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Category Theory as the Language of Modelling Environmental Interfaces – Complex Biophysical

0. Category Theory as the Language of Modelling Environmental Interfaces – Complex Biophysical Systems Dragutin T. Mihailovi ć Faculty of Agriculture, University of Novi Sad, Novi Sad , SERBIA guto@uns.ns.ac.yu. 7th EMS Annual Meeting / 8th ECAM

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Category Theory as the Language of Modelling Environmental Interfaces – Complex Biophysical

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  1. 0 Category Theory as the Language of Modelling Environmental Interfaces – Complex Biophysical Systems Dragutin T. Mihailović Faculty of Agriculture, University of Novi Sad, Novi Sad, SERBIA guto@uns.ns.ac.yu 7th EMS Annual Meeting / 8th ECAM Madrid 1-5 October, 2007 InvitedPaper (IP)

  2. 1 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  3. 2 Content + Definition of environmental interface +Modelling approach in Rosen’s sense +Self-organization + World of category theory +Conclusion (Instead) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  4. 3 Why always we have to try to explain something? There are things which are over the explanation we can get by our attempts and mind … (Paolo Cuello) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  5. 4 “Kick off meeting”, Atlanta 1996Themes on the front of sciences in 21st century Superconductivity(technological question) Contact with other civilizations (question of universality) The question about origin of the brain and functioning the consciousness- quantum teleology(question of the brain origin) Environmental problems (question of survival - question over all questions) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  6. 5 DEFINITION OF ENVIRONMENTAL INTERFACE (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  7. 6 DEFINITION OF ENVIRONMENTAL SURFACE An environmental interface can be defined as a surface between two either abiotic or biotic systems that are in relative motion and exchange mass, energy and momentum through biophysical and/or chemical processes. These processes are fluctuating temporally and spatially. “Advanced in Environmental Fluid Mechanics”,2007 Eds. C. Gualtieri and D.T. Mihailovic, Francis&Taylor, London (In press) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  8. 7 ENVIRONMENTAL SCIENCE, is the scientific study of the distribution and abundance of LIVING ORGANISMS and how the distribution and abundance are affected by INTERACTIONS between the organisms and their ENVIRONMENT . Used as a par exellance example of science dealing with COMPLEX SYSTEM (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  9. micro 8 micro meso (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  10. 9 G l o b a l L o c a l (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  11. 10 “Flying perspective” Mihailovic et al., 2002, EFM Mihailovic et al., 2002, Env. Fluid Mech. (IP) Project Meeting, The Columbia University, N.Y, 26 October 2001

  12. 11 Biophysical interfaces differentlly designed Big leaf One layer Figures designed by Dr. B. Lalic) ”Sandwich” Multilayer (IP) Lectures at Corvinus University, Budapest (Hungary), 23-25 August 2006

  13. 12 Conceptual diagram showing the link between biometeorological processes and time and space scales (Baldocchi, 2004) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  14. 13 MODELLING APPROACH (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  15. 14 How to see and how to describe? ENDOPHYSICS!! (essentially what an observer, who simply sits and watches what happens in surrounding world, will see) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  16. Environmental world in the modelling light 15 (N)atural system (F)ormal system Causality Inference in the formalism Orderliness required by the ambience Orderliness required of the self (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  17. 16 Decoding 4 Inference (N) (F) Causal 2 1 3 Encoding Comparison of these different entailment structures requires establishment of DICTIONARIES (After Robert Rosen, 1991) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  18. 17 One dictionaryfor encoding the phenomena of N into the PROPOSITIONS of F another dictionary for decoding from propositions of F back to PHENOMENA in N 1 represents causal entailment within N (essentially what an obsrver, who simply sits and watches what happens in N, will see) 2 we mast use these propositions as hypotheses 3 It generates theorems in F 4 decoding these theorems back to the phenomena - theorems we have thus generated become PREDICTIONS about N (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  19. 18 SELF-ORGANIZATION (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  20. 19 Self-organising systems are COMPLEX SYSTEMS. The term “complexity” has three levels of meaning: 1. There is self-organization and emergence in complex systems (Edmonds 1999) 2. Complex systems are not organised centrally, but in a distributed manner; there are many connections between the system´s parts (Kauffman 1993, Edmonds 1999) 3. It isdifficult to model complex systems and to predict their ehavioureven if one knows to a large extent the parts of such systems and the connections between the parts (Heylighen 1997; Edmonds 1999) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  21. 20 Open self-organized systems *the microscopic dimension of the individual element *the mesoscopic dimension of the structure limited by the structural boundary *the macroscopic dimension of the field of interaction or relevant environment limited by the system boundary. (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  22. 21 EXAMPLES (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  23. 22 EXAMPLES (Koppel et al., 2005) The american naturalist, 165,E1-E11 (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  24. 23 EXAMPLES Figure 6: GIS analysis of vegetation changes between 1982 and 1998 in two sections of the salt marsh of Paulinapolder (P) and Hellegatpolder (H) in the Westerschelde, the Netherlands. A, Position of both salt marshes in the Westerschelde. B, C, Vegetation changes at the marsh edge of the Paulinapolder and Hellgatpolder, respectively. Green depicts vegetation that remained stable between 1982 and 1998; red depicts vegetation that disappeared; yellow depicts new vegetation appearing between 1982 and 1998. Note that cliff erosion (horizontal red band in B and C) occurs simultaneously with regrowth. D, Photograph of the cliff at the right part of B, taken in 2002. E, Elevational changes measured along a government monitored transect at Paulinapolder near B (included solely for illustration). Note that cliff erosion occurs at 40 m from the start of the transect, while sedimentation occurs in front of the cliff. (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  25. 24 WORLD OF CATEGORY THEORY (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  26. 25 WORLD OF DIFFERENTIAL EQUATIONS dQi /dt = fi (dQ1, dQ2, … dQi) Qiis a quantity IDEA: putting forward the formalization of system as a finite sequence of finite sequence of differential equations DRAWBACK: There a lot LATENT assumptions (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  27. 26 WORLDOF LOGISTIC EQUATION The diagonal terms of the matrix M represent individual growth rates, while the off-diagonal terms represent the interaction between species. Fixed amount of available resources corresponds to conservation laws. Evolution gets really competitive when the total population reaches its maximum value Σ x( t) = X (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  28. 27 One can predict the population for two-cycle attractor by requiring that generation (i+2) has the same number of species as generationi: X=Xi=Xi+2=a Xi+1(1-Xi+1) bifurcation diagram containing similar plots (self-similarity). a[3.57,4) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  29. 28 Water, vegetation or any natural surface Ta z=Tg-Ta s 1-s Tg 1-s qw zn+1=azn(1-zn) Living matter Mihailovic (2007) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  30. 29 c 1-c x1 Concentration x0 Simple cell interaction via logistic equation (Gunji et al., 2004) Coupling qw Mihailovic (2007) – environmental interfaces (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  31. 30 Category theory (or topos) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  32. 31 (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  33. 32 B cell f=[XB=XA*XA,YA=XA+1] F g=[XC=XB,YC=YB*YB] F F C cell A cell gof F F F FUNCTOR F=exp(-(f,g)) (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  34. 33 We have in mind that in our system we are dealing with strictlydeterministic INITIAL FINAL There are another systems with existence of two physical times (two time arrows) INITIAL FINAL (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

  35. 34 INSTEAD OF CONCLUSION In modelling of environmental interfaces as biophysical complex systems we have to concentrate 1. Further use of category theory 2. Determining the hierarchy by Formal Conceptual Analysis 3. Considering the double arrow time 4. Use powerful cluster computers (IP) 7th EMS Annual Meeting / 8th ECAM, Madrid 1-5 October, 2007

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