The use of residuals for detecting departures from the assumptions of the linear model with full-rank covariance, whether the design matrix is full rank or not, has long been recognized as an important diagnostic tool...
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The use of residuals for detecting departures from the assumptions of the linear model with full-rank covariance, whether the design matrix is full rank or not, has long been recognized as an important diagnostic tool. Once it became feasible to compute different kinds of residual in a straight forward way, various methods have focused on their underlying properties and their effectiveness. The recursive residuals are attractive in Econometric applications where there is a natural ordering among the observations through time. New formulations for the recursive residuals for models having uncorrelated errors with equal variances are given in terms of the observation vector or the usual least-squares residuals, which do not require the computation of least-squares parameter estimates and for which the transformation matrices are expressed wholly in terms of the rows of the Theil Z matrix. Illustrations of these new formulations are given. (C) 2008 Elsevier B.V. All rights reserved.
Efficient simulation of dynamical systems becomes more and more important in industry and research. Dynamic modeling of multi-body systems yields highly nonlinear equations of motion. Usually, the accelerations are co...
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Efficient simulation of dynamical systems becomes more and more important in industry and research. Dynamic modeling of multi-body systems yields highly nonlinear equations of motion. Usually, the accelerations are computed by an explicit inversion of the mass matrix that has the dimension according to the degrees of freedom. This classical foregoing implies high computational effort. In the present contribution, an O(n) formulation is introduced for efficient (recursive) procedure. It is based on the Projection Equation in subsystem representation, structuring the problem into parts and yielding interpretable intermediate solutions. The hereby necessary inversion refers to a reduced mass matrix that has the order of the considered subsystem. Additional constraints like endpoint contact are included via corresponding constraint forces. Avoiding an inversion of the total mass matrix is again successfully applied by a recursive procedure. The impact that occurs in the transition phase between the free system and constrained system is also solved in this sense. Results for the simulation of a plane pendulum motion with changing contact scenarios are presented.
Open-chain multibody systems have been extensively studied because of their widespread application. Based on the structural characteristics of such a system, the relationship between its hinged bodies was transformed ...
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Open-chain multibody systems have been extensively studied because of their widespread application. Based on the structural characteristics of such a system, the relationship between its hinged bodies was transformed into recursive constraint relationships among the position, velocity, and acceleration of the bodies. The recursive relationships were used along with the Huston-Kane method to select the appropriate generalized coordinates and determine the partial velocity of each body and to develop an algorithm of the entire system. The algorithm was experimentally validated;it has concise steps and low susceptibility to error. Further, the algorithm can readily solve and analyze open-chain multibody systems.
This article discusses a formal belief, desire, intention (BDI)-based agent model for theory of mind (ToM). The model uses BDI concepts to describe the reasoning process of an agent that reasons about the reasoning pr...
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This article discusses a formal belief, desire, intention (BDI)-based agent model for theory of mind (ToM). The model uses BDI concepts to describe the reasoning process of an agent that reasons about the reasoning process of another agent, which is also based on BDI concepts. We discuss three different application areas and illustrate how the model can be applied to each of them. We explore a case study for each of the application areas and apply our model to it. For each case study, a number of simulation experiments are described, and their results are discussed.
The work deals with the programmed system of MOCODISS (Modeling of Continuous-Discrete Systems) that permits calculating and designing rod systems on the elastic base. The mathematical model is presented that describe...
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The work deals with the programmed system of MOCODISS (Modeling of Continuous-Discrete Systems) that permits calculating and designing rod systems on the elastic base. The mathematical model is presented that describes the dynamics of elastically attached rods with associated masses on the inhomogeneous base. Principal functional possibilities and the field of application of the programmed MOCODISS package are considered. The application is shown of the package to the problem of lateral oscillations of the rod system with elastic joints on the elastic step base.
This note contains a proof that there is no recursive function of the initial index that gives a bound for the exceptional values in Blum speed-up, but that there is a recursive bounding function of the speed-up index...
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This note contains a proof that there is no recursive function of the initial index that gives a bound for the exceptional values in Blum speed-up, but that there is a recursive bounding function of the speed-up index. All the proofs given are constructive.
A well-known result of Sacks [24] states that if A is nonrecursive, then the set {B : A less than or equal to(T) B} has measure zero. Thus, from a measure-theoretic perspective, a "good" (i.e., nonrecursive)...
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A well-known result of Sacks [24] states that if A is nonrecursive, then the set {B : A less than or equal to(T) B} has measure zero. Thus, from a measure-theoretic perspective, a "good" (i.e., nonrecursive) oracle is hard to beat in the partial order of Turing degrees. We show that analogous results hold for the standard notions of inductive inference, as well as for the notions of approximate inference.
This paper provides the closed form analytical solution to the problem of minimizing the material volume required to support a given set of bending loads with a given number of discrete structural members, subject to ...
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This paper provides the closed form analytical solution to the problem of minimizing the material volume required to support a given set of bending loads with a given number of discrete structural members, subject to material yield constraints. The solution is expressed in terms of two variables, the aspect ratio, rho(-1), and complexity of the structure, q (the total number of members of the structure is equal to q(q + 1)). The minimal material volume (normalized) is also given in closed form by a simple function of rho and q, namely, V = q(rho(-1/q) - rho(1/q)). The forces for this nonlinear problem are shown to satisfy a linear recursive equation, from node-to-node of the structure. All member lengths are specified by a linear recursive equation, dependent only on the initial conditions involving a user specified length of the structure. The final optimal design is a class 2 tensegrity structure. Our results generate the 1904 results of Michell in the special case when the selected complexity q approaches infinity. Providing the optimum interms of a given complexity has the obvious advantage of relating complexity q to other criteria, such as costs, fabrication issues, and control. If the structure is manufactured with perfect joints (no glue, welding material, etc.), the minimal mass complexity is infinite. But in the presence of any joint mass, the optimal structural complexity is finite, and indeed quite small. Hence, only simple structures (low complexity q) are needed for practical design. (c) 2009 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
We study weighted path lengths (depths) and distances for increasing tree families, For those subclasses of increasing tree families, which can be constructed via an insertion process (e.g., recursive trees, plane-ori...
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We study weighted path lengths (depths) and distances for increasing tree families, For those subclasses of increasing tree families, which can be constructed via an insertion process (e.g., recursive trees, plane-oriented recursive trees, and binary increasing trees), we can determine the limiting distribution that can be characterized as a generalized Dickman's infinitely divisible distribution.
Lindenmayer grammars have frequently been applied to represent fractal curves. In this work, the ideas behind grammar evolution are used to automatically generate and evolve Lindenmayer grammars which represent fracta...
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Lindenmayer grammars have frequently been applied to represent fractal curves. In this work, the ideas behind grammar evolution are used to automatically generate and evolve Lindenmayer grammars which represent fractal curves with a fractal dimension that approximates a predefined required value. For many dimensions, this is a nontrivial task to be performed manually. The procedure we propose closely parallels biological evolution because it acts through three different levels: a genotype (a vector of integers), a protein-like intermediate level (the Lindenmayer grammar), and a phenotype (the fractal curve). Variation acts at the genotype level, while selection is performed at the phenotype level (by comparing the dimensions of the fractal curves to the desired value).
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