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Best causal mathematical models for a nonlinear system

2005
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IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications
*

His research interests are in the areas of

doi:10.1109/tcsi.2005.846673
fatcat:waayc333h5gidnll2mbo7oxhti
*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 ...##
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Causality and strict causality for symmetric bilinear systems

1978
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Journal of Mathematical Analysis and Applications
*

It is shown that if W is a symmetric bilinear operator on a Hilbert resolution space, then the

doi:10.1016/0022-247x(78)90173-7
fatcat:q4zfdfzcjrb2pe3wmb6rvuuntq
*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*. ...##
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Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
[article]

2020
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arXiv
*
pre-print

We give an elementary introduction to the

arXiv:1908.08451v3
fatcat:j6jyvjs4onbvtovh5u52l3cti4
*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. ...##
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Mathematical theory of multi-level systems
[chapter]

1971
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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. ...

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Causal Fermion Systems: An Overview
[chapter]

2016
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Quantum Mathematical Physics
*

The

doi:10.1007/978-3-319-26902-3_15
fatcat:lmbxwvxecreqln7fqpienoobpa
*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. ...##
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On the Mathematical Foundations of Causal Fermion Systems in Minkowski Spacetime
[article]

2019
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arXiv
*
pre-print

It is inferred that the corresponding

arXiv:1909.09229v1
fatcat:hkhjo76m4jctvnanfma64woziu
*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. ...##
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Causality of translation-invariant systems

1971
*
Journal of Mathematical Analysis and Applications
*

Our final result states that the

doi:10.1016/0022-247x(71)90046-1
fatcat:o55dabor7zf35pq7wynx7jnzdm
*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. ...##
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Nonmonotonic causal theories

2004
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Artificial Intelligence
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It has been applied to several challenge problems in the

doi:10.1016/j.artint.2002.12.001
fatcat:5a5hpw6i5jewdcyyk5vmkm2w2q
*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. ...##
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The causal theory revisited

2010
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Meta Science
*

This

doi:10.1007/s11016-010-9400-9
fatcat:ffuamd7lunh7jl76edoyucnhkq
*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*". ...##
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Theories of Causal Ordering
[chapter]

1990
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Readings in Qualitative Reasoning About Physical Systems
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*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 ...

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Relativity of Causal Structure in Quantum Theory
[article]

2012
*
arXiv
*
pre-print

We will thus say that in quantum

arXiv:1110.5561v4
fatcat:2wqqa6oa6vfhfjn74jn7lulmmm
*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 ...##
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Mythical systems: mathematic and logical theory

2014
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International Journal of General Systems
*

All mythical belief

doi:10.1080/03081079.2014.947977
fatcat:f6byvtp3l5cidnchzfvwibfsa4
*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. ...##
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Testing causal quantum theory

2018
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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 ...

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Lorentzian causality theory

2019
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Living Reviews in Relativity
*

I review Lorentzian

doi:10.1007/s41114-019-0019-x
fatcat:johcsxh52jhelg6hhybv27otki
*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 ...##
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Causality theory and multiplicative transformators

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

doi:10.1016/0022-247x(80)90089-x
fatcat:ohu6qisrr5bthckxhnogveenmu
*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 ...
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