Modeling and analysis of dynamic systems with the symbolic manipulation tool Pansym
Concise graphical and/or textual notations are ubiquitously used to represent the physical structure of dynamical systems. Each different notation can be normally translated directly into mathematical expressions of system equations that allow further application of general system theoretical results and techniques for the analysis and exploitation of the studied systems, e.g. stability, controllability, sensitivity with respect to parameters, identifiability, optimization, open- and closed-loop control, etc.
The most frequently applied symbolic manipulation is differentiation, which is readily available in modern simulation programs, such as Matlab/Simulink, which do however seldom provide the analytic expressions of the simulated systems.
With the aim to overcome this limitation, i.e. to make available in symbolic form the dynamic model equations starting from a structural representation of a system, the presented software tool PANSYM has been developed over the years as a marginal project to support modeling research on biomedical systems. Although mostly still in prototypal form, the software may become useful also to others because of some interesting and unique features regarding automatic generation of: (1) ODE model equations from multidisciplinary system representations (compartmental, electrical, biochemical, bondgraphs) (DAE are transformed into ODE by computer algebra); (2) sensitivity differential equations for dependable calculations instead of numerical differentiation; (3) adjoint differential equations arising from optimal control problems; (4) source code for: (a) numerical simulation exploiting multiprocessor architectures (Fortran); (b) documentation (Latex); (c) model simulation and identification ( R ). The ad hoc coding of new formatting routines for other applications, e.g. extended Kalman filtering, and programming languages, e.g. Matlab, C++, is feasible and little time-consuming.
Latest developments include: (i) identification of population models using advanced statistical approaches, such as Nonlinear Mixed Effects Models and Bayesian inference based on Markov Chain Monte Carlo; (ii) analysis of metabolic maps with generation of dynamic equations for selected pathways.
Future plans include modeling of isotopomer dynamics for studying substrate recycling in intermediate metabolism.
Date: 2008-Jul-24 Time: 10:00:00 Room: 336
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Workshop “Metabolism and mathematical models: Two for a tango” – 2nd Edition
Title: Workshop Metabolism and mathematical models: Two for a tango – 2nd Edition
Dates: October 25-26, 2022
Location: This workshop will be held in a virtual way
The topic of this workshop is metabolism in general, with a special focus, although not exclusive, on parasitology. Besides an exploration of the biological, biochemical and biomedical aspects, the workshop will also aim at presenting some of the mathematical modelling, algorithmic theory and software development that have become crucial to explore such aspects.
This workshop is being organised in the context of two projects, both with the Inria European Team Erable. One of the projects involves a partnership with the University of São Paulo (USP), in São Paulo, Brazil, more specifically the Institute of Mathematics and Statistics (IME) and the Institute of Biomedical Sciences – Inria Associated Team Capoeira – and the other involves the Inesc-ID/IST in Portugal, ETH in Zürich and EMBL in Heidelberg – H2020 Twinning Project Olissipo.
The workshop is open to all members of these two projects but also, importantly, to the community in general.
The program and more details are available here.