This dissertation studies the colored Jones polynomial of knots and links, colored by representations of simple Lie algebras, and the stability of its coefficients. Chapter 1 provides an explicit formula for the second plethysm of an arbitrary representation of sl3. This allows for an explicit formula for the colored Jones polynomial of the trefoil, and more generally, for T(2,n) torus knots. This formula for the sl3 colored Jones polynomial of T(2,n)$ torus knots makes it possible to verify the Degree Conjecture for those knots, to efficiently compute the sl3 Witten-Reshetikhin-Turaev invariants of the Poincare sphere, and to guess a Groebner basis for the recursion ideal of the sl3 colored Jones polynomial of the trefoil. Chapter 2 gives a formulation of a stability conjecture for the coefficients of the colored Jones polynomial of a knot, colored by irreducible representations in a fixed ray of a simple Lie algebra. The conjecture is verified for all torus knots and all simple Lie algebras of rank 2. Chapter 3 supplies an efficient method to compute those q-series that come from planar graphs (i.e., reduced Tait graphs of alternating links) and compute several terms of those series for all graphs with at most 8 edges. In addition, a graph-theory proof of a theorem of Dasbach-Lin which identifies the coefficient of q^k in those series for k=0,1,2 in terms of polynomials on the number of vertices, edges and triangles of the graph is given. Chapter 4 provides a study of the structure of the stable coefficients of the Jones polynomial of an alternating link.The first four stable coefficients are identified with polynomial invariants of a (reduced) Tait graph of the link projection. A free polynomial algebra of invariants of graphs whose elements give invariants of alternating links is introduced which strictly refines the first four stable coefficients. It is conjectured that all stable coefficients are elements of this algebra, and experimental evidence for the fifth and sixth stable coefficient is given. The results are illustrated in tables of all alternating links with at most 10 crossings and all irreducible planar graphs with at most 6 vertices.

Orientadores: Luiz Antonio Barrea San Martin, Lonardo Rabelo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-22T17:26:40Z (GMT). No. of bitstreams: 1 Silva_JordanLambert_M.pdf: 1545963 bytes, checksum: 694fc3db0e24c098cadc145da4744772 (MD5) Previous issue date: 2013 / Resumo: Nesta dissertação, realizamos um estudo topológico das variedades flag reais. Encontrada a decomposição em células de Schubert de uma variedade flag, apresentamos dois invariantes topológicos sobre estas variedades: a homologia, obtida a partir do cálculo do operador fronteira da homologia celular, e a característica de Euler, cujo cálculo foi realizado para as variedades flag maximais e para as variedades grassmanianas simpléticas Lp(R2l) / Abstract: In this dissertation, we conduct a topological study of real flag manifolds. Found the Schubert cell decomposition of a flag manifold, we present two topological invariants for these manifolds: the homology, obtained from the calculation of the boundary operator of cellular homology, and the Euler characteristic, which was determinate for maximal flag manifolds and for symplectic grassmannians manifolds Lp(R2l) / Mestrado / Matematica / Mestre em Matemática

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18767号 / 理博第4025号 / 新制||理||1580(附属図書館) / 31718 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 岸本 大祐, 教授 加藤 毅, 准教授 浅岡 正幸 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

A Hessenberg variety is a subvariety of the flag variety parametrized by two maps: a Hessenberg function on $[n]$ and a linear map on $\C^n$. We study regular nilpotent Hessenberg varieties in Lie type A by focusing on the Hessenberg function $h=(n-1,n,\ldots,n)$. We first state a formula for the $f^w_{n,1}$ which generates the local defining ideal $J_{w,h}$ for any $w\in\Ss_n$. Second, we prove that there exists a convenient monomial order so that $\lead(J_{w,h})$ is squarefree. As a consequence, we conclude that each codimension-1 regular nilpotent Hessenberg variety is locally Frobenius split (in positive characteristic). / Thesis / Master of Science (MSc)

The Blue Flag program is a French international eco-award for beaches, marinas, and tour boats. With a set of 33 criteria required for obtaining the award, the Blue Flag program has sites all over the world, but none in the United States. The American Shore and Beach Preservation Association (ASBPA) sought to change that and provided an opportunity for locations in the U.S. to apply for the award. One of those applicants was the Galveston Island Park Board of Trustees in Galveston, Texas. This thesis focuses on data obtained for the park board through a survey to determine beachgoer support and interest in the Blue Flag program. Data was collected through the use of a survey and ad hoc interviews during the summer of 2021. Examined through various theoretical lenses, the data was analyzed to determine its impacts on the local community, and its relationship with other historical conservation projects. The results for this project were provided through a paper report and presentation on the findings to the client and presented at the ASBPA National Coastal Conference in October of 2021.

The aim of this thesis is to evaluate the artificial intelligence model ChatGPT as a tool in the cybersecurity domain. With the purpose of analysing and facilitating understanding of the technology’s effects on possible threats. The development of AI models has a potential to alter the knowledge required to perform malicious activities. The method for evaluating ChatGPT effectiveness in aiding actors to breach a vulnerable system is a experimental capture the flag based approach. This is a type of cyber-security challenge, simulating a target system. The goal is to find and exploit vulnerabilities on the target and obtain a so-called flag to prove the breach. ChatGPT is used as an assistant and information gathering tool in the simulations. The responses collected from ChatGPT in the simulation challenges is analysed to fulfil the thesis purpose. The results shows that ChatGPT is useful as a tool. However, as with any tool, knowledge on how to use it is required. A potential threat actor do need profound comprehension and technical knowledge to make relevant queries. 41.3% of all 46 collected responses is categorised as partly usable in conjunction with previously obtained knowledge. Furthermore, to successfully breach the simulated targets the actor need to be able to modify and deploy any suggested exploit provided by ChatGPT. The findings show a correlation between more difficult capture the flag challenges and the importance of tester knowledge. The harder challenges had a higher degree of responses categorized as partly usable compared to responses deemed directly usable. In conclusion ChatGPT do not provide enough assistance at this time to increase the potential of malicious actors with limited technical knowledge. Future work in this area includes testing internet connected and newer versions of ChatGPT and further analyse the importance of prompt engineering. / Målbilden med denna avhandling är att utvärdera AI-modellen ChatGPT som ett verktyg i en cybersäkerhets-kontext. Detta syftar till att möjliggöra utökad förståelse för teknologins effekter på möjliga hot. Utvecklingen på AI-området har potentialen att förändra kunskapsbehovet hos en aktör att genomföra olika typer av cyberangrepp. Metoden för att utvärdera ChatGPT:s möjlighet till att underlätta intrång i sårbara system är ”capture the flag” baserad. Detta är en typ av cybersäkerhetsutmaning där sårbara system simuleras. Målet är att hitta och utnyttja sårbarheter i systemen för att få tag i så kallade flagor. Dessa flaggor används sedan för att bevisa ett lyckat intrång i systemet. ChatGPT kommer att användas som en assistent och för att inhämta information under dessa simuleringar. Utdata som ChatGPT genererar kommer att samlas in och analyseras för att uppnå syftet med avhandlingen. Resultaten visar att ChatGPT är ett användbart verktyg men ett verktyg som kräver långtgående förkunskaper från användaren för att uppnå effekt. En aktör behöver besitta specifika tekniska kunskaper för att ställa relevanta frågor till AI-assistenten. 41.3% av 46 insamlade svar är kategoriserade som delvis användbara tillsammans med förkunskaper hos testaren. För att lyckas genomföra de simulerade intrången behöver aktören även kunna modifiera och implementera de förslag och lösningar som ges av ChatGPT. Resultaten visar även en korrelation mellan svårare simuleringar och vikten av testarens förkunskaper. Sammanfattningsvis ger inte ChatGPT tillräckligt hög grad av assistans för att utgöra ett hot i sig. Aktörer med begränsad teknisk kännedom kan därmed i nuläget inte utöka sin potential genom att nyttja detta verktyg. Framtida arbete innefattar liknande tester av senare, internetanslutna, versioner av ChatGPT och vidare analys av så kallad ”prompt engineering”

Leong Wai Ling Vivian. / Thesis submitted in: November 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 132-136). / Abstracts in English and Chinese. / Chapter Chapter One --- Introduction --- p.1-4 / Chapter Chapter Two --- Theoretical framework and literature review --- p.5-24 / Chapter Chapter Three --- Operationalization --- p.25-29 / Chapter Chapter Four --- Temporal staging of flag-raising ritual --- p.30-62 / Chapter Chapter Five --- Situational staging of flag-raising ritual --- p.63-120 / Chapter Chapter Six --- Conclusion --- p.121-131 / Bibliography

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-05-14T14:51:34Z No. of bitstreams: 2 Dissertação - Carlos Antônio Freitas da Silva - 2015.pdf: 659907 bytes, checksum: c43cf65b3e27833fcd6b4ab11eb79239 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-05-14T14:53:28Z (GMT) No. of bitstreams: 2 Dissertação - Carlos Antônio Freitas da Silva - 2015.pdf: 659907 bytes, checksum: c43cf65b3e27833fcd6b4ab11eb79239 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-05-14T14:53:28Z (GMT). No. of bitstreams: 2 Dissertação - Carlos Antônio Freitas da Silva - 2015.pdf: 659907 bytes, checksum: c43cf65b3e27833fcd6b4ab11eb79239 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-02-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this dissertation we will study Finsler Geometry. In particular, we will study Randers Geometry that which can be viewed as Riemannian Geometry with a pertubation. Furthermore Randers metrics are also obtained as solution to Zermelo’s Navigation Problem. We will also use classification theorems of Randers metrics of constant flag curvature and Einstein Randers metrics in terms of Zermelo’s Navigation Problem. Using Randers metrics we are going to construct a 3-parameter family of Einstein-Finsler metrics with non-constant flag curvature and to get such family we use a Killing vector field and a Riemannian metric which is the Hawking Taub-NUT metric. / Neste trabalho estudaremos a Geometria de Finsler. Em particular, estudaremos a Geometria de Randers que pode ser visto como a mais simples perturbação da Geometria Riemanniana. Além disso, veremos também que métricas de Randers podem ser obtidas como soluções do Problema Navegacional de Zermelo. Utilizaremos também resultados que caracterizam métricas de Randers com curvatura flag constante e métricas de Randers do tipo Einstein em termos do Problema Navegacional de Zermelo. Usando métricas de Randers vamos construir uma família a 3 parâmetros de métricas de Einstein-Finsler com curvatura flag não constante e para obter tal família utilizaremos um campo de Killing e uma métrica Riemanniana que é a métrica de Hawking Taub-NUT.

Argonautes are conserved RNA-binding proteins that can regulate gene expression post transcriptionally through a process known as RNA interference (RNAi). This is done through the use of small RNAs, e.g. sRNAs that act as a guide for the argonautes, allowing for sequence-specific binding to the target site. This interaction has been studied in many organisms, one of which is the model organism Dictyostelium discoideum. D. discoideum is an amoeba that has been used extensively in genetic experiments due to its unique lifestyle, and ease of use. Being a eukaryotic, unicellular organism, it proves to be a great tool for the study of regulatory systems in eukaryotes, allowing us to study this argonaute-sRNA interaction in detail. By analysing which RNAs bind to the argonautes, we can better understand which genes these proteins regulate and what role RNAi has in the organisms as a whole.  In this study, I investigate three of the five argonautes found in D. discoideum, namely agnA, agnC and agnE. By transforming FLAG-tagged versions of these genes into the amoeba, I successfully express two of these modified proteins in D. discoideum and verified expression by using antibodies designed specifically to recognise the FLAG-tags. This opens up the possibility for the characterisation of the argonaute proteins to better understand their role and function in the regulation of genes. / <p>The Biology Education Centre (IBG) is the responsible department. </p><p></p><p>Presentation has been made through Zoom. </p>

Marine tourism has been growing over the years to a diverse and large industry providing for a variety of markets. Across the world tourists enjoy activities of different types including kayaking, scuba diving, snorkelling, surfing and travelling to beaches for leisure reasons. Travelling to coastal towns with the purpose of visiting a beach has always been a great attraction for people across the world. Not only resulting in beaches becoming one of the tourism industry’s biggest markets but also a great contributor to local economies. In 200,1 South Africa adopted the Blue Flag Programme, a beach award which focuses on clean bathing water and pollution free environments. The programme was first established on the French coastline in Europe by the Foundation for Environmental Education (FEE). Since then 244 beaches and 208 marinas across 10 countries now boast with a Blue Flag award. The award requires beaches to adhere to four sets of criteria. These are water quality, environmental management, environmental education and information and safety and security. The programme also has specific periods allocated to beaches in which the beach has to meet all the stipulated standards.  Previous research has stated that the programme has great drawing power for tourists.  In contrast, other studies revealed that it has no benefits for the tourism industry, whatsoever.  Some studies have stated that it is a symbol of quality recognised by all across the world. The literature review conducted for this study revealed that the programme holds great benefits for conservation of the environment. Seen from a tourism point of view, however, it is still unclear whether the programme benefits the tourism industry or has any impact on it whatsoever. The primary goal of this dissertation is to determine the influence of Blue Flag status on the decision-making process of beach visitors when they select a beach, thereby determining whether or not the Blue Flag programme adds any value to the tourism industry. A literature review was conducted on important aspects concerning this study, namely the Blue Flag Programme, the tourist decision-making process, travel behaviour of tourists and tourist behaviour, to gain insight into the type of research. Thereafter an empirical study was conducted on six beaches in KwaZulu-Natal which involved the distribution of a self-administered questionnaire. The sampling method used for the study was quantitative, probability sampling with systematic sampling which involved the fieldworkers to approach every second person/group of people on the beach. The survey took place from 28 March to 4 April 2013. A total of 572 usable questionnaires was collected from a sample of 600 beach visitors. The data was captured using Microsoft™ Excel™ 2010 and analysed using Statistical Package for Social Sciences (SPSS version 21). Exploratory factor analyses were performed as well as a linear mixed-effect model analysis to analyse the impact of the Blue Flag Programme on tourism. To achieve the goal set for this study, two articles were produced. The aim of chapter 3 (article 1) was to determine the push and pull motives of beach visitors. The results revealed the profile of respondents to be female, married with an average age of 39 years and originating from Gauteng. They have a diploma or degree from a tertiary institute and like to visit the beach for an average of eight nights at a time. To identify the push and pull motives of beach visitors, the travel motives were first identified by means of a principal axis factoring analysis, with Oblimin and Kaiser Normalisation. The aspects yielded three factors, familiarity, family relaxation and escape and beach characteristics. The most important factor was determined to be familiarity. The analysis further revealed two push and two pull motives. The push factors are escape and relaxation (most important push motive) and familiarity. The pull motives are beach attributes (most important pull motive) and cognizance. This article showed that the familiarity of a beach plays an important role as to the motives of beach visitors as well as the fact that visitors to these beaches want to escape and relax away from everyday life. The aim of the chapter 4 (article 2) was to identify the influence of Blue Flag status on visitors’ decision-making when selecting a beach as well as to determine whether any statistically significant differences exist between the visitors to Blue Flag beaches and visitors to non-Blue Flag beaches. A principal axis factoring analysis was conducted to determine the decision-making aspects of beach visitors. This analysis yielded five actors, environmental education, safety and access, cleanliness, landscape and popularity. The most important factor was identified as cleanliness with a mean value of 4.37. Furthermore, a linear mixed-effect model analysis was conducted which identified one statistically significant difference with the factor popularity, which has a p-value of 0.002. No other differences were identified. This study thus found that Blue Flag status does not influence visitors’ decision in selecting a beach. What was interesting was the fact that the aspects which are of importance to beach visitors (such as cleanliness) form part of the criteria on which the programme is based (environmental education and information, environmental management, safety and security and water quality). Thus having Blue Flag status does impact positively on tourism. Since this was the first study of its kind in South Africa, it can benefit all beach destinations in the country. From the findings it is clear that marketing needs to be conducted regarding the Blue Flag programme and the benefits that could be reaped for both the local community and beach visitors. Furthermore, beach management can make use of the motives identified in chapter 3 as well as the decision-making aspects identified in chapter 4 to increase visitor numbers to the beach and gain competitive advantage. Tailor-made marketing strategies can be implemented which will improve the efforts of beach managers and municipalities as well as managers of the Blue Flag Programme to market the programme and raise awareness. Recommendations are made regarding further study on the Blue Flag programme to identify ways in which awareness of the programme amongst the public can be raised. Similar research can also be conducted on other environmental and tourism award systems, such as the Seaside award. This research contributes to the literature on marine tourism, seeing as this was the first time such a study was conducted in a South African setting. / MCom (Tourism Management), North-West University, Potchefstroom Campus, 2014