998 resultados para Analytic representation for propagator
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This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.
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Abstract With the phenomenal growth of electronic data and information, there are many demands for the development of efficient and effective systems (tools) to perform the issue of data mining tasks on multidimensional databases. Association rules describe associations between items in the same transactions (intra) or in different transactions (inter). Association mining attempts to find interesting or useful association rules in databases: this is the crucial issue for the application of data mining in the real world. Association mining can be used in many application areas, such as the discovery of associations between customers’ locations and shopping behaviours in market basket analysis. Association mining includes two phases. The first phase, called pattern mining, is the discovery of frequent patterns. The second phase, called rule generation, is the discovery of interesting and useful association rules in the discovered patterns. The first phase, however, often takes a long time to find all frequent patterns; these also include much noise. The second phase is also a time consuming activity that can generate many redundant rules. To improve the quality of association mining in databases, this thesis provides an alternative technique, granule-based association mining, for knowledge discovery in databases, where a granule refers to a predicate that describes common features of a group of transactions. The new technique first transfers transaction databases into basic decision tables, then uses multi-tier structures to integrate pattern mining and rule generation in one phase for both intra and inter transaction association rule mining. To evaluate the proposed new technique, this research defines the concept of meaningless rules by considering the co-relations between data-dimensions for intratransaction-association rule mining. It also uses precision to evaluate the effectiveness of intertransaction association rules. The experimental results show that the proposed technique is promising.
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Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).
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In this article we introduce the term “energy polarization” to explain the politics of energy market reform in the Russian Duma. Our model tests the impact of regional energy production, party cohesion and ideology, and electoral mandate on the energy policy decisions of the Duma deputies (oil, gas, and electricity bills and resolution proposals) between 1994 and 2003. We find a strong divide between Single-Member District (SMD) and Proportional Representation (PR) deputies High statistical significance of gas production is demonstrated throughout the three Duma terms and shows Gazprom's key position in the post-Soviet Russian economy. Oil production is variably significant in the two first Dumas, when the main legislative debates on oil privatization occur. There is no constant left–right continuum, which is consistent with the deputies' proclaimed party ideology. The pro- and anti-reform poles observed in our Poole-based single dimensional scale are not necessarily connected with liberal and state-oriented regulatory policies, respectively. Party switching is a solid indicator of Russia's polarized legislative dynamics when it comes to energy sector reform.
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Recovering position from sensor information is an important problem in mobile robotics, known as localisation. Localisation requires a map or some other description of the environment to provide the robot with a context to interpret sensor data. The mobile robot system under discussion is using an artificial neural representation of position. Building a geometrical map of the environment with a single camera and artificial neural networks is difficult. Instead it would be simpler to learn position as a function of the visual input. Usually when learning images, an intermediate representation is employed. An appropriate starting point for biologically plausible image representation is the complex cells of the visual cortex, which have invariance properties that appear useful for localisation. The effectiveness for localisation of two different complex cell models are evaluated. Finally the ability of a simple neural network with single shot learning to recognise these representations and localise a robot is examined.
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RatSLAM is a vision-based SLAM system based on extended models of the rodent hippocampus. RatSLAM creates environment representations that can be processed by the experience mapping algorithm to produce maps suitable for goal recall. The experience mapping algorithm also allows RatSLAM to map environments many times larger than could be achieved with a one to one correspondence between the map and environment, by reusing the RatSLAM maps to represent multiple sections of the environment. This paper describes experiments investigating the effects of the environment-representation size ratio and visual ambiguity on mapping and goal navigation performance. The experiments demonstrate that system performance is weakly dependent on either parameter in isolation, but strongly dependent on their joint values.
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The RatSLAM system can perform vision based SLAM using a computational model of the rodent hippocampus. When the number of pose cells used to represent space in RatSLAM is reduced, artifacts are introduced that hinder its use for goal directed navigation. This paper describes a new component for the RatSLAM system called an experience map, which provides a coherent representation for goal directed navigation. Results are presented for two sets of real world experiments, including comparison with the original goal memory system's performance in the same environment. Preliminary results are also presented demonstrating the ability of the experience map to adapt to simple short term changes in the environment.
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An algorithm to improve the accuracy and stability of rigid-body contact force calculation is presented. The algorithm uses a combination of analytic solutions and numerical methods to solve a spring-damper differential equation typical of a contact model. The solution method employs the recently proposed patch method, which especially suits the spring-damper differential equations. The resulting semi-analytic solution reduces the stiffness of the differential equations, while performing faster than conventional alternatives.
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Aim. The paper is a report of a study to demonstrate how the use of schematics can provide procedural clarity and promote rigour in the conduct of case study research. Background. Case study research is a methodologically flexible approach to research design that focuses on a particular case – whether an individual, a collective or a phenomenon of interest. It is known as the 'study of the particular' for its thorough investigation of particular, real-life situations and is gaining increased attention in nursing and social research. However, the methodological flexibility it offers can leave the novice researcher uncertain of suitable procedural steps required to ensure methodological rigour. Method. This article provides a real example of a case study research design that utilizes schematic representation drawn from a doctoral study of the integration of health promotion principles and practices into a palliative care organization. Discussion. The issues discussed are: (1) the definition and application of case study research design; (2) the application of schematics in research; (3) the procedural steps and their contribution to the maintenance of rigour; and (4) the benefits and risks of schematics in case study research. Conclusion. The inclusion of visual representations of design with accompanying explanatory text is recommended in reporting case study research methods.