Interpolyelektrolytkomplexe zylindrischer Bürstenpolymere

Die elektrostatische Wechselwirkung zwischen entgegengesetzt geladenen Polyelektrolyten führt zur spontanen Bildung von Interpolyelektrolytkomplexen. Besonders im Fokus des akademischen und biotechnologischen Interesses stehen derzeit Komplexe aus DNA und synthetischen Polykationen, da eine Anwendung dieser speziellen Interpolyelektrolytkomplexe in der nicht-viralen Gentherapie vielfältig diskutiert wird. Ziel der vorliegenden Arbeit war es, den Einfluss von Kettensteifheit auf die Bildung von Interpolyelektrolytkomplexen zu untersuchen und dabei Wege aufzuzeigen, die eine Kontrolle der Topologie von Interpolyelektrolytkomplexen ermöglichen. Neben dem topologischen Einfluss wurde untersucht, wie durch Komplexierung hochmolekularer Polyelektrolyte equilibrierbare Strukturen erhalten werden können. Als Modellsystem für diese Untersuchungen wurden zylindrische Bürstenpolymere verwendet, denen als topologischer „Kontrast“ das Komplexierungsverhalten kommerzieller PAMAM-G5-Dendrimere mit kugelförmiger Topologie gegenüber gestellt wurde. Um den Ladungsgrad des Bürstenpolymers beliebig variieren zu können, wurden Bürstenpolymere mit Poly(ethylenimin)-Seitenketten synthetisiert, deren Ladungsdichte über den Protonierungsgrad einstellbar ist. Die vorliegende Arbeit zeigt, wie diese mit Hilfe der Makromonomermethode hergestellt werden konnten. Die Komplexbildung von DNA mit semiflexiblen zylindrischen Bürstenpolymeren mit unterschiedlichen Seitenketten und Ladungsdichten in wässriger Lösung hat gezeigt, dass diese in allen untersuchten Fällen unter kinetischer Kontrolle verläuft und Nicht-Gleichgewichtsstrukturen gebildet werden. Sehr überraschend wurde festgestellt, dass die Größen der mit vorgelegter DNA gebildeten Komplexe ungeachtet des verwendeten Polykations identisch sind und DNA-Komplexe mit einem Radius von 30 bis 50 nm und einer kugelförmigen Topologie resultieren. Diese kinetisch kontrollierte Komplexbildung konnte in nicht-wässriger Lösung durch starke Reduktion der Anzahl wechselwirkender Ladungen verhindert werden, so dass eine thermodynamische Kontrolle möglich wurde. Unter diesen Bedingungen ist es gelungen, aus hochgeladenen Poly(styrolsulfonat)-Bürsten mit modifizierten Poly(ethylenimin)-Bürsten oder PAMAM-Dendrimeren Komplexe zylindrischer Topologie herzu-stellen. Für letztere konnte darüber hinaus postuliert werden, dass diese Komplexe eine dichteste Packung der PAMAM-Dendrimere darstellen, für deren Bildung das Polyanion mit seiner größeren Konturlänge und seiner zylindrischen Topologie als Templat dient.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Geometry of BV quantization and Mathai-Quillen formalism

Il formalismo Mathai-Quillen (MQ) è un metodo per costruire la classe di Thom di un fibrato vettoriale attraverso una forma differenziale di profilo Gaussiano. Lo scopo di questa tesi è quello di formulare una nuova rappresentazione della classe di Thom usando aspetti geometrici della quantizzazione Batalin-Vilkovisky (BV). Nella prima parte del lavoro vengono riassunti i formalismi BV e MQ entrambi nel caso finito dimensionale. Infine sfrutteremo la trasformata di Fourier “odd" considerando la forma MQ come una funzione definita su un opportuno spazio graduato.

Topologically correct intersection curves of tori and natural quadrics

This thesis provides efficient and robust algorithms for the computation of the intersection curve between a torus and a simple surface (e.g. a plane, a natural quadric or another torus), based on algebraic and numeric methods. The algebraic part includes the classification of the topological type of the intersection curve and the detection of degenerate situations like embedded conic sections and singularities. Moreover, reference points for each connected intersection curve component are determined. The required computations are realised efficiently by solving quartic polynomials at most and exactly by using exact arithmetic. The numeric part includes algorithms for the tracing of each intersection curve component, starting from the previously computed reference points. Using interval arithmetic, accidental incorrectness like jumping between branches or the skipping of parts are prevented. Furthermore, the environments of singularities are correctly treated. Our algorithms are complete in the sense that any kind of input can be handled including degenerate and singular configurations. They are verified, since the results are topologically correct and approximate the real intersection curve up to any arbitrary given error bound. The algorithms are robust, since no human intervention is required and they are efficient in the way that the treatment of algebraic equations of high degree is avoided.

Synthesis of Hand Exoskeletons for the Rehabilitation of Post-Stroke Patients

This dissertation presents the synthesis of a hand exoskeleton (HE) for the rehabilitation of post-stroke patients. Through the analysis of state-of-the-art, a topological classification was proposed. Based on the proposed classification principles, the rehabilitation HEs were systematically analyzed and classified. This classification is helpful to both understand the reason of proposing certain solutions for specific applications and provide some useful guidelines for the design of a new HE, that was actually the primary motivation of this study. Further to this classification, a novel rehabilitation HE was designed to support patients in cylindrical shape grasping tasks with the aim of recovering the basic functions of manipulation. The proposed device comprises five planar mechanisms, one per finger, globally actuated by two electric motors. Indeed, the thumb flexion/extension movement is controlled by one actuator whereas a second actuator is devoted to the control of the flexion/extension of the other four fingers. By focusing on the single finger mechanism, intended as the basic model of the targeted HE, the feasibility study of three different 1 DOF mechanisms are analyzed: a 6-link mechanism, that is connected to the human finger only at its tip, an 8-link and a 12-link mechanisms where phalanges and articulations are part of the kinematic chain. The advantages and drawbacks of each mechanism are deeply analyzed with respect to targeted requirements: the 12-link mechanism was selected as the most suitable solution. The dimensional synthesis based on the Burmester theory as well as kinematic and static analyses were separately done for all fingers in order to satisfy the desired specifications. The HE was finally designed and a prototype was built. The experimental results of the first tests are promising and demonstrate the potential for clinical applications of the proposed device in robot-assisted training of the human hand for grasping functions.

Aging of nuclear power plant cables: in search of non-destructive diagnostic quantities

The safety systems of nuclear power plants rely on low-voltage power, instrumentation and control cables. Inside the containment area, cables operate in harsh environments, characterized by relatively high temperature and gamma-irradiation. As these cables are related to fundamental safety systems, they must be able to withstand unexpected accident conditions and, therefore, their condition assessment is of utmost importance as plants age and lifetime extensions are required. Nowadays, the integrity and functionality of these cables are monitored mainly through destructive test which requires specific laboratory. The investigation of electrical aging markers which can provide information about the state of the cable by non-destructive testing methods would improve significantly the present diagnostic techniques. This work has been made within the framework of the ADVANCE (Aging Diagnostic and Prognostics of Low-Voltage I\&C Cables) project, a FP7 European program. This Ph.D. thesis aims at studying the impact of aging on cable electrical parameters, in order to understand the evolution of the electrical properties associated with cable degradation. The identification of suitable aging markers requires the comparison of the electrical property variation with the physical/chemical degradation mechanisms of polymers for different insulating materials and compositions. The feasibility of non-destructive electrical condition monitoring techniques as potential substitutes for destructive methods will be finally discussed studying the correlation between electrical and mechanical properties. In this work, the electrical properties of cable insulators are monitored and characterized mainly by dielectric spectroscopy, polarization/depolarization current analysis and space charge distribution. Among these techniques, dielectric spectroscopy showed the most promising results; by means of dielectric spectroscopy it is possible to identify the frequency range where the properties are more sensitive to aging. In particular, the imaginary part of permittivity at high frequency, which is related to oxidation, has been identified as the most suitable aging marker based on electrical quantities.

Topologisch kontrollierte Interpolyelektrolytkomplexe aus kettensteifen Polyelektrolyten

Interpolyelektrolytkomplexe bilden sich spontan bei Mischung von Lösungen entgegengesetzt geladener Polyelektrolyte. Dabei sind die Haupttriebkräfte der Entropiegewinn durch die Freisetzung von niedermolekularen Gegenionen sowie die elektrostatischen Wechselwirkungen. In der letzten Zeit sind sie aufgrund ihrer zahlreichen biologischen und technischen Anwendungen in den Fokus des wissenschaftlichen Interesses gerückt. Vor allem die Anwendung von Komplexen aus DNA und kationischen Polyelektrolyten in der nonviralen Gentherapie wird vielfältig diskutiert. rnIn dieser Arbeit wird eine Polystyrolsulfonat-Bürste mit einer Pfropfdichte von 100 % mit einem kationischen Tensid komplexiert und der Komplex in verschiedenen organischen Lösungsmitteln charakterisiert. Dabei zeigt sich eine signifikante Abhängigkeit des Lösungsverhaltens von der Art und der Konzentration zugesetzter Salze. Dieser Polyelektrolyt-Tensid-Komplex wird anschließend als vereinfachtes Modellsystem für die Komplexierung von DNA verwendet. Als kationische Komponente dient zunächst ein kommerzielles PAMAM-Dendrimer der 5. Generation. Dabei steht die Erhaltung der zylindrischen Topologie der anionischen Polyelektrolytbürste in den gebildeten Komplexen im Vordergrund. Durch Variation des Lösungsmittels und des Protonierungsgleichgewichts werden die experimentellen Bedingungen eingegrenzt, bei denen eine solche topologische Kontrolle möglich ist. Es zeigt sich, dass durch die Verwendung von aprotischen organischen Lösungsmitteln gute Erfolge erzielt werden können. Des Weiteren wird das Komplexierungsverhalten stark durch den Zusatz einer Säure oder einer Base beeinflusst, sodass eine topologische Kontrolle mit einem großen Überschuss einer organischen Base auch in protischen Lösungsmitteln wie Wasser und Methanol möglich wird. Anschließend wird das gleiche Polyanion noch mit einer geschützten Polylysin-Bürste in DMF komplexiert, was zur Bildung von kinetisch kontrollierten Aggregaten führt. Die Bildung dieser Aggregate kann durch den Zusatz eines großen Überschusses an Base verhindert werden und es werden zylindrische Komplexe erhalten, die nur aus einer Polylysin-Bürste bestehen. rn

Vulnerability and robustness indices against blackouts in power grids

In this dissertation some novel indices for vulnerability and robustness assessment of power grids are presented. Such indices are mainly defined from the structure of transmission power grids, and with the aim of Blackout (BO) prevention and mitigation. Numerical experiments showing how they could be used alone or in coordination with pre-existing ones to reduce the effects of BOs are discussed. These indices are introduced inside 3 different sujects: The first subject is for taking a look into economical aspects of grids’ operation and their effects in BO propagation. Basically, simulations support that: the determination to operate the grid in the most profitable way could produce an increase in the size or frequency of BOs. Conversely, some uneconomical ways of supplying energy are shown to be less affected by BO phenomena. In the second subject new topological indices are devised to address the question of "which are the best buses to place distributed generation?". The combined use of two indices, is shown as a promising alternative for extracting grid’s significant features regarding robustness against BOs and distributed generation. For this purpose, a new index based on outage shift factors is used along with a previously defined electric centrality index. The third subject is on Static Robustness Analysis of electric networks, from a purely structural point of view. A pair of existing topological indices, (namely degree index and clustering coefficient), are combined to show how degradation of the network structure can be accelerated. Blackout simulations were carried out using the DC Power Flow Method and models of transmission networks from the USA and Europe.

Tecniche regionali di stima della portata di progetto: Impatto della correlazione spaziale tra le serie di osservazioni

La stima degli indici idrometrici in bacini non strumentati rappresenta un problema che la ricerca internazionale ha affrontato attraverso il cosiddetto PUB (Predictions on Ungauged Basins – IAHS, 2002-2013). Attraverso l’analisi di un’area di studio che comprende 61 bacini del Sud-Est americano, si descrivono e applicano due tecniche di stima molto diverse fra loro: il metodo regressivo ai Minimi Quadrati Generalizzati (GLS) e il Topological kriging (TK). Il primo considera una serie di fattori geomorfoclimatici relativi ai bacini oggetto di studio, e ne estrae i pesi per un modello di regressione lineare dei quantili; il secondo è un metodo di tipo geostatistico che considera il quantile come una variabile regionalizzata su supporto areale (l’area del bacino), tenendo conto della dislocazione geografica e l’eventuale struttura annidata dei bacini d’interesse. L’applicazione di questi due metodi ha riguardato una serie di quantili empirici associati ai tempi di ritorno di 10, 50, 100 e 500 anni, con lo scopo di valutare le prestazioni di un loro possibile accoppiamento, attraverso l’interpolazione via TK dei residui GLS in cross-validazione jack-knife e con differenti vicinaggi. La procedura risulta essere performante, con un indice di efficienza di Nash-Sutcliffe pari a 0,9 per tempi di ritorno bassi ma stazionario su 0,8 per gli altri valori, con un trend peggiorativo all’aumentare di TR e prestazioni pressoché invariate al variare del vicinaggio. L’applicazione ha mostrato che i risultati possono migliorare le prestazioni del metodo GLS ed essere paragonabili ai risultati del TK puro, confermando l’affidabilità del metodo geostatistico ad applicazioni idrologiche.

Computersimulationen zum Einfluss topologischer Beschränkungen auf Polymere

Topologische Beschränkungen beeinflussen die Eigenschaften von Polymeren. Im Rahmen dieser Arbeit wird mit Hilfe von Computersimulationen im Detail untersucht, inwieweit sich die statischen Eigenschaften von kollabierten Polymerringen, Polymerringen in konzentrierten Lösungen und aus Polymerringen aufgebauten Bürsten mit topologischen Beschränkungen von solchen ohne topologische Beschränkungen unterscheiden. Des Weiteren wird analysiert, welchen Einfluss geometrische Beschränkungen auf die topologischen Eigenschaften von einzelnen Polymerketten besitzen. Im ersten Teil der Arbeit geht es um den Einfluss der Topologie auf die Eigenschaften einzelner Polymerketten in verschiedenen Situationen. Da allerdings gerade die effiziente Durchführung von Monte-Carlo-Simulationen von kollabierten Polymerketten eine große Herausforderung darstellt, werden zunächst drei Bridging-Monte-Carlo-Schritte für Gitter- auf Kontinuumsmodelle übertragen. Eine Messung der Effizienz dieser Schritte ergibt einen Beschleunigungsfaktor von bis zu 100 im Vergleich zum herkömmlichen Slithering-Snake-Algorithmus. Darauf folgt die Analyse einer einzelnen, vergröberten Polystyrolkette in sphärischer Geometrie hinsichtlich Verschlaufungen und Knoten. Es wird gezeigt, dass eine signifikante Verknotung der Polystrolkette erst eintritt, wenn der Radius des umgebenden Kapsids kleiner als der Gyrationsradius der Kette ist. Des Weiteren werden sowohl Monte-Carlo- als auch Molekulardynamiksimulationen sehr großer Ringe mit bis zu einer Million Monomeren im kollabierten Zustand durchgeführt. Während die Konfigurationen aus den Monte-Carlo-Simulationen aufgrund der Verwendung der Bridging-Schritte sehr stark verknotet sind, bleiben die Konfigurationen aus den Molekulardynamiksimulationen unverknotet. Hierbei zeigen sich signifikante Unterschiede sowohl in der lokalen als auch in der globalen Struktur der Ringpolymere. Im zweiten Teil der Arbeit wird das Skalierungsverhalten des Gyrationsradius der einzelnen Polymerringe in einer konzentrierten Lösung aus völlig flexiblen Polymerringen im Kontinuum untersucht. Dabei wird der Anfang des asymptotischen Skalierungsverhaltens, welches mit dem Modell des “fractal globules“ konsistent ist, erreicht. Im abschließenden, dritten Teil dieser Arbeit wird das Verhalten von Bürsten aus linearen Polymeren mit dem von Ringpolymerbürsten verglichen. Dabei zeigt sich, dass die Struktur und das Skalierungsverhalten beider Systeme mit identischem Dichteprofil parallel zum Substrat deutlich voneinander abweichen, obwohl die Eigenschaften beider Systeme in Richtung senkrecht zum Substrat übereinstimmen. Der Vergleich des Relaxationsverhaltens einzelner Ketten in herkömmlichen Polymerbürsten und Ringbürsten liefert keine gravierenden Unterschiede. Es stellt sich aber auch heraus, dass die bisher verwendeten Erklärungen zur Relaxationsverhalten von herkömmlichen Bürsten nicht ausreichen, da diese lediglich den anfänglichen Zerfall der Korrelationsfunktion berücksichtigen. Bei der Untersuchung der Dynamik einzelner Monomere in einer herkömmlichen Bürste aus offenen Ketten vom Substrat hin zum offenen Ende zeigt sich, dass die Monomere in der Mitte der Kette die langsamste Relaxation besitzen, obwohl ihre mittlere Verrückung deutlich kleiner als die der freien Endmonomere ist.

Higher Chern-Simons gauge theory

Higher gauge theory arises naturally in superstring theory, but many of its features remain obscure. In this thesis, after an exposition of the bacis tools in local higher gauge theory, a higher gauge Chern-Simons model is defined. We discuss the classical equations of motion as well as the behaviour of the gauge anomaly. We perform canonical quantization and we introduce two possible quantization schemes for the model. We also expound higher parallel transport in higher gauge theory, and we speculate that it can provide Wilson surfaces as topological observables for the higher gauge Chern-Simons theory.

Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

Inimmaginabile e progetto. Architettura e memoria nei luoghi della Deportazione

La memoria pubblica della Sho'ah è inscritta in una quantità proliferante di immagini e spazi memoriali. Ciò è riscontrabile in modo particolare nei principali "siti dello sterminio" assurti a simbolo nel corso degli anni, mentre molti altri "luoghi di memoria" della Deportazione soffrono di una condizione di intrinseca debolezza. Essa è riconducibile in primo luogo alla fragilità del dato materiale, i cui resti ormai privi di eloquenza risultano difficili da interpretare e conservare, in secondo luogo alla sovrapposizione di memorie concorrenti venutesi a determinare in conseguenza dei riusi successivi a cui queste strutture sono spesso andate soggette dopo la guerra, infine alla difficoltà di rendere espressione compiuta alla tragedia della Deportazione. Il caso del campo di Fossoli è paradigmatico: esso interroga la capacità del progetto di "dare forma" al palinsesto delle memorie, rendendo possibile il riconoscimento ed esplicitando una significazione delle tracce, senza aggiungere ulteriori interpretazioni. Lo spazio e il paesaggio, in quanto linguaggi indentitari, possono offrirsi come strumenti da questo punto di vista. Michel De Certeau vi fa riferimento quando afferma che lo spazio coincide con «l’effetto prodotto dalle operazioni che lo orientano, che lo circostanziano, o temporalizzano e lo fanno funzionare come unità polivalente di programmi conflittuali o di prossimità contrattuali». Lo spazio gioca un ruolo cruciale nel conformare l'esperienza del presente e allo stesso tempo nel rendere visibili le esperienze passate, compresse nella memoria collettiva. Lo scopo di questa ricerca è interrogare le potenzialità spaziali del luogo, considerate sotto il profilo culturale e semantico, come valida alternativa alla forma-monumento nella costruzione di una o più narrazioni pertinenti della memoria.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Exploring Quantum Speed-up Through Cluster-state Computers

The aim of this thesis is to investigate the nature of quantum computation and the question of the quantum speed-up over classical computation by comparing two different quantum computational frameworks, the traditional quantum circuit model and the cluster-state quantum computer. After an introductory survey of the theoretical and epistemological questions concerning quantum computation, the first part of this thesis provides a presentation of cluster-state computation suitable for a philosophical audience. In spite of the computational equivalence between the two frameworks, their differences can be considered as structural. Entanglement is shown to play a fundamental role in both quantum circuits and cluster-state computers; this supports, from a new perspective, the argument that entanglement can reasonably explain the quantum speed-up over classical computation. However, quantum circuits and cluster-state computers diverge with regard to one of the explanations of quantum computation that actually accords a central role to entanglement, i.e. the Everett interpretation. It is argued that, while cluster-state quantum computation does not show an Everettian failure in accounting for the computational processes, it threatens that interpretation of being not-explanatory. This analysis presented here should be integrated in a more general work in order to include also further frameworks of quantum computation, e.g. topological quantum computation. However, what is revealed by this work is that the speed-up question does not capture all that is at stake: both quantum circuits and cluster-state computers achieve the speed-up, but the challenges that they posit go besides that specific question. Then, the existence of alternative equivalent quantum computational models suggests that the ultimate question should be moved from the speed-up to a sort of “representation theorem” for quantum computation, to be meant as the general goal of identifying the physical features underlying these alternative frameworks that allow for labelling those frameworks as “quantum computation”.