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Page 3620 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
(CZ-KARLMP; Prague) Zero-dimensional dynamical systems, formal languages, and universality. (English summary) Theory Comput. Syst. 32 (1999), no. 4, 423-433.  ...  In addition to symbolic systems, examples of zero- dimensional dynamical systems are cellular automata and adding machines.  ... 

Page 6962 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
Summary: “We conceive finite and cellular automata as dynam- ical systems on zero-dimensional spaces and show that they are incomparable in the sense of factorization.  ...  Next we study the complexity of languages generated by zero-dimensional systems on clopen partitions of the state space.  ... 

Page 4938 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
Eindhoven University of Technology, Eindhoven, 1998. x+233 pp. ISBN 90-386-0631-1 From the summary: “To date, there are many different formal methods for describing and analyzing concurrent systems.  ...  In contrast, the self-assembly of double crossover molecules into two-dimensional sheets or three-dimensional solids is theoretically capable of universal computation.  ... 

Mathematical systems theory

R. de Groot
1977 Journal of Computational and Applied Mathematics  
, coding theory and filtering for sequential systems, general dynamical systems and categorical approach to systems.  ...  The book contains contributions by The papers fall under the following six headings : automata theory, finite dimensional linear systems, bifinear and non-linear systems, linear in£mite dimensional systems  ...  Kepler University, Linz, Austria) writes about general dynamic systems : construction and realization.  ... 
doi:10.1016/0771-050x(77)90024-9 fatcat:7tfccvyx6ndufgblekd55mn6fa

NUMERICAL MODEL OF FRACTALS IN THE PHYSICAL CHEMISTRY OF MATERIALS SCIENCE
ЧИСЛОВАЯ МОДЕЛЬ ФРАКТАЛОВ В ФИЗИКО-ХИМИИ МАТЕРИАЛОВЕДЕНИЯ

Alexander D. Izotov, Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Feodor I. Mavrikidi, Oil and Gas Research Institute, Russian Academy of Sciences
2019 Radioelectronics Nanosystems Information Technologies  
The basis of the model is the synthesis of two basic number systems of mathematics -real and p-adic numbers. A physical chemistry interpretation of p-adic numbers and their properties is given.  ...  The identity of nonlinear models of the atom and the Universe is shown, which serves as a justification for the periodicity of properties and is consistent with the hyperbolicity of the space of the general  ...  Properties are described in formal languages.  ... 
doi:10.17725/rensit.2019.11.279 fatcat:36tajykvpfedlohqtsxduoj2d4

Progress, gaps and obstacles in the classification of cellular automata

Milan Vispoel, Aisling J. Daly, Jan M. Baetens
2021 Physica D : Non-linear phenomena  
For instance, assessing how CA design choices impact the generated dynamics requires an overview of the types of dynamics that can occur.  ...  on analytical results from topological dynamics and the theory of computation on the one hand, experimental research focusing on the statistical properties of the simulated space-time patterns on the  ...  Acknowledgment We acknowledge the support from the Special Research Fund of Ghent University, Belgium (Grant N • 01Z02016).  ... 
doi:10.1016/j.physd.2021.133074 fatcat:a45fm4ac6jaajg6cobt3ej3eky

Page 2110 of Mathematical Reviews Vol. , Issue 92d [page]

1992 Mathematical Reviews  
Khanin, Feigenbaum universality and the thermodynamic formalism [MR 86g:58106] (pp. 501-540); K. M. Khanin and Ya. G.  ...  We show that the grammatical rules of the underlying language can be easily classified in a compact form by means of a universal parameter t.  ... 

From materiality to system

Louis Armand
2006 Sign Systems Studies  
— from Peirce to Lotman and Sebeok — and questions the classificatory rationale that delimits semiosis to the exclusion of a general treatment of dynamic systems.  ...  It examines the logical consequences of several major lines of argument concerning the status of semiosis with regards to the human or broadly "organic" life-world and to the "zero degree" of base materiality  ...  But the dynamic interval represented by this "zero dimensionality" can also be regarded as a gradient of dissipation, or entropic spiral, in the sense that the vortex describes an engine of possibilities  ... 
doi:10.12697/sss.2006.34.1.05 fatcat:vmehpd7mmzdpln5wm35h5ibwve

Landau–Lifshitz Hierarchy and Infinite-Dimensional Grassmann Variety

Kanehisa Takasaki
2004 Letters in Mathematical Physics  
This paper elucidates its status in Sato, Segal and Wilson's universal description of soliton equations in the language of an infinite dimensional Grassmann variety.  ...  The Landau-Lifshitz hierarchy is thereby mapped to a simple dynamical system on the set of these dressed vacua.  ...  Acknowledgements I would like to thank Takeshi Ikeda and Takashi Takebe for comments and discussion on related issues.  ... 
doi:10.1023/b:math.0000032751.45559.ef fatcat:nlh6ivhmlvfbzcrxjju4imga6e

A geometric version for the description of the dynamics of different models

O. P. Zandron
2019 Advanced Studies in Theoretical Physics  
, to models of productive systems.  ...  In many of our works, and over the years, the dynamics of different models were analyzed from a geometric point of view.  ...  Conclusions We conclude that due to it is intrinsic geometrical language, the FCE can be used as an interesting formal resource to understand the structure and the dynamics of different models, being able  ... 
doi:10.12988/astp.2019.81246 fatcat:v6wbj7xqvvfi5hhpnhaz335asu

Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos [article]

Mikhail Prokopenko, Michael Harré, Joseph Lizier, Fabio Boschetti, Pavlos Peppas, Stuart Kauffman
2019 Physics of Life Reviews   accepted
In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference  ...  Some of these interconnections are well-known, while some are clarified in this study as a result of a fine-grained comparison between recursive formal systems, Turing machines, and Cellular Automata (  ...  roles in formal systems, algorithms, and dynamical systems.  ... 
doi:10.1016/j.plrev.2018.12.003 pmid:30655222 arXiv:1711.02456v2 fatcat:pxsolfjgezbsrglhmijknbmyxi

An Object-Oriented Methodology Using Dynamic Variables for Animation and Scientific Visualization [chapter]

Russel Turner, Enrico Gobbetti, Francis Balaguer, Angelo Mangili, Daniel Thalmann, Nadia Magnenat-Thalmann
1990 CG International '90  
An object-oriented design is presented for building dynamic three-dimensional applications.  ...  The design philosophy and methodology of the toolkit are also described, as well as some of the implementation issues for the Silicon Graphics Iris 4D workstation.  ...  ACKNOWLEDGEMENTS We are grateful to Olivier Renault for his suggestions and help with the manuscript.  ... 
doi:10.1007/978-4-431-68123-6_20 fatcat:5n6gykxrabhqfgl4atwpc5jruy

Modeling Time's Arrow

Vishnu Jejjala, Michael Kavic, Djordje Minic, Chia-Hsiung Tze
2012 Entropy  
We discuss how the nonlinear dynamics of such a system provides a natural description for cosmological evolution in the early Universe.  ...  Quantum gravity, the initial low entropy state of the Universe, and the problem of time are interlocking puzzles.  ...  The work of VJ is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation.  ... 
doi:10.3390/e14040614 fatcat:odsgx64zwjhrxj6krfvn5qprom

Categories as mathematical models [article]

David I. Spivak
2015 arXiv   pre-print
A working definition of model is given, and several examples of mathematical objects, such as vector spaces, groups, and dynamical systems, are considered as categorical models.  ...  This project was supported by ONR grant N000141310260 and AFOSR grant FA9550-14-1-0031.  ...  I want to thank Allen Brown, Patrick Schultz, Tsung-Yun Tzeng, and Dmitry Vagner, as well as the referees, for their helpful comments on various drafts of this paper.  ... 
arXiv:1409.6067v3 fatcat:3snoiapex5hnhgw5bvq6iagbhq

Computation in Cellular Automata: A Selected Review [chapter]

Melanie Mitchell
2005 Non-Standard Computation  
Research Agency and the Office of Naval Research (N00014-95-1-0975).  ...  Acknowledgments Thanks to Jim Crutchfield, Howard Gutowitz, Jim Hanson, Chris Langton, Cris Moore, and Mats Nordahl for many discussions about cellular automata and for comments on an earlier draft of  ...  Parallel Formal-Language Recognition by Cellular Automata The study of formal-language recognition and generation has been a cornerstone of theoretical computer science, and the investigation of computational  ... 
doi:10.1002/3527602968.ch4 fatcat:6elcgxgiy5bjrencagl6uay2hq
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