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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Identifying the borders of mathematical knowledge

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Author(s):
Silva, Filipi Nascimento [1] ; Travencolo, Bruno A. N. [1] ; Viana, Matheus P. [1] ; Costa, Luciano da Fontoura [1, 2]
Total Authors: 4
Affiliation:
[1] Univ Sao Paulo, Inst Phys Sao Carlos, BR-13560970 Sao Paulo - Brazil
[2] Natl Inst Sci & Technol Complex Syst, Rio De Janeiro - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Journal of Physics A-Mathematical and Theoretical; v. 43, n. 32 AUG 13 2010.
Web of Science Citations: 5
Abstract

Based on a divide and conquer approach, knowledge about nature has been organized into a set of interrelated facts, allowing a natural representation in terms of graphs: each `chunk' of knowledge corresponds to a node, while relationships between such chunks are expressed as edges. This organization becomes particularly clear in the case of mathematical theorems, with their intense cross-implications and relationships. We have derived a web of mathematical theorems from Wikipedia and, thanks to the powerful concept of entropy, identified its more central and frontier elements. Our results also suggest that the central nodes are the oldest theorems, while the frontier nodes are those recently added to the network. The network communities have also been identified, allowing further insights about the organization of this network, such as its highly modular structure. (AU)

FAPESP's process: 07/02938-5 - Computational methods for characterization and analysis of neurons and glias
Grantee:Bruno Augusto Nassif Travençolo
Support type: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 07/50882-9 - Characterization and modeling of biological networks
Grantee:Matheus Palhares Viana
Support type: Scholarships in Brazil - Doctorate
FAPESP's process: 05/00587-5 - Mesh (graph) modeling and techniques of pattern recognition: structure, dynamics and applications
Grantee:Roberto Marcondes Cesar Junior
Support type: Research Projects - Thematic Grants