Discrete systems with memory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
c2011
|
| Schriftenreihe: | World Scientific series on nonlinear science
v. 75 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 429-450) and index Machine generated contents note - 1 - Cellular Automata and memory -- - 1.1 - Cellular Automata -- - 1.2 - Memory -- - Disclaimer -- - 2 - Average type memory -- - 2.1 - Average memory -- - 2.2 - Two-dimensional lattices -- - 2.2.1 - Totalistic rules -- - 2.2.2 - LIFE -- - 2.3 - One-dimensional layers -- - 2.3.1 - Elementary rules -- - 2.3.2 - Nearest and next-nearest neighbors -- - 3 - Other memories -- - 3.1 - Average-like memory -- - 3.2 - Limited trailing memory -- - 3.3 - Majority of the last three state memory -- - 3.4 - Elementary rules as memory -- - 3.5 - Minimal memory -- - 4 - Asynchrony and probabilistic rules -- - 4.1 - Asynchrony -- - 4.2 - Probabilistic rules -- - 5 - Cycles and random sequences -- - 5.1 - Cycles -- - 5.2 - Random number generation by CA -- - 6 - Three state automata -- - 6.1 - Totalistic rules -- - 6.2 - Excitable systems -- - 7 - Reversible dynamics -- - 7.1 - Characterization -- - 7.2 - Reversible rules with memory -- - 8 - Block cellular automata -- - 8.1 - Characterization -- - 8.2 - Density classification task 9 - Structurally dynamic systems -- - 9.1 - Introduction -- - 9.1.1 - Reversible SDCA -- - 9.2 - SDCA with memory -- - 9.2.1 - Two state SDCA with memory -- - 9.2.2 - Three state SDCA -- - 10 - Boolean networks -- - 10.1 - Automata on networks -- - 10.2 - Boolean networks -- - 10.3 - Automata on proximity graphs -- - 11 - Coupled layers -- - 11.1 - Coupled cellular automata -- - 11.2 - Coupled Boolean networks -- - 12 - Continuous state variable -- - 12.1 - Continuous-valued automata -- - 12.2 - Finite difference equations -- - 12.2.1 - One-dimensional maps -- - 12.2.2 - Two-dimensional maps -- - 12.3 - Plane curves -- - 12.4 - Stochastic processes -- - 13 - Spatial games -- - 13.1 - The prisoner's dilemma -- - 13.2 - Degrees of cooperation and strategies -- - 13.3 - The structurally dynamic PD (SDPD) -- - 13.4 - Pavlov versus anti-Pavlov (PAP) in the PD -- - 13.5 - Other spatial games -- - Appendices -- - Appendix - A Average memory starting at random -- - Appendix B - Dynamic with short-term memory -- - Appendix C - Heterogeneous and coupled networks -- - Appendix D - Continuous state variable -- - Appendix E - Spatial games Memory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? This book provides answers to these questions. It focuses on the study of spatially extended systems, i.e., cellular automata and other related discrete complex systems. Thus, arrays of locally connected finite state machines, or cells, update their states simultaneously, in discrete time, by the same transition rule. The classical dynamics in these systems is Markovian : only the actual configuration is taken into account to generate the next one. Generalizing the conventional view on spatially extended discrete dynamical systems evolution by allowing cells (or nodes) to be featured by some trait state computed as a function of its own previous state-values, the transition maps of the classical systems are kept unaltered, so that the effect of memory can be easily traced. The book demonstrates that discrete dynamical systems with memory are not only priceless tools for modeling natural phenomena but unique mathematical and aesthetic objects |
| Beschreibung: | 1 Online-Ressource (xi, 465 p.) |
| ISBN: | 9789814343633 9789814343640 9814343633 9814343641 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043077315 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 151126s2011 |||| o||u| ||||||eng d | ||
| 020 | |a 9789814343633 |9 978-981-4343-63-3 | ||
| 020 | |a 9789814343640 |c electronic bk. |9 978-981-4343-64-0 | ||
| 020 | |a 9814343633 |9 981-4343-63-3 | ||
| 020 | |a 9814343641 |c electronic bk. |9 981-4343-64-1 | ||
| 035 | |a (OCoLC)756782478 | ||
| 035 | |a (DE-599)BVBBV043077315 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 |a DE-1047 | ||
| 082 | 0 | |a 511.3/5 |2 23 | |
| 100 | 1 | |a Alonso-Sanz, Ramon |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Discrete systems with memory |c Ramon Alonso-Sanz |
| 264 | 1 | |a Singapore |b World Scientific |c c2011 | |
| 300 | |a 1 Online-Ressource (xi, 465 p.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a World Scientific series on nonlinear science |v v. 75 | |
| 500 | |a Includes bibliographical references (p. 429-450) and index | ||
| 500 | |a Machine generated contents note - 1 - Cellular Automata and memory -- - 1.1 - Cellular Automata -- - 1.2 - Memory -- - Disclaimer -- - 2 - Average type memory -- - 2.1 - Average memory -- - 2.2 - Two-dimensional lattices -- - 2.2.1 - Totalistic rules -- - 2.2.2 - LIFE -- - 2.3 - One-dimensional layers -- - 2.3.1 - Elementary rules -- - 2.3.2 - Nearest and next-nearest neighbors -- - 3 - Other memories -- - 3.1 - Average-like memory -- - 3.2 - Limited trailing memory -- - 3.3 - Majority of the last three state memory -- - 3.4 - Elementary rules as memory -- - 3.5 - Minimal memory -- - 4 - Asynchrony and probabilistic rules -- - 4.1 - Asynchrony -- - 4.2 - Probabilistic rules -- - 5 - Cycles and random sequences -- - 5.1 - Cycles -- - 5.2 - Random number generation by CA -- - 6 - Three state automata -- - 6.1 - Totalistic rules -- - 6.2 - Excitable systems -- - 7 - Reversible dynamics -- - 7.1 - Characterization -- - 7.2 - Reversible rules with memory -- - 8 - Block cellular automata -- - 8.1 - Characterization -- - 8.2 - Density classification task | ||
| 500 | |a 9 - Structurally dynamic systems -- - 9.1 - Introduction -- - 9.1.1 - Reversible SDCA -- - 9.2 - SDCA with memory -- - 9.2.1 - Two state SDCA with memory -- - 9.2.2 - Three state SDCA -- - 10 - Boolean networks -- - 10.1 - Automata on networks -- - 10.2 - Boolean networks -- - 10.3 - Automata on proximity graphs -- - 11 - Coupled layers -- - 11.1 - Coupled cellular automata -- - 11.2 - Coupled Boolean networks -- - 12 - Continuous state variable -- - 12.1 - Continuous-valued automata -- - 12.2 - Finite difference equations -- - 12.2.1 - One-dimensional maps -- - 12.2.2 - Two-dimensional maps -- - 12.3 - Plane curves -- - 12.4 - Stochastic processes -- - 13 - Spatial games -- - 13.1 - The prisoner's dilemma -- - 13.2 - Degrees of cooperation and strategies -- - 13.3 - The structurally dynamic PD (SDPD) -- - 13.4 - Pavlov versus anti-Pavlov (PAP) in the PD -- - 13.5 - Other spatial games -- - Appendices -- - Appendix - A Average memory starting at random -- - Appendix B - Dynamic with short-term memory -- - Appendix C - Heterogeneous and coupled networks -- - Appendix D - Continuous state variable -- - Appendix E - Spatial games | ||
| 500 | |a Memory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? This book provides answers to these questions. It focuses on the study of spatially extended systems, i.e., cellular automata and other related discrete complex systems. Thus, arrays of locally connected finite state machines, or cells, update their states simultaneously, in discrete time, by the same transition rule. The classical dynamics in these systems is Markovian : only the actual configuration is taken into account to generate the next one. Generalizing the conventional view on spatially extended discrete dynamical systems evolution by allowing cells (or nodes) to be featured by some trait state computed as a function of its own previous state-values, the transition maps of the classical systems are kept unaltered, so that the effect of memory can be easily traced. The book demonstrates that discrete dynamical systems with memory are not only priceless tools for modeling natural phenomena but unique mathematical and aesthetic objects | ||
| 650 | 7 | |a COMPUTERS / Machine Theory |2 bisacsh | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Cellular automata |x Mathematical models | |
| 650 | 4 | |a Discrete-time systems |x Mathematical models | |
| 650 | 4 | |a Dynamics | |
| 650 | 0 | 7 | |a Gedächtnis |0 (DE-588)4019614-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diskretes System |0 (DE-588)4401225-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zellularer Automat |0 (DE-588)4190671-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zellularer Automat |0 (DE-588)4190671-8 |D s |
| 689 | 0 | 1 | |a Diskretes System |0 (DE-588)4401225-1 |D s |
| 689 | 0 | 2 | |a Gedächtnis |0 (DE-588)4019614-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389645 |x Aggregator |3 Volltext |
| 912 | |a ZDB-4-EBA | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028501507 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389645 |l FAW01 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389645 |l FAW02 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804175466058219520 |
|---|---|
| any_adam_object | |
| author | Alonso-Sanz, Ramon |
| author_facet | Alonso-Sanz, Ramon |
| author_role | aut |
| author_sort | Alonso-Sanz, Ramon |
| author_variant | r a s ras |
| building | Verbundindex |
| bvnumber | BV043077315 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)756782478 (DE-599)BVBBV043077315 |
| dewey-full | 511.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/5 |
| dewey-search | 511.3/5 |
| dewey-sort | 3511.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05667nmm a2200565zcb4500</leader><controlfield tag="001">BV043077315</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">151126s2011 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814343633</subfield><subfield code="9">978-981-4343-63-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814343640</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-981-4343-64-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9814343633</subfield><subfield code="9">981-4343-63-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9814343641</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">981-4343-64-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)756782478</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043077315</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1046</subfield><subfield code="a">DE-1047</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3/5</subfield><subfield code="2">23</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Alonso-Sanz, Ramon</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Discrete systems with memory</subfield><subfield code="c">Ramon Alonso-Sanz</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore</subfield><subfield code="b">World Scientific</subfield><subfield code="c">c2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xi, 465 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">World Scientific series on nonlinear science</subfield><subfield code="v">v. 75</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (p. 429-450) and index</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Machine generated contents note - 1 - Cellular Automata and memory -- - 1.1 - Cellular Automata -- - 1.2 - Memory -- - Disclaimer -- - 2 - Average type memory -- - 2.1 - Average memory -- - 2.2 - Two-dimensional lattices -- - 2.2.1 - Totalistic rules -- - 2.2.2 - LIFE -- - 2.3 - One-dimensional layers -- - 2.3.1 - Elementary rules -- - 2.3.2 - Nearest and next-nearest neighbors -- - 3 - Other memories -- - 3.1 - Average-like memory -- - 3.2 - Limited trailing memory -- - 3.3 - Majority of the last three state memory -- - 3.4 - Elementary rules as memory -- - 3.5 - Minimal memory -- - 4 - Asynchrony and probabilistic rules -- - 4.1 - Asynchrony -- - 4.2 - Probabilistic rules -- - 5 - Cycles and random sequences -- - 5.1 - Cycles -- - 5.2 - Random number generation by CA -- - 6 - Three state automata -- - 6.1 - Totalistic rules -- - 6.2 - Excitable systems -- - 7 - Reversible dynamics -- - 7.1 - Characterization -- - 7.2 - Reversible rules with memory -- - 8 - Block cellular automata -- - 8.1 - Characterization -- - 8.2 - Density classification task</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">9 - Structurally dynamic systems -- - 9.1 - Introduction -- - 9.1.1 - Reversible SDCA -- - 9.2 - SDCA with memory -- - 9.2.1 - Two state SDCA with memory -- - 9.2.2 - Three state SDCA -- - 10 - Boolean networks -- - 10.1 - Automata on networks -- - 10.2 - Boolean networks -- - 10.3 - Automata on proximity graphs -- - 11 - Coupled layers -- - 11.1 - Coupled cellular automata -- - 11.2 - Coupled Boolean networks -- - 12 - Continuous state variable -- - 12.1 - Continuous-valued automata -- - 12.2 - Finite difference equations -- - 12.2.1 - One-dimensional maps -- - 12.2.2 - Two-dimensional maps -- - 12.3 - Plane curves -- - 12.4 - Stochastic processes -- - 13 - Spatial games -- - 13.1 - The prisoner's dilemma -- - 13.2 - Degrees of cooperation and strategies -- - 13.3 - The structurally dynamic PD (SDPD) -- - 13.4 - Pavlov versus anti-Pavlov (PAP) in the PD -- - 13.5 - Other spatial games -- - Appendices -- - Appendix - A Average memory starting at random -- - Appendix B - Dynamic with short-term memory -- - Appendix C - Heterogeneous and coupled networks -- - Appendix D - Continuous state variable -- - Appendix E - Spatial games</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Memory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? This book provides answers to these questions. It focuses on the study of spatially extended systems, i.e., cellular automata and other related discrete complex systems. Thus, arrays of locally connected finite state machines, or cells, update their states simultaneously, in discrete time, by the same transition rule. The classical dynamics in these systems is Markovian : only the actual configuration is taken into account to generate the next one. Generalizing the conventional view on spatially extended discrete dynamical systems evolution by allowing cells (or nodes) to be featured by some trait state computed as a function of its own previous state-values, the transition maps of the classical systems are kept unaltered, so that the effect of memory can be easily traced. The book demonstrates that discrete dynamical systems with memory are not only priceless tools for modeling natural phenomena but unique mathematical and aesthetic objects</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">COMPUTERS / Machine Theory</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematisches Modell</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cellular automata</subfield><subfield code="x">Mathematical models</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Discrete-time systems</subfield><subfield code="x">Mathematical models</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dynamics</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gedächtnis</subfield><subfield code="0">(DE-588)4019614-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Diskretes System</subfield><subfield code="0">(DE-588)4401225-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zellularer Automat</subfield><subfield code="0">(DE-588)4190671-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Zellularer Automat</subfield><subfield code="0">(DE-588)4190671-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Diskretes System</subfield><subfield code="0">(DE-588)4401225-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Gedächtnis</subfield><subfield code="0">(DE-588)4019614-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389645</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028501507</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389645</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389645</subfield><subfield code="l">FAW02</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043077315 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:44Z |
| institution | BVB |
| isbn | 9789814343633 9789814343640 9814343633 9814343641 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028501507 |
| oclc_num | 756782478 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xi, 465 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific |
| record_format | marc |
| series2 | World Scientific series on nonlinear science |
| spelling | Alonso-Sanz, Ramon Verfasser aut Discrete systems with memory Ramon Alonso-Sanz Singapore World Scientific c2011 1 Online-Ressource (xi, 465 p.) txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science v. 75 Includes bibliographical references (p. 429-450) and index Machine generated contents note - 1 - Cellular Automata and memory -- - 1.1 - Cellular Automata -- - 1.2 - Memory -- - Disclaimer -- - 2 - Average type memory -- - 2.1 - Average memory -- - 2.2 - Two-dimensional lattices -- - 2.2.1 - Totalistic rules -- - 2.2.2 - LIFE -- - 2.3 - One-dimensional layers -- - 2.3.1 - Elementary rules -- - 2.3.2 - Nearest and next-nearest neighbors -- - 3 - Other memories -- - 3.1 - Average-like memory -- - 3.2 - Limited trailing memory -- - 3.3 - Majority of the last three state memory -- - 3.4 - Elementary rules as memory -- - 3.5 - Minimal memory -- - 4 - Asynchrony and probabilistic rules -- - 4.1 - Asynchrony -- - 4.2 - Probabilistic rules -- - 5 - Cycles and random sequences -- - 5.1 - Cycles -- - 5.2 - Random number generation by CA -- - 6 - Three state automata -- - 6.1 - Totalistic rules -- - 6.2 - Excitable systems -- - 7 - Reversible dynamics -- - 7.1 - Characterization -- - 7.2 - Reversible rules with memory -- - 8 - Block cellular automata -- - 8.1 - Characterization -- - 8.2 - Density classification task 9 - Structurally dynamic systems -- - 9.1 - Introduction -- - 9.1.1 - Reversible SDCA -- - 9.2 - SDCA with memory -- - 9.2.1 - Two state SDCA with memory -- - 9.2.2 - Three state SDCA -- - 10 - Boolean networks -- - 10.1 - Automata on networks -- - 10.2 - Boolean networks -- - 10.3 - Automata on proximity graphs -- - 11 - Coupled layers -- - 11.1 - Coupled cellular automata -- - 11.2 - Coupled Boolean networks -- - 12 - Continuous state variable -- - 12.1 - Continuous-valued automata -- - 12.2 - Finite difference equations -- - 12.2.1 - One-dimensional maps -- - 12.2.2 - Two-dimensional maps -- - 12.3 - Plane curves -- - 12.4 - Stochastic processes -- - 13 - Spatial games -- - 13.1 - The prisoner's dilemma -- - 13.2 - Degrees of cooperation and strategies -- - 13.3 - The structurally dynamic PD (SDPD) -- - 13.4 - Pavlov versus anti-Pavlov (PAP) in the PD -- - 13.5 - Other spatial games -- - Appendices -- - Appendix - A Average memory starting at random -- - Appendix B - Dynamic with short-term memory -- - Appendix C - Heterogeneous and coupled networks -- - Appendix D - Continuous state variable -- - Appendix E - Spatial games Memory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? This book provides answers to these questions. It focuses on the study of spatially extended systems, i.e., cellular automata and other related discrete complex systems. Thus, arrays of locally connected finite state machines, or cells, update their states simultaneously, in discrete time, by the same transition rule. The classical dynamics in these systems is Markovian : only the actual configuration is taken into account to generate the next one. Generalizing the conventional view on spatially extended discrete dynamical systems evolution by allowing cells (or nodes) to be featured by some trait state computed as a function of its own previous state-values, the transition maps of the classical systems are kept unaltered, so that the effect of memory can be easily traced. The book demonstrates that discrete dynamical systems with memory are not only priceless tools for modeling natural phenomena but unique mathematical and aesthetic objects COMPUTERS / Machine Theory bisacsh Mathematisches Modell Cellular automata Mathematical models Discrete-time systems Mathematical models Dynamics Gedächtnis (DE-588)4019614-8 gnd rswk-swf Diskretes System (DE-588)4401225-1 gnd rswk-swf Zellularer Automat (DE-588)4190671-8 gnd rswk-swf Zellularer Automat (DE-588)4190671-8 s Diskretes System (DE-588)4401225-1 s Gedächtnis (DE-588)4019614-8 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389645 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Alonso-Sanz, Ramon Discrete systems with memory COMPUTERS / Machine Theory bisacsh Mathematisches Modell Cellular automata Mathematical models Discrete-time systems Mathematical models Dynamics Gedächtnis (DE-588)4019614-8 gnd Diskretes System (DE-588)4401225-1 gnd Zellularer Automat (DE-588)4190671-8 gnd |
| subject_GND | (DE-588)4019614-8 (DE-588)4401225-1 (DE-588)4190671-8 |
| title | Discrete systems with memory |
| title_auth | Discrete systems with memory |
| title_exact_search | Discrete systems with memory |
| title_full | Discrete systems with memory Ramon Alonso-Sanz |
| title_fullStr | Discrete systems with memory Ramon Alonso-Sanz |
| title_full_unstemmed | Discrete systems with memory Ramon Alonso-Sanz |
| title_short | Discrete systems with memory |
| title_sort | discrete systems with memory |
| topic | COMPUTERS / Machine Theory bisacsh Mathematisches Modell Cellular automata Mathematical models Discrete-time systems Mathematical models Dynamics Gedächtnis (DE-588)4019614-8 gnd Diskretes System (DE-588)4401225-1 gnd Zellularer Automat (DE-588)4190671-8 gnd |
| topic_facet | COMPUTERS / Machine Theory Mathematisches Modell Cellular automata Mathematical models Discrete-time systems Mathematical models Dynamics Gedächtnis Diskretes System Zellularer Automat |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389645 |
| work_keys_str_mv | AT alonsosanzramon discretesystemswithmemory |