scholarly journals Random matrices and controllability of dynamical systems

2021 ◽  
Author(s):  
John Leventides ◽  
Nick Poulios ◽  
Costas Poulios
Keyword(s):  
Probability Theory ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Linear Systems ◽  
Random Matrices ◽  
Convex Geometry ◽  
Gaussian Orthogonal Ensemble

Abstract We introduce the concept of $\epsilon $-uncontrollability for random linear systems, i.e. linear systems in which the usual matrices have been replaced by random matrices. We also estimate the $\varepsilon $-uncontrollability in the case where the matrices come from the Gaussian orthogonal ensemble. Our proof utilizes tools from systems theory, probability theory and convex geometry.

Linear Systems Theory

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

The Non-Causal Character of Renormalization Group Explanations

2018 ◽  
Author(s):  
Margaret Morrison
Keyword(s):  
Probability Theory ◽  
Renormalization Group ◽  
Dynamical Systems ◽  
Recent Literature ◽  
Mathematical Explanation ◽  
Causal Status ◽  
Physical Information ◽  
The Relationship ◽  
Structural Aspects

After reviewing some of the recent literature on non-causal and mathematical explanation, this chapter develops an argument as to why renormalization group (RG) methods should be seen as providing non-causal, yet physical, information about certain kinds of systems/phenomena. The argument centres on the structural character of RG explanations and the relationship between RG and probability theory. These features are crucial for the claim that the non-causal status of RG explanations involves something different from simply ignoring or “averaging over” microphysical details—the kind of explanations common to statistical mechanics. The chapter concludes with a discussion of the role of RG in treating dynamical systems and how that role exemplifies the structural aspects of RG explanations which in turn exemplifies the non-causal features.

scholarly journals Some elements for a history of the dynamical systems theory

2021 ◽  
Vol 31 (5) ◽  
pp. 053110
Author(s):  
Christophe Letellier ◽  
Ralph Abraham ◽  
Dima L. Shepelyansky ◽  
Otto E. Rössler ◽  
Philip Holmes ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Dynamical Systems Theory ◽  
History Of

scholarly journals The Dynamics of Musical Participation

2021 ◽  
pp. 102986492098831
Author(s):  
Andrea Schiavio ◽  
Pieter-Jan Maes ◽  
Dylan van der Schyff
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Dynamical Systems Theory ◽  
Coordination Dynamics ◽  
Musical Experience ◽  
The Core ◽  
Interactive Dynamics ◽  
Interdisciplinary Scholarship ◽  
Core Features

In this paper we argue that our comprehension of musical participation—the complex network of interactive dynamics involved in collaborative musical experience—can benefit from an analysis inspired by the existing frameworks of dynamical systems theory and coordination dynamics. These approaches can offer novel theoretical tools to help music researchers describe a number of central aspects of joint musical experience in greater detail, such as prediction, adaptivity, social cohesion, reciprocity, and reward. While most musicians involved in collective forms of musicking already have some familiarity with these terms and their associated experiences, we currently lack an analytical vocabulary to approach them in a more targeted way. To fill this gap, we adopt insights from these frameworks to suggest that musical participation may be advantageously characterized as an open, non-equilibrium, dynamical system. In particular, we suggest that research informed by dynamical systems theory might stimulate new interdisciplinary scholarship at the crossroads of musicology, psychology, philosophy, and cognitive (neuro)science, pointing toward new understandings of the core features of musical participation.

scholarly journals Coevolving institutions and the paradox of informal constraints

2021 ◽  
pp. 1-20
Author(s):  
Daniel Seligson ◽  
Anne E. C. McCants
Keyword(s):  
Economic Growth ◽  
Game Theory ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Institutional Economics ◽  
Dynamical Systems Theory ◽  
New Institutional Economics ◽  
Long Run

Abstract We can all agree that institutions matter, though as to which institutions matter most, and how much any of them matter, the matter is, paraphrasing Douglass North's words at the Nobel podium, unresolved after seven decades of immense effort. We suggest that the obstacle to progress is the paradigm of the New Institutional Economics itself. In this paper, we propose a new theory that is: grounded in institutions as coevolving sources of economic growth rather than as rules constraining growth; and deployed in dynamical systems theory rather than game theory. We show that with our approach some long-standing problems are resolved, in particular, the paradoxical and perplexingly pervasive influence of informal constraints on the long-run character of economies.

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.

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