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Results
(21
items found)
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Title:
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Conceptual
Modeling and Ontological Analysis |
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Author:
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Chris Welty.
Nicola Guarino. |
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Description:
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The slide
introduces the notions of formal ontology from
Philosophy, present basic tools for
ontology-driven conceptual analysis based on
formal ontology, explore some principled
guidelines for using these tools, and discuss
examples of using these guidelines and tools in practice. |
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Context
of Use:
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Higher Education. |
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Title:
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Resultant of Vectors |
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Author:
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William J. Devenport |
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Description:
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An educational java applet for studying vector algebra. |
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Context
of Use:
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Secondary Education,
University
Second Cycle,
University
First Cycle,
Higher Education. |
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Title:
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Set Theory |
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Author:
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Professor J.F.Baldwin |
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Description:
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The lecture slides gives a brief introduction to set theory used in the course "Discrete Mathematics ". |
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Context
of Use:
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University Graduate,
University
(Upper Div). |
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Title:
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Number Theory |
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Author:
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Professor J.F.Baldwin |
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Description:
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The lecture slides gives a brief introduction to number theory used in the course "Discrete Mathematics ". |
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Context
of Use:
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University Graduate,
University
(Upper Div). |
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Title:
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Approximation of the Newton Step by a Defect Correction Process |
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Author:
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E. Arian,A. BATTERMANN,E.W. SACHS |
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Description:
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In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced into the system. This operator is motivated by local mode analysis. The operator can be used also for preconditioning in GMRES. We give a detailed convergence analysis for the defect correction process and show the derivation of the modifying operator. Numerical tests are done on the small disturbance shape optimization problem in two dimensions for the defect correction process and for GMRES. |
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Context
of Use:
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Vocational Training,
Continuous Formation,
Professional Formation. |
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Ratings/Reviews:
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Title:
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Solving Upwind-Biased Discretizations: Defect-correction Iterations |
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Author:
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Boris Diskin,James L. Thomas |
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Description:
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A novel comprehensive half-space Fourier mode analysis (which, by the way, can take into account the influence of discretized outflow boundary conditions as well) for the defect-correction method is developed. This analysis explains many phenomena observed in solving non-elliptic equations and provides a close prediction of the actual solution behavior. It predicts the convergence rate for each iteration and the asymptotic convergence rate. As a result of this analysis, a new very efficient adaptive multigrid algorithm solving the discrete problem to within a given accuracy is proposed. Numerical simulations conform the accuracy of the analysis and the efficiency of the proposed algorithm. The results of the numerical tests are reported. |
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Context
of Use:
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Vocational Training,
Continuous Formation,
Professional Formation. |
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Title:
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Comparative Properties of Collaborative Optimization and Other Approaches to MDO |
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Author:
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Natalia M. Alexandrov,Robert Michael Lewis |
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Description:
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We discuss criteria by which one can classify, analyze, and evaluate approaches to solving multidisciplinary design optimization (MDO) problems. Central to our discussion is the often overlooked distinction between questions of formulating MDO problems and solving the resulting computational problem. We illustrate our general remarks by comparing several approaches to MDO that have been proposed. |
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Context
of Use:
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Vocational Training,
Continuous Formation,
Professional Formation. |
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Title:
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Solving Upwind-Biased Discretizations II: Multigrid Solver Using Semicoarsening |
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Author:
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Boris Diskin |
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Description:
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This paper studies a novel multigrid approach to the solution for a second order upwind- biased discretization of the convection equation in two dimensions. This approach is based on semicoarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse grids the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1. The residual asymptotic convergence rate of the proposed V (0; 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4=3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle depth (number of levels) and/or refining the target-grid mesh spacing. 2. The full multigrid algorithm (FMG) with two V (0; 2) cycles on the target grid and just one V (0; 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target discretization). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3. A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. The actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid). |
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Context
of Use:
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Vocational Training,
Continuous Formation,
Professional Formation. |
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Ratings/Reviews:
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Title:
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Reinforcement Learning: A Tutorial |
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Author:
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Mance E. Harmon,Stephanie S. Harmon |
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Description:
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The purpose of this tutorial is to provide an introduction to reinforcement learning (RL) at a level easily understood by students and researchers in a wide range of disciplines. The intent is not to present a rigorous mathematical discussion that requires a great deal of effort on the part of the reader, but rather to present a conceptual framework that might serve as an introduction to a more rigorous study of RL. The fundamental principles and techniques used to solve RL problems are presented. The most popular RL algorithms are presented. Section (1) presents an overview of RL and provides a simple example to develop intuition of the underlying dynamic programming mechanism. In Section (2) the parts of a reinforcement learning problem are discussed. These include the environment, reinforcement function, and value function. Section (3) gives a description of the most widely use d reinforcement learning algorithms. These include TD(lambda) and both the residual and direct forms of value iteration, Q-learning, and advantage learning. In Section (4) some of the ancillary issues of RL are briefly discussed, such as choosing an exploration strategy and a discount factor. The conclusion is given in Section (5). Finally, Section (6) is a glossary of commonly used terms followed by references and bibliography. |
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Context
of Use:
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Vocational Training,
Continuous Formation,
Professional Formation. |
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Title:
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Large-scale Parallel Viscous Flow Computations Using an Unstructured Multigrid Algorithm |
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Author:
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Dimitri J. Mavriplis |
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Description:
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The development and testing of a parallel unstructured agglomeration multigrid algorithm for steady-state aerodynamic flows is discussed. The agglomeration multigrid strategy uses a graph algorithm to construct the coarse multigrid levels from the given fine grid, similar to an algebraic multigrid approach, but operates directly on the non-linear system using the FAS approach. The scalability and convergence rate of the multigrid algorithm are examined on the SGI Origin 2000 and the Cray T3E. An argument is given which indicates that the asymptotic scalability of the multigrid algorithm should be similar to that of its underlying single grid smoothing scheme. For medium size problems involving several million grid points, near perfect scalability is obtained for the single grid algorithm, while only a slight drop-off in parallel efficiency is observed for the multigrid V- and W-cycles, using up to 128 processors on the SGI Origin 2000, and up to 512 processors on the Cray T3E. For a large problem using 25 million grid points, good scalability is observed for the multigrid algorithm using up to 1450 processors on a Cray T3E, even when the coarsest grid level contains fewer points than the total number of processors. |
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Context
of Use:
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Vocational Training,
Continuous Formation,
Professional Formation. |
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