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The Review of Symbolic Logic, 2018
AbstractIn a wide range of fields, the word “modular” is used to describe complex systems that can be decomposed into smaller systems with limited interactions between them. This essay argues that mathematical knowledge can fruitfully be understood as having a modular structure and explores the ways in which modularity in mathematics is epistemically ...
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AbstractIn a wide range of fields, the word “modular” is used to describe complex systems that can be decomposed into smaller systems with limited interactions between them. This essay argues that mathematical knowledge can fruitfully be understood as having a modular structure and explores the ways in which modularity in mathematics is epistemically ...
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Fundamenta Informaticae, 2006
It has been observed that various synchronisation operators underlying the modular design of concurrent systems can be explained as pullbacks in suitable categories of concurrent systems. Here, the boundaries of such approach are investigated. For this purpose we study the issue of completeness in categories of trace monoids. It turns out that (finite)
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It has been observed that various synchronisation operators underlying the modular design of concurrent systems can be explained as pullbacks in suitable categories of concurrent systems. Here, the boundaries of such approach are investigated. For this purpose we study the issue of completeness in categories of trace monoids. It turns out that (finite)
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Modular Certification of Integrated Modular Systems
2007This paper presents ongoing research into the modular certification of Integrated Modular Systems (IMS) within BAE Systems. An IMS is an open systems approach to the construction of systems from a set of standard hardware and software modules. Modular certification is the modular safety assessment of such systems. The aim is to reduce the certification
James Blow, Andrew Cox, Paul Liddell
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Progress in Neurobiology, 1991
The putative modular organization of the cerebellum can be revealed in three ways: functionally through receptive field mapping, anatomically through tract tracing studies, and biochemically by using a range of molecular probes. The present review concentrates on the last of these, the evidence for cerebellar modules that comes from molecular studies ...
R, Hawkes, C, Gravel
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The putative modular organization of the cerebellum can be revealed in three ways: functionally through receptive field mapping, anatomically through tract tracing studies, and biochemically by using a range of molecular probes. The present review concentrates on the last of these, the evidence for cerebellar modules that comes from molecular studies ...
R, Hawkes, C, Gravel
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Biosystems, 2022
The hypothesis presented here is that codes as described by Marcello Barbieri are the fundamental principle behind biological modularity. Modularity has been studied in different life science disciplines, especially in the fields of evolution and development, as well as in network biology, yet there is still no consensus on how modularity evolved ...
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The hypothesis presented here is that codes as described by Marcello Barbieri are the fundamental principle behind biological modularity. Modularity has been studied in different life science disciplines, especially in the fields of evolution and development, as well as in network biology, yet there is still no consensus on how modularity evolved ...
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The American Mathematical Monthly, 2001
Over the last 20 years, the modular function has become widely known through its miraculous intervention in two great mathematical achievements: the proof of Fermat's last theorem and the "moonshine" of the monster simple group. In both cases, the modular function appears where no one expected it, and it bridges a chasm between seemingly unrelated ...
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Over the last 20 years, the modular function has become widely known through its miraculous intervention in two great mathematical achievements: the proof of Fermat's last theorem and the "moonshine" of the monster simple group. In both cases, the modular function appears where no one expected it, and it bridges a chasm between seemingly unrelated ...
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On Sub-modularization and Morphological Heterogeneity in Modular Robotics
2013Modular robots are a kind of robots built from mechatronic modules, which can be assembled in many different ways allowing the modular robot to assume a wide range of morphologies and functions. An important question in modular robotics is to which degree modules should be heterogeneous.
A. H. Lyder +4 more
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Modular points, modular curves, modular surfaces and modular forms
1985[For the entire collection see Zbl 0547.00007.] \\par This is the written version of a talk at the Arbeitstagung at Bonn. It is centered around one example: the modular curve X\\sb 0(37). The elliptic curve E:\\quad y(y-1)=(x+1)x(x-1) is a factor of the Jacobian J\\sb 0(37).
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, 2009 Modularization can be sought for as a technique to provide context-dependent perspectives over a given shared information repository. This chapter presents an approach to database modularization where the modules represent application-specific perspectives over the shared database. The approach is meant to support the creation/definition of the modules
Parent, Christine +2 more
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Modular Groups and Modular Forms
1989In this chapter, we explain the general theory of modular forms. In §4.1, we discuss the full modular group SL 2(ℤ) and modular forms with respect to SL 2(ℤ), as an introduction to the succeeding sections. We define and study congruence modular groups in §4.2. In §4.3, we explain the relation between modular forms and Dirichlet series obtained by Hecke
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