Discrete systems with memory /:
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,...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, N.J. :
World Scientific,
©2011.
|
| Schriftenreihe: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 75. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 resource (xi, 465 pages :) |
| Bibliographie: | Includes bibliographical references (pages 429-450) and index. |
| ISBN: | 9789814343640 9814343641 1283235021 9781283235020 9786613235022 6613235024 |
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| 100 | 1 | |a Alonso-Sanz, Ramon. | |
| 245 | 1 | 0 | |a Discrete systems with memory / |c Ramon Alonso-Sanz. |
| 260 | |a Singapore ; |a Hackensack, N.J. : |b World Scientific, |c ©2011. | ||
| 300 | |a 1 online resource (xi, 465 pages :) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
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| 490 | 1 | |a World Scientific series on nonlinear science. | |
| 504 | |a Includes bibliographical references (pages 429-450) and index. |b 448 | ||
| 505 | 0 | 0 | |g Machine generated contents note: |g 1. |t Cellular Automata and memory -- |g 1.1. |t Cellular Automata -- |g 1.2. |t Memory -- |t Disclaimer -- |g 2. |t Average type memory -- |g 2.1. |t Average memory -- |g 2.2. |t Two-dimensional lattices -- |g 2.2.1. |t Totalistic rules -- |g 2.2.2. |t LIFE -- |g 2.3. |t One-dimensional layers -- |g 2.3.1. |t Elementary rules -- |g 2.3.2. |t Nearest and next-nearest neighbors -- |g 3. |t Other memories -- |g 3.1. |t Average-like memory -- |g 3.2. |t Limited trailing memory -- |g 3.3. |t Majority of the last three state memory -- |g 3.4. |t Elementary rules as memory -- |g 3.5. |t Minimal memory -- |g 4. |t Asynchrony and probabilistic rules -- |g 4.1. |t Asynchrony -- |g 4.2. |t Probabilistic rules -- |g 5. |t Cycles and random sequences -- |g 5.1. |t Cycles -- |g 5.2. |t Random number generation by CA -- |g 6. |t Three state automata -- |g 6.1. |t Totalistic rules -- |g 6.2. |t Excitable systems -- |g 7. |t Reversible dynamics -- |g 7.1. |t Characterization -- |g 7.2. |t Reversible rules with memory -- |g 8. |t Block cellular automata -- |g 8.1. |t Characterization -- |g 8.2. |t Density classification task. |
| 505 | 0 | 0 | |g 9. |t Structurally dynamic systems -- |g 9.1. |t Introduction -- |g 9.1.1. |t Reversible SDCA -- |g 9.2. |t SDCA with memory -- |g 9.2.1. |t Two state SDCA with memory -- |g 9.2.2. |t Three state SDCA -- |g 10. |t Boolean networks -- |g 10.1. |t Automata on networks -- |g 10.2. |t Boolean networks -- |g 10.3. |t Automata on proximity graphs -- |g 11. |t Coupled layers -- |g 11.1. |t Coupled cellular automata -- |g 11.2. |t Coupled Boolean networks -- |g 12. |t Continuous state variable -- |g 12.1. |t Continuous-valued automata -- |g 12.2. |t Finite difference equations -- |g 12.2.1. |t One-dimensional maps -- |g 12.2.2. |t Two-dimensional maps -- |g 12.3. |t Plane curves -- |g 12.4. |t Stochastic processes -- |g 13. |t Spatial games -- |g 13.1. |t The prisoner's dilemma -- |g 13.2. |t Degrees of cooperation and strategies -- |g 13.3. |t The structurally dynamic PD (SDPD) -- |g 13.4. |t Pavlov versus anti-Pavlov (PAP) in the PD -- |g 13.5. |t Other spatial games -- |t Appendices -- |g Appendix |t A Average memory starting at random -- |g Appendix B |t Dynamic with short-term memory -- |g Appendix C |t Heterogeneous and coupled networks -- |g Appendix D |t Continuous state variable -- |g Appendix E |t Spatial games. |
| 520 | |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. | ||
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 650 | 0 | |a Cellular automata |x Mathematical models. | |
| 650 | 0 | |a Discrete-time systems |x Mathematical models. | |
| 650 | 0 | |a Dynamics. |0 http://id.loc.gov/authorities/subjects/sh85040316 | |
| 650 | 6 | |a Automates cellulaires |x Modèles mathématiques. | |
| 650 | 6 | |a Systèmes échantillonnés |x Modèles mathématiques. | |
| 650 | 6 | |a Dynamique. | |
| 650 | 7 | |a kinetics (dynamics) |2 aat | |
| 650 | 7 | |a COMPUTERS |x Machine Theory. |2 bisacsh | |
| 650 | 7 | |a Cellular automata |x Mathematical models |2 fast | |
| 650 | 7 | |a Discrete-time systems |x Mathematical models |2 fast | |
| 650 | 7 | |a Dynamics |2 fast | |
| 758 | |i has work: |a Discrete systems with memory (Text) |1 https://id.oclc.org/worldcat/entity/E39PCG6bjVKJDcP9qxX3Pv3Qmd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Alonso-Sanz, Ramon. |t Discrete systems with memory. |d Singapore ; Hackensack, N.J. : World Scientific, ©2011 |z 9814343633 |w (OCoLC)694395036 |
| 830 | 0 | |a World Scientific series on nonlinear science. |n Series A, |p Monographs and treatises ; |v v. 75. |0 http://id.loc.gov/authorities/names/no94008495 | |
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| adam_text | |
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| author | Alonso-Sanz, Ramon |
| author_facet | Alonso-Sanz, Ramon |
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| author_variant | r a s ras |
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| contents | Cellular Automata and memory -- Cellular Automata -- Memory -- Disclaimer -- Average type memory -- Average memory -- Two-dimensional lattices -- Totalistic rules -- LIFE -- One-dimensional layers -- Elementary rules -- Nearest and next-nearest neighbors -- Other memories -- Average-like memory -- Limited trailing memory -- Majority of the last three state memory -- Elementary rules as memory -- Minimal memory -- Asynchrony and probabilistic rules -- Asynchrony -- Probabilistic rules -- Cycles and random sequences -- Cycles -- Random number generation by CA -- Three state automata -- Excitable systems -- Reversible dynamics -- Characterization -- Reversible rules with memory -- Block cellular automata -- Density classification task. Structurally dynamic systems -- Introduction -- Reversible SDCA -- SDCA with memory -- Two state SDCA with memory -- Three state SDCA -- Boolean networks -- Automata on networks -- Automata on proximity graphs -- Coupled layers -- Coupled cellular automata -- Coupled Boolean networks -- Continuous state variable -- Continuous-valued automata -- Finite difference equations -- One-dimensional maps -- Two-dimensional maps -- Plane curves -- Stochastic processes -- Spatial games -- The prisoner's dilemma -- Degrees of cooperation and strategies -- The structurally dynamic PD (SDPD) -- Pavlov versus anti-Pavlov (PAP) in the PD -- Other spatial games -- Appendices -- A Average memory starting at random -- Dynamic with short-term memory -- Heterogeneous and coupled networks -- Spatial games. |
| ctrlnum | (OCoLC)756782478 |
| 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 |
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code="g">10.2.</subfield><subfield code="t">Boolean networks --</subfield><subfield code="g">10.3.</subfield><subfield code="t">Automata on proximity graphs --</subfield><subfield code="g">11.</subfield><subfield code="t">Coupled layers --</subfield><subfield code="g">11.1.</subfield><subfield code="t">Coupled cellular automata --</subfield><subfield code="g">11.2.</subfield><subfield code="t">Coupled Boolean networks --</subfield><subfield code="g">12.</subfield><subfield code="t">Continuous state variable --</subfield><subfield code="g">12.1.</subfield><subfield code="t">Continuous-valued automata --</subfield><subfield code="g">12.2.</subfield><subfield code="t">Finite difference equations --</subfield><subfield code="g">12.2.1.</subfield><subfield code="t">One-dimensional maps --</subfield><subfield code="g">12.2.2.</subfield><subfield code="t">Two-dimensional maps --</subfield><subfield code="g">12.3.</subfield><subfield code="t">Plane curves --</subfield><subfield code="g">12.4.</subfield><subfield code="t">Stochastic processes --</subfield><subfield code="g">13.</subfield><subfield code="t">Spatial games --</subfield><subfield code="g">13.1.</subfield><subfield code="t">The prisoner's dilemma --</subfield><subfield code="g">13.2.</subfield><subfield code="t">Degrees of cooperation and strategies --</subfield><subfield code="g">13.3.</subfield><subfield code="t">The structurally dynamic PD (SDPD) --</subfield><subfield code="g">13.4.</subfield><subfield code="t">Pavlov versus anti-Pavlov (PAP) in the PD --</subfield><subfield code="g">13.5.</subfield><subfield code="t">Other spatial games --</subfield><subfield code="t">Appendices --</subfield><subfield code="g">Appendix</subfield><subfield code="t">A Average memory starting at random --</subfield><subfield code="g">Appendix B</subfield><subfield code="t">Dynamic with short-term memory --</subfield><subfield code="g">Appendix C</subfield><subfield code="t">Heterogeneous and coupled networks --</subfield><subfield code="g">Appendix D</subfield><subfield code="t">Continuous state variable --</subfield><subfield code="g">Appendix E</subfield><subfield code="t">Spatial games.</subfield></datafield><datafield tag="520" 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. 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| id | ZDB-4-EBA-ocn756782478 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:18:19Z |
| institution | BVB |
| isbn | 9789814343640 9814343641 1283235021 9781283235020 9786613235022 6613235024 |
| language | English |
| oclc_num | 756782478 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xi, 465 pages :) |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific, |
| record_format | marc |
| series | World Scientific series on nonlinear science. Monographs and treatises ; |
| series2 | World Scientific series on nonlinear science. |
| spelling | Alonso-Sanz, Ramon. Discrete systems with memory / Ramon Alonso-Sanz. Singapore ; Hackensack, N.J. : World Scientific, ©2011. 1 online resource (xi, 465 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file World Scientific series on nonlinear science. Includes bibliographical references (pages 429-450) and index. 448 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. Print version record. English. Cellular automata Mathematical models. Discrete-time systems Mathematical models. Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Automates cellulaires Modèles mathématiques. Systèmes échantillonnés Modèles mathématiques. Dynamique. kinetics (dynamics) aat COMPUTERS Machine Theory. bisacsh Cellular automata Mathematical models fast Discrete-time systems Mathematical models fast Dynamics fast has work: Discrete systems with memory (Text) https://id.oclc.org/worldcat/entity/E39PCG6bjVKJDcP9qxX3Pv3Qmd https://id.oclc.org/worldcat/ontology/hasWork Print version: Alonso-Sanz, Ramon. Discrete systems with memory. Singapore ; Hackensack, N.J. : World Scientific, ©2011 9814343633 (OCoLC)694395036 World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 75. http://id.loc.gov/authorities/names/no94008495 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=389645 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=389645 Volltext |
| spellingShingle | Alonso-Sanz, Ramon Discrete systems with memory / World Scientific series on nonlinear science. Monographs and treatises ; Cellular Automata and memory -- Cellular Automata -- Memory -- Disclaimer -- Average type memory -- Average memory -- Two-dimensional lattices -- Totalistic rules -- LIFE -- One-dimensional layers -- Elementary rules -- Nearest and next-nearest neighbors -- Other memories -- Average-like memory -- Limited trailing memory -- Majority of the last three state memory -- Elementary rules as memory -- Minimal memory -- Asynchrony and probabilistic rules -- Asynchrony -- Probabilistic rules -- Cycles and random sequences -- Cycles -- Random number generation by CA -- Three state automata -- Excitable systems -- Reversible dynamics -- Characterization -- Reversible rules with memory -- Block cellular automata -- Density classification task. Structurally dynamic systems -- Introduction -- Reversible SDCA -- SDCA with memory -- Two state SDCA with memory -- Three state SDCA -- Boolean networks -- Automata on networks -- Automata on proximity graphs -- Coupled layers -- Coupled cellular automata -- Coupled Boolean networks -- Continuous state variable -- Continuous-valued automata -- Finite difference equations -- One-dimensional maps -- Two-dimensional maps -- Plane curves -- Stochastic processes -- Spatial games -- The prisoner's dilemma -- Degrees of cooperation and strategies -- The structurally dynamic PD (SDPD) -- Pavlov versus anti-Pavlov (PAP) in the PD -- Other spatial games -- Appendices -- A Average memory starting at random -- Dynamic with short-term memory -- Heterogeneous and coupled networks -- Spatial games. Cellular automata Mathematical models. Discrete-time systems Mathematical models. Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Automates cellulaires Modèles mathématiques. Systèmes échantillonnés Modèles mathématiques. Dynamique. kinetics (dynamics) aat COMPUTERS Machine Theory. bisacsh Cellular automata Mathematical models fast Discrete-time systems Mathematical models fast Dynamics fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85040316 |
| title | Discrete systems with memory / |
| title_alt | Cellular Automata and memory -- Cellular Automata -- Memory -- Disclaimer -- Average type memory -- Average memory -- Two-dimensional lattices -- Totalistic rules -- LIFE -- One-dimensional layers -- Elementary rules -- Nearest and next-nearest neighbors -- Other memories -- Average-like memory -- Limited trailing memory -- Majority of the last three state memory -- Elementary rules as memory -- Minimal memory -- Asynchrony and probabilistic rules -- Asynchrony -- Probabilistic rules -- Cycles and random sequences -- Cycles -- Random number generation by CA -- Three state automata -- Excitable systems -- Reversible dynamics -- Characterization -- Reversible rules with memory -- Block cellular automata -- Density classification task. Structurally dynamic systems -- Introduction -- Reversible SDCA -- SDCA with memory -- Two state SDCA with memory -- Three state SDCA -- Boolean networks -- Automata on networks -- Automata on proximity graphs -- Coupled layers -- Coupled cellular automata -- Coupled Boolean networks -- Continuous state variable -- Continuous-valued automata -- Finite difference equations -- One-dimensional maps -- Two-dimensional maps -- Plane curves -- Stochastic processes -- Spatial games -- The prisoner's dilemma -- Degrees of cooperation and strategies -- The structurally dynamic PD (SDPD) -- Pavlov versus anti-Pavlov (PAP) in the PD -- Other spatial games -- Appendices -- A Average memory starting at random -- Dynamic with short-term memory -- Heterogeneous and coupled networks -- Spatial games. |
| 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 | Cellular automata Mathematical models. Discrete-time systems Mathematical models. Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Automates cellulaires Modèles mathématiques. Systèmes échantillonnés Modèles mathématiques. Dynamique. kinetics (dynamics) aat COMPUTERS Machine Theory. bisacsh Cellular automata Mathematical models fast Discrete-time systems Mathematical models fast Dynamics fast |
| topic_facet | Cellular automata Mathematical models. Discrete-time systems Mathematical models. Dynamics. Automates cellulaires Modèles mathématiques. Systèmes échantillonnés Modèles mathématiques. Dynamique. kinetics (dynamics) COMPUTERS Machine Theory. Cellular automata Mathematical models Discrete-time systems Mathematical models Dynamics |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=389645 |
| work_keys_str_mv | AT alonsosanzramon discretesystemswithmemory |