Augmentations and Rulings of Legendrian Links

For any Legendrian knot in R^3 with the standard contact structure, we show that the existence of an augmentation to any field of the Chekanov-Eliashberg differential graded algebra over Z[t,t^{-1}] is equivalent to the existence of a normal ruling of the front diagram, generalizing results of Fuchs, Ishkhanov, and Sabloff. We also show that any even graded augmentation must send t to -1.

We extend the definition of a normal ruling from J^1(S^1) given by Lavrov and Rutherford to a normal ruling for Legendrian links in #^k(S^1\times S^2). We then show that for Legendrian links in J^1(S^1) and #^k(S^1\times S^2), the existence of an augmentation to any field of the Chekanov-Eliashberg differential graded algebra over Z[t,t^{-1}] is equivalent to the existence of a normal ruling of the front diagram. For Legendrian knots, we also show that any even graded augmentation must send t to -1. We use the correspondence to give nonvanishing results for the symplectic homology of certain Weinstein 4-manifolds.

Knot/Knotting Practice in Craft and Space

Knot/knotting Practice in Craft and Space is a three part research-creation project that used a study of knotting techniques to locate craft in an expanded field of spatial practice. The first part consisted of practical, studio based exercises in which I worked with various natural and synthetic fibres to learn common knotting techniques. The second part was an art historical study that combined craft and architecture history with critical theory related to the social production of space. The third part was an exhibition of drawing and knotted objects titled Opening Closures. This document unifies the lines inquiry that define my project. The first chapter presents the art historical justification for knotting to be understood as a spatial practice. Nineteenth-century German architect and theorist Gottfried Semper’s idea that architectural form is derived from four basic material practices allies craft and architecture in my project and is the point of departure from which I make my argument. In the second chapter, to consider the methodological concerns of research-creation as a form of knowledge production and dissemination, I adopt the format of an instruction manual to conduct an analysis of knot types and to provide instructions for the production of several common knots. In the third chapter, I address the formal and conceptual underpinnings of each artwork presented in my exhibition. I conclude with a proposal for an expanded field of spatial practice by adapting art critic and theorist Rosalind Krauss’s well-known framework for assessing sculpture in 1960s.

Data-Adaptive Modeling using Convex Regression

Thesis (Ph.D.)--University of Washington, 2016-08

Unlinked Embedded Graphs

This paper is a self-contained development of an invariant of graphs embedded in three-dimensional Euclidean space using the Jones polynomial and skein theory. Some examples of the invariant are computed. An unlinked embedded graph is one that contains only trivial knots or links. Examples show that the invariant is sufficiently powerful to distinguish some different unlinked embeddings of the same graph.

Alternating surgeries

This thesis is concerned with the question of when the double branched cover of an alternating knot can arise by Dehn surgery on a knot in S^3. We approach this problem using a surgery obstruction, first developed by Greene, which combines Donaldson's Diagonalization Theorem with the $d$-invariants of Ozsvath and Szabo's Heegaard Floer homology. This obstruction shows that if the double branched cover of an alternating knot or link L arises by surgery on S^3, then for any alternating diagram the lattice associated to the Goeritz matrix takes the form of a changemaker lattice. By analyzing the structure of changemaker lattices, we show that the double branched cover of L arises by non-integer surgery on S^3 if and only if L has an alternating diagram which can be obtained by rational tangle replacement on an almost-alternating diagram of the unknot. When one considers half-integer surgery the resulting tangle replacement is simply a crossing change. This allows us to show that an alternating knot has unknotting number one if and only if it has an unknotting crossing in every alternating diagram. These techniques also produce several other interesting results: they have applications to characterizing slopes of torus knots; they produce a new proof for a theorem of Tsukamoto on the structure of almost-alternating diagrams of the unknot; and they provide several bounds on surgeries producing the double branched covers of alternating knots which are direct generalizations of results previously known for lens space surgeries. Here, a rational number p/q is said to be characterizing slope for K in S^3 if the oriented homeomorphism type of the manifold obtained by p/q-surgery on K determines K uniquely. The thesis begins with an exposition of the changemaker surgery obstruction, giving an amalgamation of results due to Gibbons, Greene and the author. It then gives background material on alternating knots and changemaker lattices. The latter part of the thesis is then taken up with the applications of this theory.

Investigating the use of LiDAR scanning as a method for the measurement of timber distortion features

Measuring the extent to which a piece of structural timber has distorted at a macroscopic scale is fundamental to assessing its viability as a structural component. From the sawmill to the construction site, as structural timber dries, distortion can render it unsuitable for its intended purposes. This rejection of unusable timber is a considerable source of waste to the timber industry and the wider construction sector. As such, ensuring accurate measurement of distortion is a key step in addressing ineffciencies within timber processing. Currently, the FRITS frame method is the established approach used to gain an understanding of timber surface profile. The method, while reliable, is dependent upon relatively few measurements taken across a limited area of the overall surface, with a great deal of interpolation required. Further, the process is unavoidably slow and cumbersome, the immobile scanning equipment limiting where and when measurements can be taken and constricting the process as a whole. This thesis seeks to introduce LiDAR scanning as a new, alternative approach to distortion feature measurement. In its infancy as a measurement technique within timber research, the practicalities of using LiDAR scanning as a measurement method are herein demonstrated, exploiting many of the advantages the technology has over current approaches. LiDAR scanning creates a much more comprehensive image of a timber surface, generating input data multiple magnitudes larger than that of the FRITS frame. Set-up and scanning time for LiDAR is also much quicker and more flexible than existing methods. With LiDAR scanning the measurement process is freed from many of the constraints of the FRITS frame and can be done in almost any environment. For this thesis, surface scans were carried out on seven Sitka spruce samples of dimensions 48.5x102x3000mm using both the FRITS frame and LiDAR scanner. The samples used presented marked levels of distortion and were relatively free from knots. A computational measurement model was created to extract feature measurements from the raw LiDAR data, enabling an assessment of each piece of timber to be carried out in accordance with existing standards. Assessment of distortion features focused primarily on the measurement of twist due to its strong prevalence in spruce and the considerable concern it generates within the construction industry. Additional measurements of surface inclination and bow were also made with each method to further establish LiDAR's credentials as a viable alternative. Overall, feature measurements as generated by the new LiDAR method compared well with those of the established FRITS method. From these investigations recommendations were made to address inadequacies within existing measurement standards, namely their reliance on generalised and interpretative descriptions of distortion. The potential for further uses of LiDAR scanning within timber researches was also discussed.

Aplicação da teoria das opções reais na análise de investimentos em concessão florestal

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Florestal, 2016.

Inverse identification of the bending stiffness of a braided polyethylene twine subject to large deformation: application to the identification of the mesh opening rigidity of fishing nets.

The evaluation of the mesh opening stiffness of fishing nets is an important issue in assessing the selectivity of trawls. It appeared that a larger bending rigidity of twines decreases the mesh opening and could reduce the escapement of fish. Nevertheless, netting structure is complex. A netting is made up of braided twines made of polyethylene or polyamide. These twines are tied with non-symmetrical knots. Thus, these assemblies develop contact-friction interactions. Moreover, the netting can be subject to large deformation. In this study, we investigate the responses of netting samples to different types of solicitations. Samples are loaded and unloaded with creep and relaxation stages, with different boundary conditions. Then, two models have been developed: an analytical model and a finite element model. The last one was used to assess, with an inverse identification algorithm, the bending stiffness of twines. In this paper, experimental results and a model for netting structures made up of braided twines are presented. During dry forming of a composite, for example, the matrix is not present or not active, and relative sliding can occur between constitutive fibres. So an accurate modelling of the mechanical behaviour of fibrous material is necessary. This study offers experimental data which could permit to improve current models of contact-friction interactions [4], to validate models for large deformation analysis of fibrous materials [1] on a new experimental case, then to improve the evaluation of the mesh opening stiffness of a fishing net

On continuous families of geometric Seifert conemanifold structures

In this paper, dedicated to Prof. Lou Kauffman, we determine the Thurston’s geometry possesed by any Seifert fibered conemanifold structure in a Seifert manifold with orbit space (Formula presented.) and no more than three exceptional fibers, whose singular set, composed by fibers, has at most three components which can include exceptional or general fibers (the total number of exceptional and singular fibers is less than or equal to three). We also give the method to obtain the holonomy of that structure. We apply these results to three families of Seifert manifolds, namely, spherical, Nil manifolds and manifolds obtained by Dehn surgery on a torus knot (Formula presented.). As a consequence we generalize to all torus knots the results obtained in [Geometric conemanifolds structures on (Formula presented.), the result of (Formula presented.) surgery in the left-handed trefoil knot (Formula presented.), J. Knot Theory Ramifications 24(12) (2015), Article ID: 1550057, 38pp., doi: 10.1142/S0218216515500571] for the case of the left handle trefoil knot. We associate a plot to each torus knot for the different geometries, in the spirit of Thurston.

Beginner's guide to fishing

With some basic knowledge and minimum skill, a beginning angler can embark on a lifetime of fun, relaxation and camaraderie with other anglers. Discussed in this booklet are several styles of fishing, types of rods, reels, knots, baits, lures, freshwater fish and aquatic habitats. You’ll find tips to improve your skills and prepare you for a fun, exciting and successful fishing trip. You’ll also learn ways to protect your aquatic resources.

A hydrodynamical view on the mass accretion onto massive halos

This Thesis presents the results of my work on how galaxy clusters form by the accretion of sub-clumps and diffuse materials, and how the accreted energy is distributed in the X-ray emitting plasma. Indeed, on scales larger than tens of millions of light years, the Universe is self-organised by gravity into a spiderweb, the Cosmic Web. Galaxy clusters are the knots of this Cosmic Web, but a strong definition of filaments (which link different knots) and their physical proprieties, is still uncertain. Even if this pattern was determined by studying the spatial distribution of galaxies in the optical band, recently, also in the X-rays probes of filamentary structures around galaxy clusters were obtained. Therefore, given these observational facilities, the galaxy clusters’ outskirts are the best candidate regions to detect filaments and study their physical characteristics. However, from X-rays observations, we have only a few detections of cosmic filaments to date. On the other hand, it is crucial to understand how the accreted energy is dissipated in the baryon content of galaxy clusters and groups. Indeed, it is well known that in the central region of galaxy clusters and groups, the baryon fraction increases with the halo mass. On the outer region, the lack of X-rays constraints influences our understanding of the evolution of baryons in the halos volume. The standard assumption of “closed-box” system, for which the baryon fraction should approach the cosmological ratio Omega_bar/Omega_m, for galaxy clusters and groups seems to be too strong, especially for less massive objects. Moreover, a complete redshift evolution of baryons in galaxy clusters and groups is still missing.

Exploration of X-ray, optical and radio emission of the radio-galaxy 3C 277.3

This thesis explores the X-ray nuclear and extended properties of the radio galaxy 3C 277.3, where a recent optical observation performed with the multi-unit spectroscopic explorer (MUSE) has revealed star-forming regions triggered by the propagation of non-thermal plasma in the intergalactic medium. This work aims to study the nuclear engine and its environment and, possibly, discover signatures of non-thermal plasma-gas interaction at high energies. 3C 277.3 was observed with the Chandra satellite five times from 2010 to 2014 for a total of about 200 ks. Data in the Chandra public archive were retrieved and analyzed. When necessary, the different pointings were combined to improve the signal-to-noise ratio. A detailed analysis of the Chandra image (obtained by combining all the observations) has revealed several emission regions. In addition to a bright nucleus, two jet knots and the northern hot spot were clearly detected by overlapping the X-ray data to a VLA map of the source at 1.4 GHz. An X-ray spectral analysis was performed for all these structures. Finally, the X-ray image was over-imposed on the MUSE data.

Constraints on the duty cycle of the remnant radio galaxy NGC 6086 in the galaxy group Abell 2162

Galaxy clusters and groups are the most massive bounded structures and the knots of the large-scale structure of the Universe. These structures reside in dark matter haloes, hosting tens to hundreds of galaxies and they are filled with hot and rarefied gas. Radio Galaxies are a peculiar class of galaxies with a luminosity in the radio band up to 10^46 erg/s between 10 MHz and 100 GHz. These galaxies are a subclass of AGN in which there is accretion on the Super Massive Black Hole. The accretion generates jets of relativistic particles and magnetic fields which lose energy through synchrotron radiation, best observable at radio frequencies. The study of the spectral ageing of the AGN plasma is fundamental to understand its evolution, interaction with the environment and to constrain the AGN duty cycle. n this thesis, we have investigated the duty cycle of the nearby remnant radio galaxy NGC 6086, located in the centre of the galaxy group Abell 2162. We have made major steps forward thanks to the new high-sensitivity interferometers in the low-frequency radio band. We have detected for the first time three filaments of emission and a second couple of lobes. We have performed an integrated and resolved analysis on the previously known inner lobes, the new filaments and the older outer lobes. We have performed an age estimate of the two pairs of lobes to give constraints on the duty cycle of the source and an estimate of its active time.