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A defence of functional modularity
Connection Science, 2003Although belief in the existence of mental modules of some form is widespread among cognitive researchers, neurally sophisticated researchers commonly resist the view that cognitive processing involves modules that are functionally independent of one another.
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2000
It is the purpose of the authors to use \(n\)th order theta functions to construct some modular forms of weight 0 on the groups \(\Gamma_0 (p)\), \(p\) a prime (Theorem 1), \(\Gamma^0(p^2)\), \(p\) a prime (Theorem 2) and \(\theta(n)=\Gamma_0 \setminus\operatorname{cap} \Gamma_\vartheta\), \(n\in\mathbb{Z}^+\) (Theorem 3).
KIRMACI, Uğur Selamet +1 more
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It is the purpose of the authors to use \(n\)th order theta functions to construct some modular forms of weight 0 on the groups \(\Gamma_0 (p)\), \(p\) a prime (Theorem 1), \(\Gamma^0(p^2)\), \(p\) a prime (Theorem 2) and \(\theta(n)=\Gamma_0 \setminus\operatorname{cap} \Gamma_\vartheta\), \(n\in\mathbb{Z}^+\) (Theorem 3).
KIRMACI, Uğur Selamet +1 more
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The modular group and modular functions
1976In the foregoing chapter we encountered unimodular transformations $$ {{c\tau + d}} $$ where a, b, c, d are integers with ad — bc = 1. This chapter studies such transformations in greater detail and also studies functions which, Iike J(τ), are invariant under unimodular transformations.
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Emergence of Functional Modularity in Robots
1998The origin and structural and functional significance of modular design in organisms represent an important issue debated in many different disciplines. To be eventually successful in clarifying the evolutionary mechanisms underpinning the emergence of modular design in complex organisms, one should be able to cover all different levels of biological ...
Calabretta R +3 more
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The Values of Modular Functions and Modular Forms
Canadian Mathematical Bulletin, 2006AbstractLet Γ0be a Fuchsian group of the first kind of genus zero and Γ be a subgroup of Γ0of finite index of genus zero. We find universal recursive relations giving theqr-series coefficients ofj0by using those of theqhs-series ofj, wherejis the canonical Hauptmodul for Γ andj0is a Hauptmodul for Γ0without zeros on the complex upper half plane(hereqℓ:=
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Functional modularity for genetic programming
Proceedings of the 11th Annual conference on Genetic and evolutionary computation, 2009In this paper we introduce, formalize, and experimentally validate a novel concept of functional modularity for Genetic Programming (GP). We rely on module definition that is most natural for GP: a piece of program code (subtree). However, as opposed to syntax-based approaches that abstract from the actual computation performed by a module, we analyze ...
Krzysztof Krawiec, Bartosz Wieloch
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