Near-optimal self-stabilising counting and firing squads

Consider a fully-connected synchronous distributed system consisting of n nodes, where up to f nodes may be faulty and every node starts in an arbitrary initial state. In the synchronous C-counting problem, all nodes need to eventually agree on a counter that is increased by one modulo C in each round for given C>1. In the self-stabilising firing squad problem, the task is to eventually guarantee that all non-faulty nodes have simultaneous responses to external inputs: if a subset of the correct nodes receive an external “go” signal as input, then all correct nodes should agree on a round (in the not-too-distant future) in which to jointly output a “fire” signal. Moreover, no node should generate a “fire” signal without some correct node having previously received a “go” signal as input. We present a framework reducing both tasks to binary consensus at very small cost. For example, we obtain a deterministic algorithm for self-stabilising Byzantine firing squads with optimal resilience f<n/3, asymptotically optimal stabilisation and response time O(f), and message size O(log f). As our framework does not restrict the type of consensus routines used, we also obtain efficient randomised solutions

self-stabilizing

Consider a fully-connected synchronous distributed system consisting of n nodes, where up to f nodes may be faulty and every node starts in an arbitrary initial state. In the synchronous C-counting problem, all nodes need to eventually agree on a counter that is increased by one modulo C in each round for given C>1. In the self-stabilising firing squad problem, the task is to eventually guarantee that all non-faulty nodes have simultaneous responses to external inputs: if a subset of the correct nodes receive an external “go” signal as input, then all correct nodes should agree on a round (in the not-too-distant future) in which to jointly output a “fire” signal. Moreover, no node should generate a “fire” signal without some correct node having previously received a “go” signal as input. We present a framework reducing both tasks to binary consensus at very small cost. For example, we obtain a deterministic algorithm for self-stabilising Byzantine firing squads with optimal resilience f<n/3, asymptotically optimal stabilisation and response time O(f), and message size O(log f). As our framework does not restrict the type of consensus routines used, we also obtain efficient randomised solutions

EFFICIENT COUNTING WITH OPTIMAL RESILIENCE

Consider a complete communication network of n nodes, where the nodes receive a common clock pulse. We study the synchronous c-counting problem: given any starting state and up to f faulty nodes with arbitrary behavior, the task is to eventually have all correct nodes labeling the pulses with increasing values modulo c in agreement. Thus, we are considering algorithms that are self-stabilizing despite Byzantine failures. In this work, we give new algorithms for the synchronous counting problem that (1) are deterministic, (2) have optimal resilience, (3) have a linear stabilization time in f (asymptotically optimal), (4) use a small number of states, and, consequently, (5) communicate a small number of bits per round. Prior algorithms either resort to randomization, use a large number of states and need high communication bandwidth, or have suboptimal resilience. In particular, we achieve an exponential improvement in both state complexity and message size for deterministic algorithms. Moreover, we present two complementary approaches for reducing the number of bits communicated during and after stabilization.Peer reviewe

Place cell physiology in a transgenic mouse model of Alzheimer's disease

Alzheimer's disease (AD) is a multifactorial neurodegenerative disorder characterized by progressive cognitive impairments (Selkoe, 2001). Hippocampal place cells are a well understood candidate for the neural basis of one type of memory in rodents; these cells identify the animal's location in an environment and are crucial for spatial memory and navigation. This PhD project aims to clarify the mechanisms responsible for the cognitive deficits in AD at the hippocampal network level, by examining place cell physiology in a transgenic mouse model of AD. I have recorded place cells in tg2576 mice, and found that aged (16 months) but not young (3 months) transgenic mice show degraded neuronal representations of the environment. The level of place cell degradation correlates with the animals' (poorer) spatial memory as tested in a forced-choice spatial alternation T-maze task and with hippocampal, but not neocortical, amyloid plaque burden. Additionally, pilot data show that physiological changes of the hippocampus in tg2576 mice seem to start as early as 3 months, when no pathological and behavioural deficits are present. However, these changes are not obvious at the neuronal level, but only at the hippocampal network level, which represent hippocampal responses to environmental changes. Place cell recording provides a sensitive assay for measuring the amount and rate of functional deterioration in animal models of dementia as well as providing a quantifiable physiological indication of the beneficial effects of potential therapies

Jagged blue frontiers: The police and the policing of boundaries in South Africa

Social and territorial boundaries have been fundamental to the approaches and practices of policing bodies in South Africa for centuries, from the mounted colonial paramilitary forces of the 1800s to the 21st century professional police. Boundaries have not only been a central mechanism that the police have consistently used to control and regulate the general population, but have also been catalysts for change in terms of operational policing strategies and tactics. This has typically been the case when a threat has been ascribed to a bounded area and/or populations that reside within the confines of the boundary, or on the other side of the boundary. The nature of the such a threat is considered to be even more severe when communities within the bounded space, or on the other side of the boundary, acquire significant quantities of firearms and ammunition, as this provides such populations with the lethal technology to defy and contest the police's coercive authority and ability to conserve boundaries relating to the maintenance of order and the enforcement of laws. South Africa is a distinctly relevant case study for an examination of the relationship between boundaries and the police as for the past three and a half centuries South Africa's diverse policing history has been profoundly framed by territorial, social and political boundaries. The police and the proto-police have been at the sharp edge of the application of authority by assorted forms of government, and have often acted to safeguard the interests of economic and political elites. That is, the police and formal policing bodies have been required to subdue and suppress groups and individuals that resisted or threatened the process of state building and resource extraction. The police were also regularly deployed to protect the territorial borders of South Africa from menacing others. By means of this historical analysis of South Africa, this thesis introduces a new concept, 'police frontierism', which illuminates the nature of the relationships between the police, policing and boundaries, and can potentially be used for future case study research. It is an alternative way of conceptualising policing, one in which police work is fundamentally framed by social and territorial boundaries. Such boundaries delineate perceived safe or 'civilised' spaces from dangerous or 'uncivilised' ones. The police tend to concentrate their resources in the frontier zone immediately adjacent to the boundary in order to preserve or extend the boundary of safety and 'civilisation', and restrict, subdue or eliminate those individuals, groups or circumstances from the 'uncivilised' spaces that a government authority or elites have deemed to be a threat to order and peace. An essential dynamic of this policing approach is that the boundary and the adjoining frontier zone strongly influence police practices and behaviour in this context. In particular, territorial and social delineations amplify and distort existing police prejudices against those communities on the other side of the boundary. The police often engage in othering, where the communities of interest are viewed negatively, and are predominantly seen as agents of disorder and law breaking. This othering may lead to an intensification of aggressive police behaviour towards the targeted communities

The Wild East: Criminal Political Economies in South Asia

The Wild East bridges political economy and anthropology to examine a variety of il/legal economic sectors and businesses such as red sanders, coal, fire, oil, sand, air spectrum, land, water, real estate, procurement and industrial labour. The 11 case studies, based across India, Pakistan and Bangladesh, explore how state regulative law is often ignored and/or selectively manipulated. The emerging collective narrative shows the workings of regulated criminal economic systems where criminal formations, politicians, police, judges and bureaucrats are deeply intertwined. By pioneering the field-study of the politicisation of economic crime, and disrupting the wider literature on South Asia’s informal economy, The Wild East aims to influence future research agendas through its case for the study of mafia-enterprises and their engagement with governance in South Asia and outside. Its empirical and theoretical contribution to debates about economic crimes in democratic regimes will be of critical value to researchers in Economics, Anthropology, Sociology, Comparative Politics, Political Science and International Relations, Criminologists and Development Studies, as well as to those inside and outside academia interested in current affairs and the relationship between crime, politics and mafia enterprises