An introduction to sequential dynamical systems:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
2007
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 248 S. 20 schw.-w. Ill., 20 schw.-w. Tab. |
| ISBN: | 0387306544 |
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| 245 | 1 | 0 | |a An introduction to sequential dynamical systems |c Henning S. Mortveit ; Christian M. Reidys |
| 264 | 1 | |a Berlin |b Springer |c 2007 | |
| 300 | |a XII, 248 S. |b 20 schw.-w. Ill., 20 schw.-w. Tab. | ||
| 336 | |b txt |2 rdacontent | ||
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| 700 | 1 | |a Reidys, Christian Michael |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804136259821502464 |
|---|---|
| adam_text | Contents
Preface
........................................................
v
1
What is a Sequential Dynamical System?
.................. 1
1.1
Sequential Dynamical Systems: A First Look
................ 1
1.2
Motivation
............................................. 4
1.3
Application Paradigms
................................... 7
1.3.1 TRANSIMS...................................... 7
1.3.2
Task Scheduling and Transport Computations
........ 13
1.4
SDS:
Characteristics and Research Questions
............... 16
1.4.1
Update Order Dependencies
........................ 16
1.4.2
Phase-Space Structure
............................. 17
1.5
Computational and Algorithmic Aspects
................... 18
1.6
Summary
............................................... 20
Problems
................................................... 20
Answers to Problems
......................................... 22
2
A Comparative Study
..................................... 23
2.1
Cellular Automata
....................................... 23
2.1.1
Background
...................................... 23
2.1.2
Structure of Cellular Automata
..................... 24
2.1.3
Elementary CA Rules
.............................. 27
2.2
Random Boolean Networks
............................... 33
2.3
Finite-State Machines (FSMs)
............................. 34
Problems
................................................... 35
Answers to Problems
......................................... 37
3
Graphs, Groups, and Dynamical Systems
.................. 39
3.1
Graphs
................................................. 39
3.1.1
Simple Graphs and Combinatorial Graphs
............ 41
3.1.2
The Adjacency Matrix of a Graph
................... 44
3.1.3
Acyclic Orientations
............................... 46
Contents
3.1.4 The Update Graph................................ 47
3.1.5
Graphs, Permutations, and Acyclic Orientations
....... 48
3.2
Group Actions
.......................................... 50
3.2.1
Groups Acting on Graphs
.......................... 51
3.2.2
Groups Acting on Acyclic Orientations
............... 52
3.3
Dynamical Systems
...................................... 56
3.3.1
Classical Continuous Dynamical Systems
............. 57
3.3.2
Classical Discrete Dynamical Systems
................ 59
3.3.3
Linear and Nonlinear Systems
....................... 61
Problems
................................................... 63
Answers to Problems
......................................... 66
Sequential Dynamical Systems
over Permutations
......................................... 69
4.1
Definitions and Terminology
.............................. 69
4.1.1
States, Vertex Functions, and Local Maps
............ 69
4.1.2
Sequential Dynamical Systems
...................... 71
4.1.3
The Phase Space of an
SDS
........................ 73
4.1.4
SDS
Analysis
—
A Note on Approach and Comments
.. 76
4.2
Basic Properties
......................................... 77
4.2.1
Decomposition of
SDS
............................. 77
4.2.2
Fixed Points
...................................... 78
4.2.3
Reversible Dynamics and Invertibility
................ 80
4.2.4
Invertible
SDS
with Symmetric Functions over Finite
Fields
............................................ 84
4.3
Equivalence
............................................. 88
4.3.1
Functional Equivalence of
SDS
...................... 90
4.3.2
Computing Equivalence Classes
..................... 91
4.3.3
Dynamical Equivalence
............................. 93
4.3.4
Enumeration of Dynamically
Nonequivalent
SDS......
97
4.4
SDS Morphisms
and Reductions
...........................103
4.4.1
Covering Maps
....................................104
4.4.2
Properties of Covering Maps
........................104
4.4.3
Reduction of
SDS
.................................105
4.4.4
Dynamical Equivalence Revisited
....................109
4.4.5
Construction of Covering Maps
.....................110
4.4.6
Covering Maps over Q™
............................
Ill
4.4.7
Covering Maps over
C¡rcn
..........................119
Problems
...................................................121
Answers to Problems
.........................................122
Phase-Space Structure of
SDS
and
Special Systems
...........................................129
5.1
Fixed Points for
SDS
over Circn and
Circ„,r
.................129
5.2
Fixed-Point Computations for General Graphs
..............137
Contents xi
5.3
Threshold
SDS
..........................................139
5.4
SDS
over
Special
Graph Classes
...........................140
5.4.1
SDS
over the Complete Graph
......................141
5.4.2
SDS
over the Circle Graph
.........................143
5.4.3
SDS
over the Line Graph
...........................145
5.4.4
SDS
over the Star Graph
...........................146
5.5
SDS
Induced by Special Function Classes
...................146
5.5.1
SDS
Induced by (norfe)fc and (naxidk)k
...............147
5.5.2
SDS
Induced by (nor*;
+
nandfe)^
....................154
Problems
...................................................158
Answers to Problems
.........................................160
Graphs, Groups, and
SDS
.................................165
6.1
SDS
with Order-Independent Periodic Points
...............165
6.1.1
Preliminaries
.....................................166
6.1.2
The Group G(Y, FY)
..............................167
6.1.3
The Class of
w-Independent SDS....................
171
6.2
The Class of «/-Independent
SDS
over
C¡rcn
.................174
6.2.1
The Groups G(Grc4, FcircJ
.........................176
6.3
A Presentation of S35
....................................178
Problems
...................................................179
Answers to Problems
.........................................182
Combinatorics of Sequential Dynamical Systems over
Words
.....................................................185
7.1
Combinatorics of
SDS
over Words
.........................187
7.1.1
Dependency Graphs
...............................187
7.1.2
Automorphisms
...................................189
7.1.3
Words
...........................................192
7.1.4
Acyclic Orientations
...............................193
7.1.5
The Mapping OY
.................................195
7.1.6
A Normal Form Result
.............................197
7.1.7
The Bijection
.....................................198
7.2
Combinatorics of
SDS
over Words II
.......................199
7.2.1
Generalized Equivalences
...........................199
7.2.2
The Bijection (PI)
................................201
7.2.3
Equivalence (P2)
..................................204
7.2.4
Phase-Space Relations
.............................206
Problems
...................................................209
Answers to Problems
.........................................210
Outlook
...................................................213
8.1
Stochastic
SDS
..........................................213
8.1.1
Random Update Order
.............................214
8.1.2
SDS
over Random Graphs
..........................217
xii Contents
8.2
Gene-Regulatory
Networks ...............................217
8.2.1
Introduction
......................................217
8.2.2 The Tryptophan-Operon...........................218
8.3
Evolutionary Optimization of SDS-Schedules
................220
8.3.1
Neutral Networks and Phenotypes of
RNA
and
SDS
... 220
8.3.2
Distances
.........................................223
8.3.3
A Replication-Deletion Scheme
......................226
8.3.4
Evolution of SDS-Schedules
.........................227
8.3.5
Pseudo-Codes
.....................................228
8.4
Discrete Derivatives
......................................229
8.5
Real-Valued and Continuous
SDS
..........................231
8.6
L-Local
SDS
............................................233
8.7
Routing
................................................234
8.7.1
Weights
..........................................234
8.7.2
Protocols as Local Maps
...........................235
References
.....................................................237
Index
..........................................................245
|
| adam_txt |
Contents
Preface
.
v
1
What is a Sequential Dynamical System?
. 1
1.1
Sequential Dynamical Systems: A First Look
. 1
1.2
Motivation
. 4
1.3
Application Paradigms
. 7
1.3.1 TRANSIMS. 7
1.3.2
Task Scheduling and Transport Computations
. 13
1.4
SDS:
Characteristics and Research Questions
. 16
1.4.1
Update Order Dependencies
. 16
1.4.2
Phase-Space Structure
. 17
1.5
Computational and Algorithmic Aspects
. 18
1.6
Summary
. 20
Problems
. 20
Answers to Problems
. 22
2
A Comparative Study
. 23
2.1
Cellular Automata
. 23
2.1.1
Background
. 23
2.1.2
Structure of Cellular Automata
. 24
2.1.3
Elementary CA Rules
. 27
2.2
Random Boolean Networks
. 33
2.3
Finite-State Machines (FSMs)
. 34
Problems
. 35
Answers to Problems
. 37
3
Graphs, Groups, and Dynamical Systems
. 39
3.1
Graphs
. 39
3.1.1
Simple Graphs and Combinatorial Graphs
. 41
3.1.2
The Adjacency Matrix of a Graph
. 44
3.1.3
Acyclic Orientations
. 46
Contents
3.1.4 The Update Graph. 47
3.1.5
Graphs, Permutations, and Acyclic Orientations
. 48
3.2
Group Actions
. 50
3.2.1
Groups Acting on Graphs
. 51
3.2.2
Groups Acting on Acyclic Orientations
. 52
3.3
Dynamical Systems
. 56
3.3.1
Classical Continuous Dynamical Systems
. 57
3.3.2
Classical Discrete Dynamical Systems
. 59
3.3.3
Linear and Nonlinear Systems
. 61
Problems
. 63
Answers to Problems
. 66
Sequential Dynamical Systems
over Permutations
. 69
4.1
Definitions and Terminology
. 69
4.1.1
States, Vertex Functions, and Local Maps
. 69
4.1.2
Sequential Dynamical Systems
. 71
4.1.3
The Phase Space of an
SDS
. 73
4.1.4
SDS
Analysis
—
A Note on Approach and Comments
. 76
4.2
Basic Properties
. 77
4.2.1
Decomposition of
SDS
. 77
4.2.2
Fixed Points
. 78
4.2.3
Reversible Dynamics and Invertibility
. 80
4.2.4
Invertible
SDS
with Symmetric Functions over Finite
Fields
. 84
4.3
Equivalence
. 88
4.3.1
Functional Equivalence of
SDS
. 90
4.3.2
Computing Equivalence Classes
. 91
4.3.3
Dynamical Equivalence
. 93
4.3.4
Enumeration of Dynamically
Nonequivalent
SDS.
97
4.4
SDS Morphisms
and Reductions
.103
4.4.1
Covering Maps
.104
4.4.2
Properties of Covering Maps
.104
4.4.3
Reduction of
SDS
.105
4.4.4
Dynamical Equivalence Revisited
.109
4.4.5
Construction of Covering Maps
.110
4.4.6
Covering Maps over Q™
.
Ill
4.4.7
Covering Maps over
C¡rcn
.119
Problems
.121
Answers to Problems
.122
Phase-Space Structure of
SDS
and
Special Systems
.129
5.1
Fixed Points for
SDS
over Circn and
Circ„,r
.129
5.2
Fixed-Point Computations for General Graphs
.137
Contents xi
5.3
Threshold
SDS
.139
5.4
SDS
over
Special
Graph Classes
.140
5.4.1
SDS
over the Complete Graph
.141
5.4.2
SDS
over the Circle Graph
.143
5.4.3
SDS
over the Line Graph
.145
5.4.4
SDS
over the Star Graph
.146
5.5
SDS
Induced by Special Function Classes
.146
5.5.1
SDS
Induced by (norfe)fc and (naxidk)k
.147
5.5.2
SDS
Induced by (nor*;
+
nandfe)^
.154
Problems
.158
Answers to Problems
.160
Graphs, Groups, and
SDS
.165
6.1
SDS
with Order-Independent Periodic Points
.165
6.1.1
Preliminaries
.166
6.1.2
The Group G(Y, FY)
.167
6.1.3
The Class of
w-Independent SDS.
171
6.2
The Class of «/-Independent
SDS
over
C¡rcn
.174
6.2.1
The Groups G(Grc4, FcircJ
.176
6.3
A Presentation of S35
.178
Problems
.179
Answers to Problems
.182
Combinatorics of Sequential Dynamical Systems over
Words
.185
7.1
Combinatorics of
SDS
over Words
.187
7.1.1
Dependency Graphs
.187
7.1.2
Automorphisms
.189
7.1.3
Words
.192
7.1.4
Acyclic Orientations
.193
7.1.5
The Mapping OY
.195
7.1.6
A Normal Form Result
.197
7.1.7
The Bijection
.198
7.2
Combinatorics of
SDS
over Words II
.199
7.2.1
Generalized Equivalences
.199
7.2.2
The Bijection (PI)
.201
7.2.3
Equivalence (P2)
.204
7.2.4
Phase-Space Relations
.206
Problems
.209
Answers to Problems
.210
Outlook
.213
8.1
Stochastic
SDS
.213
8.1.1
Random Update Order
.214
8.1.2
SDS
over Random Graphs
.217
xii Contents
8.2
Gene-Regulatory
Networks .217
8.2.1
Introduction
.217
8.2.2 The Tryptophan-Operon.218
8.3
Evolutionary Optimization of SDS-Schedules
.220
8.3.1
Neutral Networks and Phenotypes of
RNA
and
SDS
. 220
8.3.2
Distances
.223
8.3.3
A Replication-Deletion Scheme
.226
8.3.4
Evolution of SDS-Schedules
.227
8.3.5
Pseudo-Codes
.228
8.4
Discrete Derivatives
.229
8.5
Real-Valued and Continuous
SDS
.231
8.6
L-Local
SDS
.233
8.7
Routing
.234
8.7.1
Weights
.234
8.7.2
Protocols as Local Maps
.235
References
.237
Index
.245 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Mortveit, Henning S. Reidys, Christian Michael |
| author_GND | (DE-588)173979793 |
| author_facet | Mortveit, Henning S. Reidys, Christian Michael |
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| author_sort | Mortveit, Henning S. |
| author_variant | h s m hs hsm c m r cm cmr |
| building | Verbundindex |
| bvnumber | BV022260040 |
| classification_rvk | SK 810 |
| ctrlnum | (OCoLC)254900203 (DE-599)BVBBV022260040 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| index_date | 2024-07-02T16:42:32Z |
| indexdate | 2024-07-09T20:53:34Z |
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| publisher | Springer |
| record_format | marc |
| spelling | Mortveit, Henning S. Verfasser (DE-588)173979793 aut An introduction to sequential dynamical systems Henning S. Mortveit ; Christian M. Reidys Berlin Springer 2007 XII, 248 S. 20 schw.-w. Ill., 20 schw.-w. Tab. txt rdacontent n rdamedia nc rdacarrier Diskretes System (DE-588)4401225-1 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Dynamisches System (DE-588)4013396-5 s Diskretes System (DE-588)4401225-1 s DE-604 Reidys, Christian Michael Verfasser aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2738898&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015470698&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mortveit, Henning S. Reidys, Christian Michael An introduction to sequential dynamical systems Diskretes System (DE-588)4401225-1 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4401225-1 (DE-588)4013396-5 (DE-588)4123623-3 |
| title | An introduction to sequential dynamical systems |
| title_auth | An introduction to sequential dynamical systems |
| title_exact_search | An introduction to sequential dynamical systems |
| title_exact_search_txtP | An introduction to sequential dynamical systems |
| title_full | An introduction to sequential dynamical systems Henning S. Mortveit ; Christian M. Reidys |
| title_fullStr | An introduction to sequential dynamical systems Henning S. Mortveit ; Christian M. Reidys |
| title_full_unstemmed | An introduction to sequential dynamical systems Henning S. Mortveit ; Christian M. Reidys |
| title_short | An introduction to sequential dynamical systems |
| title_sort | an introduction to sequential dynamical systems |
| topic | Diskretes System (DE-588)4401225-1 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Diskretes System Dynamisches System Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2738898&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015470698&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mortveithennings anintroductiontosequentialdynamicalsystems AT reidyschristianmichael anintroductiontosequentialdynamicalsystems |