To understand the mechanism of a pressure-induced structural phase transition, it is important to know which bonding changes lead to the stabilization of the new structure. A useful approach in this regard is the quantum chemical topology, which provides a large variety of indicators for the characterization of interatomic interactions. In this work, a number of topological indicators are used to analyze the bonding changes during the pressure-induced phase transition from the cubic diamond (cd) to the β-Sn-type structure of the elements of the 14th group of the periodic table. The ability of these indicators to reflect the presence of the cd → β-Sn transition in experiment for Si, Ge and Sn and its absence for carbon is investigated. Furthermore, the effect of pressure on the interatomic interactions in the cd- and β-Sn-type structures is examined. It is observed that the energy change along the cd → β-Sn transformation pathway correlates with the evolution of certain parameters of the electron density and the electron localizability indicator (ELI-D). Accordingly, criteria of structural stability were formulated based on characteristics of interatomic interactions. These results can serve as guidelines for the investigation of other solid-state phase transformations by the topological methods.

This study is a symmetrical ethnography of the Czech development project Kola pro Afriku (Czech Bikes for Gambian Schools), which involves the collection, repairs, modification and shipment of old Czech bicycles to The Gambia. Once there, they are distributed to partner schools and offered to communing pupils. In my research, I mainly focus on the pivotal technology of the project, bicycles, and their performances. Drawing on classic ethnographies of development and (most importantly) on studies based on the actor-network theory (ANT), I gradually explore the bike collection process, their modifications and repairs, their shipment to The Gambia and their local operations. When doing so, I focus on the social topology of the bicycles and its transformations in the timespace. In this regard, the bicycles gradually appear as junk (i.e. a dysfunctional relict of stabilized networks), as a fluid collectivity and as individually fluid. Thereby, this study shows that technology transfers may lead not only to changes in the set of relations, of which the given object consists, but in the very modes, in which those relations arise. It is precisely these topological transformations that significantly contribute to the functioning of the project Kola pro Afriku. Key words: development cooperation,...

In this thesis we are studying some properties of weakly sequential homeomorphisms between Banach spaces. First, we show some results that summarize how are some clas- ses of Banach spaces (specifically separable spaces, spaces with separable dual, Asplund spaces, reflexive spaces, weakly compactly generated spaces and spaces not containing isomorphic copy of ℓ1) determined by weak topology of the space. Then we show that to preserve some properties (separability, reflexivity and being weakly compactly gene- rated) it is enough for the spaces to be weakly sequentially homeomorphic. Furthermore we show that if two spaces are weakly sequentially uniformly homeomorphic then one contains isomorphic copy of ℓ1 if and only if the other spaces has this property. Finally we construct weakly sequential homeomorphisms between some class of Banach spaces.

Ce mémoire traite de la construction d’un nouvel invariant des cobordismes lagrangiens. Cette construction est inspirée des travaux récents de Solomon dans lesquels une extension de l’homomorphisme de Calabi aux chemins lagrangiens exacts est donnée. Cette extension fut entre autres motivée par le fait que le graphe d’une isotopie hamiltonienne est un chemin lagrangien exact. Nous utilisons la suspension lagrangienne, qui associe à chaque chemin lagrangien exact un cobordisme lagrangien, pour étendre la construction de Solomon aux cobordismes lagrangiens. Au premier chapitre nous donnons une brève exposition des propriétés élémentaires des variétés symplectiques et des sous-variétés lagrangiennes. Le second chapitre traite du groupe des difféomorphismes hamiltoniens et des propriétés fondamentales de l’homomorphisme de Calabi. Le chapitre 3 est dédié aux chemins lagrangiens, l’invariant de Solomon et ses points critiques. Au dernier chapitre nous introduisons la notion de cobordisme lagrangien et construisons le nouvel invariant pour finalement analyser ses points critiques et l’évaluer sur la trace de la chirurgie de deux courbes sur le tore. Dans le cadre de ce calcul, nous serons en mesure de borner la valeur du nouvel invariant en fonction de l’ombre du cobordisme, une notion récemment introduite par Cornea et Shelukhin. / In this master's thesis, we construct a new invariant of Lagrangian cobordisms. This construction is inspired by the recent works of Solomon in which an extension of the Calabi homomorphism to exact Lagrangian paths is given. Solomon's extension was motivated by the fact that the graph of any Hamiltonian isotopy is an exact Lagrangian path. We use the Lagrangian suspension construction, which associates to every exact Lagrangian path a Lagrangian cobordism, to extend Solomon's invariant to Lagrangian cobordisms. In the first chapter, we give a brief introduction to the elementary properties of symplectic manifolds and their Lagrangian submanifolds. In the second chapter, we present an introduction to the group of Hamiltonian diffeomorphisms and discuss the fundamental properties of the Calabi homomorphism. Chapter 3 is dedicated to Lagrangian paths, Solomon's invariant and its critical points. In the last chapter, we introduce the notion of Lagrangian cobordism and we construct the new invariant. We analyze its critical points and evaluate it on the trace of the Lagrangian surgery of two curves on the torus. In this setting we further bound the new invariant in terms of the shadow of the cobordism, a notion recently introduced by Cornea and Shelukhin.

In this thesis, we will work with the nodal sets of Laplace eigenfunctions on a few simple manifolds, like the sphere and the flat torus. We will obtain bounds on the total Betti number of the nodal set that depend on the corresponding eigenvalue. Our work generalize Courant's theorem. / Dans ce mémoire, nous travaillons sur les ensembles nodaux de combinaisons de fonctions propres du laplacien, particulièrement sur la sphère et le tore plat. On bornera les nombres de Betti de ces ensembles en fonction de la valeur propre maximale. D'une certaine façon, cela généralise le fameux théorème de Courant.

In recent years, Weyl semi-metals have attracted a lot of interest in topological condensed matter, for instance for their significant potential application in quantum electronics, as the coupling between Weyl semi-metals and superconductivity, either intrinsically in the material or at the interface of a heterostructure, gives rise to a new type of topological superconductivity, which could be used to perform quantum computation operations free from decoherence. In this thesis, we investigate the low temperature magneto-transport properties of trigonal-PtBi2, a layered material, both in the presence of quantum confinement (exfoliated nano-structures) and in its absence (macro-structures). We report band structure calculations showing that trigonal-PtBi2 is a type-I Weyl semi-metal with multiple bands at the Fermi level. Shubnikov-de-Haas oscillations in macrostructures confirm the contribution to transport of carriers from multiple pockets, and magneto-transport measurements show an unusual angular dependence of the magnetoresistance with the field, which might be a manifestation of the large anisotropy of the topological band. We also report the existence of a large planar Hall effect in nano-structures, which is one of the predicted manifestations of Weyl physics. At very low temperature, below 1K, trigonal-PtBi2 becomes superconducting. We investigate the superconducting state in both macro- and nano-structures, and find that quantum confinement in nano-structures makes the superconductivity become two-dimensional. This result is confirmed by the characterization of a Berezinskii–Kosterlitz–Thouless (BKT) transition in nano-structures. This transition is very robust, as it occurs in nano-structures five times thicker than what had previously been reported for any BKT transitions in the literature. We also report on the impact of inhomogeneities on the superconducting transition.

In this work we investigate the Weyl anomaly from a new perspective. Our goal is to identify a set-up for which the classical Weyl symmetry is not broken, at the quantum level by the usual arguments related to the Euler invariants, but rather by the impact of other geometrical obstructions. Therefore, we work, mostly, in three spatiotemporal dimensions, where general arguments guarantee the absence of trace anomalies. In par- ticular, our interest here is on whether various types of singularities, emerging in the description of the differential geometry of surfaces, could induce some form of quantum inequivalence, even though the classical symmetry is at work. To this end, we work with a very special three-dimensional metric, whose nontriviality is fully in its spatial two-dimensional part. The last ingredient we use, to clean-up the way from other com- plications, is to work with physical systems where no Weyl gauge field is necessary, to have the classical invariance. The system we focus on is then the massless Dirac field the- ory (that, as well known, enjoys local Weyl symmetry) in three-dimensional conformally flat spacetimes. With these premises, the research programme consists of three steps. The first step is to find the coordinate transformations that link the conformal factor identifying the...

Wireless sensor networks are used in several multi-disciplinary areas covering a wide variety of applications. They provide distributed computing, sensing and communication in a powerful integration of capabilities. They have great long-term economic potential and have the ability to transform our lives. At the same time however, they pose several challenges – mostly as a result of their random deployment and non-renewable energy sources.Among the most important issues in wireless sensor networks are energy efficiency and radio interference. Topology control plays an important role in the design of wireless ad hoc and sensor networks; it is capable of constructing networks that have desirable characteristics such as sparser connectivity, lower transmission power and a smaller node degree.In this research a distributed topology control technique is presented that enhances energy efficiency and reduces radio interference in wireless sensor networks. Each node in the network makes local decisions about its transmission power and the culmination of these local decisions produces a network topology that preserves global connectivity. The topology that is produced consists of a planar graph that is a power spanner, it has lower node degrees and can be constructed using local information. The network lifetime is increased by reducing transmission power and the use of low node degrees reduces traffic interference. The approach to topology control that is presented in this document has an advantage over previously developed approaches in that it focuses not only on reducing either energy consumption or radio interference, but on reducing both of these obstacles. Results are presented of simulations that demonstrate improvements in performance. AFRIKAANS : Draadlose sensor netwerke word gebruik in verskeie multi-dissiplinêre areas wat 'n wye verskeidenheid toepassings dek. Hulle voorsien verspreide berekening, bespeuring en kommunikasie in 'n kragtige integrate van vermoëns. Hulle het goeie langtermyn ekonomiese potentiaal en die vermoë om ons lewens te herskep. Terselfdertyd lewer dit egter verskeie uitdagings op as gevolg van hul lukrake ontplooiing en nie-hernubare energie bronne. Van die belangrikste kwessies in draadlose sensor netwerke is energie-doeltreffendheid en radiosteuring. Topologie-beheer speel 'n belangrike rol in die ontwerp van draadlose informele netwerke en sensor netwerke en dit is geskik om netwerke aan te bring wat gewenste eienskappe het soos verspreide koppeling, laer transmissiekrag en kleiner nodus graad.In hierdie ondersoek word 'n verspreide topologie beheertegniek voorgelê wat energie-doeltreffendheid verhoog en radiosteuring verminder in draadlose sensor netwerke. Elke nodus in die netwerk maak lokale besluite oor sy transmissiekrag en die hoogtepunt van hierdie lokale besluite lewer 'n netwerk-topologie op wat globale verbintenis behou.Die topologie wat gelewer word is 'n tweedimensionele grafiek en 'n kragsleutel; dit het laer nodus grade en kan gebou word met lokale inligting. Die netwerk-leeftyd word vermeerder deur transmissiekrag te verminder en verkeer-steuring word verminder deur lae nodus grade. Die benadering tot topologie-beheer wat voorgelê word in hierdie skrif het 'n voordeel oor benaderings wat vroeër ontwikkel is omdat dit nie net op die vermindering van net energie verbruik of net radiosteuring fokus nie, maar op albei. Resultate van simulasies word voorgelê wat die verbetering in werkverrigting demonstreer. / Dissertation (MEng)--University of Pretoria, 2010. / Electrical, Electronic and Computer Engineering / unrestricted

Das Internet und darauf aufbauende Infrastrukturen haben sich als zentrale Medien zum weltweiten Abruf und Austausch von Informationen etabliert. Im Zuge dessen ist das Internet ein wichtiges Werkzeug zur globalen Vernetzung von Aktivisten und Journalisten geworden, welche dieses zudem als Plattform zur Veröffentlichung von Rechercheergebnissen und Beweismaterial verwenden. Um den Zugang zu kompromittierenden oder als unerwünscht erachteten Informationen über das Internet zu unterbinden, haben jedoch Regierungen weltweit weitreichende technische Zensurmaßnahmen implementiert. Um diesen Maßnahmen entgegenzuwirken sind Betroffene darauf angewiesen, ihre digitale Kommunikation über Geräte von Drittanbietern zu leiten, welche sich außerhalb des Einflussbereichs des Zensors befinden und deren Rolle als Umgehungsknoten für den Zensor schwer zu detektieren ist. Eine vielversprechender Ansatz zur Realisierung solcher Gegenmaßnahmen sind Friend-to-Friend (F2F) Overlay-Netzwerke. Ähnlich zu Anonymisierungsnetzwerken wie Tor und AN.ON setzen sich F2F Overlays aus den Knoten von mehreren Betreibern zusammen, wodurch ein Single Point of Failure vermieden wird. Um gegen Unterwanderung zu schützen wird jedoch die Kommunikation zwischen den Knoten in F2F Overlays auf jene Paare beschränkt, deren Betreiber sich gegenseitig vertrauen. Folglich erfordert das Aufdecken der Knoten eines F2F Overlays die Identifizierung und Kompromittierung deren Betreiber durch den Zensor mit Hilfe von Social-Engineering-Methoden. Um Anwendungsfälle wie anonymes Blogging zu unterstützen, benötigen F2F Overlays ein Routing-Protokoll, welches Datenübertragungen zwischen Knoten ohne wechselseitig vertraute Betreiber ermöglicht. Aufgrund seiner hohen Effizienz und Ausfalltoleranz gilt Routing anhand von Rooted Spanning Tree (RST) Embeddings hierfür als besonders vielversprechender Kandidat. Dabei wählen die teilnehmenden Knoten zunächst einen Knoten als Wurzel und formen, ausgehend von diesem, einen virtuellen Wurzelbaum über das F2F Overlay. Anschließend wird jedem Knoten eine virtuelle Adresse zugewiesen, welche dessen Position in dem zuvor erzeugten Wurzelbaum eindeutig repräsentiert. In F2F Overlays muss davon ausgegangen werden, dass ein Zensor, welcher einen Teil der Knotenbetreiber kompromittieren konnte, mit Hilfe eigener Knoten aktive Angriffe auf das Routing durchführt, um die Verbreitung von Inhalten zu unterbinden. Bisherige Forschung zu Routing anhand von RST Embeddings konzentriert sich jedoch primär auf die Steigerung dessen Effizienz sowie der Verbesserung dessen Robustheit gegenüber permanenter Ausfälle. In dieser Arbeit werden bisher unbekannte Angriffe auf RST-Embedding-basierte Routing-Protokolle vorgestellt, welche von bösartigen F2F-Overlay-Teilnehmern mit geringem Aufwand durchgeführt werden können. Ergänzend stellen wir anschließend Maßnahmen vor, welche derartige Routing-Protokolle inhärent robuster gegen Fehlverhalten machen. Ein wesentlicher Einflussfaktor bezüglich der Effektivität der identifizierten Angriffe ist die Tatsache, ob der gewählte Wurzelknoten ein Knoten des Angreifers ist oder nicht. Während die von uns vorgestellten Schutzmaßnahmen die Auswirkung der Angriffe auch in dem Fall begrenzen, dass der Wurzelnoten sich bösartig verhält, so erfordert das Routing von Nachrichten dabei nichtsdestotrotz erhöhten Aufwand bei gleichzeitig reduzierter Erfolgswahrscheinlichkeit. Die Wurzelwahlverfahren bisheriger RST-Embedding-basierter Routing-Protokolle können in F2F Overlays jedoch nicht auf sichere Weise umgesetzt werden, so dass ein Angreifer mit geringem Aufwand erreichen kann, dass einer seiner Knoten als Wurzel gewählt wird. Während es in F2F Overlays allgemein nicht ausgeschlossen werden kann, dass ein bösartiger Knoten als Wurzel gewählt wird, so ist es dennoch erstrebenswert, die Wahrscheinlichkeit der Wahl eines nicht-bösartigen Knotens zu erhöhen. Da bisherige Verfahren zur sicheren, verteilten Wahl eines Knotens nicht effektiv in F2F Overlays umgesetzt werden können, wird in dieser Arbeit ein neues Wurzelwahlverfahren vorgestellt. Dieses basiert auf lokalen, randomisierten Mehrheitsentscheidungen, um einen Konsens auf einen einzelnen Knoten herbeizuführen. Ergänzend dazu werden Ergebnisse einer Simulationsstudie anhand realer sozialer Graphen vorgestellt, welche belegen, dass dieser Ansatz einer Unterwanderung widersteht, wenn der Angreifer eine geringe Anzahl von Teilnehmern kompromittieren konnte. Gleichzeitig legen die Ergebnisse der Studie nahe, dass dieses Verfahren auch in F2F Overlays mit zehntausenden von Knoten in kurzer Zeit eine Einigung auf einen gemeinsamen Wurzelknoten für den Großteil der Knoten erreicht. Zur Effizienzsteigerung leiten aktuelle RST-Embedding-basierte Routing-Protokolle die Addressen anhand von Breitensuchbäumen ab. Der Aufbau derartiger Bäume erfordert jedoch, dass jeder Knoten seinem Nachbarn die eigene Hop-Distanz zum Wurzelknoten mitteilt. Dabei können Angreiferknoten gezielt inkorrekte Distanzwerte versenden, um die Anzahl der gutartigen Knoten zu maximieren, welche diese als Elternknoten wählen und folglich von anschließenden Angriffen betroffen sind. Um derartige Angriffe zu unterbinden, wird in dieser Arbeit zudem ein verteilter, selbststabilisierender Algorithmus zum Aufbau von Breitensuchbäumen vorgestellt. Dieser verwendet kryptografische Signaturen in Kombination mit Zeitstempeln, um inkorrekte sowie veraltete Distanzwerte erkennbar zu machen. Die Nutzung von RST Embeddings birgt neben Angriffen auf deren Verfügbarkeit das Risiko, dass ein interner Angreifer Informationen über die Topologie des zugrundeliegenden Netzwerkes gewinnen kann. Im Kontext von F2F Overlays ist dies problematisch, da deren Struktur dem sozialen Netzwerk deren Teilnehmern entspricht. Erlangt ein Angreifer einen Schnappschuss der Topologie eines F2F Overlays oder eines Teils davon, so kann er diesen mit der Topologie anderer sozialer Netzwerkgraphen abgleichen, um bisher unbekannte Teilnehmer aufzudecken. Das konkrete Ausmaß, in dem RST Embeddings sowie das darauf aufbauende Routing Rückschlüsse über die Topologie des Netzwerkes zulassen wurde bisher jedoch nicht untersucht. Der vierte Beitrag dieser Dissertation besteht daher aus einer detaillierten Analyse bezüglich der konkreten Informationen, welche ein interner Angreifer anhand der durch RST-Embedding-basierte Routing-Protokolle propagierten Daten gewinnen kann. / Today, the Internet plays a vital role in enabling activists and journalists to collaborate and to publish critical information on a global scale. As a consequence, governments around the globe have implemented technical censorship measures to keep citizens from accessing content that is deemed inappropriate or compromising. To address such censorship measures, a circumvention infrastructure is needed that allows affected individuals to route their online communication through third-party servers that are outside of the censor’s influence and whose use for circumvention is difficult to detect for the censor. A promising substrate to realize such an infrastructure are Friend-to-Friend (F2F) overlay networks. Similar to anonymization networks like Tor and AN.ON, F2F overlay nodes may be operated by different individuals, thus avoiding a single point of failure. To protect against infiltration, F2F overlays additionally restrict communication between participating devices to those pairs whose operators mutually trust each other. Thus, censors need to perform social engineering in order to discover operators and their nodes. To realize use cases that require communication between nodes of participants without mutual trust, such as distributed and redundant content storage or anonymous blogging, F2F overlays require a routing protocol suitable for large, dynamic networks. Among the current research on routing protocols for F2F overlays, routing based on rooted spanning tree (RST) embeddings emerged as the most promising candidate due to its high efficiency and fault tolerance. In this approach, nodes collaboratively determine a rooted spanning tree over the overlay topology and, starting from the elected root node, assign each node a virtual address that encodes its unique position in the tree. Given that a censor may compromise a fraction of the participants of an F2F overlay, it is likely that the censor will use nodes under their control to actively attack the routing protocol in order to disrupt communication. However, existing research on RST embeddings concentrates on their efficient implementation as well as resilience to permanent faults, thus leaving open in which ways such routing protocols can be attacked. Towards this end, this thesis presents previously unknown attacks that malicious participants of an F2F overlay can easily perform against state-of-the-art routing protocols. As these attacks cannot be reliably attributed to malicious nodes, we propose countermeasures that improve the inherent resilience of such protocols against misbehaving nodes. A fundamental risk that cannot completely be avoided in F2F overlays is that a malicious node may be chosen as the root node of the embedding, giving it a particularly strong position for attacks. While our proposed countermeasures limit the impact of malicious root behavior, routing in such a scenario nonetheless comes at the cost of increased routing overhead and an increased chance of routing failure. Since existing routing protocols based on RST embeddings employ insecure root election schemes, it is desirable to increase the likelihood that a benign node is chosen as root. Because existing secure protocols for node election cannot be used effectively in F2F overlays, we propose a novel root election protocol that leverages local voting algorithms to reach consensus on a single node. Simulations on real-world social graphs show that in F2F overlays, the protocol is able to reach consensus among a large fraction of nodes quickly and, in contrast to election protocols used by state-of-the-art routing algorithms, resists compromise by malicious nodes. To improve efficiency, state-of-the-art protocols embed breadth-first-search (BFS) trees for address assignment, whose formation relies on the truthful reporting of hop distances. In the presence of a benign root node, malicious nodes may deliberately propagate incorrect distance values to maximize the number of benign nodes that choose them as parent, thus increasing the impact of subsequent attacks. To defend against such misbehavior, we furthermore propose a self-stabilizing BFS formation algorithm that leverages cryptographic signatures to make incorrectly reported distances detectable. Additional to the risk of attacks aiming at the disruption of communication, RST embeddings and the routing based on them inherently leaks information about the topology of the underlying network to its participants. Such leakage is problematic in F2F overlays, as topology snapshots can be linked with graph data from further sources in order to identify participants. However, the concrete inferences malicious participants can make from the routing control data propagated by state-of-the-art protocols has not been investigated so far. The fourth contribution of this thesis therefore lies in the analysis of which information about the topology of an F2F overlay malicious participants can infer from the control data propagated by RST embedding algorithms as well as the resulting routing of messages.

We explore motivic homotopy theory over deeper bases than the spectrum of the integers: Starting from a commutative group object in a cartesian closed presentable infinity category, replacing the usual multiplicative group scheme in motivic spaces, we construct projective spaces, and show that infinite dimensional projective space is the classifying space of the group object. After passage to the stabilization, we construct a Snaith spectrum, calculate the cohomology represented by it for projective spaces and on its rationalization produce Adams operations and a splitting into summands of their eigenspaces.