6 research outputs found
Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience
- Author
- Bang-Jensen [Bang-Jensen and Gutin 02] Jorgen
- Chung [Chung 97] Fan
- Crofts [Crofts and Higham 09] J. J.
- Crofts [Crofts et al. 10] J. J.
- Estrada [Estrada and Hatano 08] E.
- Estrada [Estrada et al. 08] E.
- Estrada [Estrada et al. 09] E.
- Fortunato [Fortunato 10] S.
- Grindrod [Grindrod 02] P.
- Grindrod [Grindrod 03] P.
- Grindrod [Grindrod 11] Peter
- Higham [Higham 03] D. J.
- Kaiser [Kaiser and Hilgetag 06] M.
- Langville [Langville and Meyer 06] A. N.
- Morita [Morita et al. 01] S.
- Muchnik [Muchnik et al. 07] L.
- Newman [Newman 10] M. E. J.
- Pan [Pan et al. 10] R. K.
- Sporns [Sporns and Kotter 04] O.
- Strang [Strang 08] Gilbert
- Trusina [Trusina et al. 04] A.
- Varshney [Varshney et al. 11] L. R.
- Zhou [Zhou et al. 06] C.
- Publication venue
- 'Informa UK Limited'
- Publication date
- 01/01/2011
- Field of study
Hierarchical organisation is a common feature of many directed networks arising in nature and technology. For example, a well-defined message-passing framework based on managerial status typically exists in a business organisation. However, in many real-world networks such patterns of hierarchy are unlikely to be quite so transparent. Due to the nature in which empirical data is collated the nodes will often be ordered so as to obscure any underlying structure. In addition, the possibility of even a small number of links violating any overall “chain of command” makes the determination of such structures extremely challenging. Here we address the issue of how to reorder a directed network in order to reveal this type of hierarchy. In doing so we also look at the task of quantifying the level of hierarchy, given a particular node ordering. We look at a variety of approaches. Using ideas from the graph Laplacian literature, we show that a relevant discrete optimization problem leads to a natural hierarchical node ranking. We also show that this ranking arises via a maximum likelihood problem associated with a new range-dependent hierarchical random graph model. This random graph insight allows us to compute a likelihood ratio that quantifies the overall tendency for a given network to be hierarchical. We also develop a generalization of this node ordering algorithm based on the combinatorics of directed walks. In passing, we note that Google’s PageRank algorithm tackles a closely related problem, and may also be motivated from a combinatoric, walk-counting viewpoint. We illustrate the performance of the resulting algorithms on synthetic network data, and on a real-world network from neuroscience where results may be validated biologically
Imaginary Powers of the Dedekind Eta Function
- Author
- Publication venue
- 'Informa UK Limited'
- Publication date
- Field of study
Finding and Visualizing Graph Clusters Using PageRank Optimization
- Author
- Andersen [Andersen and Chung 07] R.
- Brandes [Brandes and Cornelsen 01] U.
- Chung [Chung 10] F.
- Chung [Chung and Zhao 10] F.
- Eades [Eades and Feng 96] P.
- Harel [Harel and Koren 02] D.
- Jeh [Jeh and Widom 03] G.
- MacQueen [MacQueen 67] J.
- Mancoridis [Mancoridis et al. 99] S.
- Newman [Newman and Girvan 04] M. E. J.
- Ng [Ng et al. 02] A.
- Zachary [Zachary 77] W. W.
- Publication venue
- 'Informa UK Limited'
- Publication date
- Field of study
Lifespan estimation of seal welded super stainless steels for water condenser of nuclear power plants
- Author
- A J Sedriks
- ASTM G150
- ASTM G48-03
- B Ozturk
- British Stainless Steel Association
- C W Kovach
- D C Agarwal
- D G Enos
- D S Janikowski
- D Tripkovic
- D Vermilyea
- E Ommedal
- G Mori
- H Strehblow
- Hyun Young Chang
- I S Hwang
- J G Kim
- J Klower
- J P Audouard
- L Lin
- M B Rockel
- N Sridhar
- O Strandmyr
- P F E II
- R C Newman
- R F A Jargelius-Pettersson
- Sujin Park
- T Okada
- T P Hoar
- U Steinsmo
- U Steinsmo
- Y R Yoo
- Y S Kim
- Y S Kim
- Y S Kim
- Young Sik Kim
- Publication venue
- 'Springer Science and Business Media LLC'
- Publication date
- Field of study
NAViGaTOR: Large Scalable and Interactive Navigation and Analysis of Large Graphs
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- Aloul [Aloul and Rawi 06] F. A.
- Altin [Altin et al. 09] A.
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- Ashburner [Ashburner et al. 00] M.
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- Barabási [Barabási and Oltvai 04] A. L.
- Bastian [Bastian et al. 09] Mathieu
- Boag [Boag et al. 02] S.
- Borgatti [Borgatti et al. 09] S. P.
- Brohee [Brohee et al. 08] S.
- Brown [Brown and Jurisica 07] K.
- Brown [Brown et al. 09] K. R.
- Cerami [Cerami et al. 06] E. G.
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- Cormen [Cormen et al. 90] Thomas H.
- Croft [Croft et al. 10] D.
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- Farin [Farin and Hansford 00] G.
- Felleman [Felleman and Van Essen 91] D. J.
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- Guerrero [Guerrero et al. 08] C.
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- Hoffmann [Hoffmann and Valencia 04] R.
- Holme [Holme et al. 02] P.
- Jensen [Jensen et al. 09] L. J.
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- Kanehisa [Kanehisa et al. 10] M.
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- Kim [Kim et al. 08] Y.
- King [King et al. 04] A. D.
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- Knuth [Knuth 93] D. E.
- Lukashin [Lukashin et al. 03] A. V.
- May [May and Lloyd 01] R. M.
- McGuffin [McGuffin and Jurisica 09] M. J.
- Milenkovic [Milenkovic 10] T.
- Milenkovic [Milenkovic and PrĹľulj 08] T.
- Milo [Milo et al. 02] R.
- Newman [Newman 03] M. E. J.
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- Palla [Palla et al. 05] G.
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- Pereira-Leal [Pereira-Leal et al. 04] J. B.
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- PrĹľulj [PrĹľulj et al. 04a] N.
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- Stumpf [Stumpf and Wiuf 05] M. P.
- Suderman [Suderman and Hallett 07] M.
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- Wernicke [Wernicke and Rasche 06] Sebastian
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- Zelezniak [Zelezniak et al. 10] A.
- Publication venue
- 'Informa UK Limited'
- Publication date
- Field of study
Rubber
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- Polski Komitet Normalizacyjny 0
- Polskl Komitet Normalizacyjny
- Polskl Komitet Normalizacyjny 0
- Polskl Komitet Normalizacyjny 0
- Polskl Komitet Norrnallzacyjny
- Popova V. V.
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- Standards Association of Australia AS 1580 Method 101.1
- Standards Association of Australia AS 1580 Method 101.3
- Standards Association of Australia AS 1580 Method 101.4
- Standards Association of Australia AS 1580 Method 101.5
- Standards Association of Australia AS 1580 Method 102.1
- Standards Association of Australia AS 1580 Method 103.1
- Standards Association of Australia AS 1580 Method 105.1
- Standards Association of Australia AS 1580 Method 105.2
- Standards Association of Australia AS 1580 Method 107.1
- Standards Association of Australia AS 1580 Method 107.2
- Standards Association of Australia AS 1580 Method 107.3
- Standards Association of Australia AS 1580 Method 108.1
- Standards Association of Australia AS 1580 Method 202.1
- Standards Association of Australia AS 1580 Method 203.1
- Standards Association of Australia AS 1580 Method 211.1
- Standards Association of Australia AS 1580 Method 401.5
- Standards Association of Australia AS 1580 Method 408.4
- Standards Association of Australia AS 2301
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- Stichting Nederlands Normalisatie-Instituut
- Stichting Nederlands Normalisatie-Instituut
- Stichting Nederlands Normalisatie-Instituut
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