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- {{Other uses|Modularity}} ...phi 0.9.1 Network Analysis and Visualization Software.png|thumb|Example of modularity measurement and colouring on a [[scale-free network]].]] ...21 KB (3,065 words) - 16:52, 21 February 2025
- ...236 |doi=10.1007/s002080050011 |issn=0025-5831}}</ref> The first notion of modularity used in the theorem statement is in terms of the non-degeneracy of the [[br ...atisfies all of the axioms except possibly for non-degeneracy. Bruguières' modularity theorem asserts that a pre-modular tensor category has non-degenerate braid ...4 KB (595 words) - 06:34, 1 March 2025
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- ...236 |doi=10.1007/s002080050011 |issn=0025-5831}}</ref> The first notion of modularity used in the theorem statement is in terms of the non-degeneracy of the [[br ...atisfies all of the axioms except possibly for non-degeneracy. Bruguières' modularity theorem asserts that a pre-modular tensor category has non-degenerate braid ...4 KB (595 words) - 06:34, 1 March 2025
- ...ees of each of the vertices (the [[degree sequence]]). In other words, the modularity contrasts the exhibited community structure in <math>G</math> with that of ...3 KB (416 words) - 01:24, 22 April 2024
- ==Modularity== ...ily of Galois representations has dimension two, by the proof of [[Serre's modularity conjecture]]. The Consani–Scholton quintic provides a non-rigid example, wh ...4 KB (495 words) - 02:48, 23 June 2024
- {{Other uses|Modularity}} ...phi 0.9.1 Network Analysis and Visualization Software.png|thumb|Example of modularity measurement and colouring on a [[scale-free network]].]] ...21 KB (3,065 words) - 16:52, 21 February 2025
- {{See also|Modularity theorem#History}} ...the formulation of the [[Taniyama–Shimura conjecture]] (now known as the [[modularity theorem]]), which states that every elliptic curve over the rational number ...8 KB (1,126 words) - 08:04, 31 December 2024
- Additivity (also called ''linearity'' or ''modularity'') means that "the whole is equal to the sum of its parts." That is, the ut ...2 KB (298 words) - 23:58, 21 April 2024
- ...ities and the [[Modularity (networks)#Resolution limit|resolution limit of modularity]]. ...ng of smaller communities into larger communities (the resolution limit of modularity), the Leiden algorithm employs an intermediate refinement phase in which co ...21 KB (3,302 words) - 23:09, 26 February 2025
- ==Modularity optimization== ...ation of [[Modularity (networks)|modularity]] as the algorithm progresses. Modularity is a scale value between −1 (non-modular clustering) and 1 (fully modular c ...21 KB (3,159 words) - 06:09, 29 January 2025
- ...[mirror symmetry (string theory)|mirror symmetry]] and extensions of the [[modularity theorem]].<ref>{{cite journal|last=Totaro|first=Burt|authorlink=Burt Totaro ...2 KB (275 words) - 05:42, 18 November 2024
- ...al [[total order#Chains|chain]] of elements, each of which obeys a certain modularity relationship. The definition encapsulates many of the nice properties of [[ | title=Poset Edge-Labellings and Left Modularity ...8 KB (1,145 words) - 08:16, 26 June 2024
- ...oth and Noriko Yui}}</ref> Currently, much of her work is focused upon the modularity of [[Calabi–Yau manifold|Calabi-Yau threefolds]]. Notably, she and [[Fernan ...4 KB (534 words) - 15:45, 25 May 2023
- {{term|modularity theorem}} {{defn|The [[modularity theorem]] (which used to be called the Taniyama–Shimura conjecture)}} ...14 KB (2,011 words) - 15:38, 26 November 2024
- ===== Application: Modularity Calculation ===== ...the observed structure against a null model: the configuration model. The modularity is computed as: ...30 KB (4,603 words) - 10:04, 19 February 2025
- ...used to support decisions in an expressive output space while maintaining modularity and tractability of training and inference. ...a way to support decisions in an expressive output space while maintaining modularity and tractability of training and inference. These constraints can express e ...13 KB (1,838 words) - 02:49, 22 December 2023
- ...ure quantifying the quality of a network’s division into communities. [12] Modularity is calculated as: ...Method''': A widely used algorithm for community detection that optimizes modularity by iteratively grouping nodes into communities. It is efficient and scalabl ...23 KB (3,190 words) - 00:28, 6 December 2024
- ...)+ v(U\cap V) = v(U)+v(V) & \forall U,V\in\mathcal{T} & \scriptstyle{\text{Modularity property}}\, ...7 KB (1,016 words) - 20:55, 28 June 2022
- ...analytic rank at most 1 (The [[modularity theorem]] later showed that the modularity assumption always holds).{{sfn|Kolyvagin|1988}} Theorem 1.1 of Nikolaev <r ...13 KB (1,727 words) - 21:30, 29 January 2025
- | title = Modularity of the Consani–Scholten quintic ...6 KB (720 words) - 19:03, 23 March 2024
- ...a proof for [[Fermat's Last Theorem]]. Both Fermat's Last Theorem and the modularity theorem were believed to be impossible to prove using previous knowledge by ...ra]] (now referred to as an ''R=T theorem'') to prove [[lift (mathematics)|modularity lifting]] theorems has been an influential development in [[algebraic numbe ...58 KB (8,759 words) - 03:42, 14 October 2024
- ...://www.csc.kth.se/~petter/Publications/ogren2012bt.pdf |chapter=Increasing Modularity of UAV Control Systems using Computer Game Behavior Trees |title=AIAA Guida ...e visually intuitive and easy to design, test, and debug, and provide more modularity, scalability, and reusability than other behavior creation methods. ...15 KB (2,159 words) - 15:21, 18 March 2024