Simulation studies of correlation functions and relaxation in polymeric systems

We investigate the statics and dynamics of a glassy,non-entangled, short bead-spring polymer melt with moleculardynamics simulations. Temperature ranges from slightlyabove the mode-coupling critical temperature to the liquidregime where features of a glassy liquid are absent. Ouraim is to work out the polymer specific effects on therelaxation and particle correlation. We find the intra-chain static structure unaffected bytemperature, it depends only on the distance of monomersalong the backbone. In contrast, the distinct inter-chainstructure shows pronounced site-dependence effects at thelength-scales of the chain and the nearest neighbordistance. There, we also find the strongest temperaturedependence which drives the glass transition. Both the siteaveraged coupling of the monomer and center of mass (CM) andthe CM-CM coupling are weak and presumably not responsiblefor a peak in the coherent relaxation time at the chain'slength scale. Chains rather emerge as soft, easilyinterpenetrating objects. Three particle correlations arewell reproduced by the convolution approximation with theexception of model dependent deviations. In the spatially heterogeneous dynamics of our system weidentify highly mobile monomers which tend to follow eachother in one-dimensional paths forming ``strings''. Thesestrings have an exponential length distribution and aregenerally short compared to the chain length. Thus, arelaxation mechanism in which neighboring mobile monomersmove along the backbone of the chain seems unlikely.However, the correlation of bonded neighbors is enhanced. When liquids are confined between two surfaces in relativesliding motion kinetic friction is observed. We study ageneric model setup by molecular dynamics simulations for awide range of sliding speeds, temperatures, loads, andlubricant coverings for simple and molecular fluids. Instabilities in the particle trajectories are identified asthe origin of kinetic friction. They lead to high particlevelocities of fluid atoms which are gradually dissipatedresulting in a friction force. In commensurate systemsfluid atoms follow continuous trajectories for sub-monolayercoverings and consequently, friction vanishes at low slidingspeeds. For incommensurate systems the velocity probabilitydistribution exhibits approximately exponential tails. Weconnect this velocity distribution to the kinetic frictionforce which reaches a constant value at low sliding speeds. This approach agrees well with the friction obtaineddirectly from simulations and explains Amontons' law on themicroscopic level. Molecular bonds in commensurate systemslead to incommensurate behavior, but do not change thequalitative behavior of incommensurate systems. However,crossed chains form stable load bearing asperities whichstrongly increase friction.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

On moduli spaces of semistable sheaves on K3 surfaces

Ich untersuche die nicht bereits durch die Arbeit "Singular symplectic moduli spaces" von Kaledin, Lehn und Sorger (Invent. Math. 164 (2006), no. 3) abgedeckten Fälle von Modulräumen halbstabiler Garben auf projektiven K3-Flächen - die Fälle mit Mukai-Vektor (0,c,0) sowie die Modulräume zu nichtgenerischen amplen Divisoren - hinsichtlich der möglichen Konstruktion neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten. Ich stelle einen Zusammenhang zu den bereits untersuchten Modulräumen und Verallgemeinerungen derselben her und erweitere bekannte Ergebnisse auf alle offenen Fälle von Garben vom Rang 0 und viele Fälle von Garben von positivem Rang. Insbesondere kann in diesen Fällen die Existenz neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten, die birational über Komponenten des Modulraums liegen, ausgeschlossen werden.

Moduli spaces of (G,h)-constellations

Given a reductive group G acting on an affine scheme X over C and a Hilbert function h: Irr G → N_0, we construct the moduli space M_Ө(X) of Ө-stable (G,h)-constellations on X, which is a common generalisation of the invariant Hilbert scheme after Alexeev and Brion and the moduli space of Ө-stable G-constellations for finite groups G introduced by Craw and Ishii. Our construction of a morphism M_Ө(X) → X//G makes this moduli space a candidate for a resolution of singularities of the quotient X//G. Furthermore, we determine the invariant Hilbert scheme of the zero fibre of the moment map of an action of Sl_2 on (C²)⁶ as one of the first examples of invariant Hilbert schemes with multiplicities. While doing this, we present a general procedure for the realisation of such calculations. We also consider questions of smoothness and connectedness and thereby show that our Hilbert scheme gives a resolution of singularities of the symplectic reduction of the action.

Use of computer algebra in the calculation of Feynman diagrams

The increasing precision of current and future experiments in high-energy physics requires a likewise increase in the accuracy of the calculation of theoretical predictions, in order to find evidence for possible deviations of the generally accepted Standard Model of elementary particles and interactions. Calculating the experimentally measurable cross sections of scattering and decay processes to a higher accuracy directly translates into including higher order radiative corrections in the calculation. The large number of particles and interactions in the full Standard Model results in an exponentially growing number of Feynman diagrams contributing to any given process in higher orders. Additionally, the appearance of multiple independent mass scales makes even the calculation of single diagrams non-trivial. For over two decades now, the only way to cope with these issues has been to rely on the assistance of computers. The aim of the xloops project is to provide the necessary tools to automate the calculation procedures as far as possible, including the generation of the contributing diagrams and the evaluation of the resulting Feynman integrals. The latter is based on the techniques developed in Mainz for solving one- and two-loop diagrams in a general and systematic way using parallel/orthogonal space methods. These techniques involve a considerable amount of symbolic computations. During the development of xloops it was found that conventional computer algebra systems were not a suitable implementation environment. For this reason, a new system called GiNaC has been created, which allows the development of large-scale symbolic applications in an object-oriented fashion within the C++ programming language. This system, which is now also in use for other projects besides xloops, is the main focus of this thesis. The implementation of GiNaC as a C++ library sets it apart from other algebraic systems. Our results prove that a highly efficient symbolic manipulator can be designed in an object-oriented way, and that having a very fine granularity of objects is also feasible. The xloops-related parts of this work consist of a new implementation, based on GiNaC, of functions for calculating one-loop Feynman integrals that already existed in the original xloops program, as well as the addition of supplementary modules belonging to the interface between the library of integral functions and the diagram generator.

The massless two-loop two-point function and zeta functions in counterterms of Feynman diagrams

The main part of this thesis describes a method of calculating the massless two-loop two-point function which allows expanding the integral up to an arbitrary order in the dimensional regularization parameter epsilon by rewriting it as a double Mellin-Barnes integral. Closing the contour and collecting the residues then transforms this integral into a form that enables us to utilize S. Weinzierl's computer library nestedsums. We could show that multiple zeta values and rational numbers are sufficient for expanding the massless two-loop two-point function to all orders in epsilon. We then use the Hopf algebra of Feynman diagrams and its antipode, to investigate the appearance of Riemann's zeta function in counterterms of Feynman diagrams in massless Yukawa theory and massless QED. The class of Feynman diagrams we consider consists of graphs built from primitive one-loop diagrams and the non-planar vertex correction, where the vertex corrections only depend on one external momentum. We showed the absence of powers of pi in the counterterms of the non-planar vertex correction and diagrams built by shuffling it with the one-loop vertex correction. We also found the invariance of some coefficients of zeta functions under a change of momentum flow through these vertex corrections.

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Neuronal differentiation and epithelial integrity: the role of Drosophila Short stop

The nervous system is the most complex organ in animals and the ordered interconnection of neurons is an essential prerequisite for normal behaviour. Neuronal connectivity requires controlled neuronal growth and differentiation. Neuronal growth essentially depends on the actin and microtubule cytoskeleton, and it has become increasingly clear, that crosslinking of these cytoskeletal fractions is a crucial regulatory process. The Drosophila Spectraplakin family member Short stop (Shot) is such a crosslinker and is crucial for several aspects of neuronal growth. Shot comprises various domains: An actin binding domain, a plakin-like domain, a rod domain, calcium responsive EF-hand motifs, a microtubule binding Gas2 domain, a GSR motif and a C-terminal EB1aff domain. Amongst other phenotypes, shot mutant animals exhibit severely reduced dendrites and neuromuscular junctions, the subcellular compartmentalisation of the transmembrane protein Fasciclin2 is affected, but it is also crucially required in other tissues, for example for the integrity of tendon cells, specialised epidermal cells which anchor muscles to the body wall. Despite these striking phenotypes, Shot function is little understood, and especially we do not understand how it can carry out functions as diverse as those described above. To bridge this gap, I capitalised on the genetic possibilities of the model system Drosophila melanogaster and carried out a structure-function analysis in different neurodevelopmental contexts and in tendon cells. To this end, I used targeted gene expression of existing and newly generated Shot deletion constructs in Drosophila embryos and larvae, analyses of different shot mutant alleles, and transfection of Shot constructs into S2 cells or cultured fibroblasts. My analyses reveal that a part of the Shot C-terminus is not essential in the nervous system but in tendon cells where it stabilises microtubules. The precise molecular mechanism underlying this activity is not yet elucidated but, based on the findings presented here, I have developed three alternative testable hypothesis. Thus, either binding of the microtubule plus-end tracking molecule EB1 through an EB1aff domain, microtubulebundling through a GSR rich motif or a combination of both may explain a context-specific requirement of the Shot C-terminus for tendon cell integrity. Furthermore, I find that the calcium binding EF-hand motif in Shot is exclusively required for a subset of neuronal functions of Shot but not in the epidermal tendon cells. These findings pave the way for complementary studies studying the impact of [Ca2+] on Shot function. Besides these differential requirements of Shot domains I find, that most Shot domains are required in the nervous system and tendon cells alike. Thus the microtubule Gas2 domain shows no context specific requirements and is equally essential in all analysed cellular contexts. Furthermore, I could demonstrate a partial requirement of the large spectrin-repeat rod domain of Shot in neuronal and epidermal contexts. I demonstrate that this domain is partially required in processes involving growth and/or tissue stability but dispensable for cellular processes where no mechanical stress resistance is required. In addition, I demonstrate that the CH1 domain a part of the N-terminal actin binding domain of Shot is only partially required for all analysed contexts. Thus, I conclude that Shot domains are functioning different in various cellular environments. In addition my study lays the base for future projects, such as the elucidation of Shot function in growth cones. Given the high degree of conservation between Shot and its mammalian orthologues MACF1/ACF7 and BPAG1, I believe that the findings presented in this study will contribute to the general understanding of spectraplakins across species borders.

The Euler number of OGradys 10-dimensional symplectic manifold

Wir berechnen die Eulerzahl der 10-dimensionalen exzeptionellen irreduziblen symplektischen Mannigfaltigkeit, die von O Grady konstruiert wurde. Die Idee besteht darin, zunächst eine Lagrangefaserung zu konstruieren und dann die Eulerzahlen der Fasern zu berechnen. Es stellt sich heraus, dass fast alle Fasern die Eulerzahl 0 haben, und deswegen reduziert sich das Problem auf die Berechnung der Eulerzahlen der übrigen Fasern. Diese Fasern sind Modulräume von halbstabilen Garben auf singulären Kurven. Der Hauptteil dieser Dissertation ist der Berechnung der Eulerzahlen dieser Modulräume gewidmet. Diese Resultate sind von unabhängigem Interesse.

Reinforcement Lernen mit Regularisierungsnetzwerken

Die Arbeit behandelt das Problem der Skalierbarkeit von Reinforcement Lernen auf hochdimensionale und komplexe Aufgabenstellungen. Unter Reinforcement Lernen versteht man dabei eine auf approximativem Dynamischen Programmieren basierende Klasse von Lernverfahren, die speziell Anwendung in der Künstlichen Intelligenz findet und zur autonomen Steuerung simulierter Agenten oder realer Hardwareroboter in dynamischen und unwägbaren Umwelten genutzt werden kann. Dazu wird mittels Regression aus Stichproben eine Funktion bestimmt, die die Lösung einer "Optimalitätsgleichung" (Bellman) ist und aus der sich näherungsweise optimale Entscheidungen ableiten lassen. Eine große Hürde stellt dabei die Dimensionalität des Zustandsraums dar, die häufig hoch und daher traditionellen gitterbasierten Approximationsverfahren wenig zugänglich ist. Das Ziel dieser Arbeit ist es, Reinforcement Lernen durch nichtparametrisierte Funktionsapproximation (genauer, Regularisierungsnetze) auf -- im Prinzip beliebig -- hochdimensionale Probleme anwendbar zu machen. Regularisierungsnetze sind eine Verallgemeinerung von gewöhnlichen Basisfunktionsnetzen, die die gesuchte Lösung durch die Daten parametrisieren, wodurch die explizite Wahl von Knoten/Basisfunktionen entfällt und so bei hochdimensionalen Eingaben der "Fluch der Dimension" umgangen werden kann. Gleichzeitig sind Regularisierungsnetze aber auch lineare Approximatoren, die technisch einfach handhabbar sind und für die die bestehenden Konvergenzaussagen von Reinforcement Lernen Gültigkeit behalten (anders als etwa bei Feed-Forward Neuronalen Netzen). Allen diesen theoretischen Vorteilen gegenüber steht allerdings ein sehr praktisches Problem: der Rechenaufwand bei der Verwendung von Regularisierungsnetzen skaliert von Natur aus wie O(n**3), wobei n die Anzahl der Daten ist. Das ist besonders deswegen problematisch, weil bei Reinforcement Lernen der Lernprozeß online erfolgt -- die Stichproben werden von einem Agenten/Roboter erzeugt, während er mit der Umwelt interagiert. Anpassungen an der Lösung müssen daher sofort und mit wenig Rechenaufwand vorgenommen werden. Der Beitrag dieser Arbeit gliedert sich daher in zwei Teile: Im ersten Teil der Arbeit formulieren wir für Regularisierungsnetze einen effizienten Lernalgorithmus zum Lösen allgemeiner Regressionsaufgaben, der speziell auf die Anforderungen von Online-Lernen zugeschnitten ist. Unser Ansatz basiert auf der Vorgehensweise von Recursive Least-Squares, kann aber mit konstantem Zeitaufwand nicht nur neue Daten sondern auch neue Basisfunktionen in das bestehende Modell einfügen. Ermöglicht wird das durch die "Subset of Regressors" Approximation, wodurch der Kern durch eine stark reduzierte Auswahl von Trainingsdaten approximiert wird, und einer gierigen Auswahlwahlprozedur, die diese Basiselemente direkt aus dem Datenstrom zur Laufzeit selektiert. Im zweiten Teil übertragen wir diesen Algorithmus auf approximative Politik-Evaluation mittels Least-Squares basiertem Temporal-Difference Lernen, und integrieren diesen Baustein in ein Gesamtsystem zum autonomen Lernen von optimalem Verhalten. Insgesamt entwickeln wir ein in hohem Maße dateneffizientes Verfahren, das insbesondere für Lernprobleme aus der Robotik mit kontinuierlichen und hochdimensionalen Zustandsräumen sowie stochastischen Zustandsübergängen geeignet ist. Dabei sind wir nicht auf ein Modell der Umwelt angewiesen, arbeiten weitestgehend unabhängig von der Dimension des Zustandsraums, erzielen Konvergenz bereits mit relativ wenigen Agent-Umwelt Interaktionen, und können dank des effizienten Online-Algorithmus auch im Kontext zeitkritischer Echtzeitanwendungen operieren. Wir demonstrieren die Leistungsfähigkeit unseres Ansatzes anhand von zwei realistischen und komplexen Anwendungsbeispielen: dem Problem RoboCup-Keepaway, sowie der Steuerung eines (simulierten) Oktopus-Tentakels.

Pseudodifferential analysis in Psi*-algebras on transmission spaces, infinite solving ideal chains and K-theory for conformally compact spaces

The present thesis is a contribution to the theory of algebras of pseudodifferential operators on singular settings. In particular, we focus on the $b$-calculus and the calculus on conformally compact spaces in the sense of Mazzeo and Melrose in connection with the notion of spectral invariant transmission operator algebras. We summarize results given by Gramsch et. al. on the construction of $Psi_0$-and $Psi*$-algebras and the corresponding scales of generalized Sobolev spaces using commutators of certain closed operators and derivations. In the case of a manifold with corners $Z$ we construct a $Psi*$-completion $A_b(Z,{}^bOmega^{1/2})$ of the algebra of zero order $b$-pseudodifferential operators $Psi_{b,cl}(Z, {}^bOmega^{1/2})$ in the corresponding $C*$-closure $B(Z,{}^bOmega^{12})hookrightarrow L(L^2(Z,{}^bOmega^{1/2}))$. The construction will also provide that localised to the (smooth) interior of Z the operators in the $A_b(Z, {}^bOmega^{1/2})$ can be represented as ordinary pseudodifferential operators. In connection with the notion of solvable $C*$-algebras - introduced by Dynin - we calculate the length of the $C*$-closure of $Psi_{b,cl}^0(F,{}^bOmega^{1/2},R^{E(F)})$ in $B(F,{}^bOmega^{1/2}),R^{E(F)})$ by localizing $B(Z, {}^bOmega^{1/2})$ along the boundary face $F$ using the (extended) indical familiy $I^B_{FZ}$. Moreover, we discuss how one can localise a certain solving ideal chain of $B(Z, {}^bOmega^{1/2})$ in neighbourhoods $U_p$ of arbitrary points $pin Z$. This localisation process will recover the singular structure of $U_p$; further, the induced length function $l_p$ is shown to be upper semi-continuous. We give construction methods for $Psi*$- and $C*$-algebras admitting only infinite long solving ideal chains. These algebras will first be realized as unconnected direct sums of (solvable) $C*$-algebras and then refined such that the resulting algebras have arcwise connected spaces of one dimensional representations. In addition, we recall the notion of transmission algebras on manifolds with corners $(Z_i)_{iin N}$ following an idea of Ali Mehmeti, Gramsch et. al. Thereby, we connect the underlying $C^infty$-function spaces using point evaluations in the smooth parts of the $Z_i$ and use generalized Laplacians to generate an appropriate scale of Sobolev spaces. Moreover, it is possible to associate generalized (solving) ideal chains to these algebras, such that to every $ninN$ there exists an ideal chain of length $n$ within the algebra. Finally, we discuss the $K$-theory for algebras of pseudodifferential operators on conformally compact manifolds $X$ and give an index theorem for these operators. In addition, we prove that the Dirac-operator associated to the metric of a conformally compact manifold $X$ is not a Fredholm operator.

Early steps in ventral nerve cord development in chelicerates and myriapods and formation of brain compartments in spiders

The central point of this work is the investigation of neurogenesis in chelicerates and myriapods. By comparing decisive mechanisms in neurogenesis in the four arthropod groups (Chelicerata, Crustacea, Insecta, Myriapoda) I was able to show which of these mechanisms are conserved and which developmental modules have diverged. Thereby two processes of embryonic development of the central nervous system were brought into focus. On the one hand I studied early neurogenesis in the ventral nerve cord of the spiders Cupiennius salei and Achaearanea tepidariorum and the millipede Glomeris marginata and on the other hand the development of the brain in Cupiennius salei.rnWhile the nervous system of insects and crustaceans is formed by the progeny of single neural stem cells (neuroblasts), in chelicerates and myriapods whole groups of cells adopt the neural cell fate and give rise to the ventral nerve cord after their invagination. The detailed comparison of the positions and the number of the neural precursor groups within the neuromeres in chelicerates and myriapods showed that the pattern is almost identical which suggests that the neural precursors groups in these arthropod groups are homologous. This pattern is also very similar to the neuroblast pattern in insects. This raises the question if the mechanisms that confer regional identity to the neural precursors is conserved in arthropods although the mode of neural precursor formation is different. The analysis of the functions and expression patterns of genes which are known to be involved in this mechanism in Drosophila melanogaster showed that neural patterning is highly conserved in arthropods. But I also discovered differences in early neurogenesis which reflect modifications and adaptations in the development of the nervous systems in the different arthropod groups.rnThe embryonic development of the brain in chelicerates which was investigated for the first time in this work shows similarities but also some modifications to insects. In vertebrates and arthropods the adult brain is composed of distinct centres with different functions. Investigating how these centres, which are organised in smaller compartments, develop during embryogenesis was part of this work. By tracing the morphogenetic movements and analysing marker gene expressions I could show the formation of the visual brain centres from the single-layered precheliceral neuroectoderm. The optic ganglia, the mushroom bodies and the arcuate body (central body) are formed by large invaginations in the peripheral precheliceral neuroectoderm. This epithelium itself contains neural precursor groups which are assigned to the respective centres and thereby build the three-dimensional optical centres. The single neural precursor groups are distinguishable during this process leading to the assumption that they carry positional information which might subdivide the individual brain centres into smaller functional compartments.rn

Conceptual and normative issues of memory enhancement

Our growing understanding of human mind and cognition and the development of neurotechnology has triggered debate around cognitive enhancement in neuroethics. The dissertation examines the normative issues of memory enhancement, and focuses on two issues: (1) the distinction between memory treatment and enhancement; and (2) how the issue of authenticity concerns memory interventions, including memory treatments and enhancements. rnThe first part consists of a conceptual analysis of the concepts required for normative considerations. First, the representational nature and the function of memory are discussed. Memory is regarded as a special form of self-representation resulting from a constructive processes. Next, the concepts of selfhood, personhood, and identity are examined and a conceptual tool—the autobiographical self-model (ASM)—is introduced. An ASM is a collection of mental representations of the system’s relations with its past and potential future states. Third, the debate between objectivist and constructivist views of health are considered. I argue for a phenomenological account of health, which is based on the primacy of illness and negative utilitarianism.rnThe second part presents a synthesis of the relevant normative issues based on the conceptual tools developed. I argue that memory enhancement can be distinguished from memory treatment using a demarcation regarding the existence of memory-related suffering. That is, memory enhancements are, under standard circumstances and without any unwilling suffering or potential suffering resulting from the alteration of memory functions, interventions that aim to manipulate memory function based on the self-interests of the individual. I then consider the issue of authenticity, namely whether memory intervention or enhancement endangers “one’s true self”. By analyzing two conceptions of authenticity—authenticity as self-discovery and authenticity as self-creation, I propose that authenticity should be understood in terms of the satisfaction of the functional constraints of an ASM—synchronic coherence, diachronic coherence, and global veridicality. This framework provides clearer criteria for considering the relevant concerns and allows us to examine the moral values of authenticity. rn