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49
Stochastic Complexity Measures for Physiological Signal Analysis
, 1996
"... Traditional feature extraction methods describe signals in terms of amplitude and frequency. This paper takes a paradigm shift and investigates four stochastic complexity features. Their advantages are demonstrated on synthetic and physiological signals, the latter recorded during periods of Cheyne ..."
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Cited by 35 (16 self)
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Traditional feature extraction methods describe signals in terms of amplitude and frequency. This paper takes a paradigm shift and investigates four stochastic complexity features. Their advantages are demonstrated on synthetic and physiological signals, the latter recorded during periods of CheyneStokes respiration, anesthesia, sleep and motor cortex investigation. 1 Introduction Physiological signals have a wide variety of forms. To describe them traditional feature measures typically extract amplitude and frequency information. This makes comparison of signals which have different bandwidths difficult. In addition such measures do not allow comparison within subject groups as the absolute frequency of rhythms may differ from person to person and may depend on other factors such as patient sex and age. Hence, other methods are desirable. When visually inspecting signals, one of the first impressions they give to the observer is that of their `complexity'. Some signals seem to vary ...
A Study of the Passive Gait of a CompassLike Biped Robot: Symmetry and Chaos
 INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
, 1998
"... The focus of this work is a systematic study of the passive gait of a compasslike planar biped robot on inclined slopes. The robot is kinematically equivalent to a double pendulum, possessing two kneeless legs with point masses and a third point mass at the "hip" joint. Three parameters, namely the ..."
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Cited by 30 (4 self)
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The focus of this work is a systematic study of the passive gait of a compasslike planar biped robot on inclined slopes. The robot is kinematically equivalent to a double pendulum, possessing two kneeless legs with point masses and a third point mass at the "hip" joint. Three parameters, namely the ground slope angle and the normalized mass and length of the robot describe its gait. We show that in response to a continuous change in any one of its parameters the symmetric and steady stable gait of the unpowered robot gradually evolves through a regime of bifrcations characterized by progressively complicated asymmetric gaits eventually arriving at an apparently chaotic gait where no two steps are identical. The robot can maintain this gait indefinitely. A
Compasslike biped robot  Part I: Stability and bifurcation of passive gaits
, 1996
"... It is wellknown that a suitably designed unpowered mechanical biped robot can "walk" down an inclined plane with a steady gait. The characteristics of the gait (e.g., velocity, step period, step length) depend on the geometry and the inertial properties of the robot and the slope of the plane. The ..."
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Cited by 22 (4 self)
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It is wellknown that a suitably designed unpowered mechanical biped robot can "walk" down an inclined plane with a steady gait. The characteristics of the gait (e.g., velocity, step period, step length) depend on the geometry and the inertial properties of the robot and the slope of the plane. The energy required to maintain the steady motion comes from the conversion of the biped's gravitational potential energy as it descends. Investigation of such passive "natural" motions may potentially lead us to strategies useful for controlling active walking machines as well as to understand human locomotion. In this report we demonstrate the existence and the stability of symmetric and asymmetric passive gaits using a simple nonlinear biped robot model. Kinematically the robot is identical to a double pendulum (similar to the Acrobot and the Pendubot) and is able to walk with the socalled compass gait. We also identify perioddoubling bifurcation in this passive gait which eventually lead...
Nonlinear brain dynamics as macroscopic manifestation of underlying manybody dynamics
, 2006
"... ..."
Bifurcation and Chaos in a Simple Passive Bipedal Gait
 IEEE International Conference on Robotics and Automation
, 1997
"... This paper proposes an analysis of the behavior of perhaps the simplest biped robot: the compass gait model. It has been shown previously that such a robot can walk down a slope indefinitely without any actuation. Passive motions of this nature are of particular interest since they may lead us to st ..."
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Cited by 14 (1 self)
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This paper proposes an analysis of the behavior of perhaps the simplest biped robot: the compass gait model. It has been shown previously that such a robot can walk down a slope indefinitely without any actuation. Passive motions of this nature are of particular interest since they may lead us to strategies for controlling active walking machines as well as to a better understanding of human locomotion. We show here that, depending on the parameters of the system, passive compass gait may exhibit 1periodic, 2 n periodic and chaotic gaits proceeding from cascades of perioddoubling bifurcations. Since compass equations are quite involved (they combine nonlinear differential and algebraic equations in a 4dimensional space), our investigations rely, in part, on numerical simulations. 1 Motivation At the INRIA RhoneAlpes Laboratory of Grenoble, France, we are working on the development of an anthropomorphic biped walker. The envisioned prototype will have reasonable adaptation capabi...
Maximum entropy change and least action principle for nonequilibrium systems, Invited talk at the Twelfth United
 Nations/European Space Agency Workshop on Basic Space Science
, 2004
"... A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their actions, we show that the maximum path information leads to a path ..."
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Cited by 5 (3 self)
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A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their actions, we show that the maximum path information leads to a path probability distribution in exponentials of action. This means that the most probable paths are just the paths of least action. This distribution naturally leads to important laws of normal diffusion. A conclusion of this work is that, for probabilistic mechanics or irregular dynamics, the principle of maximization of path information is equivalent to the least action principle for regular dynamics. We also show that an average path information between the initial phase volume and the final phase volume can be related to the entropy change defined with natural invariant measure of dynamic system. Hence the principles of least action and maximum path information suggest the maximum entropy change. This result is used for some chaotic systems evolving in fractal phase space in order to derive their invariant measures. 1 1
A New Gait Parameterization Technique By Means of Cyclogram Moments: Application to human slope walking
"... A new parameterization technique for the systematic characterization of human walking gait in diverse external conditions is proposed in this work. By parameterization we mean a quantitative expression of certain gait descriptors as the function of an external parameter, such as the ground slope. Th ..."
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Cited by 4 (0 self)
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A new parameterization technique for the systematic characterization of human walking gait in diverse external conditions is proposed in this work. By parameterization we mean a quantitative expression of certain gait descriptors as the function of an external parameter, such as the ground slope. The mathematical quantities derived from the geometric features of the hipknee cyclograms are the main gait descriptors considered in this study. We demonstrate that these descriptors, expressed in a general setting as the geometric moments of the cyclogram contours, can meaningfully reflect the evolution of the gait kinematics on different slopes. We provide a new interpretation of the cyclogram perimeter and discover two potential invariants of slopewalking gait. Experimental slopewalking data obtained at 1 interval within the range of13 to +13 (+23.1%) on a variableinclination treadmill was used in this study.
On the Dynamics of a Vertically Driven Damped Planar Pendulum
"... The dynamics of the planar pendulum with parametric vertical timeperiodic forcing is considered. Analytical and numerical methods are employed to study the various dynamical features of the system. A rigorous analysis is presented in order to show that, in presence of friction, the upward equilibri ..."
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Cited by 4 (4 self)
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The dynamics of the planar pendulum with parametric vertical timeperiodic forcing is considered. Analytical and numerical methods are employed to study the various dynamical features of the system. A rigorous analysis is presented in order to show that, in presence of friction, the upward equilibrium position becomes asymptotically stable when the period of the forcing is below an appropriate threshold; this is illustrated by performing numerical computations and advanced visualization techniques. Also the dynamics of the system far from its equilibrium points is systematically investigated by using Poincare sections and phase portraits. The attractors and the associated basins of attraction are computed. Furthermore we calculate the Lyapunov exponents to show that for some parameter values the dynamics of the pendulum shows sensitivity to initial conditions. 1 Introduction Over the last decades parametrically excited nonlinear oscillators have begun to be extensively studied, both t...
On the Dynamics of P Systems
 PREPROCEEDINGS OF FIFTH WORKSHOP IN MEMBRANE COMPUTING, WMC5
, 2004
"... P systems are considered in the dynamical perspective of biological and biochemical systems. In this sense, the focus of computational processes is in their behavioral patterns rather than in their final states encoding answers to initial inputs. The framework of "state transition dynamics" is ou ..."
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Cited by 2 (0 self)
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P systems are considered in the dynamical perspective of biological and biochemical systems. In this sense, the focus of computational processes is in their behavioral patterns rather than in their final states encoding answers to initial inputs. The framework of "state transition dynamics" is outlined where general dynamical concepts are formulated in completely discrete terms. A metabolic algorithm is defined which computes the evolution of P systems when initial states and reaction parameters are given. This algorithm is applied to the analysis of important oscillatory phenomena of biological interest.
Information Dynamics In Physiological Control Systems
, 1997
"... Causality is often measured by means of the correlation function. This function has been shown to be restrictive at best and false at worst. The accurate determination of causal relationships is part of the content of this work. To measure associations, strategies and methods other than simple corre ..."
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Cited by 1 (1 self)
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Causality is often measured by means of the correlation function. This function has been shown to be restrictive at best and false at worst. The accurate determination of causal relationships is part of the content of this work. To measure associations, strategies and methods other than simple correlation are required. In the first part, signals of differing natures are translated into a common domain, known in pattern recognition as feature space. This allows the determination of association over a large number of signals. In the second part, states within the mapping space are determined using clustering methods to form symbol sequences. In the last part of the thesis, interactions are determined using both symbol sequences and unsegmented feature vectors. Interactions are estimated based on the correlation function and directed transinformation, which is a generalisation of the correlation measure. All procedures are applied not only to synthetic data but also to signal recordings ...