− | Most [[complex system]] models are often formulated in terms of concepts drawn from statistical physics, information theory and non-linear dynamics; however, such approaches are not focused on, or do not include, the conceptual part of complexity related to organization and topological attributes or algebraic topology, such as network connectivity of genomes, interactomes and biological organisms that are very important.<ref name="Rosen" /><ref>^ Heylighen, Francis (2008). "Complexity and Self-Organization". In Bates, Marcia J.; Maack, Mary Niles. Encyclopedia of Library and Information Sciences. CRC. {{ISBN|978-0-8493-9712-7}}</ref><ref>"abstract relational biology (ARB)". PlanetPhysics. Retrieved 2010-03-17.</ref> Recently, the two complementary approaches based both on [[information theory]], [[network topology]]/[[graph theory|abstract graph theory]] concepts are being combined for example in the fields of [[neuroscience]] and [[cognition|human cognition]].<ref name="springerlink" /><ref>http://hdl.handle.net/10101/npre.2011.6115.1 Wallace, Rodrick. When Spandrels Become Arches: Neural crosstalk and the evolution of consciousness. Available from Nature Precedings (2011)</ref> It is generally agreed that there is a [[hierarchy]] of complexity levels of organization that should be considered as distinct from that of the levels of reality in [[ontology]].<ref name="springerlink" /><ref>{{cite journal | author = Poli R | year = 2001a | title = The Basic Problem of the Theory of Levels of Reality | url = | journal = Axiomathes | volume = 12 | issue = 3–4| pages = 261–283 | doi = 10.1023/A:1015845217681 | s2cid = 55743057 }}</ref><ref>{{cite journal | author = Poli R | year = 1998 | title = Levels | url = | journal = Axiomathes | volume = 9 | issue = 1–2| pages = 197–211 | doi=10.1007/bf02681712| pmid = 8053082 }}</ref> The hierarchy of complexity levels of organization in the biosphere is also recognized in modern classifications of taxonomic ranks, such as: [[domain (biology)|biological domain]] and biosphere, [[Kingdom (biology)|biological kingdom]], [[Phylum]], [[Class (biology)|biological class]], [[Order (biology)|order]], [[Family (biology)|family]], [[genus]] and [[species]]. Because of their dynamic and composition variability, intrinsic "fuzziness", autopoietic attributes, ability to self-reproduce, and so on, organisms do not fit into the 'standard' definition of general systems, and they are therefore 'super-complex' in both their function and structure; organisms can be thus be defined in CSB only as '[[meta-system]]s' of simpler dynamic systems<ref name="springerlink" /><ref>[http://pespmc1.vub.ac.be/MST.html Metasystem Transition Theory], [[Valentin Turchin]], [[Cliff Joslyn]], 1993-1997</ref> Such a meta-system definition of organisms, species, 'ecosystems', and so on, is not equivalent to the definition of a ''system of systems'' as in [[Autopoiesis|Autopoietic System]]s Theory,;<ref>[http://archonic.net Reflexive Autopoietic Systems Theory]</ref> it also differs from the definition proposed for example by K.D. Palmer in meta-system engineering,<ref>[http://archonic.net/incosewg/ppframe.htm Meta-system Engineering], Kent D. Palmer, 1996</ref> organisms being quite different from machines and [[Automata theory|automata]] with fixed input-output transition functions, or a continuous [[dynamical system]] with fixed [[phase space]],<ref>Hoff, M.A., Roggia, K.G., Menezes, P.B.:(2004). Composition of Transformations: A Framework for Systems with Dynamic Topology. ''International Journal of Computing Anticipatory System's'' 14:259–270</ref> contrary to the Cartesian philosophical thinking; thus, organisms cannot be defined merely in terms of a quintuple ''A'' of ''(states, startup state, input and output sets/alphabet, transition function)'',<ref>[[John E. Hopcroft]], [[Rajeev Motwani]], [[Jeffrey D. Ullman]].2000. [[Introduction to Automata Theory, Languages, and Computation]] (2nd Edition)Pearson Education. {{ISBN|0-201-44124-1}}</ref> although 'non-deterministic automata', as well as 'fuzzy automata' have also been defined. Tessellation or [[cellular automaton|cellular automata]] provide however an intuitive, visual/computational insight into the lower levels of complexity, and have therefore become an increasingly popular, discrete model studied in computability theory, applied mathematics, physics, computer science, theoretical biology/systems biology, cancer simulations and microstructure modeling. Evolving cellular automata using genetic algorithms<ref>The Evolutionary Design of Collective Computation in Cellular Automata, James P. Crutchfeld, Melanie Mitchell, Rajarshi Das (In J. P. Crutchfield and P. K. Schuster (editors), Evolutionary Dynamics|Exploring the Interplay of Selection, Neutrality, Accident, and Function. New York: Oxford University Press, 2002.)</ref><ref>Evolving Cellular Automata with Genetic Algorithms: A Review of Recent Work, Melanie Mitchell, James P. Crutchfeld, Rajarshi Das (In Proceedings of the First International Conference on Evolutionary Computation and Its Applications (EvCA'96). Moscow, Russia: Russian Academy of Sciences, 1996.)</ref><ref>{{cite journal | doi = 10.1073/pnas.0307811100 | last1 = Peak | first1 = West | last2 = Messinger | first2 = Mott | year = 2004 | title = Evidence for complex, collective dynamics and emergent, distributed computation in plants | journal = Proceedings of the National Academy of Sciences of the USA | volume = 101 | issue = 4| pages = 918–922 |bibcode = 2004PNAS..101..918P | pmid = 14732685 | last3 = Messinger | first3 = SM | last4 = Mott | first4 = KA | pmc = 327117}}</ref> is also an emerging field attempting to bridge the gap between the tessellation automata and the higher level complexity approaches in CSB. | + | Most [[complex system]] models are often formulated in terms of concepts drawn from statistical physics, information theory and non-linear dynamics; however, such approaches are not focused on, or do not include, the conceptual part of complexity related to organization and topological attributes or algebraic topology, such as network connectivity of genomes, interactomes and biological organisms that are very important.<ref name="Rosen" /><ref>^ Heylighen, Francis (2008). "Complexity and Self-Organization". In Bates, Marcia J.; Maack, Mary Niles. Encyclopedia of Library and Information Sciences. CRC.</ref><ref>"abstract relational biology (ARB)". PlanetPhysics. Retrieved 2010-03-17.</ref> Recently, the two complementary approaches based both on [[information theory]], [[network topology]]/[[graph theory|abstract graph theory]] concepts are being combined for example in the fields of [[neuroscience]] and [[cognition|human cognition]].<ref name="springerlink" /><ref>http://hdl.handle.net/10101/npre.2011.6115.1 Wallace, Rodrick. When Spandrels Become Arches: Neural crosstalk and the evolution of consciousness. Available from Nature Precedings (2011)</ref> It is generally agreed that there is a [[hierarchy]] of complexity levels of organization that should be considered as distinct from that of the levels of reality in [[ontology]].<ref name="springerlink" /><ref>{{cite journal | author = Poli R | year = 2001a | title = The Basic Problem of the Theory of Levels of Reality | url = | journal = Axiomathes | volume = 12 | issue = 3–4| pages = 261–283 | doi = 10.1023/A:1015845217681 | s2cid = 55743057 }}</ref><ref>{{cite journal | author = Poli R | year = 1998 | title = Levels | url = | journal = Axiomathes | volume = 9 | issue = 1–2| pages = 197–211 | doi=10.1007/bf02681712| pmid = 8053082 }}</ref> The hierarchy of complexity levels of organization in the biosphere is also recognized in modern classifications of taxonomic ranks, such as: [[domain (biology)|biological domain]] and biosphere, [[Kingdom (biology)|biological kingdom]], [[Phylum]], [[Class (biology)|biological class]], [[Order (biology)|order]], [[Family (biology)|family]], [[genus]] and [[species]]. Because of their dynamic and composition variability, intrinsic "fuzziness", autopoietic attributes, ability to self-reproduce, and so on, organisms do not fit into the 'standard' definition of general systems, and they are therefore 'super-complex' in both their function and structure; organisms can be thus be defined in CSB only as '[[meta-system]]s' of simpler dynamic systems<ref name="springerlink" /><ref>[http://pespmc1.vub.ac.be/MST.html Metasystem Transition Theory], [[Valentin Turchin]], [[Cliff Joslyn]], 1993-1997</ref> Such a meta-system definition of organisms, species, 'ecosystems', and so on, is not equivalent to the definition of a ''system of systems'' as in [[Autopoiesis|Autopoietic System]]s Theory,;<ref>[http://archonic.net Reflexive Autopoietic Systems Theory]</ref> it also differs from the definition proposed for example by K.D. Palmer in meta-system engineering,<ref>[http://archonic.net/incosewg/ppframe.htm Meta-system Engineering], Kent D. Palmer, 1996</ref> organisms being quite different from machines and [[Automata theory|automata]] with fixed input-output transition functions, or a continuous [[dynamical system]] with fixed [[phase space]],<ref>Hoff, M.A., Roggia, K.G., Menezes, P.B.:(2004). Composition of Transformations: A Framework for Systems with Dynamic Topology. ''International Journal of Computing Anticipatory System's'' 14:259–270</ref> contrary to the Cartesian philosophical thinking; thus, organisms cannot be defined merely in terms of a quintuple ''A'' of ''(states, startup state, input and output sets/alphabet, transition function)'',<ref>[[John E. Hopcroft]], [[Rajeev Motwani]], [[Jeffrey D. Ullman]].2000. [[Introduction to Automata Theory, Languages, and Computation]] (2nd Edition)Pearson Education. </ref> although 'non-deterministic automata', as well as 'fuzzy automata' have also been defined. Tessellation or [[cellular automaton|cellular automata]] provide however an intuitive, visual/computational insight into the lower levels of complexity, and have therefore become an increasingly popular, discrete model studied in computability theory, applied mathematics, physics, computer science, theoretical biology/systems biology, cancer simulations and microstructure modeling. Evolving cellular automata using genetic algorithms<ref>The Evolutionary Design of Collective Computation in Cellular Automata, James P. Crutchfeld, Melanie Mitchell, Rajarshi Das (In J. P. Crutchfield and P. K. Schuster (editors), Evolutionary Dynamics|Exploring the Interplay of Selection, Neutrality, Accident, and Function. New York: Oxford University Press, 2002.)</ref><ref>Evolving Cellular Automata with Genetic Algorithms: A Review of Recent Work, Melanie Mitchell, James P. Crutchfeld, Rajarshi Das (In Proceedings of the First International Conference on Evolutionary Computation and Its Applications (EvCA'96). Moscow, Russia: Russian Academy of Sciences, 1996.)</ref><ref>{{cite journal | doi = 10.1073/pnas.0307811100 | last1 = Peak | first1 = West | last2 = Messinger | first2 = Mott | year = 2004 | title = Evidence for complex, collective dynamics and emergent, distributed computation in plants | journal = Proceedings of the National Academy of Sciences of the USA | volume = 101 | issue = 4| pages = 918–922 |bibcode = 2004PNAS..101..918P | pmid = 14732685 | last3 = Messinger | first3 = SM | last4 = Mott | first4 = KA | pmc = 327117}}</ref> is also an emerging field attempting to bridge the gap between the tessellation automata and the higher level complexity approaches in CSB. |