4 resultados para Infinite horizon problems

em CORA - Cork Open Research Archive - University College Cork - Ireland


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There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

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The concept of police accountability is not susceptible to a universal or concise definition. In the context of this thesis it is treated as embracing two fundamental components. First, it entails an arrangement whereby an individual, a minority and the whole community have the opportunity to participate meaningfully in the formulation of the principles and policies governing police operations. Second, it presupposes that those who have suffered as victims of unacceptable police behaviour should have an effective remedy. These ingredients, however, cannot operate in a vacuum. They must find an accommodation with the equally vital requirement that the burden of accountability should not be so demanding that the delivery of an effective police service is fatally impaired. While much of the current debate on police accountability in Britain and the USA revolves around the issue of where the balance should be struck in this accommodation, Ireland lacks the very foundation for such a debate as it suffers from a serious deficit in research and writing on police generally. This thesis aims to fill that gap by laying the foundations for an informed debate on police accountability and related aspects of police in Ireland. Broadly speaking the thesis contains three major interrelated components. The first is concerned with the concept of police in Ireland and the legal, constitutional and political context in which it operates. This reveals that although the Garda Siochana is established as a national force the legal prescriptions concerning its role and governance are very vague. Although a similar legislative format in Britain, and elsewhere, have been interpreted as conferring operational autonomy on the police it has not stopped successive Irish governments from exercising close control over the police. The second component analyses the structure and operation of the traditional police accountability mechanisms in Ireland; namely the law and the democratic process. It concludes that some basic aspects of the peculiar legal, constitutional and political structures of policing seriously undermine their capacity to deliver effective police accountability. In the case of the law, for example, the status of, and the broad discretion vested in, each individual member of the force ensure that the traditional legal actions cannot always provide redress where individuals or collective groups feel victimised. In the case of the democratic process the integration of the police into the excessively centralised system of executive government, coupled with the refusal of the Minister for Justice to accept responsibility for operational matters, project a barrier between the police and their accountability to the public. The third component details proposals on how the current structures of police accountability in Ireland can be strengthened without interfering with the fundamentals of the law, the democratic process or the legal and constitutional status of the police. The key elements in these proposals are the establishment of an independent administrative procedure for handling citizen complaints against the police and the establishment of a network of local police-community liaison councils throughout the country coupled with a centralised parliamentary committee on the police. While these proposals are analysed from the perspective of maximising the degree of police accountability to the public they also take into account the need to ensure that the police capacity to deliver an effective police service is not unduly impaired as a result.

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Case-Based Reasoning (CBR) uses past experiences to solve new problems. The quality of the past experiences, which are stored as cases in a case base, is a big factor in the performance of a CBR system. The system's competence may be improved by adding problems to the case base after they have been solved and their solutions verified to be correct. However, from time to time, the case base may have to be refined to reduce redundancy and to get rid of any noisy cases that may have been introduced. Many case base maintenance algorithms have been developed to delete noisy and redundant cases. However, different algorithms work well in different situations and it may be difficult for a knowledge engineer to know which one is the best to use for a particular case base. In this thesis, we investigate ways to combine algorithms to produce better deletion decisions than the decisions made by individual algorithms, and ways to choose which algorithm is best for a given case base at a given time. We analyse five of the most commonly-used maintenance algorithms in detail and show how the different algorithms perform better on different datasets. This motivates us to develop a new approach: maintenance by a committee of experts (MACE). MACE allows us to combine maintenance algorithms to produce a composite algorithm which exploits the merits of each of the algorithms that it contains. By combining different algorithms in different ways we can also define algorithms that have different trade-offs between accuracy and deletion. While MACE allows us to define an infinite number of new composite algorithms, we still face the problem of choosing which algorithm to use. To make this choice, we need to be able to identify properties of a case base that are predictive of which maintenance algorithm is best. We examine a number of measures of dataset complexity for this purpose. These provide a numerical way to describe a case base at a given time. We use the numerical description to develop a meta-case-based classification system. This system uses previous experience about which maintenance algorithm was best to use for other case bases to predict which algorithm to use for a new case base. Finally, we give the knowledge engineer more control over the deletion process by creating incremental versions of the maintenance algorithms. These incremental algorithms suggest one case at a time for deletion rather than a group of cases, which allows the knowledge engineer to decide whether or not each case in turn should be deleted or kept. We also develop incremental versions of the complexity measures, allowing us to create an incremental version of our meta-case-based classification system. Since the case base changes after each deletion, the best algorithm to use may also change. The incremental system allows us to choose which algorithm is the best to use at each point in the deletion process.

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While people in Catholic parishes in Ireland appear keenly aware of parish boundaries, these understandings are more often oral than cartographic. There is no digital map of all of the Catholic parishes in Ireland. However, the institutional Catholic Church insists that no square kilometre can exist outside of a parish boundary. In this paper, I explain a process whereby the Catholic parishes of Ireland were produced digitally. I will outline some of the technical challenges of digitizing such boundaries. In making these maps, it is not only a question of drawing lines but mapping people’s understanding of their locality. Through an example of one part of the digitisation project, I want to talk about how verifying maps with local people often complicates something which may have at first sight seemed simple. The paper ends on a comparison with how other communities of interest are territorialised in Ireland and elsewhere to draw out some broader theoretical and theological issues of concern.