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Les termes : un modèle algébrique de représentation et de structuration de données symboliques

Marie-Catherine Daniel-Vatonne, Colin de la Higuera (1993)

Mathématiques et Sciences Humaines

Nos travaux se situent dans le cadre de l'analyse conceptuelle des données. Notre objectif est de généraliser les représentations par variables binaires ou nominales en y adjoignant la modélisation de structures internes. Le problème est de ne pas perdre en complexité algorithmique ce qui est gagné en puissance de représentation. Selon ces considérations, décrire les données et des classes de données par des structures arborescentes semble un bon compromis. Le système de représentation que nous...

Les types de données syntaxiques du système ℱ

Samir Farkh, Karim Nour (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Nous présentons dans ce papier une définition purement syntaxique des types entrées et des types sorties du système ℱ . Nous définissons les types de données syntaxiques comme étant des types entrées et sorties. Nous démontrons que les types à quantificateurs positifs sont des types de données syntaxiques et qu’un type entrée est un type sortie. Nous imposons des restrictions sur la règle d’élimination des quantificateurs pour démontrer qu’un type sortie est un type entrée.

Les types de données syntaxiques du système ℱ

Samir Farkh, Karim Nour (2010)

RAIRO - Theoretical Informatics and Applications

We give in this paper a purely syntactical definition of input and output types of system ℱ . We define the syntactical data types as input and output types. We show that any type with positive quantifiers is a syntactical data type and that an input type is an output type. We give some restrictions on the ∀-elimination rule in order to prove that an output type is an input type.

Lexical Error Compensation in Handwritten-Based Mathematical Information Retrieval

Ahmadi, Seyed Ali, Youssef, Abdou (2008)

Towards Digital Mathematics Library. Birmingham, United Kingdom, July 27th, 2008

Entering mathematical queries, in general, can be a demanding task. Mathematical notation is two-dimensional and cannot be easily typed with a standard QWERTY keyboard. Handwriting appears to be the most intuitive and promising method to express mathematical queries. Recognition technology for handwritten mathematical notation has never been applied in math search. The objective of this research is to design and implement an automated symbol-recognition error compensation system for the handwritten-based...

Lexicographic combinations of preference relations in the context of Possibilistic Decision Theory.

Lluís Godo, Adriana Zapico (2006)

Mathware and Soft Computing

In Possibilistic Decision Theory (PDT), decisions are ranked by a pressimistic or by an optimistic qualitative criteria. The preference relations induced by these criteria have been axiomatized by corresponding sets of rationality postulates, both à la von Neumann and Morgenstern and à la Savage. In this paper we first address a particular issue regarding the axiomatic systems of PDT à la von Neumann and Morgenstern. Namely, we show how to adapt the axiomatic systems for the pessimistic and optimistic...

Linear discriminant analysis with a generalization of the Moore-Penrose pseudoinverse

Tomasz Górecki, Maciej Łuczak (2013)

International Journal of Applied Mathematics and Computer Science

The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when the number of features exceeds that of observations. In this case, the covariance estimates do not have full rank, and thus cannot be inverted. There are a number of ways to deal with this problem. In this paper, we propose improving LDA in this...

Linear size test sets for certain commutative languages

Štěpán Holub, Juha Kortelainen (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We prove that for each positive integer n , the finite commutative language E n = c ( a 1 a 2 ⋯ a n ) possesses a test set of size at most 5 n . Moreover, it is shown that each test set for E n has at least n - 1 elements. The result is then generalized to commutative languages L containing a word w such that (i) alph ( w ) = alph ( L ) ; and (ii) each symbol a ∈ alph ( L ) occurs at least twice in w if it occurs at least twice in some word of L : each such L possesses a test set of size 11 n , where n = Card ( alph ( L ) ) . The considerations rest on the analysis of some basic types of word equations....

Linear size test sets for certain commutative languages

Štěpán Holub, Juha Kortelainen (2010)

RAIRO - Theoretical Informatics and Applications

We prove that for each positive integer n, the finite commutative language En = c(a1a2...an) possesses a test set of size at most 5n. Moreover, it is shown that each test set for En has at least n-1 elements. The result is then generalized to commutative languages L containing a word w such that (i) alph(w) = alph}(L); and (ii) each symbol a ∈ alph}(L) occurs at least twice in w if it occurs at least twice in some word of L: each such L possesses a test set of size 11n, where n = Card(alph(L))....

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