The Experts below are selected from a list of 37863 Experts worldwide ranked by ideXlab platform
L Dangio - One of the best experts on this subject based on the ideXlab platform.
-
daisy a new software tool to test global identifiability of biological and physiological systems
Computer Methods and Programs in Biomedicine, 2007Co-Authors: Giuseppina Bellu, Stefania Audoly, Maria Pia Saccomani, L DangioAbstract:A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a Differential Algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/.
-
parameter identifiability of nonlinear systems the role of initial conditions
Automatica, 2003Co-Authors: Maria Pia Saccomani, Stefania Audoly, L DangioAbstract:Identifiability is a fundamental prerequisite for model identification; it concerns uniqueness of the model parameters determined from the input-output data, under ideal conditions of noise-free observations and error-free model structure. In the late 1980s concepts of Differential Algebra have been introduced in control and system theory. Recently, Differential Algebra tools have been applied to study the identifiability of dynamic systems described by polynomial equations. These methods all exploit the characteristic set of the Differential ideal generated by the polynomials defining the system. In this paper, it will be shown that the identifiability test procedures based on Differential Algebra may fail for systems which are started at specific initial conditions and that this problem is strictly related to the accessibility of the system from the given initial conditions. In particular, when the system is not accessible from the given initial conditions, the ideal I having as generators the polynomials defining the dynamic system may not correctly describe the manifold of the solution. In this case a new ideal that includes all Differential polynomials vanishing at the solution of the dynamic system started from the initial conditions should be calculated. An identifiability test is proposed which works, under certain technical hypothesis, also for systems with specific initial conditions.
-
a new Differential Algebra algorithm to test identifiability of nonlinear systems with given initial conditions
Conference on Decision and Control, 2001Co-Authors: Pia M Saccomani, Stefania Audoly, Giuseppina Bellu, L DangioAbstract:A priori global identifiability is a fundamental prerequisite for model identification. It concerns uniqueness of the parametric structure of a dynamic model describing given input and output functions measured during an experiment. Assessing a priori global identifiability is particularly difficult for nonlinear dynamic models. Various approaches have been proposed in the literature, but no solution exists in the general case. The introduction of concepts of Differential Algebra and in particular the concept of characteristic set of a Differential ideal introduced by Ritt (1950) have proven very useful tools in identifiability analysis. Yet the construction of an efficient algorithm still remains a difficult task. An improvement on existing algorithms has been published by some of the present the authors (Saccomani et al., 2000). Unfortunately this algorithm, like all other algorithms based on Differential Algebra, may run into difficulties for systems which are started at certain specific initial conditions. We propose a new version of the algorithm which gives the correct answer even if the system is started at special states from which the accessibility property is not guaranteed.
-
global identifiability of nonlinear models of biological systems
IEEE Transactions on Biomedical Engineering, 2001Co-Authors: Stefania Audoly, Giuseppina Bellu, L Dangio, Maria Pia Saccomani, Claudio CobelliAbstract:A prerequisite for well-posedness of parameter estimation of biological and physiological systems is a priori global identifiability, a property which concerns uniqueness of the solution for the unknown model parameters. Assessing a priori global identifiability is particularly difficult for nonlinear dynamic models. Various approaches have been proposed in the literature but no solution exists in the general case. Here, the authors present a new algorithm for testing global identifiability of nonlinear dynamic models, based on Differential Algebra. The characteristic set associated to the dynamic equations is calculated in an efficient way and computer Algebra techniques are used to solve the resulting set of nonlinear Algebraic equations. The algorithm is capable of handling many features arising in biological system models, including zero initial conditions and time-varying parameters. Examples of usage of the algorithm for analyzing a priori global identifiability of nonlinear models of biological and physiological systems are presented.
Stefania Audoly - One of the best experts on this subject based on the ideXlab platform.
-
daisy a new software tool to test global identifiability of biological and physiological systems
Computer Methods and Programs in Biomedicine, 2007Co-Authors: Giuseppina Bellu, Stefania Audoly, Maria Pia Saccomani, L DangioAbstract:A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a Differential Algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/.
-
parameter identifiability of nonlinear systems the role of initial conditions
Automatica, 2003Co-Authors: Maria Pia Saccomani, Stefania Audoly, L DangioAbstract:Identifiability is a fundamental prerequisite for model identification; it concerns uniqueness of the model parameters determined from the input-output data, under ideal conditions of noise-free observations and error-free model structure. In the late 1980s concepts of Differential Algebra have been introduced in control and system theory. Recently, Differential Algebra tools have been applied to study the identifiability of dynamic systems described by polynomial equations. These methods all exploit the characteristic set of the Differential ideal generated by the polynomials defining the system. In this paper, it will be shown that the identifiability test procedures based on Differential Algebra may fail for systems which are started at specific initial conditions and that this problem is strictly related to the accessibility of the system from the given initial conditions. In particular, when the system is not accessible from the given initial conditions, the ideal I having as generators the polynomials defining the dynamic system may not correctly describe the manifold of the solution. In this case a new ideal that includes all Differential polynomials vanishing at the solution of the dynamic system started from the initial conditions should be calculated. An identifiability test is proposed which works, under certain technical hypothesis, also for systems with specific initial conditions.
-
a new Differential Algebra algorithm to test identifiability of nonlinear systems with given initial conditions
Conference on Decision and Control, 2001Co-Authors: Pia M Saccomani, Stefania Audoly, Giuseppina Bellu, L DangioAbstract:A priori global identifiability is a fundamental prerequisite for model identification. It concerns uniqueness of the parametric structure of a dynamic model describing given input and output functions measured during an experiment. Assessing a priori global identifiability is particularly difficult for nonlinear dynamic models. Various approaches have been proposed in the literature, but no solution exists in the general case. The introduction of concepts of Differential Algebra and in particular the concept of characteristic set of a Differential ideal introduced by Ritt (1950) have proven very useful tools in identifiability analysis. Yet the construction of an efficient algorithm still remains a difficult task. An improvement on existing algorithms has been published by some of the present the authors (Saccomani et al., 2000). Unfortunately this algorithm, like all other algorithms based on Differential Algebra, may run into difficulties for systems which are started at certain specific initial conditions. We propose a new version of the algorithm which gives the correct answer even if the system is started at special states from which the accessibility property is not guaranteed.
-
global identifiability of nonlinear models of biological systems
IEEE Transactions on Biomedical Engineering, 2001Co-Authors: Stefania Audoly, Giuseppina Bellu, L Dangio, Maria Pia Saccomani, Claudio CobelliAbstract:A prerequisite for well-posedness of parameter estimation of biological and physiological systems is a priori global identifiability, a property which concerns uniqueness of the solution for the unknown model parameters. Assessing a priori global identifiability is particularly difficult for nonlinear dynamic models. Various approaches have been proposed in the literature but no solution exists in the general case. Here, the authors present a new algorithm for testing global identifiability of nonlinear dynamic models, based on Differential Algebra. The characteristic set associated to the dynamic equations is calculated in an efficient way and computer Algebra techniques are used to solve the resulting set of nonlinear Algebraic equations. The algorithm is capable of handling many features arising in biological system models, including zero initial conditions and time-varying parameters. Examples of usage of the algorithm for analyzing a priori global identifiability of nonlinear models of biological and physiological systems are presented.
Maria Pia Saccomani - One of the best experts on this subject based on the ideXlab platform.
-
daisy a new software tool to test global identifiability of biological and physiological systems
Computer Methods and Programs in Biomedicine, 2007Co-Authors: Giuseppina Bellu, Stefania Audoly, Maria Pia Saccomani, L DangioAbstract:A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a Differential Algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/.
-
parameter identifiability of nonlinear systems the role of initial conditions
Automatica, 2003Co-Authors: Maria Pia Saccomani, Stefania Audoly, L DangioAbstract:Identifiability is a fundamental prerequisite for model identification; it concerns uniqueness of the model parameters determined from the input-output data, under ideal conditions of noise-free observations and error-free model structure. In the late 1980s concepts of Differential Algebra have been introduced in control and system theory. Recently, Differential Algebra tools have been applied to study the identifiability of dynamic systems described by polynomial equations. These methods all exploit the characteristic set of the Differential ideal generated by the polynomials defining the system. In this paper, it will be shown that the identifiability test procedures based on Differential Algebra may fail for systems which are started at specific initial conditions and that this problem is strictly related to the accessibility of the system from the given initial conditions. In particular, when the system is not accessible from the given initial conditions, the ideal I having as generators the polynomials defining the dynamic system may not correctly describe the manifold of the solution. In this case a new ideal that includes all Differential polynomials vanishing at the solution of the dynamic system started from the initial conditions should be calculated. An identifiability test is proposed which works, under certain technical hypothesis, also for systems with specific initial conditions.
-
global identifiability of nonlinear models of biological systems
IEEE Transactions on Biomedical Engineering, 2001Co-Authors: Stefania Audoly, Giuseppina Bellu, L Dangio, Maria Pia Saccomani, Claudio CobelliAbstract:A prerequisite for well-posedness of parameter estimation of biological and physiological systems is a priori global identifiability, a property which concerns uniqueness of the solution for the unknown model parameters. Assessing a priori global identifiability is particularly difficult for nonlinear dynamic models. Various approaches have been proposed in the literature but no solution exists in the general case. Here, the authors present a new algorithm for testing global identifiability of nonlinear dynamic models, based on Differential Algebra. The characteristic set associated to the dynamic equations is calculated in an efficient way and computer Algebra techniques are used to solve the resulting set of nonlinear Algebraic equations. The algorithm is capable of handling many features arising in biological system models, including zero initial conditions and time-varying parameters. Examples of usage of the algorithm for analyzing a priori global identifiability of nonlinear models of biological and physiological systems are presented.
Min Cheng - One of the best experts on this subject based on the ideXlab platform.
-
Differential Algebraic method for arbitrary order curvilinear-axis combined geometric-chromatic aberration analysis
Journal of Physics D: Applied Physics, 2003Co-Authors: Min Cheng, Tiantong Tang, Zhenhua YaoAbstract:The principle of Differential Algebra is applied to analyse and calculate arbitrary order curvilinear-axis combined geometric–chromatic aberrations of electron optical systems. Expressions of Differential Algebraic form of high order combined aberrations are obtained and arbitrary order combined aberrations can be calculated numerically. As an example, a typical wide electron beam focusing system with curved optical axes named magnetic immersion lens has been studied. All the second-order and third-order combined geometric–chromatic aberrations of the lens have been calculated, and the patterns of the corresponding geometric aberrations and combined aberrations have been given as well.
-
high order combined geometric chromatic aberrations of magnetic electron lenses using Differential Algebra
Journal of Physics D, 2002Co-Authors: Min Cheng, Tiantong TangAbstract:In this paper, high-order geometric and chromatic aberrations of magnetic electron lenses are dealt with together by using the Differential Algebraic method. High-order geometric-chromatic aberration analytic expressions are obtained and arbitrary order combined aberrations can be calculated. As an example, a Glaser's bell-shaped magnetic electron lens has been studied and the second- and third-order combined geometric-chromatic aberration coefficients have been calculated. The aberration figures of the combined second-order aberrations are also presented. This developed method can be of great utility in high-order combined aberration analysis and correction for high-resolution charged particle optical systems.
Zhenhua Yao - One of the best experts on this subject based on the ideXlab platform.
-
Differential Algebraic method for arbitrary order curvilinear-axis combined geometric-chromatic aberration analysis
Journal of Physics D: Applied Physics, 2003Co-Authors: Min Cheng, Tiantong Tang, Zhenhua YaoAbstract:The principle of Differential Algebra is applied to analyse and calculate arbitrary order curvilinear-axis combined geometric–chromatic aberrations of electron optical systems. Expressions of Differential Algebraic form of high order combined aberrations are obtained and arbitrary order combined aberrations can be calculated numerically. As an example, a typical wide electron beam focusing system with curved optical axes named magnetic immersion lens has been studied. All the second-order and third-order combined geometric–chromatic aberrations of the lens have been calculated, and the patterns of the corresponding geometric aberrations and combined aberrations have been given as well.