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A defence of functional modularity

Connection Science, 2003
Although 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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On the modular functions.

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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The modular group and modular functions

1976
In 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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The Values of Modular Functions and Modular Forms

Canadian Mathematical Bulletin, 2006
AbstractLet 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, 2009
In 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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The Modular Function

1987
By SL2 we mean the group of 2 x 2 matrices with determinant 1. We write SL2 (R) for those elements of SL2 having coefficients in a ring R. In practice, the ring R will be Z, Q, R. We call SL2 (Z) the modular group.
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Emergence of Functional Modularity in Robots

1998
The 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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Symmetrization of Modular Aggregation Functions

2010
Ordered modular aggregation functions (OMAF in short) can be seen as symmetrized modular aggregation functions and they are characterized by comonotone modularity. As such, OMAFs generalize OWA operators. We show a one-to-one correspondence between idempotent OMAFs and copula-based integrals with respect to a symmetric capacity.
Radko Mesiar   +1 more
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Modular network function virtualization

2017 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), 2017
Network functions like load balancers and stateful firewalls which traditionally have been packaged in a single proprietary device are now being virtuahzed in software across multiple physical devices networked together to achieve greater flexibility and scale. A virtualization can become very complex.
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