86 resultados para Martingale representation theorem


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1. Biodiversity, water quality and ecosystem processes in streams are known to be influenced by the terrestrial landscape over a range of spatial and temporal scales. Lumped attributes (i.e. per cent land use) are often used to characterise the condition of the catchment; however, they are not spatially explicit and do not account for the disproportionate influence of land located near the stream or connected by overland flow. 2. We compared seven landscape representation metrics to determine whether accounting for the spatial proximity and hydrological effects of land use can be used to account for additional variability in indicators of stream ecosystem health. The landscape metrics included the following: a lumped metric, four inverse-distance-weighted (IDW) metrics based on distance to the stream or survey site and two modified IDW metrics that also accounted for the level of hydrologic activity (HA-IDW). Ecosystem health data were obtained from the Ecological Health Monitoring Programme in Southeast Queensland, Australia and included measures of fish, invertebrates, physicochemistry and nutrients collected during two seasons over 4 years. Linear models were fitted to the stream indicators and landscape metrics, by season, and compared using an information-theoretic approach. 3. Although no single metric was most suitable for modelling all stream indicators, lumped metrics rarely performed as well as other metric types. Metrics based on proximity to the stream (IDW and HA-IDW) were more suitable for modelling fish indicators, while the HA-IDW metric based on proximity to the survey site generally outperformed others for invertebrates, irrespective of season. There was consistent support for metrics based on proximity to the survey site (IDW or HA-IDW) for all physicochemical indicators during the dry season, while a HA-IDW metric based on proximity to the stream was suitable for five of the six physicochemical indicators in the post-wet season. Only one nutrient indicator was tested and results showed that catchment area had a significant effect on the relationship between land use metrics and algal stable isotope ratios in both seasons. 4. Spatially explicit methods of landscape representation can clearly improve the predictive ability of many empirical models currently used to study the relationship between landscape, habitat and stream condition. A comparison of different metrics may provide clues about causal pathways and mechanistic processes behind correlative relationships and could be used to target restoration efforts strategically.

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The present study investigated how object locations learned separately are integrated and represented as a single spatial layout in memory. Two experiments were conducted in which participants learned a room-sized spatial layout that was divided into two sets of five objects. Results suggested that integration across sets was performed efficiently when it was done during initial encoding of the environment but entailed cost in accuracy when it was attempted at the time of memory retrieval. These findings suggest that, once formed, spatial representations in memory generally remain independent and integrating them into a single representation requires additional cognitive processes.

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This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

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This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

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Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In previous work we introduced a method to update the reference views in a topological map so that a mobile robot could continue to localize itself in a changing environment using omni-directional vision. In this work we extend this longterm updating mechanism to incorporate a spherical metric representation of the observed visual features for each node in the topological map. Using multi-view geometry we are then able to estimate the heading of the robot, in order to enable navigation between the nodes of the map, and to simultaneously adapt the spherical view representation in response to environmental changes. The results demonstrate the persistent performance of the proposed system in a long-term experiment.

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Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In this work, we introduce a method to update the reference views in a hybrid metrictopological map so that a mobile robot can continue to localize itself in a changing environment. The updating mechanism, based on the multi-store model of human memory, incorporates a spherical metric representation of the observed visual features for each node in the map, which enables the robot to estimate its heading and navigate using multi-view geometry, as well as representing the local 3D geometry of the environment. A series of experiments demonstrate the persistence performance of the proposed system in real changing environments, including analysis of the long-term stability.

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Building information models are increasingly being utilised for facility management of large facilities such as critical infrastructures. In such environments, it is valuable to utilise the vast amount of data contained within the building information models to improve access control administration. The use of building information models in access control scenarios can provide 3D visualisation of buildings as well as many other advantages such as automation of essential tasks including path finding, consistency detection, and accessibility verification. However, there is no mathematical model for building information models that can be used to describe and compute these functions. In this paper, we show how graph theory can be utilised as a representation language of building information models and the proposed security related functions. This graph-theoretic representation allows for mathematically representing building information models and performing computations using these functions.

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Representation of facial expressions using continuous dimensions has shown to be inherently more expressive and psychologically meaningful than using categorized emotions, and thus has gained increasing attention over recent years. Many sub-problems have arisen in this new field that remain only partially understood. A comparison of the regression performance of different texture and geometric features and investigation of the correlations between continuous dimensional axes and basic categorized emotions are two of these. This paper presents empirical studies addressing these problems, and it reports results from an evaluation of different methods for detecting spontaneous facial expressions within the arousal-valence dimensional space (AV). The evaluation compares the performance of texture features (SIFT, Gabor, LBP) against geometric features (FAP-based distances), and the fusion of the two. It also compares the prediction of arousal and valence, obtained using the best fusion method, to the corresponding ground truths. Spatial distribution, shift, similarity, and correlation are considered for the six basic categorized emotions (i.e. anger, disgust, fear, happiness, sadness, surprise). Using the NVIE database, results show that the fusion of LBP and FAP features performs the best. The results from the NVIE and FEEDTUM databases reveal novel findings about the correlations of arousal and valence dimensions to each of six basic emotion categories.

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Late in 2009, the Australian Workplace Relations Ministers' Council endorsed the model Work Health and Safety Bill 2009, which is to be adopted by all Australian governments (federal, state and territory) from 01 January 2012. This paper describes and analyses two key sets of provisions in this model legislation. The first establishes a 'primary' duty of care imposed not on 'employers' but on persons conducting a business or undertaking, and owed to all kinds of workers engaged, directed or influenced by the person conducting the business or undertaking. The second encompasses broad duties on all persons conducting a business or undertaking to consult with workers who carry out work for the business or undertaking and who are directly affected by a work health and safety issue, and to facilitate the election of health and safety representatives representing all workers who carry out work for the business or undertaking. These provisions arguably make a significant contribution to solving a problem faced by occupational safety and health regulators around the world – modifying regulation to accommodate all forms of precarious work.

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This Australian Indigenous creactive work and its Treatise promote ways of thinking about practice and research that extend well beyond the current discourse. It invites re-thinking on how research can be practice-led in new ways, and what that might mean for future students. When discussing the challenges of today, this work signifies how "Western Style" thinking and theory is wanting in so many ways. It engages a new dynamic and innovative way of theorising, encouraging future students to apply their full capacity of energy and wisdom. (Extract from examiners' reports.)

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A tag-based item recommendation method generates an ordered list of items, likely interesting to a particular user, using the users past tagging behaviour. However, the users tagging behaviour varies in different tagging systems. A potential problem in generating quality recommendation is how to build user profiles, that interprets user behaviour to be effectively used, in recommendation models. Generally, the recommendation methods are made to work with specific types of user profiles, and may not work well with different datasets. In this paper, we investigate several tagging data interpretation and representation schemes that can lead to building an effective user profile. We discuss the various benefits a scheme brings to a recommendation method by highlighting the representative features of user tagging behaviours on a specific dataset. Empirical analysis shows that each interpretation scheme forms a distinct data representation which eventually affects the recommendation result. Results on various datasets show that an interpretation scheme should be selected based on the dominant usage in the tagging data (i.e. either higher amount of tags or higher amount of items present). The usage represents the characteristic of user tagging behaviour in the system. The results also demonstrate how the scheme is able to address the cold-start user problem.

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This project is a step forward in the study of text mining where enhanced text representation with semantic information plays a significant role. It develops effective methods of entity-oriented retrieval, semantic relation identification and text clustering utilizing semantically annotated data. These methods are based on enriched text representation generated by introducing semantic information extracted from Wikipedia into the input text data. The proposed methods are evaluated against several start-of-art benchmarking methods on real-life data-sets. In particular, this thesis improves the performance of entity-oriented retrieval, identifies different lexical forms for an entity relation and handles clustering documents with multiple feature spaces.