Article
Finger tapping movements of Parkinson's disease patients automatically rated using nonlinear delay differential equations.
Institute for Neural Computation, University of California at San Diego, La Jolla, California 92093-0523, USA.
Chaos (Woodbury, N.Y.) (impact factor:
1.8).
03/2012;
22(1):013119.
DOI:10.1063/1.3683444
Source: PubMed
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Article: Relation between observability and differential embeddings for nonlinear dynamics.
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ABSTRACT: In the analysis of a scalar time series, which lies on an m-dimensional object, a great number of techniques will start by embedding such a time series in a d-dimensional space, with d>m. Therefore there is a coordinate transformation phi(s) from the original phase space to the embedded one. The embedding space depends on the observable s(t). In theory, the main results reached are valid regardless of s(t). In a number of practical situations, however, the choice of the observable does influence our ability to extract dynamical information from the embedded attractor. This may arise in problems in nonlinear dynamics such as model building, control and synchronization. To some degree, ease of success will depend on the choice of the observable simply because it is related to the observability of the dynamics. In this paper the observability matrix for nonlinear systems, which uses Lie derivatives, is revisited. It is shown that such a matrix can be interpreted as the Jacobian matrix of phi(s)--the map between the original phase space and the differential embedding induced by the observable--thus establishing a link between observability and embedding theory.Physical Review E 06/2005; 71(6 Pt 2):066213. · 2.26 Impact Factor -
Article: Frequently asked questions about global modeling.
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ABSTRACT: When a global model is attempted from experimental data, some preprocessing might be required. Therefore it is only natural to wonder what kind of effects the preprocessing might have on the modeling procedure. This concern is manifested in the form of recurrent frequently asked questions, such as "how does the preprocessing affect the underlying dynamics?" This paper aims at providing answers to important questions related to (i) data interpolation, (ii) data smoothing, (iii) data-estimated derivatives, (iv) model structure selection, and (v) model validation. The answers provided will hopefully remove some of those doubts and one shall be more confident not only on global modeling but also on various data analyses which may be also dependent on data preprocessing.Chaos (Woodbury, N.Y.) 07/2009; 19(2):023103. · 1.80 Impact Factor -
Article: Parkinsonism: onset, progression and mortality.
Neurology 06/1967; 17(5):427-42. · 8.31 Impact Factor
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Keywords
10-s bouts
algorithmic rating
algorithmic scores
clinical observations
degenerative condition
motor behaviors
neurological specialist
nonlinear delay differential equation
Parkinson's disease
Parkinson's patients
progression
severity
six-dimensional numerical descriptor
subjective ratings
time series
time-series
two sets
unified Parkinson's disease rating scale scores
uniformly
Yahr scale