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A mathematical and computational framework for reliable real-time solution of parametrized partial differential equations

Christophe Prud'homme, Dimitrios V. Rovas, Karen Veroy, Anthony T. Patera (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are (i) (provably) rapidly convergent global reduced–basis approximations — Galerkin projection onto a space W N spanned...

A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations

Christophe Prud'homme, Dimitrios V. Rovas, Karen Veroy, Anthony T. Patera (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are (i) (provably) rapidly convergent global reduced–basis approximations — Galerkin projection onto a space WN spanned...

A mathematical framework for learning and adaption: (generalized) random systems with complete connections.

Ulrich Herkenrath, Radu Theodorescu (1981)

Trabajos de Estadística e Investigación Operativa

The aim of this paper is to show that the theory of (generalized) random systems with complete connection may serve as a mathematical framework for learning and adaption. Chapter 1 is of an introductory nature and gives a general description of the problems with which one is faced. In Chapter 2 the mathematical model and some results about it are explained. Chapter 3 deals with special learning and adaption models.

A matrix inequality based design method for consensus problems in multi-agent systems

Shohei Okuno, Joe Imae, Tomoaki Kobayashi (2009)

International Journal of Applied Mathematics and Computer Science

In this paper, we study a consensus problem in multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus...

A method for knowledge integration

Martin Janžura, Pavel Boček (1998)

Kybernetika

With the aid of Markov Chain Monte Carlo methods we can sample even from complex multi-dimensional distributions which cannot be exactly calculated. Thus, an application to the problem of knowledge integration (e. g. in expert systems) is straightforward.

A method for learning scenario determination and modification in intelligent tutoring systems

Adrianna Kozierkiewicz-Hetmańska, Ngoc Thanh Nguyen (2011)

International Journal of Applied Mathematics and Computer Science

Computers have been employed in education for years. They help to provide educational aids using multimedia forms such as films, pictures, interactive tasks in the learning process, automated testing, etc. In this paper, a concept of an intelligent e-learning system will be proposed. The main purpose of this system is to teach effectively by providing an optimal learning path in each step of the educational process. The determination of a suitable learning path depends on the student's preferences,...

A method of constructing the frame of a directed graph

Ichiro Hofuku, Kunio Oshima (2013)

International Journal of Applied Mathematics and Computer Science

In web search engines, such as Google, the ranking of a particular keyword is determined by mathematical tools, e.g., Pagerank or Hits. However, as the size of the network increases, it becomes increasingly difficult to use keyword ranking to quickly find the information required by an individual user. One reason for this phenomenon is the interference of superfluous information with the link structure. The World Wide Web can be expressed as an enormous directed graph. The purpose of the present...

A methodology for constructing fuzzy rule-based classification systems.

José María Fernández Garrido, Ignacio Requena Ramos (2000)

Mathware and Soft Computing

In this paper, a methodology to obtain a set of fuzzy rules for classification systems is presented. The system is represented in a layered fuzzy network, in which the links from input to hidden nodes represents the antecedents of the rules, and the consequents are represented by links from hidden to output nodes. Specific genetic algorithms are used in two phases to extract the rules. In the first phase an initial version of the rules is extracted, and in second one, the labels are refined. The...

A methodology for developing knowledge-based systems.

Juan Luis Castro, José Jesús Castro-Sánchez, Antonio Espin, José Manuel Zurita (1998)

Mathware and Soft Computing

This paper presents a methodology for developing fuzzy knowledge based systems (KBS), which permits a complete automatization. This methodology will be useful for approaching more complex problems that those in which machine learning from examples are successful.

A metric for evaluating software architecture and communication models consistency

Jean-Yves Lafaye, Georges Louis (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Among several alternative viewpoints for building software quality metrics, evaluating the consistency between different models in a software specification or implementation appears to be fruitful. An obvious difficulty is that different models are usually expressed by means of different concepts, and then, confronting heterogeneous representations is not straightforward. In this paper, we propose a solution for measuring the consistency between the architecture and the communication models. After...

A metric for evaluating software architecture and communication models consistency

Jean-Yves Lafaye, Georges Louis (2010)

RAIRO - Theoretical Informatics and Applications

Among several alternative viewpoints for building software quality metrics, evaluating the consistency between different models in a software specification or implementation appears to be fruitful. An obvious difficulty is that different models are usually expressed by means of different concepts, and then, confronting heterogeneous representations is not straightforward. In this paper, we propose a solution for measuring the consistency between the architecture and the communication models. After...

A mixed–FEM and BEM coupling for a three-dimensional eddy current problem

Salim Meddahi, Virginia Selgas (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed–FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.

A mixed–FEM and BEM coupling for a three-dimensional eddy current problem

Salim Meddahi, Virginia Selgas (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed–FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.

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