Coordination and Control of Autonomous Mobile Robots Swarms by using Particle Swarm Optimization Algorithm and Consensus Theory

This thesis presents some different techniques designed to drive a swarm of robots in an a-priori unknown environment in order to move the group from a starting area to a final one avoiding obstacles. The presented techniques are based on two different theories used alone or in combination: Swarm Intelligence (SI) and Graph Theory. Both theories are based on the study of interactions between different entities (also called agents or units) in Multi- Agent Systems (MAS). The first one belongs to the Artificial Intelligence context and the second one to the Distributed Systems context. These theories, each one from its own point of view, exploit the emergent behaviour that comes from the interactive work of the entities, in order to achieve a common goal. The features of flexibility and adaptability of the swarm have been exploited with the aim to overcome and to minimize difficulties and problems that can affect one or more units of the group, having minimal impact to the whole group and to the common main target. Another aim of this work is to show the importance of the information shared between the units of the group, such as the communication topology, because it helps to maintain the environmental information, detected by each single agent, updated among the swarm. Swarm Intelligence has been applied to the presented technique, through the Particle Swarm Optimization algorithm (PSO), taking advantage of its features as a navigation system. The Graph Theory has been applied by exploiting Consensus and the application of the agreement protocol with the aim to maintain the units in a desired and controlled formation. This approach has been followed in order to conserve the power of PSO and to control part of its random behaviour with a distributed control algorithm like Consensus.

A novel functional renormalization group framework for gauge theories and gravity

In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for krightarrowinfty and the standard effective action rnfor krightarrow0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NLsigmaM) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or field strength. Crucial to the practical use of this expansion is the development of new techniques to manage functional traces such as the algorithm proposed in this thesis. This allows to project the flow of all terms in the EAA which are analytic in the fields. As an application we show how the low energy effective action for quantum gravity emerges as the result of integrating the RG flow. In any treatment of theories with local symmetries that introduces a reference scale, the question of preserving gauge invariance along the flow emerges as predominant. In the EAA framework this problem is dealt with the use of the background field formalism. This comes at the cost of enlarging the theory space where the EAA lives to the space of functionals of both fluctuation and background fields. In this thesis, we study how the identities dictated by the symmetries are modified by the introduction of the cutoff and we study so called bimetric truncations of the EAA that contain both fluctuation and background couplings. In particular, we confirm the existence of a non-Gaussian fixed point for QEG, that is at the heart of the Asymptotic Safety scenario in quantum gravity; in the enlarged bimetric theory space where the running of the cosmological constant and of Newton's constant is influenced by fluctuation couplings.

Diffusion maps in the Subriemannian motion group and perceptual grouping

Il presente lavoro è motivato dal problema della constituzione di unità percettive a livello della corteccia visiva primaria V1. Si studia dettagliatamente il modello geometrico di Citti-Sarti con particolare attenzione alla modellazione di fenomeni di associazione visiva. Viene studiato nel dettaglio un modello di connettività. Il contributo originale risiede nell'adattamento del metodo delle diffusion maps, recentemente introdotto da Coifman e Lafon, alla geometria subriemanniana della corteccia visiva. Vengono utilizzati strumenti di teoria del potenziale, teoria spettrale, analisi armonica in gruppi di Lie per l'approssimazione delle autofunzioni dell'operatore del calore sul gruppo dei moti rigidi del piano. Le autofunzioni sono utilizzate per l'estrazione di unità percettive nello stimolo visivo. Sono presentate prove sperimentali e originali delle capacità performanti del metodo.

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.

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

Highly accurate quantum chemistry : spin-orbit splittings via multireference coupled-cluster methods and applications in heavy-atom main-group chemistry

Diese Dissertation demonstriert und verbessert die Vorhersagekraft der Coupled-Cluster-Theorie im Hinblick auf die hochgenaue Berechnung von Moleküleigenschaften. Die Demonstration erfolgt mittels Extrapolations- und Additivitätstechniken in der Single-Referenz-Coupled-Cluster-Theorie, mit deren Hilfe die Existenz und Struktur von bisher unbekannten Molekülen mit schweren Hauptgruppenelementen vorhergesagt wird. Vor allem am Beispiel von cyclischem SiS_2, einem dreiatomigen Molekül mit 16 Valenzelektronen, wird deutlich, dass die Vorhersagekraft der Theorie sich heutzutage auf Augenhöhe mit dem Experiment befindet: Theoretische Überlegungen initiierten eine experimentelle Suche nach diesem Molekül, was schließlich zu dessen Detektion und Charakterisierung mittels Rotationsspektroskopie führte. Die Vorhersagekraft der Coupled-Cluster-Theorie wird verbessert, indem eine Multireferenz-Coupled-Cluster-Methode für die Berechnung von Spin-Bahn-Aufspaltungen erster Ordnung in 2^Pi-Zuständen entwickelt wird. Der Fokus hierbei liegt auf Mukherjee's Variante der Multireferenz-Coupled-Cluster-Theorie, aber prinzipiell ist das vorgeschlagene Berechnungsschema auf alle Varianten anwendbar. Die erwünschte Genauigkeit beträgt 10 cm^-1. Sie wird mit der neuen Methode erreicht, wenn Ein- und Zweielektroneneffekte und bei schweren Elementen auch skalarrelativistische Effekte berücksichtigt werden. Die Methode eignet sich daher in Kombination mit Coupled-Cluster-basierten Extrapolations-und Additivitätsschemata dafür, hochgenaue thermochemische Daten zu berechnen.

The Making of a Shiite Bourgeoisie in Lebanon Political Mobilisation, Economic Resources and Formation of a Social Group

The thesis analyses the making of the Shiite middle- and upper/entrepreneurial-class in Lebanon from the 1960s till the present day. The trajectory explores the historical, political and social (internal and external) factors that brought a sub-proletariat to mobilise and become an entrepreneurial bourgeoisie in the span of less than three generations. This work proposes the main theoretical hypothesis to unpack and reveal the trajectory of a very recent social class that through education, diaspora, political and social mobilisation evolved in a few years into a very peculiar bourgeoisie: whereas Christian-Maronite middle class practically produced political formations and benefited from them and from Maronite’s state supremacy (National Pact, 1943) reinforcing the community’s status quo, Shiites built their own bourgeoisie from within, and mobilised their “cadres” (Boltanski) not just to benefit from their renovated presence at the state level, but to oppose to it. The general Social Movement Theory (SMT), as well as a vast amount of the literature on (middle) class formation are therefore largely contradicted, opening up new territories for discussion on how to build a bourgeoisie without the state’s support (Social Mobilisation Theory, Resource Mobilisation Theory) and if, eventually, the middle class always produces democratic movements (the emergence of a social group out of backwardness and isolation into near dominance of a political order). The middle/upper class described here is at once an economic class related to the control of multiple forms of capital, and produced by local, national, and transnational networks related to flows of services, money, and education, and a culturally constructed social location and identity structured by economic as well as other forms of capital in relation to other groups in Lebanon.

Clutch-size adjustments and skew models: effects on reproductive partitioning and group stability

Reproductive skew theory seeks to integrate social and ecological factors thought to influence the division of reproduction among group-living animals. However, most reproductive skew models only examine interactions between individuals of the same sex. Here, we suggest that females can influence group stability and conflict among males by modifying their clutch size and may do so if they benefit from the presence of subordinate male helpers or from reduced conflict. We develop 3 models, based on concessions-based, restraint, and tug-of-war models, in which female clutch size is variable and ask when females will increase their clutch size above that which would be optimal in the absence of male-male conflict. In concessions-based and restraint models, females should increase clutch size above their optima if the benefits of staying for subordinate males are relatively low. Relatedness between males has no effect on clutch size. When females do increase clutch size, the division of reproduction between males is not influenced by relatedness and does not differ between restraint and concessions-based models. Both of these predictions are in sharp contrast to previous models. In tug-of-war models, clutch size is strongly influenced by relatedness between males, with the largest clutches, but the fewest surviving offspring, produced when males are unrelated. These 3 models demonstrate the importance of considering third-party interests in the decisions of group-living organisms.

Single Molecular Conductance of Tolanes: Experimental and Theoretical Study on the Junction Evolution Dependent on the Anchoring Group

Employing a scanning tunneling microscopy based beak junction technique and mechanically controlled break junction experiments, we investigated tolane (diphenylacetylene)-type single molecular junctions having four different anchoring groups (SH, pyridyl (PY), NH2, and CN) at a solid/liquid interface. The combination of current–distance and current–voltage measurements and their quantitative statistical analysis revealed the following sequence for junction formation probability and stability: PY > SH > NH2 > CN. For all single molecular junctions investigated, we observed the evolution through multiple junction configurations, with a particularly well-defined binding geometry for PY. The comparison of density functional theory type model calculations and molecular dynamics simulations with the experimental results revealed structure and mechanistic details of the evolution of the different types of (single) molecular junctions upon stretching quantitatively.

Efficient team actions: Outline of a theory of teams in sport

So far, social psychology in sport has preliminary focused on team cohesion, and many studies and meta analyses tried to demonstrate a relation between cohesiveness of a team and it's performance. How a team really co-operates and how the individual actions are integrated towards a team action is a question that has received relatively little attention in research. This may, at least in part, be due to a lack of a theoretical framework for collective actions, a dearth that has only recently begun to challenge sport psychologists. In this presentation a framework for a comprehensive theory of teams in sport is outlined and its potential to integrate the following presentations is put up for discussion. Based on a model developed by von Cranach, Ochsenbein and Valach (1986), teams are information processing organisms, and team actions need to be investigated on two levels: the individual team member and the group as an entity. Elements to be considered are the task, the social structure, the information processing structure and the execution structure. Obviously, different task require different social structures, communication and co-ordination. From a cognitivist point of view, internal representations (or mental models) guide the behaviour mainly in situations requiring quick reactions and adaptations, were deliberate or contingency planning are difficult. In sport teams, the collective representation contains the elements of the team situation, that is team task and team members, and of the team processes, that is communication and co-operation. Different meta-perspectives may be distinguished and bear a potential to explain the actions of efficient teams. Cranach, M. von, Ochsenbein, G., & Valach, L. (1986).The group as a self-active system: Outline of a theory of group action. European Journal of Social Psychology, 16, 193-229.

Neighbourhood Diversity and Social Trust: An Empirical Analysis of Interethnic Contact and Group-specific Effects

To date, neighbourhood studies on ethnic diversity and social trust have revealed inconclusive findings. In this paper, three innovations are proposed in order to systemise the knowledge about neighbourhood ethnic diversity and the development of social trust. First, it is proposed to use a valid trust measure that is sensitive to the local neighbourhood context. Second, the paper argues for a conception of organically evolved neighbourhoods, rather than using local administrative units as readily available proxies for neighbourhood divisions. Thirdly, referring to intergroup contact theory and group-specific effects of diversity, the paper challenges the notion that ethnic diversity has overwhelmingly negative effects on social trust.

Voter Participation in the 1998 Bundestag Elections: A Theoretical Modification and Empirical Application of Downs’ Theory of Voter Participation

This article seeks to contribute to the illumination of the so-called 'paradox of voting' using the German Bundestag elections of 1998 as an empirical case. Downs' model of voter participation will be extended to include elements of the theory of subjective expected utility (SEU). This will allow a theoretical and empirical exploration of the crucial mechanisms of individual voters' decisions to participate, or abstain from voting, in the German general election of 1998. It will be argued that the infinitely low probability of an individual citizen's vote to decide the election outcome will not necessarily reduce the probability of electoral participation. The empirical analysis is largely based on data from the ALLBUS 1998. It confirms the predictions derived from SEU theory. The voters' expected benefits and their subjective expectation to be able to influence government policy by voting are the crucial mechanisms to explain participation. By contrast, the explanatory contribution of perceived information and opportunity costs is low.

Outline of a theory of efficient teams in Sport.

Introduction So far, social psychology in sport has preliminary focused on team cohesion, and many studies and meta-analyses tried to demonstrate a relation between cohesiveness of a team and its performance. How a team really co-operates and how the individual actions are integrated towards a team action is a question that has received relatively little attention in research. This may, at least in part, be due to a lack of a theoretical framework for collective actions, a dearth that has only recently begun to challenge sport psychologists. Objectives In this presentation a framework for a comprehensive theory of teams in sport is outlined and its potential to integrate research in the domain of team performance and, more specifically, the following presentations, is put up for discussion. Method Based on a model developed by von Cranach, Ochsenbein and Valach (1986), teams are considered to be information processing organisms, and team actions need to be investigated on two levels: the individual team member and the group as an entity. Elements to be considered are the task, the social structure, the information processing structure and the execution structure. Obviously, different task require different social structures, communication processes and co-ordination of individual movements. Especially in rapid interactive sports planning and execution of movements based on feedback loops are not possible. Deliberate planning may be a solution mainly for offensive actions, whereas defensive actions have to adjust to the opponent team's actions. Consequently, mental representations must be developed to allow a feed-forward regulation of team member's actions. Results and Conclusions Some preliminary findings based on this conceptual framework as well as further consequences for empirical investigations will be presented. References Cranach, M.v., Ochsenbein, G. & Valach, L. (1986). The group as a self-active system: Outline of a theory of group action. European Journal of Social Psychology, 16, 193-229.