Self-Stabilization in the Distributed Systems of Finite State Machines

The notion of self-stabilization was first proposed by Dijkstra in 1974 in his classic paper. The paper defines a system as self-stabilizing if, starting at any, possibly illegitimate, state the system can automatically adjust itself to eventually converge to a legitimate state in finite amount of time and once in a legitimate state it will remain so unless it incurs a subsequent transient fault. Dijkstra limited his attention to a ring of finite-state machines and provided its solution for self-stabilization. In the years following his introduction, very few papers were published in this area. Once his proposal was recognized as a milestone in work on fault tolerance, the notion propagated among the researchers rapidly and many researchers in the distributed systems diverted their attention to it. The investigation and use of self-stabilization as an approach to fault-tolerant behavior under a model of transient failures for distributed systems is now undergoing a renaissance. A good number of works pertaining to self-stabilization in the distributed systems were proposed in the yesteryears most of which are very recent. This report surveys all previous works available in the literature of self-stabilizing systems

Algorithmes auto-stabilisants pour la construction de structures couvrantes réparties

This thesis deals with the self-stabilizing construction of spanning structures over a distributed system. Self-stabilization is a paradigm for fault-tolerance in distributed algorithms. It guarantees that the system eventually satisfies its specification after transient faults hit the system. Our model of distributed system assumes locally shared memories for communicating, unique identifiers for symmetry-breaking, and distributed daemon for execution scheduling, that is, the weakest proper daemon. More generally, we aim for the weakest possible assumptions, such as arbitrary topologies, in order to propose the most versatile constructions of distributed spanning structures. We present four original self-stabilizing algorithms achieving k-clustering, (f,g)-alliance construction, and ranking. For every of these problems, we prove the correctness of our solutions. Moreover, we analyze their time and space complexity using formal proofs and simulations. Finally, for the (f,g)-alliance problem, we consider the notion of safe convergence in addition to self-stabilization. It enforces the system to first quickly satisfy a specification that guarantees a minimum of conditions, and then to converge to a more stringent specification.Cette thèse s'intéresse à la construction auto-stabilisante de structures couvrantes dans un système réparti. L'auto-stabilisation est un paradigme pour la tolérance aux fautes dans les algorithmes répartis. Plus précisément, elle garantit que le système retrouve un comportement correct en temps fini après avoir été perturbé par des fautes transitoires. Notre modèle de système réparti se base sur des mémoires localement partagées pour la communication, des identifiants uniques pour briser les symétries et un ordonnanceur inéquitable, c'est-à-dire le plus faible des ordonnanceurs. Dans la mesure du possible, nous nous imposons d'utiliser les plus faibles hypothèses, afin d'obtenir les constructions les plus générales de structures couvrantes réparties. Nous présentons quatre algorithmes auto-stabilisants originaux pour le k-partitionnement, la construction d'une (f,g)-alliance et l'indexation. Pour chacun de ces problèmes, nous prouvons la correction de nos solutions. De plus, nous analysons leur complexité en temps et en espace à l'aide de preuves formelles et de simulations. Enfin, pour le problème de (f,g)-alliance, nous prenons en compte la notion de convergence sûre qui vient s'ajouter à celle d'auto-stabilisation. Elle garantit d'abord que le comportement du système assure rapidement un minimum de conditions, puis qu'il continue de converger jusqu'à se conformer à une spécification plus exigeante

A self-stabilizing algorithm for finding a minimal 2-dominating set assuming the distributed demon model

AbstractA 2-dominating set in a distributed system is a set of processors such that each processor outside the set has at least two neighbors in the set. In applications, a 2-dominating set can be considered as an ideal place in the system for allocating resources, and a minimal 2-dominating set allows for the minimum of resources to be allocated. Since a maximal independent set can be viewed as a minimal 1-dominating set, the problem of finding a minimal 2-dominating set extends the problem of finding a maximal independent set in some sense. The distributed demon model for self-stabilizing systems is a natural generalization of the central demon model introduced by Dijkstra. In the past, only a few self-stabilizing algorithms under the distributed demon model have been obtained without using any transformer, and most of these algorithms are for ring networks only. In this paper, we propose a self-stabilizing algorithm that can find a minimal 2-dominating set in any general network in which the distributed demon model is assumed. This proposed algorithm is not obtained via any transformer. We also verify the correctness of the proposed algorithm

Magnetic and orbital ordering in cuprates and manganites

The mechanisms of magnetic and orbital interactions due to double exchange (DE) and superexchange (SE) in transition metal oxides with degenerate e_g orbitals are presented. Specifically, we study the effective spin-orbital models derived for the d^9 ions as in KCuF_3, and for the d^4 ions as in LaMnO_3, for spins S=1/2 and S=2, respectively. Such models are characterized by three types of elementary excitations: spin waves, orbital waves, and spin-and-orbital waves. The SE interactions between Cu^{2+} (d^9) ions are inherently frustrated, which leads to a new mechanism of spin liquid which operates in three dimensions. The SE between Mn^{3+} (d^4) ions explains the A-type antiferromagnetic order in LaMnO_3 which coexists with the orbital order. In contrast, the ferromagnetic metallic phase and isotropic spin waves observed in doped manganites are explained by DE for degenerate e_g orbitals. It is shown that although a hole does not couple to spin excitations in ferromagnetic planes of LaMnO_3, the orbital excitations change the energy scale for the coherent hole propagation and cause a large redistribution of spectral weight. Finally, we point out some open problems in the present understanding of doped manganites.Comment: 155 pages, 66 figure

Topological data analysis of organoids

Organoids are multi-cellular structures which are cultured in vitro from stem cells to resemble specific organs (e.g., colon, liver) in their three- dimensional composition. The gene expression and the tissue composition of organoids constantly affect each other. Dynamic changes in the shape, cellular composition and transcriptomic profile of these model systems can be used to understand the effect of mutations and treatments in health and disease. In this thesis, I propose new techniques in the field of topological data analysis (TDA) to analyse the gene expression and the morphology of organoids. I use TDA methods, which are inspired by topology, to analyse and quantify the continuous structure of single-cell RNA sequencing data, which is embedded in high dimensional space, and the shape of an organoid. For single-cell RNA sequencing data, I developed the multiscale Laplacian score (MLS) and the UMAP diffusion cover, which both extend and im- prove existing topological analysis methods. I demonstrate the utility of these techniques by applying them to a published benchmark single-cell data set and a data set of mouse colon organoids. The methods validate previously identified genes and detect additional genes with known involvement cancers. To study the morphology of organoids I propose DETECT, a rotationally invariant signature of dynamically changing shapes. I demonstrate the efficacy of this method on a data set of segmented videos of mouse small intestine organoid experiments and show that it outperforms classical shape descriptors. I verify the method on a synthetic organoid data set and illustrate how it generalises to 3D to conclude that DETECT offers rigorous quantification of organoids and opens up computationally scalable methods for distinguishing different growth regimes and assessing treatment effects. Finally, I make a theoretical contribution to the statistical inference of the method underlying DETECT

A Multi Agent System for Flow-Based Intrusion Detection Using Reputation and Evolutionary Computation

The rising sophistication of cyber threats as well as the improvement of physical computer network properties present increasing challenges to contemporary Intrusion Detection (ID) techniques. To respond to these challenges, a multi agent system (MAS) coupled with flow-based ID techniques may effectively complement traditional ID systems. This paper develops: 1) a scalable software architecture for a new, self-organized, multi agent, flow-based ID system; and 2) a network simulation environment suitable for evaluating implementations of this MAS architecture and for other research purposes. Self-organization is achieved via 1) a reputation system that influences agent mobility in the search for effective vantage points in the network; and 2) multi objective evolutionary algorithms that seek effective operational parameter values. This paper illustrates, through quantitative and qualitative evaluation, 1) the conditions for which the reputation system provides a significant benefit; and 2) essential functionality of a complex network simulation environment supporting a broad range of malicious activity scenarios. These results establish an optimistic outlook for further research in flow-based multi agent systems for ID in computer networks

Space-time residual minimization for parabolic partial differential equations

Many processes in nature and engineering are governed by partial differential equations (PDEs). We focus on parabolic PDEs, that describe time-dependent phenomena like heat conduction, chemical concentration, and fluid flow. Even if we know that a unique solution exists, we can express it in closed form only under very strict circumstances. So, to understand what it looks like, we turn to numerical approximation. Historically, parabolic PDEs are solved using time-stepping. One first discretizes the PDE in space as to obtain a system of coupled ordinary differential equations in time. This system is then solved using the vast theory for ODEs. While efficient in terms of memory and computational cost, time-stepping schemes take global time steps, which are independent of spatial position. As a result, these methods cannot efficiently resolve details in localized regions of space and time. Moreover, being inherently sequential, they have limited possibilities for parallel computation. In this thesis, we take a different approach and reformulate the parabolic evolution equation as an equation posed in space and time simultaneously. Space-time methods mitigate the aforementioned issues, and moreover produce approximations to the unknown solution that are uniformly quasi-optimal. The focal point of this thesis is the space-time minimal residual (MR) method introduced by R. Andreev, that finds the approximation that minimizes both PDE- and initial error. We discuss its theoretical properties, provide numerical algorithms for its computation, and discuss its applicability in data assimilation (the problem of fusing measured data to its underlying PDE)

Interaction dynamics and autonomy in cognitive systems

The concept of autonomy is of crucial importance for understanding life and cognition. Whereas cellular and organismic autonomy is based in the self-production of the material infrastructure sustaining the existence of living beings as such, we are interested in how biological autonomy can be expanded into forms of autonomous agency, where autonomy as a form of organization is extended into the behaviour of an agent in interaction with its environment (and not its material self-production). In this thesis, we focus on the development of operational models of sensorimotor agency, exploring the construction of a domain of interactions creating a dynamical interface between agent and environment. We present two main contributions to the study of autonomous agency: First, we contribute to the development of a modelling route for testing, comparing and validating hypotheses about neurocognitive autonomy. Through the design and analysis of specific neurodynamical models embedded in robotic agents, we explore how an agent is constituted in a sensorimotor space as an autonomous entity able to adaptively sustain its own organization. Using two simulation models and different dynamical analysis and measurement of complex patterns in their behaviour, we are able to tackle some theoretical obstacles preventing the understanding of sensorimotor autonomy, and to generate new predictions about the nature of autonomous agency in the neurocognitive domain. Second, we explore the extension of sensorimotor forms of autonomy into the social realm. We analyse two cases from an experimental perspective: the constitution of a collective subject in a sensorimotor social interactive task, and the emergence of an autonomous social identity in a large-scale technologically-mediated social system. Through the analysis of coordination mechanisms and emergent complex patterns, we are able to gather experimental evidence indicating that in some cases social autonomy might emerge based on mechanisms of coordinated sensorimotor activity and interaction, constituting forms of collective autonomous agency