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Picture codes

Symeon Bozapalidis, Archontia Grammatikopoulou (2006)

RAIRO - Theoretical Informatics and Applications

We introduce doubly-ranked (DR) monoids in order to study picture codes. We show that a DR-monoid is free iff it is pictorially stable. This allows us to associate with a set C of pictures a picture code B(C) which is the basis of the least DR-monoid including C. A weak version of the defect theorem for pictures is established. A characterization of picture codes through picture series is also given.

Planning identification experiments for cell signaling pathways: An NFκB case study

Krzysztof Fujarewicz (2010)

International Journal of Applied Mathematics and Computer Science

Mathematical modeling of cell signaling pathways has become a very important and challenging problem in recent years. The importance comes from possible applications of obtained models. It may help us to understand phenomena appearing in single cells and cell populations on a molecular level. Furthermore, it may help us with the discovery of new drug therapies. Mathematical models of cell signaling pathways take different forms. The most popular way of mathematical modeling is to use a set of nonlinear...

Poids des duaux des codes BCH de distance prescrite 2 a + 1 et sommes exponentielles

Éric Férard (2002)

Bulletin de la Société Mathématique de France

Soit n un entier pair. On considère un code BCH binaire C n de longueur 2 n - 1 et de distance prescrite 2 a + 1 avec a 3 . Le poids d’un mot non nul du dual de  C n peut s’exprimer en fonction d’une somme exponentielle. Nous montrerons que cette somme n’atteint pas la borne de Weil et nous proposerons une amélioration de celle-ci. En conséquence, nous obtiendrons une amélioration de la borne de Carlitz-Uchiyama sur le poids des mots du dual de C n .

Polyabelian loops and Boolean completeness

François Lemieux, Cristopher Moore, Denis Thérien (2000)

Commentationes Mathematicae Universitatis Carolinae

We consider the question of which loops are capable of expressing arbitrary Boolean functions through expressions of constants and variables. We call this property Boolean completeness. It is a generalization of functional completeness, and is intimately connected to the computational complexity of various questions about expressions, circuits, and equations defined over the loop. We say that a loop is polyabelian if it is an iterated affine quasidirect product of Abelian groups; polyabelianness...

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