Related papers: Alternative to Ritt's Pseudodivision for finding t…
Ritt-Wu's algorithm of characteristic sets is the most representative for triangularizing sets of multivariate polynomials. Pseudo-division is the main operation used in this algorithm. In this paper we present a new algorithmic scheme for…
Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies…
In this paper, we give an overview of the differential algebra approach to identifiability, and then note a very simple observation about input-output equivalence and identifiability, that describes the identifiability equivalence between…
Invariant sets are a key ingredient for verifying safety and other properties of cyber-physical systems that mix discrete and continuous dynamics. We adapt the elimination-theoretic Rosenfeld-Gr\"{o}bner algorithm to systematically obtain…
In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
In this preliminary work, we present nonstandard time-stepping strategies to solve differential equations based on the algebraic estimation method applied to the estimation of time-derivative, which provides interesting properties of…
Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
A key step in mechanistic modelling of dynamical systems is to conduct a structural identifiability analysis. This entails deducing which parameter combinations can be estimated from a given set of observed outputs. The standard…
Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a…
In this paper we introduce a working generalization of the theory of Gr\"obner bases for algebras of partial difference polynomials with constant coefficients. One obtains symbolic (formal) computation for systems of linear or non-linear…
Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Grobner bases algorithm is a well-known method to solve this problem. However, a serious drawback exists in the Grobner bases based…
In this study, we propose a method for extracting the hidden algebraic structures of model parameters that are uniquely determined by observed time-series data and unidentifiable state-space models, explicitly and exhaustively. State-space…
We discuss issues of structural and practical identifiability of partially observed differential equations which are often applied in systems biology. The development of mathematical methods to investigate structural non-identifiability has…
We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…
Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…
Structural identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. The method of input-output equations is one method for…
Identifiability is a necessary condition for successful parameter estimation of dynamic system models. A major component of identifiability analysis is determining the identifiable parameter combinations, the functional forms for the…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…