Effective visualization of graphs is a powerful tool to help understand the relationships among the graph's underlying objects and to interact with them. Several styles for drawing graphs have emerged over the last three decades. Polyline drawing is a widely used style for drawing graphs, where each node is mapped to a distinct point in the plane and each edge is mapped to a polygonal chain between their corresponding nodes. Some common optimization criteria for such a drawing are defined in terms of area requirement, number of bends per edge, angular resolution, number of distinct line segments, edge crossings, and number of planar layers. In this thesis we develop algorithms for drawing graphs that optimize different aesthetic qualities of the drawing. Our algorithms seek to simultaneously optimize multiple drawing aesthetics, reveal potential trade-offs among them, and improve many previous graph drawing algorithms. We start by exploring probable trade-offs in the context of planar graphs. We prove that every $n$-vertex planar triangulation $G$ with maximum degree $\Delta$ can be drawn with at most $2n+t-3$ segments and $O(8^t \cdot \Delta^{2t})$ area, where $t$ is the number of leaves in a Schnyder tree of $G$. We then show that one can improve the area by allowing the edges to have bends. Since compact drawings often suffer from bad angular resolution, we seek to compute polyline drawings with better angular resolution. We develop a polyline drawing algorithm that is simple and intuitive, yet implies significant improvement over known results. At this point we move our attention to drawing nonplanar graphs. We prove that every thickness-$t$ graph can be drawn on $t$ planar layers with $\min\{O(2^{t/2} \cdot n^{1-1/\beta}), 2.25n +O(1)\}$ bends per edge, where $\beta = 2^{\lceil (t-2)/2 \rceil }$. Previously, the bend complexity, i.e., the number of bends per edge, was not known to be sublinear for $t>2$. We then examine the case when the number of available layers is restricted. The layers may now contain edge crossings. We develop a technique to draw complete graphs on two layers, which improves previous upper bounds on the number of edge crossings in such drawings. / October 2016

Planar cell polarity (PCP) is a developmental signaling mechanism that establishes a polarity within the plane of an epithelium. PCP has been shown to play a role in guiding numerous neurodevelopmental processes such as convergent extension, neuron migration, and axon pathfinding. Certain commissural neurons in the dorsal spinal cord make a series of guidance decisions en route to the brain: first, a ventral projection along the D-V axis, followed by a midline crossing, and after exiting the floorplate, a dorso-anterior turn along the A-P axis. Here, we provide in vivo evidence that the axons of the Commissural Primary Ascending (CoPAs) neurons in zebrafish require the PCP genes fzd3a, vangl2, and scribble for rostral pathfinding both before and after crossing the midline. Dorsoventral guidance of CoPA axons is unaltered in fzd3a, vangl2, and scribble mutants, suggesting that the PCP signaling pathway only controls A-P guidance of CoPAs. Our results have provided evidence for two potential non- mutually exclusive models: (i) A-P axon guidance is achieved by cell-autonomous Wnt-Frizzled signaling or that (ii) A-P axon guidance is achieved by non-cell-autonomous PCP signaling in the neuroepithelial environment. The single-cell nature of the CoPA axon system allows for simple genetic manipulation and visualization, which will potentially elucidate the validity of either model. Scribble (Scrib), a member of the LAP family, plays a critical role in establishing and regulating cell polarization in epithelia and during cell migration. In zebrafish, Scrib mutants have defects in convergent extension (CE) cell movements and facial branchiomotor neuron (FBMN) migration. Despite our understanding of Scrib’s genetic role in neurodevelopment, little is known about the subcellular localization of endogenous Scrib in vivo during CE and FBMN migration. We have generated a monoclonal antibody against the C-terminus of zebrafish Scrib and have shown that this antibody is specific against endogenous Scrib in both western blot and immunocytochemical applications. Confocal microscopy of Scrib immunocytochemistry shows that at various developmental stages, Scrib distinctly localizes to basolateral membranes of non polarized epithelium, to the membrane in mesodermal cells undergoing CE, and to the membrane of migrating FBMNs. Furthermore, the distribution of Scrib puncta along membranes of FBMN- FBMN contact is significantly altered in the PCP mutant pk1b. Further application of our newly generated Scrib antibody will potentially lead to new insight on Scrib’s role in neurodevelopment.

The famous Four Color Theorem states that any planar graph can be properly colored using at most four colors. However, if we want to properly color the square of a planar graph (or alternatively, color the graph using distinct colors on vertices at distance up to two from each other), we will always require at least \Delta + 1 colors, where \Delta is the maximum degree in the graph. For all \Delta, Wegner constructed planar graphs (even without 3-cycles) that require about \frac{3}{2} \Delta colors for such a coloring. To prove a stronger upper bound, we consider only planar graphs that contain no 4-cycles and no 5-cycles (but which may contain 3-cycles). Zhu, Lu, Wang, and Chen showed that for a graph G in this class with \Delta \ge 9, we can color G^2 using no more than \Delta + 5 colors. In this thesis we improve this result, showing that for a planar graph G with maximum degree \Delta \ge 32 having no 4-cycles and no 5-cycles, at most \Delta + 3 colors are needed to properly color G^2. Our approach uses the discharging method, and the result extends to list-coloring and other related coloring concepts as well.

In zebrafish, CoPA (Commissural Primary Ascending) is the first among ascending commissural axons to pathfind anteriorly and form the spinal commissure. One pathway that guides their anterior growth is the planar cell polarity (PCP) signaling pathway, but it is not fully known how PCP signaling regulates anterior guidance. We examined CoPA pathfinding in various PCP mutants to determine if anterior-posterior (A-P) guidance of CoPAs is dependent on PCP signaling. We found that certain PCP mutants exhibited anterior pathfinding defects, with approximately half of all affected CoPAs migrating incorrectly posteriorly. By using a translation-blocking DCC (Deleted in Colorectal Cancer) morpholino to prevent CoPA midline crossing, we discovered that CoPA axons in Fzd3a and Scribble mutants show severe defects in A-P guidance, which suggest that PCP influences A-P guidance of CoPAs prior to and after midline crossing.

The effect of inorganic electrolytes on the determination of relative permittivity and concentration of water solutions of 1,4 dioxane was studied in this work. The method used was dielectrimetry, and NaCl, KCl, CsCl and LiCl at various concentrations were tested electrolytes. The interfering effect of these electrolytes was found for concentrations above 0.05 mmol l-1. It was also found that the interfering factor is purely the solution conductivity independent on the ion kind. The measurements were carried out with both the planar and the tubular detection cell having the electrodes insulated from the solution. The cell was connected to the differentiator (the voltage is the analytical signal) or multivibrator (the frequency is the analytical signal). A good agreement between experimental results and the modeled calculation for the detector with differentiator was also obtained.

Increasing the power density of power electronic converters while reducing or maintaining the same cost, offers a higher potential to meet the current trend inrelation to various power electronic applications. High power density converters can be achieved by increasing the switching frequency, due to which the bulkiest parts, such as transformer, inductors and the capacitor's size in the convertercircuit can be drastically reduced. In this regard, highly integrated planar magnetics are considered as an effective approach compared to the conventional wire wound transformers in modern switch mode power supplies (SMPS). However, as the operating frequency of the transformers increase from several hundred kHz to MHz, numerous problems arise such as skin and proximity effects due to the induced eddy currents in the windings, leakage inductance and unbalanced magnetic flux distribution. In addition to this, the core losses whichare functional dependent on frequency gets elevated as the operating frequency increases. Therefore, this thesis provides an insight towards the problems related to the high frequency magnetics and proposes a solution with regards to different aspects in relation to designing high power density, energy efficient transformers.The first part of the thesis concentrates on the investigation of high power density and highly energy efficient coreless printed circuit board (PCB) step-down transformers useful for stringent height DC-DC converter applications, where the core losses are being completely eliminated. These transformers also maintain the advantages offered by existing core based transformers such as, high coupling coefficient, sufficient input impedance, high energy efficiency and wide frequencyband width with the assistance of a resonant technique. In this regard, several coreless PCB step down transformers of different turn’s ratio for power transfer applications have been designed and evaluated. The designed multilayered coreless PCB transformers for telecom and PoE applications of 8,15 and 30W show that the volume reduction of approximately 40 - 90% is possible when compared to its existing core based counterparts while maintaining the energy efficiency of the transformers in the range of 90 - 97%. The estimation of EMI emissions from the designed transformers for the given power transfer application proves that the amount of radiated EMI from a multilayered transformer is lessthan that of the two layered transformer because of the decreased radius for thesame amount of inductance.The design guidelines for the multilayered coreless PCB step-down transformer for the given power transfer application has been proposed. The designed transformer of 10mm radius has been characterized up to the power level of 50Wand possesses a record power density of 107W/cm3 with a peak energy efficiency of 96%. In addition to this, the design guidelines of the signal transformer fordriving the high side MOSFET in double ended converter topologies have been proposed. The measured power consumption of the high side gate drive circuitvitogether with the designed signal transformer is 0.37W. Both these signal andpower transformers have been successfully implemented in a resonant converter topology in the switching frequency range of 2.4 – 2.75MHz for the maximum load power of 34.5W resulting in the peak energy efficiency of converter as 86.5%.This thesis also investigates the indirect effect of the dielectric laminate on the magnetic field intensity and current density distribution in the planar power transformers with the assistance of finite element analysis (FEA). The significanceof the high frequency dielectric laminate compared to FR-4 laminate in terms of energy efficiency of planar power transformers in MHz frequency region is also explored.The investigations were also conducted on different winding strategies such as conventional solid winding and the parallel winding strategies, which play an important role in the design and development of a high frequency transformer and suggested a better choice in the case of transformers operating in the MHz frequency region.In the second part of the thesis, a novel planar power transformer with hybrid core structure has been designed and evaluated in the MHz frequency region. The design guidelines of the energy efficient high frequency planar power transformerfor the given power transfer application have been proposed. The designed corebased planar transformer has been characterized up to the power level of 50W and possess a power density of 47W/cm3 with maximum energy efficiency of 97%. This transformer has been evaluated successfully in the resonant converter topology within the switching frequency range of 3 – 4.5MHz. The peak energy efficiency ofthe converter is reported to be 92% and the converter has been tested for the maximum power level of 45W, which is suitable for consumer applications such as laptop adapters. In addition to this, a record power density transformer has been designed with a custom made pot core and has been characterized in thefrequency range of 1 - 10MHz. The power density of this custom core transformer operating at 6.78MHz frequency is 67W/cm3 and with the peak energy efficiency of 98%.In conclusion, the research in this dissertation proposed a solution for obtaining high power density converters by designing the highly integrated, high frequency(1 - 10MHz) coreless and core based planar magnetics with energy efficiencies inthe range of 92 - 97%. This solution together with the latest semiconductor GaN/SiC switching devices provides an excellent choice to meet the requirements of the next generation ultra flat low profile switch mode power supplies (SMPS).

The newly discovered iron based superconductors have captivated the attention of the scientific community due to the unusual mechanism behind their superconductivity and their promise as the next generation high temperature superconductors. After a century of superconductor research, the physical mechanism behind high temperature superconductivity is still not understood. These new materials bring renewed hope in elucidating the pairing mechanism responsible with high temperature superconductors and achieving the ultimate goal of the field, room temperature superconductivity. Consequently, a deeper understanding of the intriguing properties of iron based materials is essential. A great deal about the pairing mechanism of Cooper electron pairs can be inferred from the symmetry of their pairing wave function or order parameter. One of the most involved probes for studying the pairing symmetry is the London penetration depth. The low temperature behavior of London penetration depth in superconductors is directly related to the density of states and provides a powerful tool for investigating low-lying quasiparticle energy and, for this very reason, can give valuable hints on superconducting gap symmetry. The work presented focuses on investigating the pairing symmetry in the Fe1+y(Te1−xSex) system using a radio-frequency tunnel diode oscillator (TDO) technique for precise measurements of the temperature dependence of their in-plane penetration depth. The TDO technique, based on an original concept involving the use of planar inductors in an novel configuration, was implemented on a dilution refrigerator to investigate a significant number of single crystal samples, with nominal Se concentrations of 36%, 40%, 43% and 45% respectively, down to temperatures as low as 50 mK. A systematic study together with a comprehensive analysis regarding the order parameter symmetry in the Fe1+y(Te1−xSex) system is presented. In many cases we found that London penetration depth shows an upturn below at low temperatures, indicative of a paramagnetic-type contribution. Also the low-temperature behavior of penetration depth is best described by a quadratic power law with no systematic dependence on the Se concentration. Most importantly, in the limit of T → 0, in some samples we observed a narrow region of linear temperature dependence, suggestive of nodes in the superconducting gap of Fe1+y(Te1−xSex).

Bobbin lace is a 500-year-old art form in which threads are braided together in an alternating manner to produce a lace fabric. A key component in its construction is a small pattern, called a bobbin lace ground, that can be repeated periodically to fill a region of any size. In this thesis we present a mathematical model for bobbin lace grounds representing the structure as the pair (Δ(G), ζ (v)) where Δ(G) is a topological embedding of a 2-regular digraph, G, on a torus and ζ(v) is a mapping from the vertices of G to a set of braid words. We explore in depth the properties that Δ(G) must possess in order to produce workable lace patterns. Having developed a solid, logical foundation for bobbin lace grounds, we enumerate and exhaustively generate patterns that conform to that model. We start by specifying an equivalence relation and define what makes a pattern prime so that we can identify unique representatives. We then prove that there are an infinite number of prime workable patterns. One of the key properties identified in the model is that it must be possible to partition Δ(G) into a set of osculating circuits such that each circuit has a wrapping index of (1,0); that is, the circuit wraps once around the meridian of the torus and does not wrap around the longitude. We use this property to exhaustively generate workable patterns for increasing numbers of vertices in G by gluing together lattice paths in an osculating manner. Using a backtracking algorithm to process the lattice paths, we identify over 5 million distinct prime patterns. This is well in excess of the roughly 1,000 found in lace ground catalogues. The lattice paths used in our approach are members of a family of partially directed lattice paths that have not been previously reported. We explore these paths in detail, develop a recurrence relation and generating function for their enumeration and present a bijection between these paths and a subset of Motzkin paths. Finally, to draw out of the extremely large number of patterns some of the more aesthetically interesting cases for lacemakers to work on, we look for examples that have a high degree of symmetry. We demonstrate, by computational generation, that there are lace ground representatives from each of the 17 planar periodic symmetry groups. / Graduate / 0389 / 0984 / 0405 / veronikairvine@gmail.com

Approved for public release; distribution is unlimited / Computer simulation studies of a frequency domain adaptive beamforming algorithm are presented. These simulation studies were conducted to determine the multiple broadband target localization capability and the full angular coverage capability of the algorithm. The algorithm was evaluated at several signal-to-noise ratios with varying sampling rates. The number of iterations that the adaptive algorithm took to reach a minimum estimation error was determined. Results of the simulation studies indicate that the algorithm can localize multiple broadband targets and has full angular coverage capability. / http://archive.org/details/computersimulati00behr / Lieutenant, United States Navy

Nesta tese desenvolveram-se projetos e modelos de indutores planares para circuitos integrados de radiofrequência nas arquiteturas espiral e cross para as tecnologias CMOS AMS 0,35 ?m e IBM 0,13 ?m, visando representar o desempenho destes na faixa de frequências de corrente contínua até 90% da frequência de ressonância. A modelagem empregada utiliza um circuito elétrico equivalente com nove elementos para representar indutores, para o qual é apresentado um processo para extração dos valores dos seus componentes a partir de dados simulados ou medidos. Foi apresentada uma versão estendida da arquitetura cross original, mais flexível e tratável por algoritmos, com uma indutância 25% maior que a arquitetura espiral de mesma área. Utilizou-se planejamento de experimentos para elaborar conjuntos de amostras de indutores com dimensões geométricas variadas nas arquiteturas e tecnologias estudadas, para os quais desenvolveu-se um conjunto de algoritmos específicos para o projeto dos indutores a partir de suas dimensões. A simulação eletromagnética do layout de cada amostra gerou os resultados empregados no desenvolvimento do processo de extração dos valores dos componentes do circuito equivalente, os quais foram relacionados às dimensões geométricas dos indutores através de equações de projeto elaboradas por meio de análise de regressão multivariada e modelos lineares generalizados. Tanto o processo de extração dos valores dos componentes, como as equações de projeto foram validados estatisticamente pela comparação dos resultados das simulações dos respectivos circuitos equivalentes com os resultados das simulações eletromagnéticas dos layouts dos indutores em cada arquitetura e tecnologia, demonstrando a correspondência entre estes. Discrepâncias observadas em alta frequência entre os resultados de simulação eletromagnética dos indutores e seus respectivos circuitos equivalentes são associados a limitações do modelo de circuito usado, que não considera os fenômenos de correntes de Foucault (correntes de turbilhonamento) e efeito pelicular. O processo de modelagem desenvolvido, devido a sua generalidade, pode ser aplicado ao desenvolvimento de outros modelos de circuito elétrico para indutores, ou mesmo para modelagem de outros componentes passivos para circuitos integrados, como capacitores, resistores e transformadores. / In this thesis were developed designs and models for planar inductors for radiofrequency integrated circuits in the spiral and cross architectures for AMS 0.35 ?m and IBM 0.13 ?m CMOS technologies, aiming to represent the inductors performance in the frequency range of direct current up to 90% of resonant frequency. The employed modeling used an equivalent circuit for inductors with nine elements, for which a process for extracting the values of its components from simulated or measured data is presented. An extended version of the original cross architecture was presented, more flexible and treatable by algorithms, with an inductance 25% larger than the spiral architecture of the same area. Design of experiments was used to elaborate sets of inductor samples with different geometric dimensions in the studied architectures and technologies. Algorithms were developed to design the layout of each inductor considering its architecture and specific dimensions. The layout electromagnetic simulation of each sample generated the results used in the process developed for extracting the values of the components of the equivalent circuit model, which were related to the geometric dimensions of the inductors through design equations elaborated by multivariate regression analysis and generalized linear models. Both the component extraction process and the design equations were statistically validated by comparing the simulation results of the respective equivalent circuit models with the results of the electromagnetic simulations of the inductor layouts in each architecture and technology, demonstrating matching between them. Observed discrepancies at high frequency between the electromagnetic simulation results for the inductors and their respective equivalent circuits are associated with limitations of the circuit model used, which does not consider eddy currents and skin effect phenomena. The modeling process developed, due to its generality, can be applied to the development of other electric circuit models for inductors, or even to model other passive components for integrated circuits, such as capacitors, resistors and transformers.