Topics in the General Theory of Structures

ISBN-13: 9789401081993 / Angielski / Miękka / 2011 / 208 str.

E.R. Caianiello;M.A. Aizerman

Opis

This volume is about "Structure." The search for "structure," always the pursuit of sciences within their specific areas and perspectives, is witnessing these days a dra matic revolution. The coexistence and interaction of so many structures (atoms, hu mans, cosmos and all that there is in between) would be unconceivable according to many experts, if there were not, behind it all, some gen eral organizational principle. s that (at least in some asymptotic way) make possible so many equilibria among species and natural objects, fan tastically tuned to an extremely high degree of precision. The evidence accumulates to an increasingly impressive degree; a concrete example comes from physics, whose constant aim always was and is that of searching for "ultimate laws," out of which everything should follow, from quarks to the cosmos. Our notions and philosophy have un dergone major revolutions, whenever the "unthinkable" has been changed by its wonderful endeavours into "fact." Well, it is just from physics that evidence comes: even if the "ultimate" could be reached, it would not in any way be a terminal point. When "complexity" comes into the game, entirely new notions have to be invented; they all have to do with "structure," though this time in a much wider sense than would have been understood a decade or so ago."

Spis treści

1. Introduction.- 2. Structure and Modularity in Self-Organizing Complex Systems.- 3. Hierarchy and Modularity in Natural Languages.- 4. Dynamic Approach to Analysis of Structures Described by Graphs (Foundations of Graph-Dynamics).- 5. Structural Properties of Voting Systems.- 6. Application of Predicate Calculus to the Study of Structures of Systems.- 7. Tournament Functions in Problems of Collective Choices.- 8. C-Calculus: An Overview.- 9. On Some Analytic Aspects of C-Calculus.- 10. A New Method Based on C-Calculus for Some Problems of Cell Movement Analysis.- 11. Systems and Uncertainty: A Geometrical Approach.