otherusesof Modularity Many organisms consist of modules , both anatomically and in their metabolism . Anatomical modules are usually segments or organs. When we look at illustrations of metabolic reactions, we find that they, too, are modular we can clearly identify, for instance, the citric acid cycle as a complex network that has only a few interfaces with other such modules. This principle holds true at various different scales we can identify smaller modules within such larger networks that are similarly self contained. We say that metabolic modularity is Scale free network scale free . In addition to showing scalefree and small world network small world properties, biological networks appear to exhibit modularity in topological structure. In the field of network biology, the definition of nodes and edges in a given network depends on the type of network examined. For example, in a protein interaction network , nodes correspond with individual proteins and edges represent the interactions between them either through direct physical interaction, or compound mediated . Metabolic network s, on the other hand, contain metabolite nodes and edges that represent the specific enzymes that connect them in catalyzing biochemical reactions . As with any type of network, modularity in biological networks allows sub groups of nodes and edges to function in a semi autonomous fashion . The concept of modularity resurfaces at the scale of organs and developmental units. Why are there distinct cell types organised into spatial aggregations organs , and what are the benefits of having a segmentation ... that modularity imparts a certain degree of evolvability to a system by allowing specific features ... are more constrained. It is thought that there exists an Optimality theory optimal degree of modularity ... Homologues, Natural Kinds, and the Evolution of Modularity http 7e.devbio.com article.php?ch 23 ... celldynamics research pdfs vonDassowMunro99.pdf Modularity in Animal Development ... more details
Other uses ModularityModularity is a benefit function used in the analysis of Complex network networks ... into modules or communities. Good divisions, which have high values of the modularity, are those ... connections between different modules. The most common use of the modularity is as a basis for optimization ... number of groups. The modularity of this division is defined to be the fraction of the edges ... in the same group, the modularity, denoted Q , is then given by math Q frac 1 2m sum ij left A ij ... and c sub i sub , c sub j sub is the Kronecker delta symbol. The value of the modularity lies in the range ... on the basis of chance. Matrix formulation An alternative formulation of the modularity, useful ... called modularity matrix, which has elements math B ij A ij frac k i k j 2m . math All rows and columns of the modularity matrix sum to zero, which means that the modularity of an undivided network ... the modularity. The general form of the modularity for arbitrary numbers of communities is equivalent ... ref Resolution limit Modularity compares the number of edges inside a cluster with the expected ..., if a network is large enough, the expected number of edges between two groups of nodes in modularity ... be interpreted by modularity as a sign of a strong correlation between the two clusters, and optimizing modularity would lead to the merge of the two clusters, independently of the clusters features ... edges, and represent the best identifiable communities, would be merged by modularity optimization ... doi 10.1073 pnas.0605965104 issue 1 pmc 1765466 ref For this reason, optimizing modularity in large ... for methods like modularity optimization, which rely on a global null model. ref cite journal ... main approaches to solve the resolution limit within the modularity context the addition of a resistance ... of modularity, which controls the relative importance between internal links of the communities and the null model ref name rb06 . Optimizing modularity for values of these parameters in their respective ... more details
dablink The concept of modularity is also used in other fields. See modularity . Modularity of mind is the notion that a mind may, at least in part, be composed of separate innate structures which have established evolution arily developed functional purposes. Proponents believe this view is implied by Noam Chomsky s concept of a universal grammar universal , generative grammar . Such universal features of language are taken by proponents of the modularity theory to imply the existence of an underlying language acquisition language acquisition device structure in the brain. This device is postulated to be autonomous and specialized for learning language rapidly a module. Fodor s Modularity of Mind Historically, questions regarding the functional architecture of the mind have been divided into two different theories of the nature of the faculties. The first can be characterized as a horizontal view because it refers to mental processes as if they are interactions between faculties such as memory ... lobe. This simplistic view of modularity has been disproven over the course of the last century. In the 1980s, however, Jerry Fodor revived the idea of the modularity of mind, although without the notion ... most articulate proponents with the 1983 publication of Modularity of Mind . ref Fodor, Jerry A. 1983 . Modularity of Mind An Essay on Faculty Psychology . Cambridge, Mass. MIT Press. ISBN 0 262 56025 ... in the same sense as reflexes. Although he argued for the modularity of lower level cognitive processes in Modularity of Mind he also argued that higher level cognitive processes are not modular ... to as the cognitive impenetrability of the module. Evolutionary psychology Other perspectives on modularity .... Arguments against modularity In contrast to modular mental structure, some theories posit domain ... processes has yet to be developed. See also Modularity Language module Visual modularity Society of Mind ..., R. 2006 . Modularity in cognition Framing the debate. Psychological Review , 113, 628 647. http ... more details
Configurable modularity is a term coined by Raoul de Campo of IBM Research and later expanded on by Nate Edwards of the same organization, denoting the ability to reuse independent components by changing their interconnections, but not their internals. ref N.P. Edwards, On the Architectural Requirements of an Engineered System , IBM Research Report, RC 6688 28797 , T.J. Watson Research Center, Yorktown Heights, NY, 8 18 1977 ref In Edwards view this characterizes all successful reuse systems, and indeed all systems which can be described as engineered . References references Category Theoretical computer science comp sci stub ... more details
In mathematics the modularity theorem previously known as the Taniyama Shimura Weil conjecture and by several related names establishes a connection between elliptic curve s over the field of rational number s and modular form s. It was fully proved jointly by Christophe Breuil , Brian Conrad , Fred Diamond , and Richard Taylor mathematician Richard Taylor in 2001, borrowing many of the techniques used in Andrew Wiles Wiles s proof of Fermat s Last Theorem proof of Fermat s Last Theorem . The modularity theorem is a special case of more general conjectures due to Robert Langlands . The Langlands program seeks to attach an automorphic form or automorphic representation a suitable generalization of a modular form to more general objects of arithmetic algebraic geometry, such as to every elliptic curve over a number field . Most cases of these extended conjectures have not yet been proved. Statement The theorem states that any elliptic curve over Q can be obtained via a rational map with integer coefficient s from the classical modular curve math X 0 N math for some integer N this is a curve with integer coefficients with an explicit definition. This mapping is called a modular parametrization of level N . If N is the smallest integer for which such a parametrization can be found which by the modularity theorem itself is now known to be a number called the conductor , then the parametrization may be defined in terms of a mapping generated by a particular kind of modular form of weight ... curve Isogeny isogeny . The modularity theorem implies a closely related analytic statement to an elliptic ... from the modularity theorem. Some modular forms of weight two, in turn, correspond to holomorphic differential .... The now fully proved conjecture became known as the modularity theorem. Several theorems in number theory similar to Fermat s Last Theorem follow from the modularity theorem. For example no cube ... last3 Diamond first3 Fred last4 Taylor first4 Richard title On the modularity of elliptic curves over ... more details
Cleanup date January 2007 In cognitive neuroscience , visual modularity is an organizational concept concerning how Visual perception vision works. The way in which the primate visual system operates is currently under intense scientific scrutiny. One dominant thesis is that different properties of the visual world color , Motion physics motion , shape form and so forth require different computational solutions which are implemented in anatomically functionally distinct regions that operate independently that is, in a modular fashion. ref name calpar1 cite journal last Calabretta, first R. coauthors Parisi, D. year 2005 title Evolutionary Connectionism and Mind Brain Modularity journal Modularity. Understanding the development and evolution of complex natural systems publisher MIT Press location Cambridge, MA doi 10.1098 rstb.2005.1807 pages 309 330 pmid 16524839 volume 361 issue 1467 pmc ... Color processing Similar converging evidence suggests modularity for color. Beginning with Gowers ... Form processing Another clinical case that would a priori suggest a module for modularity in visual ... terminating in the inferotemporal cortex rather than an isolated module. Functional modularity One of the first uses of the term module or modularity occurs in the influential book Modularity of Mind ... to beliefs and is cognitively impenetrable. Much of the confusion concerning modularity exists ... behavioral deficits following brain insult thus taken as evidence for modularity . In addition, evidence ... e.g. V1 see Leventhal et al., 1995 thus taken as evidence against modularity . That these streams ... access to the information are all evidence for visual modularity. See also Modularity Society ... Connectionism and Mind Brain Modularity. In W. Callabaut & D. Rasskin Gutman , Modularity. Understanding ..., J. A. 1983 . The Modularity of Mind An Essay on Faculty Psychology. Cambridge, Mass. MIT Press, a Bradford ... pmid 6850272 DEFAULTSORT Visual Modularity Category Cognitive science Category Neuroscience Category ... more details
Unreferenced stub auto yes date December 2009 Cleanup jargon date December 2008 IOS Software Modularity is an extension to the Cisco IOS operating system that allows for an In Service Software Upgrade ISSU of router or switch functionality. IOS Software Modularity appears in version 12.2 18 SXF4 which is available for the Catalyst 6500 Catalyst switch . IOS Software Modularity is based on the QNX microkernel . DEFAULTSORT Ios Software Modularity Category Cisco products Software stub ... more details
Unreferenced date March 2007 Portal Software Testing Modularity driven testing is a term used in the testing of software . Test Script Modularity Framework The test script modularity framework requires the creation of small, independent scripts that represent modules, sections, and functions of the application under test. These small scripts are then used in a hierarchical fashion to construct larger tests, realizing a particular test case. Of all the frameworks, this one should be the simplest to grasp and master. It is a well known programming strategy to build an abstraction layer in front of a component to hide the component from the rest of the application. This insulates the application from modifications in the component and provides modularity in the application design. The test script modularity framework applies this principle of abstraction or encapsulation in order to improve the maintainability and scalability of automated test suites. DEFAULTSORT Modularity Driven Testing Category Software testing ... more details
Unreferenced date December 2009 A modular elliptic curve is an elliptic curve E that admits a parametrisation X sub 0 sub N E by a modular curve . This is not the same as a modular curve that happens to be an elliptic curve, and which could be called an elliptic modular curve. The modularity theorem , formerly known as the Taniyama Shimura conjecture asserts that every elliptic curve defined over the rational numbers is modular. Equivalent formulations Equivalent to the above formulation of modularity is that the L series of E agrees with the L series of a normalized eigenform. DEFAULTSORT Modular Elliptic Curve Category Elliptic curves ... more details
modularity provides the application as a collection of separate executable files which may be independently ... use of the monolithic term described enormous main frame applications with no usable modularity ... more details
Multiple issues orphan February 2009 context October 2009 unreferenced December 2009 Expert subject Computer science date November 2008 In a Flexible Rake Receiver , signal electrical engineering signal reception is performed with a single correlator engine and a stream computing stream buffer computer science buffer storing the entire delay spread of baseband input output I O sample signal sample s. The primary advantage of the proposed approach is flexible Multipath propagation multipath allocation supporting enhanced modularity programming modularity of the receiver and resource sharing among multiple channel communications channel decoder s. See also Signal processing DEFAULTSORT Flexible Rake Receiver Category Receiver radio Comp sci stub ... more details
The term Weil conjecture may refer to The Weil conjectures about zeta functions of varieties over finite fields, proved by Dwork, Grothendieck, Deligne and others. The Modularity theorem Taniyama Shimura Weil conjecture about elliptic curves, proved by Wiles and others. The Weil conjecture on Tamagawa numbers about the Tamagawa number of an algebraic group , proved by Kottwitz and others. mathdab ... more details
Unreferenced date December 2009 Orphan date December 2009 A Modular weapon or Modular Weapons System citation needed date December 2010 is a weapon that allows for many modifications. Modularity has become a major attribute looked for by today s military and law enforcement because they can bulk buy one or two models of rifle, then bulk buy hundreds of add on modules grenade launcher s, laser pointer s, telescopic sight scopes or flashlight torches which can be used with every other rifle. One of these rifles is the XM8 rifle XM8 , which was being considered as a M16 rifle M16 and a M4 carbine M4 replacement in the US military. It was competing with the Robinson Arms XCR , FN SCAR , H&K 416 . The main advantage of these rifles is that one rifle model can be purchased with several addons and an entire army be equipped with the same rifle base Urban warfare Urban soldiers Mechanized infantry Special forces Marksman Marksmen Sharpshooters Sniper s All of these different units can use the same base rifle model. Some modularity has previously seen with the M16 rifle M16 series the M4 carbine M4 and the M249 Squad Automatic Weapon M249 . They all used the same ammunition and the M249 could also hold and use an M16 magazine STANAG 5.56 mm KE . DEFAULTSORT Modular Weapon Category Personal weapons ... more details
unreferenced date February 2011 Open Form is a term coined by Earle Brown in the 1950s to describe works where the structure and form of the piece was left open to interpretation by the composer while the materials notes, rhythms, etc were pre composed. Brown s early experiments in this area were extreme and abstract a collection of works titled FOLIO and FOUR SYSTEMS are emblematic of his initial experiments. Over his career, he developed an approach to Open Form that integrated unique approaches to modularity in form that he compared to the mobiles of Alexander Calder . Within this framework, bits of music would be composed as numbered or cued events and grouped into pages . Events could be superimposed within a single page, played at different speeds, etc and one could navigate through a work at varying paces, returning to previous pages, skipping forward, backward, etc. In each work, a slightly different approach was taken, but this general logic of modularity remained. Anthony Braxton has developed these ideas in his own way, integrating even greater multiplicity and laying in his Ghost Trance Music structures within which secondary and tertiary compositions may become overlaid by the performers. Walter Thompson has extended these ideas through a vast language of conducting gestures called soundpainting . John Zorn extended these ideas in his game pieces, most famously in Cobra. Uncategorized date February 2011 ... more details
Brian Conrad b. November 20, 1970, New York City , is an United States American mathematician and number theory number theorist , working at Stanford University . Previously he was at the University of Michigan . Conrad s most famous accomplishment is his work on proving the modularity theorem , also known as the Taniyama Shimura Conjecture. He proved this in 1999 with Christophe Breuil , Fred Diamond and Richard Taylor mathematician Richard Taylor , while holding a joint postdoctoral position at Harvard University and the Institute for Advanced Study in Princeton, New Jersey . Conrad got his bachelor s degree from Harvard in 1992, where he won a prize for his undergraduate thesis. He did his doctoral work under Andrew Wiles . He received his Ph.D. from Princeton University in 1996 with a dissertation entitled Finite Honda Systems And Supersingular Elliptic Curves . He was also featured as an extra in NOVA TV series Nova s The Proof . His identical twin brother Keith Conrad , also a number theory number theorist , is a professor at the University of Connecticut . External links http math.stanford.edu conrad Homepage at Stanford University http abel.math.harvard.edu rtaylor st.ps On the modularity of elliptic curves over Q Proof of Taniyama Shimura coauthored by Conrad. Brian Conrad, Fred Diamond, Richard Taylor http abel.math.harvard.edu rtaylor cdt.dvi Modularity of certain potentially Barsotti Tate Galois representations , Journal of the American Mathematical Society 12 1999 , pp. 521&ndash 567. Also contains the proof C. Breuil, B. Conrad, F. Diamond, R. Taylor http www.ihes.fr breuil PUBLICATIONS STW.pdf On the modularity of elliptic curves over Q wild 3 adic exercices , Journal of the American Mathematical Society 14 2001 , 843 939. Persondata Metadata see Wikipedia Persondata . NAME Conrad, Brian ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH November 20, 1970 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Conrad, Brian Category 20th century mathem ... more details
Orphan date February 2009 The TASCAM SX 1 family of audio mixer s and recorder s built by TASCAM that utilize a 32x8x8 mixer and 16 track hard disk recorder to capture sound. The SX 1 is quite versatile for a sixteen track mixer, built to professional standards, higher quality then the four track mixers used by The Beatles among others. Anticipating the need for modularity in an expanding world, most SX family mixers possess an expansion slot . Sources http www.tascam.com Products SX 1 sx1vision.pdf Tascam website Category Audio mixing Audio tech stub ... more details
A factorette is an informal term used to describe a unit of composability of a larger Software factory . A factorette is a Software factory . A factorette is used as a contextual term to describe a software factory that extends another software factory. A factorette typically but not exclusively presents a single view point called A Single View Point Factory . That is, a factory that addresses at least one concern technology pattern aspect of a larger solution architecture etc. Factorettes enables Modularity programming modularization or Composability of a Software factory . References http msdn.microsoft.com en us library aa905331.aspx The EFx Architectural Guidance Software Factory Category Microsoft software factories Comp sci stub ... more details
Grammatical Framework GF is a type theoretic grammar formalism based on Martin L f type theory . GF particularly addresses four aspects of grammars multilinguality, semantics, modularity and grammar engineering, and reuse of grammars in different formats and as software components. References Citation last Ranta first Aarne title Grammatical Framework A Type Theoretical Grammar Formalism journal Journal of Functional Programming volume 14 issue 2 pages 145 189 year 2004 url http www.cs.chalmers.se aarne articles gf jfp.ps.gz External links http gf.digitalgrammars.com Grammatical Framework homepage . Category Grammar frameworks ling stub ... more details
Unreferenced auto yes date December 2009 Genetic architecture refers to the underlying genetic basis of a phenotype phenotypic Trait biological trait . A synonymous term is the genotype phenotype map , the way that genotypes map to the phenotypes. The genotype phenotype map has been analyzed in terms of several principal axes epistasis, polygeny, pleiotropy, quasi continuity, modularity, phenotypic plasticity, robustness, and evolvability. Epistasis when the alleles at one Locus genetics locus change the phenotypic effects of genetic variation at another locus, the two genes are said to exhibit epistasis in their interactions. Polygeny when multiple genes contribute to a particular phenotypic character, the map is said to possess polygeny . The genetic architecture in cases of polygeny can be further characterized by the spectrum of contributions of the genes, e.g. many genes of small effect vs. few genes of large effect. Pleiotropy when multiple phenotypic characters are affected by a single genetic variation, the map is said to possess pleiotropy . Quasi continuity when small genetic changes map to small phenotypic changes, the map is said to possess Lewontin quasi continuity Lewontin . Modularity when two different phenotypic characters can be mapped to mostly non overlapping sets of genes, the map is said to possess modularity , though this concept is still in flux in the scientific literature. Phenotypic plasticity Plasticity when a single genotype gives rise to a spectrum of phenotypes, the phenotype is said to have plasticity . The plasticity may occur as different phenotypes among different individuals of the same genotype, or different phenotypes within the lifetime of a single individual, or different phenotypes in response to specific environmental conditions. Mutational robustness when the same phenotype occurs in an organism despite a variety of environmental perturbations, it is said to be robust . When the same phenotype is produced despite mutations ... more details
Evolutionary Logic is the idea that logical rules can be reduction philosophy reduced to biology. It is a theory of rationality in which rational and logical rules emerged for pragmatic reasons, and are therefore not special laws. The formal systems of logic have ordinarily been studied independently, but continual progress in evolutionary theory suggests that biology and logic could be intimately interrelated. Evolutionary Logic suggests that the principles of reasoning are neither fixed, absolute, independent, nor elemental. Instead it is the evolutionary dynamic that is elemental. William S. Cooper argues in the book The Evolution of Reason that logical rules are derived directly from evolutionary principles. ref William S. Cooper. The Evolution of Reason Logic as a Branch of Biology . Cambridge Studies in Philosophy and Biology. ISBN 978 0521540254 ref Logical rules are derived directly from evolutionary principles, and therefore, have no metaphysical status of their own. Modularity theory of mind main Modularity of mind The Modularity theory of mind is the notion that a mind, at least in part, may be composed of separate innate structures which have established evolutionarily developed functional purposes. Individuals including Noam Chomsky , Steven Pinker , Leda Cosmides , John Tooby , and David Buss , believed that all brain functions were founded on specific modules there would be modules for language, for mating, religion, etc, and so logic. Archaeologist Steven Mithen writes in The Prehistory of Mind 1996 , there is evidence that our ancestors began with a generic intelligence, such as we find in apes. Others have suggested that ancestors developed three major specialized modules one for naive physics one for manufacture of instruments and one for culture and the politics of coexistence. ref Lu s Moniz Pereira. Evolutionary Psychology and the Unity of Sciences Towards an evolutionary epistemology http centria.di.fct.unl.pt lmp publications online papers Ev ... more details
Context date October 2009 In systems engineering , modular design or modularity in design is an approach that subdivides a system into smaller parts modules that can be independently created and then used in different systems to drive multiple functionalities. A modular system can be characterized by the following 1 Functional partitioning into discrete scalable, reusable modules consisting of isolated, self contained functional elements 2 Rigorous use of well defined modular interfaces, including object oriented descriptions of module functionality 3 Ease of change to achieve technology transparency and, to the extent possible, make use of industry standards for key interfaces. ref cite web url http nesipublic.spawar.navy.mil part5 releases 1.3.0 WebHelp glossary m.htm title Glossary Modular Design publisher Net Centric Enterprise Solutions for Interoperability US Government accessdate September 2007 ref Besides reduction in cost due to lesser customization, and less learning time , and flexibility in design, modularity offers other benefits such as augmentation adding new solution by merely plugging in a new module , and exclusion. Examples of modular systems are car s, computers and high rise buildings. Earlier examples include loom s, railroad signal ing systems, telephone exchanges , pipe organ s and electric power distribution systems. Computers use modularity to overcome changing customer demands and to make the manufacturing process more adaptive to change see modular .... A downside to modularity and this depends on the extent of modularity is that modular systems are not optimized ... gex index.htm Clark, K.B. and Baldwin, C.Y., Design Rules. Vol. 1 The Power of Modularity Cambridge ... of Modularity in Design Harvard Business School, 2002 http www.people.hbs.edu cbaldwin DR2 DR1Option.pdf http www.cs.drexel.edu yfcai Presentations Modularity 20in 20Design CMU.ppt Modularity in Design Formal Modeling & Automated Analysis http www.connected.org media modular.html Modularity upgrading ... more details
10.1103 PhysRevE.69.066133 ref Modularity maximization One of the most widely used methods for community detection is modularity maximization. ref name fast Modularity networks Modularity is a benefit function that measures the quality of a particular division of a network into communities. The modularity ... or more that have particularly high modularity. Since exhaustive search over all possible divisions ... of modularity optimization is however questionable on the one hand, it has been shown that modularity ... Modularity networks Resolution limit resolution limit ref cite journal author S. Fortunato and M ... issue 1 pmc 1765466 ref on the other hand the landscape of modularity values is characterized by a huge degeneracy of partitions with high modularity, close to the absolute maximum, which may be very ... 2010 title The performance of modularity maximization in practical contexts journal Phys. Rev. E ... modularity in a local way. Second, it aggregates nodes of the same community and builds a new network whose nodes are the communities. These steps are repeated iteratively until a maximum of modularity ... have been employed. For instance, researchers have compared the modularity networks modularity values ... with highest modularity. Another approach involves applying algorithms to networks that have ... more details
, now known as the Modularity Theorem although this implies Fermat s Last Theorem, Serre proves it directly ... title Serre s modularity conjecture The level one case year 2006 journal Duke Mathematical Journal ... last2 Wintenberger first2 Jean Pierre year 2009 title Serre s modularity conjecture I journal ... last Khare first Chandrashekhar last2 Wintenberger first2 Jean Pierre year 2009 title Serre s modularity ... s Modularity Conjecture Serre s Modularity Conjecture 50 minute lecture by Ken Ribet given on October ... more details
SIMSCRIPT II.5 is the latest incarnation of SIMSCRIPT , one of the oldest computer simulation language s. Although military contractor CACI released it in 1971 , it still enjoys wide use in large scale military and air traffic control simulations. SIMSCRIPT II.5 is a powerful, free form, English like, general purpose simulation programming language. It supports the application of software engineering principles, such as structured programming and modularity, which impart orderliness and manageability to simulation models. ref cite book first Edward C. last Russell title Building Simulation models with SIMSCRIPT II.5 publisher CACI location Los Angeles year 1983 ref External links http www.simscript.net products products.html CACI SIMSCRIPT page References references Category Simulation programming languages ... more details
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