Correlations of higher order in networks of spiking neurons:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Freiburg (Breisgau)
2016
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Enthält Sonderabdrucke |
| Beschreibung: | ca. 110 verschieden gezählte Seiten Illustrationen 30 cm |
Internformat
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| 245 | 1 | 0 | |a Correlations of higher order in networks of spiking neurons |c Stojan Jovanović |
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Datensatz im Suchindex
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CORRELATIONS OF HIGHER ORDER IN
NETWORKS OF SPIKING NEURONS
AUTHOR:
STOJAN JOVANOVIC
BORN IN
BELGRADE, SERBIA
PROF. DR. STEFAN
ROTTER
SUPERVISORS:
PROF. DR. JOHN HERTZ
PROF. DR. JEANETTE
HELLGREN KOTALESKI
A THESIS SUBMITTED IN FULFILMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
IN THE
ALBERT-LUDWIGS UNIVERSITAET FREIBURG IM BREISGAU, (FACULTY OF BIOLOGY)
AND FOR DEGREE OF PHD IN COMPUTER SCIENCE IN
KTH, ROYAL INSTITUTE OF TECHNOLOGY, STOCKHOLM, (DEPT, OF COMPUTATIONAL
SCIENCE AND TECHNOLOGY, SCHOOL OF COMPUTER SCIENCE AND COMMUNICATION)
THESIS PRINTED IN SWEDEN BY US-AB, STOCKHOLM, SEPTEMBER 2016
CONTENTS
DECLARATION OF AUTHORSHIP IV
ABSTRACT V
ABSTRAKT VI
ZUSAMENFASSUNG VII
ACKNOWLEDGEMENTS VIII
CONTENTS IX
1 INTRODUCTION 1
1.1 SCOPE OF THE
THESIS............................................................................................
2
1.1.1 CUMULANT DENSITIES OF THE ILAWKCS POINT
PROCESS............................... 2
1.1.2 THIRD-ORDER CORRELATIONS AND TOPOLOGY IN A BALANCED NEURONAL NET
WORK
........................................................................................................
3
1.2 LIST, OF PUBLICATIONS, INCLUDED IN THIS THESIS
....................................................
4
1.3 CONTRIBUTION TO
PAPERS......................................................................
4
2 NETWORK CONNECTIVITY AND DYNAMICS 5
2.1 NEURONS AND NEURONAL NETWORK DYNAMICS IN EXPERIMENTAL SETTINGS
..............
5
2.1.1 NEURONAL NETWORK CONNECTIVITY
..........................................................
6
2.1.2 ROLE OF CORRELATION IN NETWORK DYNAMICS
...........................................
6
2.1.3 OSCILLATIONS AND CORRELATIONS
................................................................
7
2.2 THEORETICAL MODELS IN THE STUDY OF NEURAL NETWORKS
......................................
7
2.3 CORRELATIONS OF HIGHER ORDER IN THEORETICAL MODELS
.........................................
8
2.4 GRAPH THEORY - A WAY TO DESCRIBE NETWORK CONNECTIVITY
...................................
.10
3 METHODS 12
3.1 POINT-PROCESS
MODELS.............................................................................................12
3.1.1 BASIC
DEFINITIONS.......................................................................................12
3.1.2 POISSON POINT PROCESS
.......................................................
................
14
3.1.3 HAVVKCS POINT PROCESS
.........................................................15
3.2 STATISTICAL MEASURES OF
DEPENDENCE.................................................................17
3.2.1 COVARIANCE OF TWO RANDOM VARIABLES
.....................................................
17
3.2.2 THE THIRD-ORDER JOINT CUM
ULANT
..............................................................
18
3.2.3 JOINT EUMULANTS OF ORDER
N
.....................................................................19
3.3 LAPLACE FUNCTIONALS OF POINT PROCESSES
...........................................................20
3.3.1 DEFINITION OF A LAPLACE FUNCTIONAL
...........................................................
21
3.3.2 CUMULANT DENSIT IES OF A POINT
PROCESS..................................................21
3.3.3 LAPLACE FUNCTIONAL OF A HAWKES PROCESS
...............................................23
4 RESULTS 27
4.1 CUMULANT DENSITIES OF HAWKES POINT PROCESSES
..............................................
27
4.1.1 MATHEMATICAL PRELIMINARIES
....................................................................
27
4.1.1.1 THE CONDIT IONAL RATE PROCESS
...............................................
27
4.1.1.2 EXPECTED NUMBER OF EVENTS AND THE MARTINGALE PROPERTY . 29
4.1.1.3 THE CLUSTER REPRESENTATION OF A HAWKES PROCESS
........................
30
4.1.2 THE FIRST
CUMULANT....................................................................................32
4.1.3 THE SECOND CUMULANT
..............................................................................33
4.1.3.1 THE CONDITIONAL RATE REPRESENTATION
......................................33
4.1.3.2 LIRE CLUSTER REPRESENTATION
.....................................................36
4.1.4 THE THIRD CUMULANT
.................................................................................39
4.1.4.1 THE. CONDITIONAL RATE
REPRESENTATION......................................39
4.1.4.2 THE CLUSTER PROCESS REPRESENTATION
.......................................
41
4.1.5 CUMULANT OF ORDER
N
................................................................................
42
4.2 THIRD-ORDER CORRELATIONS IN BALANCED NEURONAL
NETWORKS...................................51
4.2.1
PRELIMINARIES.............................................................................................51
4.2.2 THE AVERAGE THIRD CUMULANT
.................................................................
52
4.2.3
3
IN TERMS OF TOPOLOGICAL M
OTIFS
...........................................................
53
4.2.4 EXPLICIT FORMULA FOR
..............................................................................57
4.2.5 K
-3
IN THE LIMIT OF LARGE NETWORKS
...........................................................60
5 DISCUSSION 61
5.1 HIGHER-ORDER CORRELATIONS AND CONNECTIVITY IN THE HAWKES POINT
PROCESS
M
ODEL......................................................................................................................61
5.2 HOW NETWORK TOPOLOGY AFFECTS CORRELATIONS OF THIRD ORDER
...............................
62
BIBLIOGRAPHY 65
APPENDICES
PAPER A 76
PAPER B
86
|
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| spelling | Jovanović, Stojan Verfasser (DE-588)1124844597 aut Correlations of higher order in networks of spiking neurons Stojan Jovanović Freiburg (Breisgau) 2016 ca. 110 verschieden gezählte Seiten Illustrationen 30 cm txt rdacontent n rdamedia nc rdacarrier Enthält Sonderabdrucke Dissertation Albert-Ludwigs Universität Freiburg im Breisgau und der KTH Stockholm$2016 2016 (DE-588)4113937-9 Hochschulschrift gnd-content B:DE-101 application/pdf http://d-nb.info/1125486465/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029811143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jovanović, Stojan Correlations of higher order in networks of spiking neurons |
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| title | Correlations of higher order in networks of spiking neurons |
| title_auth | Correlations of higher order in networks of spiking neurons |
| title_exact_search | Correlations of higher order in networks of spiking neurons |
| title_full | Correlations of higher order in networks of spiking neurons Stojan Jovanović |
| title_fullStr | Correlations of higher order in networks of spiking neurons Stojan Jovanović |
| title_full_unstemmed | Correlations of higher order in networks of spiking neurons Stojan Jovanović |
| title_short | Correlations of higher order in networks of spiking neurons |
| title_sort | correlations of higher order in networks of spiking neurons |
| topic_facet | Hochschulschrift |
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