A Fixed Point Framework for Recovering Signals from Nonlinear Transformations

A feature of the brain processing the visualization of objects is such that objects that are much farther away from the eye look smaller than closer objects to the eye. We show that a family of nonlinear transformations, also to be called compactifications, simulate qualitatively this property of keeping objects in perspective. These transformations project objects in a plane on a spherical shell. It is shown then that an observer located at a fixed point on the axis of the sphere visualizes the projected objects on the sphere in perspective. Namely, that objects that are farther away from the observation point seem smaller. Examples are provided. This is a departure from the traditional approaches using linearity and projections of objects from one plane into another plane.

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Mental equilibrium: Identifying fixed-point attractors in the stream of thought

PsycEXTRA Dataset ◽

10.1037/e633872013-031 ◽

2003 ◽

Author(s):

Robin R. Vallacher ◽

Andrzej Nowak ◽

Matthew Rockloff

Keyword(s):

Fixed Point

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ON THE RANDOM FIXED POINT THEOREMS IN ABSTRACT SPACE

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30707-0 ◽

1981 ◽

Vol 1 (2) ◽

pp. 133-144 ◽

Cited By ~ 2

Author(s):

Shaozhong Chen ◽

Zuoshu Liu

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Abstract Space ◽

Random Fixed Point

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Fixed point model for adaptive token passing bus protocol

IEE Proceedings E Computers and Digital Techniques ◽

10.1049/ip-e.1992.0007 ◽

1992 ◽

Vol 139 (1) ◽

pp. 50 ◽

Cited By ~ 2

Author(s):

P.G. Harrison ◽

F. Naraghi

Keyword(s):

Fixed Point ◽

Point Model ◽

Token Passing

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Bifurcation in a Simple Model of the Cardiovascular System

Methods of Information in Medicine ◽

10.1055/s-0038-1634285 ◽

2000 ◽

Vol 39 (02) ◽

pp. 118-121 ◽

Cited By ~ 5

Author(s):

S. Akselrod ◽

S. Eyal

Keyword(s):

Nonlinear Dynamics ◽

Blood Pressure ◽

Heart Rate ◽

Fixed Point ◽

Cardiovascular System ◽

Modified Model ◽

Mayer Waves ◽

Sustained Oscillations ◽

Human Cardiovascular System ◽

Physiological Values

Abstract:A simple nonlinear beat-to-beat model of the human cardiovascular system has been studied. The model, introduced by DeBoer et al. was a simplified linearized version. We present a modified model which allows to investigate the nonlinear dynamics of the cardiovascular system. We found that an increase in the -sympathetic gain, via a Hopf bifurcation, leads to sustained oscillations both in heart rate and blood pressure variables at about 0.1 Hz (Mayer waves). Similar oscillations were observed when increasing the -sympathetic gain or decreasing the vagal gain. Further changes of the gains, even beyond reasonable physiological values, did not reveal another bifurcation. The dynamics observed were thus either fixed point or limit cycle. Introducing respiration into the model showed entrainment between the respiration frequency and the Mayer waves.

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