Systemic Modeling of Chaotic EEG During Human Sleep

2021 ◽  
Author(s):  
Mahmoud Alipour ◽  
Seyed Mohammad Reza Hashemi Gholpayeghani
Keyword(s):  
Phase Space ◽  
Sensitivity And Specificity ◽  
Chaotic Attractor ◽  
Sleep Cycle ◽  
Sleep Stages ◽  
Exponential Regression ◽  
Attractor Dynamic ◽  
Chaotic Nature ◽  
Definition Of ◽  
Geometric Changes

Abstract One of the most challenging discussions about EEG is the chaotic nature of this biological signal. In the present study, we attempt to provide an analysis to demonstrate sleep EEG chaoticity. We model changes of sleep attractor dynamic in phase space by exponential regression. Our model demonstrates that the sleep attractor is the sleep cycle attractor whose size shrinks during successive cycles by presenting a new definition of the sleep cycle. We study the EEG dynamics of different sleep stages by presenting two new features based on phase space properties. We show that each stage has a unique chaotic attractor. We model geometric changes of these attractors during successive sleep cycles. Our model achieves an accuracy, sensitivity, and specificity of 89.15%, 82.84%, and 81.62% classifying sleep stages.

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

Can early neurological improvement after mechanical thrombectomy be used as a surrogate for final stroke outcome?

2018 ◽  
Vol 11 (5) ◽  
pp. 450-454 ◽  
Author(s):  
Sebastien Soize ◽  
Guillaume Fabre ◽  
Matthias Gawlitza ◽  
Isabelle Serre ◽  
Serge Bakchine ◽  
...  
Keyword(s):  
Sensitivity And Specificity ◽  
Mechanical Thrombectomy ◽  
Characteristic Curve ◽  
Optimal Threshold ◽  
Future Research ◽  
Nihss Score ◽  
Neurological Improvement ◽  
Good Outcome ◽  
Optimal Thresholds ◽  
Definition Of

Background and purposeWe aimed to identify the best definition of early neurological improvement (ENI) at 2 and 24 hours after mechanical thrombectomy (MT) and determine its ability to predict a good functional outcome at 3 months.MethodsThis retrospective analysis was based on a prospectively collected registry of patients treated by MT for ischemic stroke from May 2010 to March 2017. We included patients treated with stent-retrievers with National Institute of Health Stroke Scale (NIHSS) score before treatment and at 2 and/or 24 hours after treatment and modified Rankin Score (mRS) at 3 months. Receiver operating characteristic curve analysis was performed to estimate optimal thresholds for ENI at 2 and 24 hours. The relationship between optimal ENI definitions and good outcome at 3 months (mRS 0–2) was assessed by logistic regression.ResultsThe analysis included 246 patients. At 2 hours, the optimal threshold to predict a good outcome at 3 months was improvementin the NIHSS score of >1 point (AUC 0.83,95% CI 0.77 to 0.87), with sensitivity and specificity 78.3% (62.2–85.7%) and 84.6% (77.2–90.3%), respectively, and OR 12.67 (95% CI 4.69 to 31.10, p<0.0001). At 24 hours, the optimal threshold was an improvementin the NIHSS score of >4 points (AUC 0.93, 95% CI 0.89 to 0.96), with sensitivity and specificity 93.8% (87.7–97.5%) and 83.2% (75.7–89.2%), respectively, and OR 391.32 (95% CI 44.43 to 3448.35, p<0.0001).ConclusionsENI 24 hours after thrombectomy appears to be a straightforward surrogate of long-term endpoints and may have value in future research.

scholarly journals A VARIATIONAL FORMULATION OF SYMPLECTIC NONCOMMUTATIVE MECHANICS

2007 ◽  
Vol 04 (05) ◽  
pp. 789-805 ◽  
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principle ◽  
Configuration Space ◽  
Variational Formulation ◽  
Noncommutative Space ◽  
First Order ◽  
Dynamical Properties ◽  
Definition Of ◽  
Space Noncommutativity

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity, we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [18]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

The Role of Neural Networks in Computerized Classification of the Electrocardiogram

2011 ◽  
pp. 60-80
Author(s):  
Chris D. Nugent ◽  
Dewar D. Finlay ◽  
Mark P. Donnelly ◽  
Norman D. Black
Keyword(s):  
Neural Networks ◽  
Research Effort ◽  
Body Surface Potential ◽  
Potential Mapping ◽  
Rule Set ◽  
Chaotic Nature ◽  
Definition Of ◽  
Cardiac Diagnosis ◽  
Electrocardiogram Ecg

Electrical forces generated by the heart are transmitted to the skin through the body’s tissues. These forces can be recorded on the body’s surface and are represented as an electrocardiogram (ECG). The ECG can be used to detect many cardiac abnormalities. Traditionally, ECG classification algorithms have used rule based techniques in an effort to model the thought and reasoning process of the human expert. However, the definition of an ultimate rule set for cardiac diagnosis has remained somewhat elusive, and much research effort has been directed at data driven techniques. Neural networks have emerged as a strong contender as the highly non-linear and chaotic nature of the ECG represents a well-suited application for this technique. This study presents an overview of the application of neural networks in the field of ECG classification, and, in addition, some preliminary results of adaptations of conventional neural classifiers are presented. From this work, it is possible to highlight issues that will affect the acceptance of this technique and, in addition, identify challenges faced for the future. The challenges can be found in the intelligent processing of larger amounts of ECG information which may be generated from recording techniques such as body surface potential mapping.

Nonlinear dynamics of forced transitional jets: periodic and chaotic attractors

1994 ◽  
Vol 263 ◽  
pp. 93-132 ◽  
Author(s):  
George Broze ◽  
Fazle Hussain
Keyword(s):  
Phase Diagram ◽  
Phase Space ◽  
Lyapunov Exponent ◽  
Conceptual Model ◽  
Chaotic Attractor ◽  
Excitation Frequency ◽  
Chaotic Attractors ◽  
Largest Lyapunov Exponent ◽  
Open Flow ◽  
Vortex Pairing

Conclusive experimental evidence is presented for the existence of a low-dimensional temporal dynamical system in an open flow, namely the near field of an axisymmetric, subsonic free jet. An initially laminar jet (4 cm air jet in the Reynolds number range 1.1 × 104 [Lt ] ReD × 9.1 × 104) with a top-hat profile was studied using single-frequency, longitudinal, bulk excitation. Two non-dimensional control parameters – forcing frequency StD (≡fexD/Ue, where fez is the excitation frequency, D is the jet exit diameter and Ue is the exit velocity) and forcing amplitude af (≡ u’f/Ue, where u’f is the jet exit r.m.s. longitudinal velocity fluctuation at the excitation frequency) – were varied over the ranges 10-4 < af < 0.3 and 0.3 < StD < 3.0 in order to construct a phase diagram. Periodic and chaotic states were found over large domains of the parameter space. The periodic attractors correspond to stable pairing (SP) and stable double pairing (SDP) of rolled-up vortices. One chaotic attractor, near SP in the parameter space, results from nearly periodic modulations of pairing (NPMP) of vortices. At large scales (i.e. approximately the size of the attractor) in phase space, NPMP exhibits approximately quasi-periodic behaviour, including modulation sidebands around ½fex in u-spectra, large closed loops in its Poincaré sections, correlation dimension v ∼ 2 and largest Lyapunov exponent λ1 ∼ 0. But investigations at smaller scales (i.e. distances greater than, but of the order of, trajectory separation) in phase space reveal chaos, as shown by v > 2 and λ1 > 0. The other chaotic attractor, near SDP, results from nearly periodic modulations of the first vortex pairing but chaotic modulations of the second pairing and has a broadband spectrum, a dimension 2.5 [Lt ] v [Lt ] 3 and the largest Lyapunov exponent 0.2 [Lt ] λ1 [Lt ] 0.7 bits per orbit (depending on measurement locations in physical and parameter spaces).A definition that distinguishes between physically and dynamically open flows is proposed and justified by our experimental results. The most important conclusion of this study is that a physically open flow, even one that is apparently dynamically open due to convective instability, can exhibit dynamically closed behaviour as a result of feedback. A conceptual model for transitional jets is proposed based on twodimensional instabilities, subharmonic resonance and feedback from downstream vortical structures to the nozzle lip. Feedback was quantified and shown to affect the exit fundamental–subharmonic phase difference ϕ – a crucial variable in subharmonic resonance and, hence, vortex pairing. The effect of feedback, the sensitivity of pairings to ϕ, the phase diagram, and the documented periodic and chaotic attractors demonstrate the validity of the proposed conceptual model.

scholarly journals Dynamics and Control of Humanoid Robots: A Geometrical Approach

2010 ◽  
Vol 1 (4) ◽  
Author(s):  
Vladimir G. Ivancevic ◽  
Tijana T. Ivancevic
Keyword(s):  
Phase Space ◽  
Hamiltonian Dynamics ◽  
Fitness Function ◽  
Hamiltonian Formalism ◽  
Humanoid Robots ◽  
Geometrical Approach ◽  
Dynamics And Control ◽  
Definition Of ◽  
Configuration Manifold ◽  
And Control

AbstractThis paper reviews modern geometrical dynamics and control of humanoid robots. This general Lagrangian and Hamiltonian formalism starts with a proper definition of humanoid's configuration manifold, which is a set of all robot's active joint angles. Based on the ‘covariant force law’, the general humanoid's dynamics and control are developed. Autonomous Lagrangian dynamics is formulated on the associated ‘humanoid velocity phase space’, while autonomous Hamiltonian dynamics is formulated on the associated ‘humanoid momentum phase space’. Neural-like hierarchical humanoid control naturally follows this geometrical prescription. This purely rotational and autonomous dynamics and control is then generalized into the framework of modern non-autonomous biomechanics, defining the Hamiltonian fitness function. The paper concludes with several simulation examples.

scholarly journals Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime

2017 ◽  
Vol 29 (04) ◽  
pp. 1750014 ◽  
Author(s):  
Michał Wrochna ◽  
Jochen Zahn
Keyword(s):  
Phase Space ◽  
Cauchy Surface ◽  
Gauge Field Theories ◽  
Subsidiary Condition ◽  
Yang Mills ◽  
Special Cases ◽  
Hadamard States ◽  
Hyperbolic Spacetimes ◽  
Definition Of ◽  
Classical Phase Space

We investigate linearized gauge theories on globally hyperbolic spacetimes in the BRST formalism. A consistent definition of the classical phase space and of its Cauchy surface analogue is proposed. We prove that it is isomorphic to the phase space in the ‘subsidiary condition’ approach of Hack and Schenkel in the case of Maxwell, Yang–Mills, and Rarita–Schwinger fields. Defining Hadamard states in the BRST formalism in a standard way, their existence in the Maxwell and Yang–Mills case is concluded from known results in the subsidiary condition (or Gupta–Bleuler) formalism. Within our framework, we also formulate criteria for non-degeneracy of the phase space in terms of BRST cohomology and discuss special cases. These include an example in the Yang–Mills case, where degeneracy is not related to a non-trivial topology of the Cauchy surface.

scholarly journals CANONICAL TRANSFORMATIONS IN THREE-DIMENSIONAL PHASE-SPACE

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4769-4788 ◽  
Author(s):  
TEKİN DERELİ ◽  
ADNAN TEĞMEN ◽  
TUĞRUL HAKİOĞLU
Keyword(s):  
Phase Space ◽  
Canonical Transformation ◽  
Generating Functions ◽  
General Framework ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Canonical Transformations ◽  
Dimensional Phase Space ◽  
Nambu Bracket ◽  
Definition Of

Canonical transformation in a three-dimensional phase-space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed. Finally, we show that the decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.

Nasal Endoscopy and the Definition and Diagnosis of Chronic Rhinosinusitis

2002 ◽  
Vol 126 (6) ◽  
pp. 623-627 ◽  
Author(s):  
James A. Stankiewicz ◽  
James M. Chow
Keyword(s):  
Computed Tomography ◽  
Chronic Rhinosinusitis ◽  
Sensitivity And Specificity ◽  
Nasal Polyps ◽  
Ct Scanning ◽  
Current Treatment ◽  
Current Definition ◽  
Treatment Paradigm ◽  
Definition Of ◽  
High Degree

OBJECTIVES: Although endoscopy has been shown by a few authors to be a valuable tool for the diagnosis of chronic rhinosinusitis, its true role in the evaluation of the patient with chronic rhinosinusitis has not been elucidated. The current definition of chronic rhinosinusitis is a symptom-based definition, and objective testing such as endoscopy or computed tomography (CT) is not included. However, the current treatment paradigm for chronic rhinosinusitis is dependent on the definition for diagnosis. Patients are treated with 4 weeks of antibiotics and decongestant/antihistamines/steroids based on the definition. This study aims to evaluate in a prospective fashion the place of endoscopy in the diagnosis of chronic rhinosinusitis. STUDY DESIGN: A group of 78 patients meeting the definition of chronic rhinosinusitis were subjected to same-day endoscopy and CT scanning. RESULTS: Seventeen (22%) of 78 patients had positive endoscopic and CT results. There were 20 (26%) of 78 patients with negative endoscopic and positive CT results. Six (8%) patients had positive endoscopic and negative CT results, and 35 (45%) had negative endoscopic and negative CT results. Overall, 37 (47%) patients had positive CT results, and 41 (53%) patients had negative CT results. Endoscopy showing the presence of purulence, nasal polyps, or watery congested mucosa correlated well with CT results. Negative endoscopy correlated with CT results in 65% of patients. CONCLUSION: The use of endoscopy to corroborate the diagnosis in nonpolypoid or nonpurulent rhinosinusitis in previously unoperated patients is questioned. Patients who meet the subjective definition of chronic rhinosinusitis should have a high degree of sensitivity and specificity with endoscopy or CT. The fact this is not the case questions the accuracy of the definition and the treatment paradigm. SIGNIFICANCE: According to this study, positive endoscopic results correlated well with CT, and negative endoscopic results correlated in 71% of patients with negative CT results.

Sign in / Sign up

Export Citation Format

Share Document