2,367 research outputs found
Observability and Structural Identifiability of Nonlinear Biological Systems
Observability is a modelling property that describes the possibility of
inferring the internal state of a system from observations of its output. A
related property, structural identifiability, refers to the theoretical
possibility of determining the parameter values from the output. In fact,
structural identifiability becomes a particular case of observability if the
parameters are considered as constant state variables. It is possible to
simultaneously analyse the observability and structural identifiability of a
model using the conceptual tools of differential geometry. Many complex
biological processes can be described by systems of nonlinear ordinary
differential equations, and can therefore be analysed with this approach. The
purpose of this review article is threefold: (I) to serve as a tutorial on
observability and structural identifiability of nonlinear systems, using the
differential geometry approach for their analysis; (II) to review recent
advances in the field; and (III) to identify open problems and suggest new
avenues for research in this area.Comment: Accepted for publication in the special issue "Computational Methods
for Identification and Modelling of Complex Biological Systems" of Complexit
Dynamical compensation and structural identifiability: analysis, implications, and reconciliation
The concept of dynamical compensation has been recently introduced to
describe the ability of a biological system to keep its output dynamics
unchanged in the face of varying parameters. Here we show that, according to
its original definition, dynamical compensation is equivalent to lack of
structural identifiability. This is relevant if model parameters need to be
estimated, which is often the case in biological modelling. This realization
prompts us to warn that care should we taken when using an unidentifiable model
to extract biological insight: the estimated values of structurally
unidentifiable parameters are meaningless, and model predictions about
unmeasured state variables can be wrong. Taking this into account, we explore
alternative definitions of dynamical compensation that do not necessarily imply
structural unidentifiability. Accordingly, we show different ways in which a
model can be made identifiable while exhibiting dynamical compensation. Our
analyses enable the use of the new concept of dynamical compensation in the
context of parameter identification, and reconcile it with the desirable
property of structural identifiability
Consistency of maximum likelihood estimation for some dynamical systems
We consider the asymptotic consistency of maximum likelihood parameter
estimation for dynamical systems observed with noise. Under suitable conditions
on the dynamical systems and the observations, we show that maximum likelihood
parameter estimation is consistent. Our proof involves ideas from both
information theory and dynamical systems. Furthermore, we show how some
well-studied properties of dynamical systems imply the general statistical
properties related to maximum likelihood estimation. Finally, we exhibit
classical families of dynamical systems for which maximum likelihood estimation
is consistent. Examples include shifts of finite type with Gibbs measures and
Axiom A attractors with SRB measures.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1259 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Identification of cellular automata: theoretical remarks
Land use evolution during forty years in a large set of European cities is analysed by means of a cellular automaton. In one hand (the operational level), the use of this modelling tool allows: a: to study the transition rules in land use and the proximity effects on these rules; b: to compare the different case -studies, otherwise very difficult to be confronted; c: to define scenarios of evolution, on the bases of the past trends. On the other hand (methodological level), availability of a large data-base (significant time series for a set of comparable cases) allows: a: to manage, in a scientific way, the problem of calibration and validation of a cellular automaton (a crucial problem - we have to blame - usually neglected in territorial applications); b: to verify, empirically, potentialities and limits of cellular automata, compared to other models for the analysis of spatial dynamics.
A study of parameter identification
A set of definitions for deterministic parameter identification ability were proposed. Deterministic parameter identificability properties are presented based on four system characteristics: direct parameter recoverability, properties of the system transfer function, properties of output distinguishability, and uniqueness properties of a quadratic cost functional. Stochastic parameter identifiability was defined in terms of the existence of an estimation sequence for the unknown parameters which is consistent in probability. Stochastic parameter identifiability properties are presented based on the following characteristics: convergence properties of the maximum likelihood estimate, properties of the joint probability density functions of the observations, and properties of the information matrix
A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone
Recommended standardized procedures for determining exhaled lower respiratory
nitric oxide and nasal nitric oxide have been developed by task forces of the
European Respiratory Society and the American Thoracic Society. These
recommendations have paved the way for the measurement of nitric oxide to
become a diagnostic tool for specific clinical applications. It would be
desirable to develop similar guidelines for the sampling of other trace gases
in exhaled breath, especially volatile organic compounds (VOCs) which reflect
ongoing metabolism. The concentrations of water-soluble, blood-borne substances
in exhaled breath are influenced by: (i) breathing patterns affecting gas
exchange in the conducting airways; (ii) the concentrations in the
tracheo-bronchial lining fluid; (iii) the alveolar and systemic concentrations
of the compound. The classical Farhi equation takes only the alveolar
concentrations into account. Real-time measurements of acetone in end-tidal
breath under an ergometer challenge show characteristics which cannot be
explained within the Farhi setting. Here we develop a compartment model that
reliably captures these profiles and is capable of relating breath to the
systemic concentrations of acetone. By comparison with experimental data it is
inferred that the major part of variability in breath acetone concentrations
(e.g., in response to moderate exercise or altered breathing patterns) can be
attributed to airway gas exchange, with minimal changes of the underlying blood
and tissue concentrations. Moreover, it is deduced that measured end-tidal
breath concentrations of acetone determined during resting conditions and free
breathing will be rather poor indicators for endogenous levels. Particularly,
the current formulation includes the classical Farhi and the Scheid series
inhomogeneity model as special limiting cases.Comment: 38 page
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