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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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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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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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Symmetrization of Modular Aggregation Functions
2010Ordered 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), 2017Network 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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1996
For a lattice \(L\) and a group \(G\) a map \(\mu: L\to G\) is called a modular function if for all \(x,y\in L\), we have \(\mu(x\vee y)+ \mu(x\wedge y)= \mu(x)+ \mu(y)\). The important examples that provide much of the motivation for the study of modular functions are furnished by measures on Boolean algebras and linear operators on vector lattices ...
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For a lattice \(L\) and a group \(G\) a map \(\mu: L\to G\) is called a modular function if for all \(x,y\in L\), we have \(\mu(x\vee y)+ \mu(x\wedge y)= \mu(x)+ \mu(y)\). The important examples that provide much of the motivation for the study of modular functions are furnished by measures on Boolean algebras and linear operators on vector lattices ...
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Zeta-Functions of Modular Curves
2006This work gives an exposition and a generalization of classical results due to M. Eichler [1] and G. Shimura [2], which give the expression of congruence-zeta-functions of some modular curves in terms of Hecke polynomials. The central point in these papers is the famous congruence relation which links the local factor of the Mellin transforms of ...
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