A Gröbner fan method for biochemical network modeling

Dimitrova, Elena; Jarrah, Abdul Salam; Laubenbacher, Reinhard; Stigler, Brandilyn

doi:10.1145/1277548.1277566

Cited by 27 publications

(27 citation statements)

References 6 publications

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“…It would therefore be desirable to have a method available that infers not only a wiring diagram but a dynamic description of the system. Another advantage of the method presented here is that there are methods closely related to the one presented here which are able to do just that (Laubenbacher & Stigler 2004;Dimitrova, Jarrah et al 2007). However, typically more data are required to be able to infer accurate models.…”

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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“…As can be seen, though Eqs. (13) and (14) consist of different monomials from the target PDS, their dynamics are similar to the target ones, and the perturbed data points are approximately on the graphs of their dynamics. If the number of monomials is empirically reduced, and if there are more monomials being considered than those in the order ideal, then it might be necessary to consider Eq.…”

Section: Reconstruction Of the Lorenz Attractormentioning

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%

“…In [30], the complicated polynomials created by interpolating time series data were simplified by using the Gröbner basis [12] computed from the data. Although there are several studies based on this approach [13,22,31,44], they are limited to discrete-time finite-state PDSs and the assumption of noise-free quantized data (e.g., Boolean). This is partly because computational algebraic approaches require strict symbolic computations, and thus, they are very sensitive to perturbations of 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 baggage of statistical techniques to analyse designs whose point coordinates are "approximately" known, could be supplemented by transferring the algebraic notion of border bases [44] to statistics. The techniques in Section 2 are applied to reverse engineering in particular for the identification of biochemical networks [25].…”

Section: Advanced Topicsmentioning

confidence: 99%