Pathwise Sensitivity Analysis in Transient Regimes

The instantaneous relative entropy (IRE) and the corresponding instanta- neous Fisher information matrix (IFIM) for transient stochastic processes are pre- sented in this paper. These novel tools for sensitivity analysis of stochastic models serve as an extension of the well known relative entropy rate (RER) and the corre- sponding Fisher information matrix (FIM) that apply to stationary processes. Three cases are studied here, discrete-time Markov chains, continuous-time Markov chains and stochastic differential equations. A biological reaction network is presented as a demonstration numerical example

Structural identifiability of dynamic systems biology models

22 páginas, 5 figuras, 2 tablas.-- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.A powerful way of gaining insight into biological systems is by creating a nonlinear differential equation model, which usually contains many unknown parameters. Such a model is called structurally identifiable if it is possible to determine the values of its parameters from measurements of the model outputs. Structural identifiability is a prerequisite for parameter estimation, and should be assessed before exploiting a model. However, this analysis is seldom performed due to the high computational cost involved in the necessary symbolic calculations, which quickly becomes prohibitive as the problem size increases. In this paper we show how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability. We present results about models whose identifiability had not been previously determined, report unidentifiabilities that had not been found before, and show how to modify those unidentifiable models to make them identifiable. This method helps prevent problems caused by lack of identifiability analysis, which can compromise the success of tasks such as experiment design, parameter estimation, and model-based optimization. The procedure is called STRIKE-GOLDD (STRuctural Identifiability taKen as Extended-Generalized Observability with Lie Derivatives and Decomposition), and it is implemented in a MATLAB toolbox which is available as open source software. The broad applicability of this approach facilitates the analysis of the increasingly complex models used in systems biology and other areasAFV acknowledges funding from the Galician government (Xunta de Galiza, Consellería de Cultura, Educación e Ordenación Universitaria http://www.edu.xunta.es/portal/taxonomy/term/206) through the I2C postdoctoral program, fellowship ED481B2014/133-0. AB and AFV were partially supported by grant DPI2013-47100-C2-2-P from the Spanish Ministry of Economy and Competitiveness (MINECO). AFV acknowledges additional funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 686282 (CanPathPro). AP was partially supported through EPSRC projects EP/M002454/1 and EP/J012041/1.Peer reviewe

On parameter and structural identifiability: nonunique reconstructiability/observability for identifiable systems, other ambiguities and new definitions.

A number of inconsistencies, misunderstandings and ambiguities have arisen in the recent literature regarding identifiability concepts, evidenced in part by the number of "point-counterpoint" notes and comments published on this subject. It appears that the problem is due fundamentally to a lack of a unified set of definitions. A partially new, simple and hopefully complete set of definitions is proposed here for deterministic models. They are based on an extended model, termed the "constrained structure"-appropriate for complete analysis of identifiability properties of a system. They rely minimally on special jargon and are consistent with reported definitions for notions of stochastic identifiability. Relationships with other definitions are discussed and it is also shown that an important class of identifiable models are not necessarily uniquely observable/reconstructible. The latter problem has important implications in applications

Separating Shape Graphs

Abstract. Detailed memory models that expose individual fields are necessary to precisely analyze code that makes use of low-level aspects such as, pointers to fields and untagged unions. Yet, higher-level representations that collect fields into records are often used because they are typically more convenient and efficient in modeling the program heap. In this paper, we present a shape graph representation of memory that exposes individual fields while largely retaining the convenience of an object-level model. This representation has a close connection to particular kinds of formulas in separation logic. Then, with this representation, we show how to extend the Xisa shape analyzer for low-level aspects, including pointers to fields, C-style nested structures and unions, malloc and free, and array values, with minimal changes to the core algorithms (e.g., materialization and summarization).