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Complex Hadamard Matrices contained in a Bose–Mesner algebra

Takuya Ikuta, Akihiro Munemasa (2015)

Special Matrices

Acomplex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying HH* = nI, where * stands for the Hermitian transpose and I is the identity matrix of order n. In this paper, we first determine the image of a certain rational map from the d-dimensional complex projective space to Cd(d+1)/2. Applying this result with d = 3, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose–Mesner algebra of a certain 3-class symmetric...

Complexité et automates cellulaires linéaires

Valérie Berthé (2010)

RAIRO - Theoretical Informatics and Applications

The aim of this paper is to evaluate the growth order of the complexity function (in rectangles) for two-dimensional sequences generated by a linear cellular automaton with coefficients in / l , and polynomial initial condition. We prove that the complexity function is quadratic when l is a prime and that it increases with respect to the number of distinct prime factors of l.

Composition and structure of social networks

Ove Frank (1997)

Mathématiques et Sciences Humaines

Social networks representing one or more relationships between individuals and one or more categorical characteristics of the individuals exhibit both structure and composition. Probabilistic models of such networks can be used for analyzing the interrelations between structural and compositional variables, for instance in order to find how structure can be explained by composition or how structure explains composition. Different models are discussed and different statistical methods are employed...

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