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Space Representation (space + representation)

Distribution by Scientific Domains

Engineering	33%

Selected Abstracts

Granularity in Relational Formalisms,With Application to Time and Space Representation

COMPUTATIONAL INTELLIGENCE, Issue 4 2001
Jérôme Euzenat
Temporal and spatial phenomena can be seen at a more or less precise granularity, depending on the kind of perceivable details. As a consequence, the relationship between two objects may differ depending on the granularity considered. When merging representations of different granularity, this may raise problems. This paper presents general rules of granularity conversion in relation algebras. Granularity is considered independently of the specific relation algebra, by investigating operators for converting a representation from one granularity to another and presenting six constraints that they must satisfy. The constraints are shown to be independent and consistent and general results about the existence of such operators are provided. The constraints are used to generate the unique pairs of operators for converting qualitative temporal relationships (upward and downward) from one granularity to another. Then two fundamental constructors (product and weakening) are presented: they permit the generation of new qualitative systems (e.g. space algebra) from existing ones. They are shown to preserve most of the properties of granularity conversion operators. [source]

Recursive penalized least squares solution for dynamical inverse problems of EEG generation

HUMAN BRAIN MAPPING, Issue 4 2004
Okito Yamashita
Abstract In the dynamical inverse problem of electroencephalogram (EEG) generation where a specific dynamics for the electrical current distribution is assumed, we can impose general spatiotemporal constraints onto the solution by casting the problem into a state space representation and assuming a specific class of parametric models for the dynamics. The Akaike Bayesian Information Criterion (ABIC), which is based on the Type II likelihood, was used to estimate the parameters and evaluate the model. In addition, dynamic low-resolution brain electromagnetic tomography (LORETA), a new approach for estimating the current distribution is introduced. A recursive penalized least squares (RPLS) step forms the main element of our implementation. To obtain improved inverse solutions, dynamic LORETA exploits both spatial and temporal information, whereas LORETA uses only spatial information. A considerable improvement in performance compared to LORETA was found when dynamic LORETA was applied to simulated EEG data, and the new method was applied also to clinical EEG data. Hum. Brain Mapp. 21:221,235, 2004. © 2004 Wiley-Liss, Inc. [source]

Design spaces, measures and metrics for evaluating quality of time operators and consequences leading to improved algorithms by design,illustration to structural dynamics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005
X. Zhou
Abstract For the first time, for time discretized operators, we describe and articulate the importance and notion of design spaces and algorithmic measures that not only can provide new avenues for improved algorithms by design, but also can distinguish in general, the quality of computational algorithms for time-dependent problems; the particular emphasis is on structural dynamics applications for the purpose of illustration and demonstration of the basic concepts (the underlying concepts can be extended to other disciplines as well). For further developments in time discretized operators and/or for evaluating existing methods, from the established measures for computational algorithms, the conclusion that the most effective (in the sense of convergence, namely, the stability and accuracy, and complexity, namely, the algorithmic formulation and algorithmic structure) computational algorithm should appear in a certain algorithmic structure of the design space amongst comparable algorithms is drawn. With this conclusion, and also with the notion of providing new avenues leading to improved algorithms by design, as an illustration, a novel computational algorithm which departs from the traditional paradigm (in the sense of LMS methods with which we are mostly familiar with and widely used in commercial software) is particularly designed into the perspective design space representation of comparable algorithms, and is termed here as the forward displacement non-linearly explicit L-stable (FDEL) algorithm which is unconditionally consistent and does not require non-linear iterations within each time step. From the established measures for comparable algorithms, simply for illustration purposes, the resulting design of the FDEL formulation is then compared with the commonly advocated explicit central difference method and the implicit Newmark average acceleration method (alternately, the same conclusion holds true against controllable numerically dissipative algorithms) which pertain to the class of linear multi-step (LMS) methods for assessing both linear and non-linear dynamic cases. The conclusions that the proposed new design of the FDEL algorithm which is a direct consequence of the present notion of design spaces and measures, is the most effective algorithm to-date to our knowledge in comparison to the class of second-order accurate algorithms pertaining to LMS methods for routine and general non-linear dynamic situations is finally drawn through rigorous numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source]

An algorithm for the structural analysis of state space: synthesis of nonlinear observers

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2001
Virgilio López-Moralès
Abstract The problem addressed is the linearization of multi-input multi-output (MIMO) nonlinear systems by a generalized state coordinates transformation and generalized input,output injection, in order to design an observer. This observer will have linear error dynamics. The goal is to bring together two observers design approaches: a structural one and a numerical one. Necessary and sufficient conditions for the existence of a linearizing generalized state transformation are obtained by an algebraic way and without computing the input,output differential equations. The main result tests integrability conditions of differential one-forms derived from the state space representation and is applicable to a large subclass of nonlinear systems. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Permanent-transitory Decomposition in Var Models With Cointegration and Common Cycles

OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 4 2000
Alain Hecq
In this paper we derive permanent-transitory decompositions of non-stationary multiple times series generated by (r)nite order Gaussian VAR(p) models with both cointegration and serial correlation common features. We extend existing analyses to the two classes of reduced rank structures discussed in Hecq, Palm and Urbain (1998). Using the corresponding state space representation of cointegrated VAR models in vector error correction form we show how decomposition can be obtained even in the case where the number of common feature and cointegration vectors are not equal to the number of variables. As empirical analysis of US business fluctuations shows the practical relevance of the approach we propose. [source]

Interference of probabilities and number field structure of quantum models

ANNALEN DER PHYSIK, Issue 10 2003
A. Khrennikov
Abstract We study the probabilistic consequences of the choice of the basic number field in the quantum formalism. We demonstrate that by choosing a number field for a linear space representation of quantum model it is possible to describe various interference phenomena. We analyse interference of probabilistic alternatives induced by real, complex, hyperbolic (Clifford) and p -adic representations. [source]