The regular models of a logic program are a particular type of partial (3-valued) models which correspond to stable partial models with minimal undefinedness. In this paper, we explore graphical conditions on the dependence graph of a normal logic program to analyze the existence, unicity and multiplicity of non-trivial regular models for the program. We show three main results: 1) a necessary condition for the existence of non-trivial regular models, 2) a sufficient condition for the unicity of regular models, and 3) two upper bounds for the number of regular models based on positive feedback vertex sets […]
Tue, Oct 1, 2024
Chemical Reaction Networks (CRNs) are a standard formalism used in chemistry and biology to model complex molecular interaction systems. In the perspective of systems biology, they are a central tool to analyze the high-level functions of the cell in terms of their low-level molecular interactions. In the perspective of synthetic biology, they constitute a target programming language to implement in chemistry new functions either in vitro, in artificial vesicles, or in living cells […]
Mon, Jul 1, 2024
Tropical geometry can be used to find the order of time scales of variables in chemical reaction networks and search for model reductions [SGF+15]. In this report, we consider the problem of solving tropical equilibration problems in ODE systems of the BioModels model repository. We are interested in the existence of solutions both in R and Z […]
Fri, Apr 1, 2022
The Turing completeness result for continuous chemical reaction networks (CRN) shows that any computable function over the real numbers can be computed by a CRN over a finite set of formal molecular species using at most bimolecular reactions with mass action law kinetics. The proof uses a previous result of Turing completeness for functions defined by polynomial ordinary differential equations (PODE), the dualrail encoding of real variables by the difference of concentration between two molecular species, and a back-end quadratization transformation to restrict to elementary reactions with at most two reactants. In this paper, we present a polynomialization algorithm of quadratic time complexity to transform a system of elementary differential equations in PODE […]
Wed, Sep 1, 2021
In this short paper extracted from [7], we present a polynomialization algorithm of quadratic time complexity to transform a system of elementary differential equations in polynomial differential equations (PODE). This algorithm is used as a front-end transformation in a pipeline to compile any elementary mathematical function, either of time or of some input variable, into a finite Chemical Reaction Network (CRN) which computes it. We illustrate the performance of our compiler on a benchmark of elementary functions which serve as formal specification of CRN design problems in synthetic biology, and as comparison basis with natural CRNs exhibiting similar behaviours […]
Wed, Sep 1, 2021
Chemical reaction networks (CRNs) are a standard formalism used in chemistry and biology to reason about the dynamics of molecular interaction networks. In their interpretation by ordinary differential equations, CRNs provide a Turing-complete model of analog computattion, in the sense that any computable function over the reals can be computed by a finite number of molecular species with a continuous CRN which approximates the result of that function in one of its components in arbitrary precision. The proof of that result is based on a previous result of Bournez et al […]
Tue, Sep 1, 2020
Chemical Reaction Networks (CRNs) provide a useful abstraction of molecular interaction networks in which molecular structures as well as mass conservation principles are abstracted away to focus on the main dynamical properties of the network structure. In their interpretation by ordinary differential equations, we say that a CRN with distinguished input and output species computes a positive real function $f : R+ → R+$, if for any initial concentration x of the input species, the concentration of the output molecular species stabilizes at concentration f (x). The Turing-completeness of that notion of chemical analog computation has been established by proving that any computable real function can be computed by a CRN over a finite set of molecular species […]
Tue, Sep 1, 2020
With the automation of biological experiments and the increase of quality of single cell data that can now be obtained by phospho-proteomic and time lapse videomicroscopy, automating the building of mechanistic models from these data time series becomes conceivable and a necessity for many new applications. While learning numerical parameters to fit a given model structure to observed data is now a quite well understood subject, learning the structure of the model is a more challenging problem that previous attempts failed to solve without relying quite heavily on prior knowledge about that structure. In this paper, we consider mechanistic models based on chemical reaction networks (CRN) with their continuous dynamics based on ordinary differential equations, and finite time series about the time evolution of concentration of molecular species for a given time horizon and a finite set of perturbed initial conditions […]
Sun, Sep 1, 2019
With the automation of biological experiments and the increase of quality of single cell data that can now be obtained by phosphoproteomic and time lapse videomicroscopy, automating the building of mechanistic models from these time series data becomes conceivable and a necessity for many new applications. While learning numerical parameters to fit a given model structure to observed data is now a quite well understood subject, learning the structure of the model is a more challenging problem that previous attempts failed to solve without relying quite heavily on prior knowledge about that structure. In this paper , we consider mechanistic models based on chemical reaction networks (CRN) with their continuous dynamics based on ordinary differential equations, and finite time series about the time evolution of concentration of molecular species for a given time horizon and a finite set of perturbed initial conditions […]
Sat, Jun 1, 2019
Biochemical reaction networks are one of the most widely used formalism in systems biology to describe the molecular mechanisms of high-level cell processes. However modellers also reason with influence diagrams to represent the positive and negative influences between molecular species and may find an influence network useful in the process of building a reaction network. In this paper, we introduce a formalism of influence networks with forces, and equip it with a hierarchy of Boolean, Petri net, stochastic and differential semantics, similarly to reaction networks with rates […]
Sat, Dec 1, 2018