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Best causal mathematical models for a nonlinear system

A. Torokhti, P. Howlett, C. Pearce
2005 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
His research interests are in the areas of mathematical modelling of nonlinear systems, mathematical signal processing, operator approximation, applied statistics, and operator equations.  ...  Anatoli Torokhti is an Associate Professor at the School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA, Australia.  ...  Best Causal Mathematical Models for a Nonlinear System Anatoli Torokhti, Phil Howlett, and Charles Pearce Abstract-We provide new causal mathematical models of a nonlinear system which are specifications  ... 
doi:10.1109/tcsi.2005.846673 fatcat:waayc333h5gidnll2mbo7oxhti

Causality and strict causality for symmetric bilinear systems

Avraham Feintuch
1978 Journal of Mathematical Analysis and Applications  
It is shown that if W is a symmetric bilinear operator on a Hilbert resolution space, then the causality and strict causality of W is equivalent to the causality and strict causality of the bipower map  ...  INTRODUCTION Due to the great success in the theory of causality and stability of linear inputoutput systems (see [S, 6, 7] ), in recent years attempts have been made to extends parts of this theory to  ...  nonlinear systems.  ... 
doi:10.1016/0022-247x(78)90173-7 fatcat:q4zfdfzcjrb2pe3wmb6rvuuntq

Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts [article]

Felix Finster, Maximilian Jokel
2020 arXiv   pre-print
We give an elementary introduction to the theory of causal fermion systems, with a focus on the underlying physical ideas and the conceptual and mathematical foundations.  ...  Acknowledgments: We would like to thank the participants of the conference "Progress and visions in quantum theory in view of gravity" held in Leipzig in October 2018 for fruitful and inspiring discussions  ...  Causal fermion systems provide a mathematically consistent theory which gives General Relativity and Quantum Theory as limiting cases.  ... 
arXiv:1908.08451v3 fatcat:j6jyvjs4onbvtovh5u52l3cti4

Mathematical theory of multi-level systems [chapter]

M. D. Mesarović
1971 Lecture notes in mathematics  
theory. (9) Mathematical theory of multi-level systems M.D.  ...  A mathematical theory of co-ordination for systems described in Banach spaces is presented.  ... 
doi:10.1007/bfb0070126 fatcat:nhqicx6b6zfk3j4sdokmyvk3bm

Causal Fermion Systems: An Overview [chapter]

Felix Finster
2016 Quantum Mathematical Physics  
The theory of causal fermion systems is an approach to describe fundamental physics. We here introduce the mathematical framework and give an overview of the objectives and current results.  ...  The theory of causal fermion systems is an approach to describe fundamental physics.  ...  Causal fermion systems evolved from an attempt to combine several physical principles in a coherent mathematical framework.  ... 
doi:10.1007/978-3-319-26902-3_15 fatcat:lmbxwvxecreqln7fqpienoobpa

On the Mathematical Foundations of Causal Fermion Systems in Minkowski Spacetime [article]

Marco Oppio
2019 arXiv   pre-print
It is inferred that the corresponding causal fermion systems are regular and have a smooth manifold structure.  ...  The emergence of the concept of a causal fermion system is revisited and further investigated for the vacuum Dirac equation in Minkowski spacetime.  ...  The general mathematical set-up of the theory In this section we introduce the basic set-up of the theory, together with all the main mathematical objects of interest.  ... 
arXiv:1909.09229v1 fatcat:hkhjo76m4jctvnanfma64woziu

Causality of translation-invariant systems

V.K Balakrishnan
1971 Journal of Mathematical Analysis and Applications  
Our final result states that the system is causal if the system function when regularized in a particular way is a vector-valued entire function satisfying certain growth conditions.  ...  INTRODUCTION The purpose of this paper is to obtain a complete frequency-domain characterization for the causality of a linear system which is not necessarily passive.  ... 
doi:10.1016/0022-247x(71)90046-1 fatcat:o55dabor7zf35pq7wynx7jnzdm

Nonmonotonic causal theories

Enrico Giunchiglia, Joohyung Lee, Vladimir Lifschitz, Norman McCain, Hudson Turner
2004 Artificial Intelligence  
It has been applied to several challenge problems in the theory of commonsense knowledge.  ...  We study the relationship between this formalism and other work on nonmonotonic reasoning and knowledge representation, and discuss its implementation, called the Causal Calculator.  ...  Fig. 1 . 1 The transition system corresponding to the causal theories SD m . For any action description D and any nonnegative integer m, the causal theory D m is defined as follows.  ... 
doi:10.1016/j.artint.2002.12.001 fatcat:5a5hpw6i5jewdcyyk5vmkm2w2q

The causal theory revisited

Ward Struyve
2010 Meta Science  
This theory forms the subject of Riggs' book "Quantum Causality".  ...  The de Broglie-Bohm theory, or Causal Theory as Riggs prefers to call it, is a theory about particles that follow trajectories in a deterministic way, influenced by the wavefunction.  ...  This theory forms the subject of Riggs' book "Quantum Causality".  ... 
doi:10.1007/s11016-010-9400-9 fatcat:ffuamd7lunh7jl76edoyucnhkq

Theories of Causal Ordering [chapter]

Johan de Kleer, John Seely Brown
1990 Readings in Qualitative Reasoning About Physical Systems  
Causal ordering is a general technique not out/v applicable to qualitative reasoning.  ...  However, when feedback is present, our qualitative physics determines a causal ordering around feedback loops as well.  ...  Distributed systems, such as airplane wings, the weather. flow in a river, 1is the better reference on causal ordcring THEORIES OF CAUSAL ORDERING 35 are characterized by partial differential equations  ... 
doi:10.1016/b978-1-4832-1447-4.50068-7 fatcat:4vus7whbjrcrbcqe3b3aghwaxa

Relativity of Causal Structure in Quantum Theory [article]

Marco Zaopo
2012 arXiv   pre-print
We will thus say that in quantum theory we have relativity of causal structure.  ...  Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time.  ...  It suggests that to formulate a properly quantum theory of cosmological processes, we should look for a mathematical formalism to calculate probabilities of these processes such that the causal structure  ... 
arXiv:1110.5561v4 fatcat:2wqqa6oa6vfhfjn74jn7lulmmm

Mythical systems: mathematic and logical theory

J. Nescolarde-Selva, J.L. Usó-Doménech, M. Lloret-Climent
2014 International Journal of General Systems  
All mythical belief systems have a numinous-religious nature.  ...  Human society is a multilevel system with a material structure (society), an ideological superstructure (belief systems, values, etc) and a supersuperstructure with two parts: mythical (origin and justification  ...  However, as Schweder (1977) had pointed out the human mind is inclined to seek connections between events where there is no good evidence for a causal connection.  ... 
doi:10.1080/03081079.2014.947977 fatcat:f6byvtp3l5cidnchzfvwibfsa4

Testing causal quantum theory

Adrian Kent
2018 Proceedings of the Royal Society A  
Causal quantum theory assumes that measurements or collapses are well-defined physical processes, localized in space-time, and never give perfectly reliable outcomes and that the outcome of one measurement  ...  Although the theory has unusual properties, it is not immediately evident that it is inconsistent with experiment to date. I discuss its implications and experimental tests.  ...  First, we accept the empirical success of non-relativistic quantum theory when dealing with individual systems, and take this as evidence that the basic mathematical formalism of quantum theory is an essential  ... 
doi:10.1098/rspa.2018.0501 pmid:30602934 pmcid:PMC6304019 fatcat:mlp7h4bkgnby7cwu24w5mfny3m

Lorentzian causality theory

E. Minguzzi
2019 Living Reviews in Relativity  
I review Lorentzian causality theory paying particular attention to the optimality and generality of the presented results.  ...  The paper is almost self-contained thanks to a systematic logical exposition of the many different topics that compose the theory.  ...  This rather abstract point of view does a good job in mathematically framing Causality Theory but provides little insights on the motivations that brought researchers from mathematical relativity to its  ... 
doi:10.1007/s41114-019-0019-x fatcat:johcsxh52jhelg6hhybv27otki

Causality theory and multiplicative transformators

R.M De Santis, A Feintuch
1980 Journal of Mathematical Analysis and Applications  
The concept of a multiplicative transforrnator formalized by Brodskii, Gokhberg, and Krein in a by now classical 1967 paper can play in causality theory a role similar to that played by the more familiar  ...  inds an alternative point of view (a system cascade connection representation in lieu of a parallel connection), a more compact formulation of some proofs and results, a natural tool for a generalization  ...  The question of the canonical causality decomposition, the connections between causality and other system theoretic concepts, the causality of the inverse of a causal system, have, for instance, all been  ... 
doi:10.1016/0022-247x(80)90089-x fatcat:ohu6qisrr5bthckxhnogveenmu
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