Results 21 to 30 of about 212,419 (273)
Modular Forms on Hecke's Modular Groups [PDF]
Proceedings of the American Mathematical Society, 1973 Let H={-r=x+iy:y>0}. Let A>0, k>O, y=I1. Let M(Q, k, y) denote the set of functions f for which f(r)= .D=o ane2'i"rli and f(-1/T)=y(&/i)kf(T), for all T r H. Let MO(A, k, y) denote the set of feM(A, k. y) for which f((T)=O(yc) uniformly for all x as y-+, for some real c.
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Challenges in identifying and interpreting organizational modules in morphology [PDF]
, 2017 Form is a rich concept that agglutinates information about the proportions and topological arrangement of body parts. Modularity is readily measurable in both features, the variation of proportions (variational modules) and the organization of topology ...
Esteve-Altava, B
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Size reduction of complex networks preserving modularity [PDF]
, 2007 The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality.
A Arenas +8 more
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Global vs local modularity for network community detection. [PDF]
PLoS ONE, 2018 Community structures are ubiquitous in various complex networks, implying that the networks commonly be composed of groups of nodes with more internal links and less external links.
Shi Chen +7 more
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Additive Approximation Algorithms for Modularity Maximization [PDF]
, 2016 The modularity is a quality function in community detection, which was introduced by Newman and Girvan (2004). Community detection in graphs is now often conducted through modularity maximization: given an undirected graph $G=(V,E)$, we are asked to find
Kawase, Yasushi +2 more
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Convergent evolution of modularity in metabolic networks through different community structures
BMC Evolutionary Biology, 2012 Background It has been reported that the modularity of metabolic networks of bacteria is closely related to the variability of their living habitats. However, given the dependency of the modularity score on the community structure, it remains unknown ...
Zhou Wanding, Nakhleh Luay
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Deterministic Modularity Optimization [PDF]
, 2007 We study community structure of networks. We have developed a scheme for maximizing the modularity Q based on mean field methods. Further, we have defined a simple family of random networks with community structure; we understand the behavior of these ...
Albert +22 more
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Modular Curves, Modular Surfaces and Modular Fourfolds [PDF]
, 2007 This article surveys some recent work of the author on Hilbert modular fourfolds X. After some preliminaries on the cohomology and special, codimension 2 cycles Z on X of Hirzebruch-Zagier type, a proof of the Tate conjecture for X over abelian fields is exposed. It is followed by a description of a method to construct classes in the Bloch's Chow group
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SIAM Journal on Discrete Mathematics, 2022 A rank-$r$ integer matrix $A$ is $Δ$-modular if the determinant of each $r \times r$ submatrix has absolute value at most $Δ$. The class of $1$-modular, or unimodular, matrices is of fundamental significance in both integer programming theory and matroid theory.
Oxley, James, Walsh, Zach
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Abelian Surfaces over totally real fields are Potentially Modular [PDF]
, 2018 We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. As a consequence, we obtain the expected meromorphic continuation and functional equations of their Hasse--Weil zeta functions.
Boxer, George +3 more
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