolic triangulations called PSHT. These are hyperbolic variants of the Uniform Infinite Planar Triangulation (UIPT), and were introduced by Nicolas Curien in 2014. We first establish a near-critical scaling limit result: if we let the hyperbolicity parameter go to its critical value at the same time as the distances are renormalized, the PSHT converge to a random metric space that we call the hyperbolic Brownian plane. We also study precise metric properties of the PSHT and of the hyperbolic Brownian plane, such as the structure of their infinite geodesics. We obtain as well new properties of the Poisson boundary of the PSHT.Finally, we are interested in another natural model of hyperbolic random maps: supercritical causal maps, which are obtained from supercritical Galton--Watson trees by adding edges between vertices at the same height. We establish metric hyperbolicity results about these maps, as well as properties of the simple random walk (including a positive speed result). Some of the properties we obtain are robust, and may be generalized to any planar map containing a supercritical Galton--Watson tree.

The aim of this thesis is to acquaint with the various types of the planar transmission lines and discuss their properties. Subsequently, the development of the real models of selected lines and verification their properties by simulations using COMSOL Multiphysics. The second part deals with the modeling of the semiconductor substrate, which replacing the dielectric substrate used for the transmission lines in the first part. The final part deals with the verification of calculation results in a specialized program TiberCAD.

This master's thesis deals with a design of a planar parabolic reflector antenna. The thesis is divided into several parts. The first section is dedicated to the theory of the parabolic antenna design and a basic introduction of the SIW technology which is used for the realization of an antenna prototype. The second chapter deals with the design of individual parts of the antenna (i. e. a primary and secondary reflector and an antenna feeder excited by a waveguide) for particular assignment. The third part is focused on modeling the designed antenna using ANSYS HFSS. Other parts of the thesis include a conversion of the proposed antenna to the SIW technology and a design of a transition between the antenna and a feeding waveguide WR15. The last part of the thesis deals with measuring of the reflection coefficient and the radiation pattern of the fabricated antenna prototype.

A theoretical investigation of one-dimensional planar photonic crystal waveguides is carried out. These waveguides consist of a dielectric layer sandwiched between two semiinfinite periodic dielectric structures. Using a novel approach, exact analytical solutions for guided modes in such waveguides are presented. The se rigorous solutions allow one to distinguish clearly between the index-guiding regime and guidance due to the photonic crystal effect. In the first part of this investigation, a rigorous analysis of the reflection of uniform plane waves from a semi- infinite periodic dielectric structure is undertaken. Both parallel and perpendicular polarizations for the incident plane wave are considered. Exact expressions for the reflection coefficients corresponding to two polarization cases are obtained using an impedance approach. The results for the reflection coefficient are then used to study propagation properties of guided modes in one-dimensional photonic crystal waveguides with semiinfinite periodic cladding regions. Characteristic equations, from which propagation constants of guided modes can be obtained, and solutions for electromagnetic fields of these modes are derived. Solutions for both TE (transverse electric) and TM (transverse magnetic) modes are presented. Numerical results for the propagation constant and field distributions of several lower-order modes are presented. The solutions unique to photonic crystal waveguides are emphasized. / Master of Science

Dieses Manuskript entstand aus Vorlesungen über Geodätische Berechnungen an der Hochschule für Technik und Wirtschaft Dresden. Da diese Lehrveranstaltung im ersten oder zweiten Semester stattfindet, werden noch keine Methoden der höheren Mathematik benutzt. Das Themenspektrum beschränkt sich deshalb weitgehend auf elementare Berechnungen in der Ebene.:0 Vorwort 1 Ebene Trigonometrie 1.1 Winkelfunktionen 1.2 Berechnung schiefwinkliger ebener Dreiecke 1.3 Berechnung schiefwinkliger ebener Vierecke 2 Ebene Koordinatenrechnung 2.1 Kartesische und Polarkoordinaten 2.2 Erste Geodätische Grundaufgabe 2.3 Zweite Geodätische Grundaufgabe 3 Flächenberechnung und Flächenteilung 3.1 Flächenberechnung aus Maßzahlen. 3.2 Flächenberechnung aus Koordinaten 3.3 Absteckung und Teilung gegebener Dreiecksflächen 3.4 Absteckung und Teilung gegebener Vierecksflächen 4 Kreis und Ellipse 4.1 Kreisbogen und Kreissegment 4.2 Näherungsformeln für flache Kreisbögen 4.3 Sehnen-Tangenten-Verfahren 4.4 Grundlegendes über Ellipsen 4.5 Abplattung und Exzentrizitäten 4.6 Die Meridianellipse der Erde 4.7 Flächeninhalt und Bogenlängen 5 Ebene Einschneideverfahren 5.1 Bogenschnitt 5.2 Vorwärtsschnitt 5.3 Anwendung: Geradenschnitt 5.4 Anwendung: Kreis durch drei Punkte 5.5 Schnitt Gerade ⎼ Kreis oder Strahl ⎼ Kreis 5.6 Rückwärtsschnitt 5.7 Anwendung: Rechteck durch fünf Punkte 6 Ebene Koordinatentransformationen 6.1 Elementare Transformationsschritte 6.2 Rotation und Translation. 6.3 Rotation, Skalierung und Translation 6.4 Ähnlichkeitstransformation mit zwei identischen Punkten 6.5 Anwendung: Hansensche Aufgabe 6.6 Anwendung: Kleinpunktberechnung 6.7 Anwendung: Rechteck durch fünf Punkte 6.8 Ebene Helmert-Transformation 6.9 Bestimmung der Parameter bei Rotation und Translation 6.10 Ebene Affintransformation 7 Lösungen / This manuscript evolved from lectures on Geodetic Computations at the University of Applied Sciences Dresden (Germany). Since this lecture is given in the first or second semester, no advanced mathematical methods are used. The range of topics is limited to elementary computations in the plane.:0 Vorwort 1 Ebene Trigonometrie 1.1 Winkelfunktionen 1.2 Berechnung schiefwinkliger ebener Dreiecke 1.3 Berechnung schiefwinkliger ebener Vierecke 2 Ebene Koordinatenrechnung 2.1 Kartesische und Polarkoordinaten 2.2 Erste Geodätische Grundaufgabe 2.3 Zweite Geodätische Grundaufgabe 3 Flächenberechnung und Flächenteilung 3.1 Flächenberechnung aus Maßzahlen. 3.2 Flächenberechnung aus Koordinaten 3.3 Absteckung und Teilung gegebener Dreiecksflächen 3.4 Absteckung und Teilung gegebener Vierecksflächen 4 Kreis und Ellipse 4.1 Kreisbogen und Kreissegment 4.2 Näherungsformeln für flache Kreisbögen 4.3 Sehnen-Tangenten-Verfahren 4.4 Grundlegendes über Ellipsen 4.5 Abplattung und Exzentrizitäten 4.6 Die Meridianellipse der Erde 4.7 Flächeninhalt und Bogenlängen 5 Ebene Einschneideverfahren 5.1 Bogenschnitt 5.2 Vorwärtsschnitt 5.3 Anwendung: Geradenschnitt 5.4 Anwendung: Kreis durch drei Punkte 5.5 Schnitt Gerade ⎼ Kreis oder Strahl ⎼ Kreis 5.6 Rückwärtsschnitt 5.7 Anwendung: Rechteck durch fünf Punkte 6 Ebene Koordinatentransformationen 6.1 Elementare Transformationsschritte 6.2 Rotation und Translation. 6.3 Rotation, Skalierung und Translation 6.4 Ähnlichkeitstransformation mit zwei identischen Punkten 6.5 Anwendung: Hansensche Aufgabe 6.6 Anwendung: Kleinpunktberechnung 6.7 Anwendung: Rechteck durch fünf Punkte 6.8 Ebene Helmert-Transformation 6.9 Bestimmung der Parameter bei Rotation und Translation 6.10 Ebene Affintransformation 7 Lösungen

This thesis introduces exact (ILP- and SAT/PBS-based) algorithms for the Minimum Genus Problem and the Maximum Planar Subgraph Problem. It also considers general limits of approximation algorithms for the Maximum Planar Subgraph Problem.

Particle image velocimetry (PIV) is used to make volume-flow-rate measurements at the exit of a turbulent, planar nozzle. The objective of this report is to assess a range of data acquisition and processing parameters. Data is acquired for volume flow rates of Reynolds numbers between 10,000 and 100,000 for both two-component (2C) and stereo PIV. The parameters are systematically changed one at a time and evaluated using differences in uncertainty, calculation time, and volume- flow-rate deviation. Data acquisition parameters follow the trends of previous work. A multitude of processing parameters were varied for several PIV processing methods. Recommendations for each method are developed and listed with potential drawbacks. 2C PIV was found to underestimate volume-flow-rate by 3-4% depending on the integration scheme and stereo PIV underestimated volume-flow-rate by 2%.

A new laser based flow interrogation system, capable of simultaneous measurement of planar three-component velocity data, was constructed and tested. The Virginia Tech Doppler Global Velocimeter (DGV) system was designed for use in the Virginia Tech Stability Wind Tunnel as a tool for investigating complex three-dimensional separated flow regions. The systems was designed for robustness, ease of use, and for acquisition of low uncertainty velocity data. A series of tests in the Stability Tunnel were conducted to determine the how well the new DGV system met these goals. Extensive calibration tests proved the system is capable of measuring the frequency shifts of scattered laser light, and therefore velocity. However, equipment failures and inadequate flow seed density prevented accurate velocity measurements in the separated wake region behind a 6:1 prolate spheroid. Detailed uncertainty analysis techniques demonstrated that, under the proper conditions, the system is capable of making velocity measurements with approximately +/- 2m/s uncertainty. / Master of Science