Kant's antinomies are exercises designed to illustrate the limits of human reasoning. He skillfully juxtaposes pairs of arguments and exposes the dangerous propensity for human reasoning to stretch beyond the conditioned and into the transcendental ideas of the unconditional. Kant believes this is a natural process and affirms the limits of pure reason in so much as they should prevent us from believing that we can truly know anything about the unconditional. His first antimony addresses the possibility of a beginning in time or no beginning in time. This thesis will focus on this first antinomy and critically assesses it in set theoretic terms. It is this author's belief that the mathematical nuances of infinite sets and the understanding of mathematical objects bear relevance to the proper interpretation of this antinomy. Ultimately, this composition will illustrate that Kant's argument in the first antinomy is flawed because it fails to account for infinite bounded sets and a conceptualization of the infinite as a mathematical object of reason.

This thesis investigates several problems in social network analysis on misinformation prevention with an emphasis on finding solutions that can scale to massive online networks. In particular, it considers two problem formulations related to the spread of misinformation in a network that cover the elimination of existing misinformation and the prevention of future dissemination of misinformation. Additionally, a comprehensive comparison of several algorithms for the feedback arc set (FAS) problem is presented in order to identify an approach that is both scalable and computes a lightweight solution. The feedback arc set problem is of particular interest since several notable problems in social network analysis, including the elimination of existing misinformation, crucially rely on computing a small FAS as a preliminary. The elimination of existing misinformation is modelled as a graph searching game. The problem can be summarized as constructing a search strategy that will leave the graph clear of any misinformation at the end of the searching process in as few steps as possible. Despite the problem being NP-hard, even on directed acyclic graphs, this thesis presents an efficient approximation algorithm and provides new experimental results that compares the performance of the approximation algorithm to the lower bound on several large online networks. In particular, new scalability goals are achieved through careful algorithmic engineering and a highly optimized pre-processing step. The minimum feedback arc set problem is an NP-hard problem on graphs that seeks a minimum set of arcs which, when removed from the graph, leave it acyclic. A comprehensive comparison of several approximation algorithms for computing a minimum feedback arc set is presented with the goal of comparing the quality of the solutions and the running times. Additionally, careful algorithmic engineering is applied for multiple algorithms in order to improve their scalability. In particular, two approaches that are optimized (one greedy and one randomized) result in simultaneously strong performance for both feedback arc set size and running time. The experiments compare the performance of a wide range of algorithms on a broad selection of large online networks and reveal that the optimized greedy and randomized implementations outperform the other approaches by simultaneously computing a feedback arc set of competitive size and scaling to web-scale graphs with billions of vertices and tens of billions of arcs. Finally, the algorithms considered are extended to the probabilistic case in which arcs are realized with some fixed probability and a detailed experimental comparison is provided. \sloppy Finally, the problem of preventing the spread of misinformation propagating through a social network is considered. In this problem, a ``bad'' campaign starts propagating from a set of seed nodes in the network and the notion of a limiting (or ``good'') campaign is used to counteract the effect of misinformation. The goal is to identify a set of $k$ users that need to be convinced to adopt the limiting campaign so as to minimize the number of people that adopt the ``bad'' campaign at the end of both propagation processes. \emph{RPS} (Reverse Prevention Sampling), an algorithm that provides a scalable solution to the misinformation prevention problem, is presented. The theoretical analysis shows that \emph{RPS} runs in $O((k + l)(n + m)(\frac{1}{1 - \gamma}) \log n / \epsilon^2 )$ expected time and returns a $(1 - 1/e - \epsilon)$-approximate solution with at least $1 - n^{-l}$ probability (where $\gamma$ is a typically small network parameter). The time complexity of \emph{RPS} substantially improves upon the previously best-known algorithms that run in time $\Omega(m n k \cdot POLY(\epsilon^{-1}))$. Additionally, an experimental evaluation of \emph{RPS} on large datasets is presented where it is shown that \emph{RPS} outperforms the state-of-the-art solution by several orders of magnitude in terms of running time. This demonstrates that misinformation prevention can be made practical while still offering strong theoretical guarantees. / Graduate

CoordenaÃÃo de AperfeiÃoamento de NÃvel Superior / Seja I : ∑n → Mn+1 uma imersÃo de uma variedade conexa n-dimensional ∑ em uma variedade Riemanniana completa conexa (n + 1)-dimensional M sem pontos conjugados. Suponha que a uniÃo das geodÃsicas tangentes a I nÃo cobrem M. Sobre essa hipÃtese temos dois resultados: 1. Se a cobertura universal de ∑ Ã compacta, entÃo M Ã simplesmente conexa. 2. Se I Ã um mergulho prÃprio e M Ã simplesmente conexa, entÃo I(∑) Ã um grÃfico normal sobre um subconjunto aberto de uma esfera geodÃsica. AlÃm disso, existe um conjunto estrelado aberto A M tal que A Ã uma variedade com fronteira I(∑). / Let I : ∑n → Mn+1 be an immersion of an n-dimensional connected manifold ∑ in an (n + 1)-dimensional connected completed Riemannian manifold M without conjugate points. Assume that the union of geodesics tangent to I does not cover M. Under these hypotheses we have two results: 1. M is simply connected provided that the universal covering of ∑ is compact. 2. If I is a proper embedding and M is simply connected, then I(∑) is a normal graph over an open subset os a geodesic sphere. Furthermore, there exists an open star-shaped set A M such that A is a manifold with the boundary I(∑).

Konjunktionsfelet är ett tankefel som uppstår vid sannolikhetsbedömningar. Detta tankefel inträffar då en sammanslagning av två alternativ bedöms som mer sannolikt än ett av alternativen fristående, vilket är felaktigt enligt sannolikhetsteori. Syftet med föreliggande enkätstudie var att undersöka om konjunktionsfelet förekom vid sannolikhetsbedömningar i en klinisk psykologisk kontext. Urvalsgruppen bestod av psykologstudenter under senare delen av utbildningen (termin 9 och 10, N = 30), en grupp med gedigen psykologisk kunskap, grundläggande kunskap inom statistik samt eventuell förkunskap om konjunktionsfelet. Ett möjligt sätt att minska förekomsten av konjunktionsfelet är att förtydliga relationen mellan kategorier och subkategorier vid en sannolikhetsbedömning. Studien undersökte även ifall ett informationsmoment, som förtydligade denna relation, kunde minska deltagarnas benägenhet att begå konjunktionsfel. Ett frågeformulär utformades för att undersöka dessa frågeställningar. Formuläret innehöll 12 uppgifter i en klinisk psykologisk kontext samt informationsmomentet. Resultatet visade att konjunktionsfelet uppvisades i genomsnitt 51% av de sex inledande frågorna. Efter att ha tagit del av informationsmomentet minskade andelen konjunktionsfel till 30% i resterande sex frågor. Slutligen undersöktes om förkunskap påverkade andelen begångna konjunktionsfel. Det framkom att deltagare med en högre förkunskap begick färre konjunktionsfel än de med lägre. Slutsatsen av studien var att psykologstudenterna, trots sina kunskaper, begick konjunktionsfelet vid sannolikhetsbedömningar i en klinisk psykologisk kontext. Vidare minskade andelen konjunktionsfel efter informationsmomentet. Dessa resultat kan beaktas i psykologiska bedömningssituationer för att minska risken för konjunktionsfel. Att undersöka om liknande resultat även kan uppnås bland yrkesverksamma psykologer kan vara av intresse för framtida forskning.

The purpose of this paper is to investigate some of the properties of convex sets in the plane through synthetic geometry.

The purpose of this thesis is to present an axiomatic foundation for the development of the natural numbers from two points of view. It makes no claim at originality other than at the point of organization and presentation of previously developed works.

Let G be a Polish group. We say that G is an algebraically determined Polish group if given any Polish group L and any algebraic isomorphism from L to G, then the algebraic isomorphism is a topological isomorphism. We will prove a general theorem that gives useful sufficient conditions for a semidirect product of two Polish groups to be algebraically determined. This will smooth the way for the proofs for some special groups. For example, let H be a separable Hilbert space and let G be a subset of the unitary group U(H) acting transitively on the unit sphere. Assume that -I in G and G is a Polish topological group in some topology such that H x G to H, (x,U) to U(x) is continuous, then H x G is a Polish topological group. Hence H x G is an algebraically determined Polish group. In addition, we apply the above the above result on the unitary group U(A) of a separable irreducible C*-algebra A with identity acting transitively on the unit sphere in a separable Hilbert space H and proved that the natural semidirect product H x U(A) is an algebraically determined Polish group. A similar theorem is true for the natural semidirect product R^{n} x G(n), where G(n) = GL(n,R), or GL^{+}(n,R), or SL(n,R), or |SL(n,R)|={A in GL(n,R) : |det(A)|=1}. On the other hand, it is known that the Heisenberg group H_{3}(R) , (R, +), (R{0}, x), and GL^{+}(n,R) are not algebraically determined Polish groups.

A reflection on the costume and scenic design process for the theoretical production of the musical Notre-Dame de Paris, composed by Riccardo Cocciante with lyrics by Luc Plamondon. This record contains the steps of the design process, from the analysis of the libretto and the dramaturgical research to the final presentation of the costume and scenic design elements.

Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.

Since the introduction of the lipid emulsion formulation in 1986, propofol has become established for induction as well as for maintenance of anaesthesia in veterinary practice1 including cats2;3-8. Propofol is rapidly metabolized by hepatic glucuronidation in most species and it has also been shown to undergo extrahepatic metabolism9-13, so that total body clearance may exceed liver blood flow in certain species. Because of their highly carniverous diet, cats are little exposed to antiherbivory compounds so that they have become deficient in UGP-glucuronosyltransferase (UGT)14. Consequently, a number of drugs are eliminated slowly15;16, often giving rise to prolonged half-lives of the parent drugs. Cats are therefore sensitive to the adverse effects of many drugs and toxins that are normally glucuronidated before elimination. It is therefore likely that the disposition of propofol may differ markedly from that of humans and other animal species17. Adam et al18 reported that for the cremophor propofol formulation in cats, volumes of distribution were smaller and elimination halflives were longer than those of pigs, rats and rabbits. In addition, pulmonary uptake has been demonstrated to occur in cats,19 however propofol’s pharmacokinetics have not been studied formally. The purpose of this study was to determine the pharmacokinetic behaviour of propofol after single intravenous injections. In comparison with man, the apparent central volume of distribution in domestic cats is small (0.56L.kg-1 body weight vs. 0.228L.kg-1) for the human pharmacokinetic parameter set of Marsh et al20 and the clearance (0.0086 L.kg-1.min-1 vs. 0.027 L.kg- 1.min-1) is approximately 2½ times slower in cats when compared with humans. Slow clearance should not influence recovery from anaesthesia following standard induction doses, because the early decreases in blood concentrations are predominantly due to redistribution of drug to various tissues (similar to the disposition of thiopentone which exhibits a slow total body clearance21. However it is possible that drug may accumulate within the body after prolonged infusions, resulting in delayed recovery times. This phenomenon is best described by calculating “context-sensitive” decrement-times by computer simulation22-24. Computer software♣ were used to calculate the 20%, 50% and 80% context-sensitive decrement times for the cat pharmacokinetic model. For comparative purposes, similar calculations were performed for an adult human male (weight 70 kg) using the pharmacokinetic parameter-set of Marsh et al20. Assuming that recovery from anaesthesia occurs after a 50% decrease in blood concentrations has taken place, it is apparent from the 50% context-senstive decrement-time graph that for infusions lasting up to 20 minutes (during which concentrations are kept constant), recovery can be expected to be rapid and predictable. However if infusions are administered for longer than 20 minutes, the recovery times of the “average” cat increase rapidly, reaching a plateau of 36 minutes, while recovery times of the human remain short, albeit increasing slowly. Awakening times become dramatically prolonged and unpredictable in both cats and humans if propofol concentrations are required to decrease by 80% for recovery to occur. Under these circumstances the 80% decrement time after a two-hour infusion is approximately two hours in cats and 45 minutes in humans. On the other hand, if dosing is conservative, so that blood concentrations need to decrease by only 20% for awakening to occur, then recovery times are short and predictable, being only a few minutes, regardless of the duration of the preceding infusion. These findings are in accordance with those of Pascoe et al25 who reported that cats took longer to recover after a short (30 min) infusion than after a long (150 min) infusion. In their crossover study, the propofol infusion rates were adjusted so that the cats were maintained at a light level of anaesthesia at which they responded sluggishly to pedal stimulation. It is therefore likely that propofol concentrations were kept steady and were similar during the 30-minute as well as during the 150-minute infusions. Delayed recovery has also been reported when propofol was administered to cats on consecutive days26. Conclusions and clinical relevance: We recommend that propofol infusions be administered to cats only for fairly short procedures and that for prolonged surgery, maintenance of anaesthesia should be accomplished using other drugs. In order to decrease the propofol dose, premedication and analgesic supplements should be co-administered to provide “balanced” anaesthesia. ♣ TIVA Trainer version 8, author Frank Engbers, Leiden University Medical Centre Copyright / Dissertation (MMedVet)--University of Pretoria, 2009. / Companion Animal Clinical Studies / unrestricted