The diploma thesis is entitled "Internal Risks of a Critical Infrastructure Entity from the Public Sector". It deals with the analysis and evaluation of the internal risks of a critical infrastructure entity, namely a large business center in one of the regional cities of the Czech Republic, with an emphasis on ensuring the continuity of its function and expressing recommendations for adjusting existing risks. The first part of the thesis is devoted to the definition of initial theoretical knowledge and essential terms related to the solving issue of critical infrastructure. In the next sections, the work focuses specifically on the shopping center object and the analysis of the current state of its internal risks, which first reveals possible sources of risk in each part of the shopping center, then describes how to determine the degree of criticality of rooms, risk assessment and last but not least proposes and gives recommendations for action against the risks identified.

The vision of automated driving demands a highly available system, especially in safety-critical functionalities. In automated driving when a driver is not binding to be a part of the control loop, the system needs to be operational even after failure of a critical component until driver regain the control of vehicle. In pursuit of such a fail-operational behavior, the developed design process with software redundancy in contrast to conventional dedicated backup requires the support of automatic configurator for scheduling relevant parameters to ensure real-time behavior of the system. Multiple implementation methods are introduced to provide an automatic service which also considers task criticality before assigning task to the processor. Also, a generic method is developed to generate adaptation plans automatically for an already monitoring and reconfiguration service to handle fault occurring environment.

Das Auftreten von Supraleitung in Systemen mit schweren Fermionen, erstmals entdeckt in CeCu_2Si_2, wird mit der Nähe zu einem quantenkritischen Punkt in Verbindung gebracht. Daraus ergibt sich ein komplexes Zusammenspiel von Magnetismus und Supraleitung, das in der vorliegenden Arbeit durch Messungen der spezifischen Wärme, der Wechselfeldsuszeptibilität und durch inelastische Neutronenstreuexperimente an verschiedenen Einkristallen von CeCu_2(Si_{1-x}Ge_x)_2 untersucht wird. Der Schwerpunkt liegt auf der genauen Charakterisierung des magnetischen Anregungsspektrums von CeCu_2Si_2 des S-Typs. Die Ergebnisse der Neutronenstreumessungen implizieren stark, dass die Kopplung der supraleitenden Cooper-Paare durch überdämpfte Spinfluktuationen vermittelt wird, die in der Umgebung eines Quantenphasenübergangs gehäuft auftreten. Unter Substitution einiger Si- durch Ge-Atome in CeCu_2Si_2 stabilisiert sich die magnetische Ordnung, und die Supraleitung wird zunehmend unterdrückt. Neutronenstreumessungen ergeben, dass dies bei 2 % Ge-Substitution dazu führt, dass sich Magnetismus und Supraleitung gegenseitig verdrängen, während sie bei 10 % Ge-Substitution mikroskopisch koexistieren. - (Die Dissertation ist veröffentlicht im Logos Verlag Berlin GmbH, Berlin, Deutschland, http://www.logos-verlag.de, ISBN: 978-3-8325-2456-2) / The occurrence of superconductivity in systems with heavy fermions, discovered for the first time in CeCu_2Si_2, is often linked to the vicinity of a quantum critical point. This results in a complex interplay of magnetism and superconductivity, which is studied by means of specific heat and ac susceptibility measurements as well as neutron scattering experiments on different single crystals of CeCu_2(Si_{1-x}Ge_x)_2 in the present thesis. The focus is put on the detailed characterisation of the magnetic excitation spectrum in S-type CeCu_2Si_2. Neutron scattering results strongly imply that the coupling of superconducting Cooper pairs is mediated by overdamped spin fluctuations, which accumulate in the vicinity of a quantum phase transition. By substituting Si by Ge atoms in CeCu_2Si_2 magnetic order is stabilised and superconductivity successively suppressed. Neutron scattering experiments demonstrate that 2 % Ge substitution leads to magnetic order being displaced by superconductivity on decreasing temperature, whereas both coexist microscopically in the case of 10 % Ge substitution.

Spiking neural networks (SNN) are dynamic models of biological neurons, that communicates with event-based signals called spikes. SNN that reproduce observed properties of biological senses like vision are developed to better understand how such systems function, and to learn how more efficient sensor systems can be engineered. A branching parameter describes the average probability for spikes to propagate between two different neuron populations. The adaptation of branching parameters towards critical values is known to be important for maximizing the sensitivity and dynamic range of SNN. In this thesis, a recently proposed SNN model for visual feature learning and pattern recognition known as the E-I Net model is studied and extended with a critical branching mechanism. The resulting modified E-I Net model is studied with numerical experiments and two different types of sensory queues. The experiments show that the modified E-I Net model demonstrates critical branching and power-law scaling behavior, as expected from SNN near criticality, but the power-laws are broken and the stimuli reconstruction error is higher compared to the error of the original E-I Net model. Thus, on the basis of these experiments, it is not clear how to properly extend the E-I Net model properly with a critical branching mechanism. The E-I Net model has a particular structure where the inhibitory neurons (I) are tuned to decorrelate the excitatory neurons (E) so that the visual features learned matches the angular and frequency distributions of feature detectors in visual cortex V1 and different stimuli are represented by sparse subsets of the neurons. The broken power-laws correspond to different scaling behavior at low and high spike rates, which may be related to the efficacy of inhibition in the model.

In this thesis, we evaluate how well isolation can be achieved between two virtual machines within a mixed criticality system on a multi-core processor. We achieve this isolation with Jailhouse, an open-source, minimalist hypervisor. We then enhance Jailhouse with core throttling, a technique we use to minimize inter-core interference between VMs. Then, we run workloads with and without core throttling to determine the effect throttling has on interference between a non-real time VM and a real-time VM. We find that Jailhouse provides excellent isolation between VMs even without throttling, and that core throttling suppresses the remaining inter-core interference to a large extent.

The vicinity of continuous quantum phase transitions displays unique properties such as scaling behavior and incoherent excitation spectra which are not found in any stable phase of matter. This fascinating quantum critical regime is crucial for progress on key problems of modern condensed matter physics. The three research projects of this thesis challenge and refine our understanding of quantum criticality in different ways. Part I concerns unexpected quantum critical behavior near the Mott transition. The bandwidth-controlled Mott transition in the half-filled one-band Hubbard model is one of the most paradigmatic phenomena of strongly correlated physics. Within the approximation of dynamical mean-field theory (DMFT) this metal-insulator transition is of first order at low temperatures, with the transition line ending at a critical temperature. Surprisingly, numerical calculations with DMFT and experiments in organic salts consistently found quantum critical scaling of the resistivity above the critical temperature. The aim of this project is to explain this unexpected scaling in the absence of a quantum critical point in the phase diagram. To this end, we perform extensive DMFT simulations with the numerical renormalization group as a state-of-the-art impurity solver. We find that the quantum critical scaling can be traced back to the metastable insulator at the boundary of the coexistence region at T = 0 which exhibits previously unknown scale-invariance on the frequency axis. In Part II we study how magnetic quantum criticality is affected by the coupling to additional non-critical degrees of freedom. Considering typical electronic energy scales the study of quantum critical phenomena in magnets requires very low temperatures in the sub-100mK range. In this regime additional effects which are typically neglected in the theoretical modeling may become important. Here we focus on one particular example, which is the hyperfine coupling to nuclear spins. We investigate the fate of the quantum critical behavior at lowest temperatures and determine crossover scales below which a purely electronic description is no longer sufficient. Explicit calculations for paradigmatic models on the level of mean-field theory plus Gaussian fluctuations reveal that the quantum phase transition can be shifted or smeared in the presence of nuclear spins. More exotic effects of nuclear spins, e.g. in spin liquids, are discussed on a qualitative level. Part III is devoted to the discussion of domain-driven phase transitions in easy-axis ferromagnets.This work is motivated by an experimental study of LiHoF4, a dipolar easy-axis ferromagnet that displays a well-studied quantum phase transition from a ferromagnetic to a paramagnetic phase as function of a transverse field. Measurements of the ac susceptibility found a well-defined phase transition even in tilted fields where the Ising symmetry is explicitly broken and Landau theory of the microscopic order parameter predicts a crossover. We are able to explain and model the transition in tilted fields by the inclusion of domain effects, i.e., by taking into account the spontaneous breaking of translational symmetry by mesoscale pattern formation in the ferromagnetic phase. The modeling of stray-field energies as effective antiferromagnetic couplings between magnetization components in different domains is in excellent quantitative agreement with the experimental results.:1 Phases and their transitions . . . . . . . . . . . . . . . . . . . . 4 1.1 Thermal and quantum phase transitions . . . . . . . . . . . . . . . . . . . . 4 1.2 Theoretical description of phase transitions . . . . . . . . . . . . . . . . . . 8 1.3 Project overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 I Mott quantum criticality in the one-band Hubbard model . . . . . . . . . . .15 2 Introduction to the Mott transition . . . . . . . . . . . . . . . . . . . . 16 2.1 Metal-insulator transitions and the Hubbard model . . . . . . . . . . . . . . 16 2.2 A local perspective: the idea of dynamical mean-field theory . . . . . . . . . 19 2.3 Quantum critical scaling near the Mott transition . . . . . . . . . . . . . . . 21 3 Dynamical mean-field theory (DMFT) . . . . . . . . . . . . . . . . . . . . 25 3.1 Single-impurity Anderson model . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Theoretical foundations of DMFT . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Wilson's numerical renormalization group . . . . . . . . . . . . . . . . . . . 32 3.4 Implementation and choice of parameters . . . . . . . . . . . . . . . . . . . 36 4 Power-law spectra and quantum critical scaling . . . . . . . . . . . . . . . . . . 38 4.1 Scale-invariant solutions of DMFT . . . . . . . . . . . . . . . . . . . . . . . 38 4.2 Spectral power laws at T=0 in the metastable insulator . . . . . . . . . . . 40 4.3 Finite-temperature crossovers in the spectral function . . . . . . . . . . . . 47 4.4 Resistivity scaling driven by spectral power laws . . . . . . . . . . . . . . . 50 4.5 Scaling analysis of the dynamic susceptibility . . . . . . . . . . . . . . . . . 58 4.6 Ideas and obstacles towards an analytical understanding . . . . . . . . . . . 62 4.7 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 II Limits on magnetic quantum criticality from nuclear spins . . . . . . . . . . . . .65 5 Stability of magnetic transitions to hyperfine coupling . . . . . . . . . . . . . . . .66 5.1 Nuclear spins near quantum criticality . . . . . . . . . . . . . . . . . . . . . 66 5.2 Introduction to nuclear spins and hyperfine coupling . . . . . . . . . . . . . 67 5.3 Magnetic phases in the presence of nuclear spins . . . . . . . . . . . . . . . 69 5.4 Two scenarios for magnetic quantum criticality plus nuclear spins . . . . . . 70 6 Paradigmatic models for magnetic quantum phase transitions . . . . . . . . . 73 6.1 Transverse-field Ising model . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.2 Coupled-dimer model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6.3 Frustrated spin models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7 Crossover scales introduced by nuclear spins . . . . . . . . . . . . . . . . . . .83 7.1 Shifted transitions: transverse-field Ising magnets . . . . . . . . . . . . . . . 83 7.2 Smeared transitions: coupled-dimer magnets . . . . . . . . . . . . . . . . . . 90 7.3 Additional transitions due to nuclear spins . . . . . . . . . . . . . . . . . . . 98 7.4 Exotic magnetic quantum phase transitions plus nuclear spins . . . . . . . . 101 7.5 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 III Domain-driven phase transitions in easy-axis ferromagnets . . . . . . . . 105 8 Easy-axis ferromagnet LiHoF4 . . . . . . . . . . . . . . . . . . . . 106 8.1 Easy-axis ferromagnets in tilted fields . . . . . . . . . . . . . . . . . . . . . 106 8.2 LiHoF4 and its phase transitions . . . . . . . . . . . . . . . . . . . . . . . . 109 9 Modeling of microscopic degrees of freedom in LiHoF4 . . . . . . . . . . . . 112 9.1 Landau theory in tilted fields . . . . . . . . . . . . . . . . . . . . . . . . . . 112 9.2 Crystal field effects and microscopic Hamiltonian . . . . . . . . . . . . . . . 113 9.3 Crossovers in the microscopic model . . . . . . . . . . . . . . . . . . . . . . 118 10 Modeling of mesoscopic degrees of freedom in LiHoF4 . . . . . . . . . . . . . . .123 10.1 Domains in ferromagnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 10.2 Modeling of domain effects as effective interactions . . . . . . . . . . . . . . 127 10.3 Combined mean-field Hamiltonian and domain optimization . . . . . . . . . 130 10.4 Nature of the phase transition in tilted fields . . . . . . . . . . . . . . . . . 132 10.5 Domain-driven phase transition at T = 0 . . . . . . . . . . . . . . . . . . . . 135 10.6 Domain-driven phase transition at finite temperatures . . . . . . . . . . . . 141 10.7 Comparison with experimental results . . . . . . . . . . . . . . . . . . . . . 146 10.8 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 IV Summary & Outlook . . . . . . . . . . . . . . . . . . . . 151 V Appendices . . . . . . . . . . . . . . . . . . . . 155 A Part I: NRG level spectra . . . . . . . . . . . . . . . . . . . . 156 B Part I: Analytical properties of scale-invariant DMFT solutions . . . . . . . . . . .159 B.1 Kondo perturbation theory as an impurity solver . . . . . . . . . . . . . . . 159 B.2 Analytical properties of a power-law self-energy . . . . . . . . . . . . . . . . 166 C Part I: Scaling analysis of the resistivity . . . . . . . . . . . . . . . . . . 168 D Part II: Solution of the transverse-field Ising model with nuclear spins . . . . . . 172 D.1 Holstein-Primakoff representation of the electronic and nuclear spins . . . . 172 D.2 Determination of the classical reference state . . . . . . . . . . . . . . . . . 174 D.3 Excitation spectrum of the coupled nuclear-electronic model . . . . . . . . . 175 D.4 Magnetization, susceptibility, and heat capacity . . . . . . . . . . . . . . . . 177 E Part II: Solution of the coupled-dimer model with nuclear spins . . . . . . . . . . . 181 E.1 Bond-operator description of the electronic spins . . . . . . . . . . . . . . . 181 E.2 Determination to the electronic ground state . . . . . . . . . . . . . . . . . 185 E.3 Holstein-Primakoff representation of the nuclear spins . . . . . . . . . . . . 188 E.4 Excitation spectrum of the coupled nuclear-electronic model . . . . . . . . . 189 E.5 Staggered magnetization and susceptibility . . . . . . . . . . . . . . . . . . 192 F Part III: Calculation of domain-induced effective interactions . . . . . . . . . . . . . 198 Bibliography . . . . . . . . . . . . . . . . . . . . 203

Réduire la consommation énergétique des systèmes temps réel embarqués multiprocesseurs est devenu un enjeu important notammentpour augmenter leur autonomie. Nous réduisons la consommation statique des processeurs en exploitant leurs états basseconsommation. Dans un état basse-consommation, la consommation énergétique est fortement réduite mais un délai de transition et une pénalité sont nécessaires pour revenir à l'état actif. Nous proposons dans cette thèse les premiers algorithmes d'ordonnancement tempsréel multiprocesseurs optimaux pour réduire la consommation énergétique des systèmes temps réel dur et des systèmes temps réel àcriticité mixte. Ces algorithmes d'ordonnancement permettent d'activer les état basse-consommation les plus économes en énergie.Chaque algorithme d'ordonnancement est divisé en deux parties. La première partie hors-ligne génère un ordonnancement en utilisant laprogrammation linéaire en nombres entiers pour minimiser la consommation énergétique. La seconde partie est en-ligne et augmente lataille des périodes d'inactivité les tâches terminent leur exécution plus tôt que prévu. Dans le cadre des systèmes temps réel à criticitémixte, nous profitons du fait que les tâches de plus faible criticité peuvent tolérer des dépassements d'échéances pour être plus agressifhors-ligne afin de réduire davantage la consommation énergétique. Les résultats montrent que les algorithmes proposés utilisent demanière plus efficace les états basse-consommation. La consommation énergétique lorsque ceux-ci sont activés est en effet jusqu'à dix fois plus faible qu'avec les algorithmes d'ordonnancement multiprocesseurs existants. / Reducing the energy consumption of multiprocessor real-time embedded systems is a growing concern to increase their autonomy. In thisthesis, we aim to reduce the energy consumption of the processors, it includes both static and dynamic consumption and it is nowdominated by static consumption as the semiconductor technology moves to deep sub-micron scale. Existing solutions mainly focused ondynamic consumption. On the other hand, we target static consumption by efficiently using the low-power states of the processors. In alow-power state, the processor is not active and the deeper the low-power state is, the lower is the energy consumption but the higher isthe transition delay to come back to the active state. In this thesis, we propose the first optimal multiprocessor real-time schedulingalgorithms minimizing the static energy consumption. They optimize the duration of the idle periods to activate the most appropriate lowpowerstates. We target hard real-time systems with periodic tasks and also mixed-criticality systems where tasks with lower criticalitiescan tolerate deadline misses, therefore allowing us to be more aggressive while trying to reduce the energy consumption. We use anadditional task to model the idle time and mixed integer linear programming to compute offline a schedule minimizing the energyconsumption. Evaluations have been performed using existing optimal multiprocessor real-time scheduling algorithms. Results show thatthe energy consumption while processors are idle is up to ten times reduced with our solutions compared to the existing multiprocessor real-time scheduling algorithms.

We extend the study of learning and generalization in feed forward Boolean networks to random Boolean networks (RBNs). We explore the relationship between the learning capability and the network topology, the system size, the training sample size, and the complexity of the computational tasks. We show experimentally that there exists a critical connectivity Kc that improves the generalization and adaptation in networks. In addition, we show that in finite size networks, the critical K is a power-law function of the system size N and the fraction of inputs used during the training. We explain why adaptation improves at this critical connectivity by showing that the network ensemble manifests maximal topological diversity near Kc. Our work is partly motivated by self-assembled molecular and nanoscale electronics. Our findings allow to determine an automata network topology class for efficient and robust information processing.

Kollektive biologische Systeme sammeln Informationen und leiten diese intern weiter, um Umweltveränderungen zu detektieren und auf sie zu reagieren. In Tiergruppen können die probabilistischen Entscheidungen von Individuen durch diese kollektive Informationsverarbeitung verbessert werden. Die dem sozialen Austausch zu Grunde liegenden Sinneswahrnehmungen finden jedoch in gängigen Modellen kollektiven Verhaltens kaum Beachtung. Hier untersuche ich, wie der individuelle Zugang zu sozialen Informationen durch visuelle Wahrnehmung und räumliche Gruppenstruktur geformt wird. Zuerst untersuche ich Fluchtwellen in Fischschwärmen in zwei als unterschiedlich riskant wahrgenommenen Kontexten mithilfe empirisch ermittelter visueller Interaktionsnetzwerke. Die beobachtete strukturelle Änderung der Gruppen zwischen den Kontexten erweist sich als essenziell, um die Änderung der Fluchtwellengröße zu erklären und optimiert potenziell die kollektive Informationsverarbeitung im jeweiligen Kontext. Von optimaler Informationsverarbeitung wird in biologischen Systemen oft angenommen, dass sie an Phasenübergängen in deren kollektiver Dynamik stattfindet, sogenannten kritischen Punkten. Die beobachtete strukturelle Änderung ändert den Abstand des Schwarmverhaltens zu einem solchen kritischen Punkt. Jedoch bleiben die Gruppen subkritisch in beiden Kontexten, vermutlich aus Notwendigkeit, tatsächliche Warnungen zu verstärken und falsche zu unterdrücken. Im zweiten Teil vergleiche ich visuelle Netzwerke mit anderen räumlichen Netzwerken bezüglich ihrer Struktur und dem Verhalten von Ausbreitungsprozessen auf ihnen. Einzig visuelle Netzwerke zeigen bei mittleren Gruppendichten Optima in zentralen Netzwerkeigenschaften und behalten realistische Eigenschaften bei hohen und niedrigen Dichten. Abschließend entwickle ich eine analytische Näherung zentraler Netzwerkeigenschaften solcher visuellen Netzwerke. / Collective biological systems gather information and propagate it internally to detect and react to environmental changes. In animal groups the probabilistic decisions of individuals can be improved by this collective information processing. Animals rely on sensory cues for social communication, yet common models of collective behavior neglect this sensory basis of interactions. Here, I investigate how an individual’s access to social information is shaped by visual sensory limitations and spatial group structure. First, escape waves in fish schools are studied under two levels of perceived environmental risk using empirically inferred visual interaction networks. Group-structural change is found to be crucial to explain the observed differences in size of escape waves and potentially optimize collective information processing according to the state of the environment. Optimal information processing in biological systems is often hypothesized to occur at phase transitions in their collective dynamics, so-called critical points. Here, the observed change in group structure modifies the schools’ distance to a critical point. Yet groups stay subcritical in both experimental setups, which may manage a trade-off between sensitivity to true alarms and robustness to false ones. In a second part, visual networks are compared to other spatial networks in structure and behavior of spreading processes on them. Visual networks show a unique dependence on group density with optima in network structural measures at intermediate densities, making them more realistic than other networks at high and low densities. Finally, an analytical approximation of central properties of visual networks is developed. Overall, this thesis identifies group structure as a potential control mechanism of collective information processing, highlights the trade-off associated with criticality in noisy systems and provides a systematic study and analytic approximation of visual sensory networks.

[pt] Cenários de falhas em plataformas offshore constituem riscos ambientais, sociais e econômicos significativos devido à amplitude dos danos que podem ser provocados. Portanto, neste contexto, a adoção de boas práticas de gestão de manutenção é necessária, permitindo a continuidade operacional, através da integridade de ativos. No entanto, há ainda uma necessidade de estudos com uma abordagem holística para uma avaliação multinível de ativos, através de abordagens modernas que mitiguem as limitações da análise de modos e efeitos de falha (FMEA) tradicional. Desse modo, esta pesquisa propõe um framework para a análise FMEA que considera a subjetividade e as importâncias relativas dos critérios de risco, através de uma abordagem integrada que utiliza sistemas hierárquicos de inferência e modelos multicritério, como o Best-Worst Method (BWM) e o fuzzy VIsekriterijumsko KOmpromisno Rangiranje (VIKOR) para fornecer uma classificação estruturada de ativos, orientando o gestor na priorização de manutenção. Esse framework foi validado por meio de um estudo empírico em uma plataforma do tipo Floating Production Storage and Offloading (FPSO), que abordou a problemática da corrosão externa para gestão de manutenção, com base na coleta de dados triangulados. Portanto, a presente pesquisa traz contribuições teóricas ao preencher lacunas através da propositura e aplicação de metodologias integradas, e contribuições práticas ao fornecer aos gestores, responsáveis pela formulação de planos de manutenção, elementos objetivos para uma tomada de decisão mais eficaz, sob o paradigma da confiabilidade. Esse framework pode ser aplicado em outros domínios através do ajuste de critérios avaliativos. / [en] Failure scenarios in offshore platforms pose significant environmental, social, and economic risks due to the magnitude of potential damages they can cause. Therefore, in this context, the adoption of good maintenance management practices is necessary, enabling operational continuity through asset integrity. However, there is still a need for studies with a holistic approach for a multi-level assessment of assets, using modern approaches to mitigate the limitations of traditional Failure Mode and Effects Analysis (FMEA). Thus, this research proposes a framework for FMEA that considers the subjectivity and relative importance of risk criteria, through an integrated approach using hierarchical inference systems and multi-criteria models such as the Best-Worst Method (BWM) and fuzzy VIsekriterijumsko KOmpromisno Rangiranje (VIKOR) to provide a structured classification of assets, guiding managers in maintenance prioritization. This framework was validated through an empirical study on a Floating Production Storage and Offloading (FPSO) platform, addressing the issue of external corrosion for maintenance management, based on triangulated data collection. Therefore, this research brings theoretical contributions by filling gaps through the proposal and application of integrated methodologies, and practical contributions by providing managers responsible for formulating maintenance plans with objective elements for more effective decision-making under the reliability paradigm. This framework can be applied in other domains by adjusting evaluative criteria.