Reverse-engineering of polynomial dynamical systems

Jarrah, Abdul Salam; Laubenbacher, Reinhard; Stigler, Brandilyn; Stillman, Michael

doi:10.1016/j.aam.2006.08.004

Cited by 78 publications

(91 citation statements)

References 16 publications

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“…Network of ecological interactions inferred for the Culicidae subnetwork from Table 1. Filled edges represent edges that are found in both, the subnetwork built in (Zhang 2007) and ( Jarrah et al 2007); dashed edges represent the relationships found in but not in (Zhang 2007); white edges represent edges missing in ( Jarrah et al 2007) from those found in (Zhang 2007). …”

Section: Contribution Of Mathematical Inference Methodsmentioning

confidence: 99%

Inference of Ecological Interaction Networks

Vera-Licona

Laubenbacher

2008

Annales Zoologici Fennici

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The inference of the interactions between organisms in an ecosystem from observational data is an important problem in ecology. This paper presents a mathematical inference method, originally developed for the inference of biochemical networks in molecular biology, adapted for the inference of networks of ecological interactions. The method is applied to a network of invertebrate families (taxa) in a rice field.

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Section: Contribution Of Mathematical Inference Methodsmentioning

confidence: 99%

Inference of Ecological Interaction Networks

Vera-Licona

Laubenbacher

2008

Annales Zoologici Fennici

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“…Reconstruction of dynamical systems from time series data is an important and common challenge in a wide range of research fields [2,3,5,6,9,[21][22][23]30,41,45]. In this task, dynamical systems are typically described by the following n-dimensional system of autonomous ordinary differential equations (ODEs):…”

Section: Introductionmentioning

confidence: 99%

“…, x n ) ∈ R n . Many models of f i exist, and polynomial dynamical systems (PDSs) have been extensively studied [6,18,22,[30][31][32]43,47]. In this case, f i are described by polynomials (i.e., linear combinations of monomials).…”

Section: Introductionmentioning

confidence: 99%

“…In recent studies, computational algebra has been exploited to theoretically reduce the number of monomials considered, and this has led to the successful reconstruction of the discrete-time finite-state PDSs of gene networks [13,22,30,31,44,46]. In [30], the complicated polynomials created by interpolating time series data were simplified by using the Gröbner basis [12] computed from the data.…”

Section: Introductionmentioning

confidence: 99%

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Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems

Kera

Hasegawa

2016

Nonlinear Dyn

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Reconstruction of nonlinear dynamical systems from noisy time series data has attracted much attention in recent years, and it has broad applications in many fields, especially in theoretical biology. Here, we propose a reconstruction algorithm based on the noise-tolerant algebraic approach that can infer underlying continuous-time polynomial dynamical systems from the observed time series data. The advantages of our approach are that it can handle nonlinearity, and it can be applied to noisy systems. Our approach reduces the range of monomials to be considered without any a priori knowledge as many other studies does. We apply the proposed method to two oscillatory systems (the FitzHugh-Nagumo and the Oregonator) subject to noise, where the conventional fitting methods based on L 1 and L 2 regularizations often fail. Our numerical experiments show that the proposed method accurately reconstructs the continuous-time polynomial dynamical systems. We also apply the method to a chaotic system and show the effectiveness of our approach.

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“…The algorithm in [13] starts with only data as input and computes all possible minimal wiring diagrams of polynomial models that fit the given data and outputs a most likely one, based on one of several possible model scoring methods. It does not depend on the choice of a term order.…”

Section: Network Inferencementioning

confidence: 99%

On the Algebraic Geometry of Polynomial Dynamical Systems

Jarrah

Laubenbacher

2008

Emerging Applications of Algebraic Geometry

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Abstract. This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks. It is shown that several problems relating to their structure and dynamics, as well as control theory, can be formulated and solved in the language of algebraic geometry.

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Reverse-engineering of polynomial dynamical systems

Cited by 78 publications

References 16 publications

Inference of Ecological Interaction Networks

Inference of Ecological Interaction Networks

Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems

On the Algebraic Geometry of Polynomial Dynamical Systems

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