Towards an “Erlangen program” for general linear systems theory

2005 ◽  
pp. 32-51 ◽  
Author(s):  
R. Creutzburg ◽  
V. G. Labunets ◽  
E. V. Labunets
Keyword(s):  
Systems Theory ◽  
Linear Systems ◽  
General Linear ◽  
Erlangen Program

Towards an “Erlangen Program” for general linear systems theory

1994 ◽  
pp. 52-71
Author(s):  
Reiner Creutzburg ◽  
Valerij G. Labunets ◽  
Ekaterina V. Labunets
Keyword(s):  
Systems Theory ◽  
Linear Systems ◽  
General Linear ◽  
Erlangen Program

Linear Systems Theory

2018 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Systems Theory ◽  
Linear Systems

scholarly journals Validating Linear Systems Analysis for Laminar fMRI: Temporal Additivity for Stimulus Duration Manipulations

2020 ◽  
Author(s):  
Jelle A. van Dijk ◽  
Alessio Fracasso ◽  
Natalia Petridou ◽  
Serge O. Dumoulin
Keyword(s):  
Systems Theory ◽  
Linear Systems ◽  
Blood Oxygenation ◽  
Ultra High Field ◽  
Feedback Information ◽  
Oxygenation Level ◽  
Early Visual Cortex ◽  
Magnetic Resonance Imaging Mri ◽  
And Function ◽  
The Relationship

AbstractAdvancements in ultra-high field (7 T and higher) magnetic resonance imaging (MRI) scanners have made it possible to investigate both the structure and function of the human brain at a sub-millimeter scale. As neuronal feedforward and feedback information arrives in different layers, sub-millimeter functional MRI has the potential to uncover information processing between cortical micro-circuits across cortical depth, i.e. laminar fMRI. For nearly all conventional fMRI analyses, the main assumption is that the relationship between local neuronal activity and the blood oxygenation level dependent (BOLD) signal adheres to the principles of linear systems theory. For laminar fMRI, however, directional blood pooling across cortical depth stemming from the anatomy of the cortical vasculature, potentially violates these linear system assumptions, thereby complicating analysis and interpretation. Here we assess whether the temporal additivity requirement of linear systems theory holds for laminar fMRI. We measured responses elicited by viewing stimuli presented for different durations and evaluated how well the responses to shorter durations predicted those elicited by longer durations. We find that BOLD response predictions are consistently good predictors for observed responses, across all cortical depths, and in all measured visual field maps (V1, V2, and V3). Our results suggest that the temporal additivity assumption for linear systems theory holds for laminar fMRI. We thus show that the temporal additivity assumption holds across cortical depth for sub-millimeter gradient-echo BOLD fMRI in early visual cortex.

Teaching linear systems theory using Cramer's rule

1990 ◽  
Vol 33 (3) ◽  
pp. 258-267 ◽  
Author(s):  
R.E. Klein
Keyword(s):  
Systems Theory ◽  
Linear Systems ◽  
Cramer’S Rule

Generation of Synthetic Seismograms Using Linear Systems Theory

1971 ◽  
Vol 8 (11) ◽  
pp. 1409-1422 ◽  
Author(s):  
O. G. Jensen ◽  
R. M. Ellis
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Systems Theory ◽  
Linear Systems ◽  
Time Domain ◽  
Synthetic Seismograms ◽  
Elastic Wave Propagation ◽  
Arbitrary Angle ◽  
Teleseismic Events

The linear systems theory for elastic wave propagation in a multilayered crust has been extended to time domain solutions. Attenuation is specifically included. This direct time domain approach allows the computation of synthetic seismograms for P or SV waveforms incident at an arbitrary angle at the base of the crustal section. To demonstrate the utility of the technique, seismograms are computed for various conditions and comparisons made with teleseismic events recorded in central Alberta.

Observers in Linear Systems Theory

2015 ◽  
pp. 943-947
Author(s):  
A. Astolfi ◽  
Panos J. Antsaklis
Keyword(s):  
Systems Theory ◽  
Linear Systems

Realizations in Linear Systems Theory

2015 ◽  
pp. 1128-1132
Author(s):  
Panos J. Antsaklis ◽  
A. Astolfi
Keyword(s):  
Systems Theory ◽  
Linear Systems

scholarly journals Quantum Linear Systems Theory

2016 ◽  
Vol 8 (1) ◽  
pp. 67-93 ◽  
Author(s):  
Ian R. Petersen
Keyword(s):  
Systems Theory ◽  
Linear Systems

Distributed self-triggered control for coupled general linear systems via static output feedback

2015 ◽  
Author(s):  
Jianfeng Zhao ◽  
Linying Xiang ◽  
Fei Chen ◽  
Weiyao Lan
Keyword(s):  
Linear Systems ◽  
Output Feedback ◽  
General Linear ◽  
Static Output Feedback ◽  
Static Output
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