High dimensional reference architectures presented here allows
confronting and prevailing over the growing complexity of polytopic
projects implementations. Such projects should be envisaged giving
that conventional systems operations, equipments, methodologies or
organizations will reach their limits for self-evolvability in high
complexity conditions. Self-evolvable high complexity systems are
based on high dimensional polytopic reference architectures.
Polytope is the general term of the sequence: point, line, polygon,
polyhedron and so on.The polytopic projects are targeting the
artificiality, not only for materials where it is well known and
applied, but also for biological, cognitive, intelligent and
mathematical systems. The book highlights the polytopic projects
basic similarity despite the noticeable difference as domains of
application. The roads to follow and the algebra of changing roads
are emphasized. The book is divided in 9 chapters. Chapter 1
introduces the Polytopic Roadmap to 4D and beyond. The role for the
dialogue of processes in duality of the non-Aristotelian Logic of
Contradiction and of Included Middle is emphasized for different
domains. Chapter 2 refers to chemical systems. Supramolecular
chemistry, metal organic frameworks, MOF, and reaction networks,
are the examples considered in the frame of polytopic chemistry.
Chapter 3 refers to biological systems. Biological dynamical
hierarchies and quasi-species are the considered case studies.
Technological and scientific projects targeting artificiality for
cells and viruses are considered. Chapter 4 refers to cognitive
systems. Developmental stages, formal and relational concepts
analysis, and neural coding are considered here. The roles of the
4D systems of systems of systems and of conceptual 4D-cube are
emphasized. Artificiality for cognitive systems is the object of
study. Chapter 5 refers to mathematical systems. Modeling levels
and the 4D digital twins are discussed. Hopf monoids as tools for
the study of combinations and separations, dual graded graphs and
V-models are informally presented. Chapter 6 refers to application
of formal concept analysis, FCA, for high dimensional separations,
nesting and drug delivery. Chapter 7 refers to polytopic
engineering systems as multiscale transfer,
distributors-collectors, cyclic operations, middle vessel columns,
mixing, assembly and designs. Equipments have been characterized
using Polytopic Roadmaps and classified by Periodic Tables. Chapter
8 introduces polytopic industry, economy, society and
sustainability. Chapter 9 outlines new domains of interest as arts
and architecture, transdisciplinarity, complex systems and unity of
sciences and engineering. Polytopic Roadmaps are proposed as Method
for experts from various fields to synthesize their thinking and
capabilities into new projects implementation to face and surpass
high complexity. A repetitive finding of this book is that
self-evolvability observed in physical systems is based on the same
directed sequence of reference architectures as the
self-evolvability of concepts in our mind. Continuing to develop
the field of self-evolvable systems and presenting the polytopic
roadmaps for 4D and beyond advances in ever growing complexity
domains, the book will be useful to engineers, researchers,
entrepreneurs and students in different branches of production,
complex systems sciences and engineering, ecology and applied
mathematics.
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