My Way in Mathematics: From Ergodic Theory Through Scattering to J-inner Matrix Functions and Passive Linear Systems Theory

2016 ◽  
pp. 1-25
Author(s):  
Damir Z. Arov
Keyword(s):  
Systems Theory ◽  
Linear Systems ◽  
Ergodic Theory ◽  
Matrix Functions

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.

scholarly journals Category Theory for Autonomous and Networked Dynamical Systems

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 302 ◽  
Author(s):  
Jean-Charles Delvenne
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Ergodic Theory ◽  
Category Theory ◽  
Open Systems ◽  
Topological Dynamics ◽  
Control Problems ◽  
Natural Conditions ◽  
Discussion Paper ◽  
Open Systems Theory

In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions. We also provide a purely categorical proof of the existence of the maximal equicontinuous factor in topological dynamics. We then show how to define open systems (that can interact with their environment), interconnect them, and define control problems for them in a unified way.

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

Fourier Analysis in Systems Theory

2009 ◽  
Author(s):  
Robert J Marks II
Keyword(s):  
Fourier Analysis ◽  
Systems Theory ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Homogeneous Systems ◽  
Single Output ◽  
System Operator ◽  
Single Input ◽  
Necessary And Sufficient

In the most general sense, any process wherein a stimulus generates a corresponding response can be dubbed a system. For a temporal system with single input, f (t), and single output, g(t), the relation can be written as . . . g(t) = S{ f (t)} (3.1) . . . where S{·} is the system operator. This is illustrated in Figure 3.1. There exist numerous system types. We define them here in terms of continuous signals. The equivalents in discrete time are given as an exercise. For homogeneous systems, amplifying or attenuating the input likewise amplifying or attenuating the output. For any constant, a,. . . S{a f(t)} = aS{ f (t)} (3.2) If the response of the sum is the sum of the responses, the system is said to be additive. Specifically,. . . S{ f1(t) + f2(t)} = S{ f1(t)} + S{ f2(t)} (3.3) . . . Systems that are both homogeneous and additive are said to be linear. The criteria in (3.2) and (3.3) can be combined into a single necessary and sufficient condition for linearity.. . . S{a f1(t) + bf2(t)} = aS{ f1(t)} + bS{ f2(t)} (3.4) . . . where a and b are constants. All linear systems produce a zero output when the input is zero. . . . S{0} = 0. (3.5). . . To show this, we use (3.4) with a = −b and f1(t) = f2(t). Note that, because of (3.5), the system defined by . . . g(t) = b f(t) + c . . . where b and c¹ 0 are constants, is not linear. It is not homogeneous since . . . S{a f} = b f + c ≠aS{ f} = a (b f + c) .

scholarly journals Characterization of toxicokinetics and toxicodynamics with linear systems theory: application to lead-associated cognitive decline.

2001 ◽  
Vol 109 (4) ◽  
pp. 361-368 ◽  
Author(s):  
J M Links ◽  
B S Schwartz ◽  
D Simon ◽  
K Bandeen-Roche ◽  
W F Stewart
Keyword(s):  
Cognitive Decline ◽  
Systems Theory ◽  
Linear Systems ◽  
Theory Application
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