國立虎尾科技大學 |

Second Order Networks with spatial structure.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Second Order Networks with spatial structure./
Author:	Fuller, Samantha.
Description:	1 online resource (37 pages)
Notes:	Source: Masters Abstracts International, Volume: 56-01.
Contained By:	Masters Abstracts International56-01(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369084566

Second Order Networks with spatial structure.
Fuller, Samantha.

Second Order Networks with spatial structure. - 1 online resource (37 pages)

Source: Masters Abstracts International, Volume: 56-01.

Thesis (M.S.)

Includes bibliographical references

Synchronization of spiking activity across neurons plays a role in many processes in the brain. Using the framework of Second Order Networks (SONETs) paired with a global ring structure, we looked at the relationships between the connectivity statistics and two key eigenvalue quantities related to the synchrony of the network---the largest eigenvalue of the connectivity matrix and the variance of the eigenvalues of the Laplacian. Previously, Zhao et al. (2011) examined these relationships in the case of homogeneous SONETs, in which there is no spatial variation in the network. In this work, we broaden our view to SONETs where we allow the connection probabilities to depend on the spatial structure of the network. First, we develop an algorithm to generate SONETs which allows us to specify both the global and local geometry of the network. We then randomly generated a wide range of SONETs to examine the relationships between the connectivity statistics and the eigenvalue quantities of the resulting networks. We find that two of the second order statistics, namely those corresponding to the frequency of convergent connections and to the frequency of chain connections, primarily influence the values of the two eigenvalue quantities. Our results are remarkably similar to those of the homogeneous case, indicating that the qualitative relationship we see between synchrony and second order statstics should extend to a larger class of networks. We also find that for the networks we considered, the parameters used to describe the overall geometry of the network had a minimal influence on the two key eigenvalue quantities.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369084566Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Second Order Networks with spatial structure.
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006 m o u
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008 190606s2016 xx obm 000 0 eng d
020 $a 9781369084566
035 $a (MiAaPQ)AAI10153320
035 $a (MiAaPQ)umn:17288
035 $a AAI10153320
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Fuller, Samantha. $3 1180512
245 1 0 $a Second Order Networks with spatial structure.
264 0 $c 2016
300 $a 1 online resource (37 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Masters Abstracts International, Volume: 56-01.
500 $a Adviser: Duane Nykamp.
502 $a Thesis (M.S.) $c University of Minnesota $d 2016.
504 $a Includes bibliographical references
520 $a Synchronization of spiking activity across neurons plays a role in many processes in the brain. Using the framework of Second Order Networks (SONETs) paired with a global ring structure, we looked at the relationships between the connectivity statistics and two key eigenvalue quantities related to the synchrony of the network---the largest eigenvalue of the connectivity matrix and the variance of the eigenvalues of the Laplacian. Previously, Zhao et al. (2011) examined these relationships in the case of homogeneous SONETs, in which there is no spatial variation in the network. In this work, we broaden our view to SONETs where we allow the connection probabilities to depend on the spatial structure of the network. First, we develop an algorithm to generate SONETs which allows us to specify both the global and local geometry of the network. We then randomly generated a wide range of SONETs to examine the relationships between the connectivity statistics and the eigenvalue quantities of the resulting networks. We find that two of the second order statistics, namely those corresponding to the frequency of convergent connections and to the frequency of chain connections, primarily influence the values of the two eigenvalue quantities. Our results are remarkably similar to those of the homogeneous case, indicating that the qualitative relationship we see between synchrony and second order statstics should extend to a larger class of networks. We also find that for the networks we considered, the parameters used to describe the overall geometry of the network had a minimal influence on the two key eigenvalue quantities.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Minnesota. $b Mathematics. $3 1180493
773 0 $t Masters Abstracts International $g 56-01(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10153320 $z click for full text (PQDT)