A computer scientist point of view on Hilbert's differential theorem of zeros

What is a solution of a system of polynomial differential equations ? This paper provides an original presentation of well-known theorems, with a computer scientist flavor, relying on an improved normal form algorithm

A Normal Form Algorithm for Regular Differential Chains

International audienceThis paper presents a new algorithm for computing the normal form of a differential rational fraction modulo differential ideals presented by regular differential chains. An application to the computation of power series solutions is presented and illustrated with the new DifferentialAlgebra MAPLE package

Computing differential characteristic sets by change of ordering

submitted to the Journal of Symbolic ComputationWe describe an algorithm for converting a characteristic set of a prime differential ideal from one ranking into another. This algorithm was implemented in many different languages and has been applied within various software and projects. It permitted to solve formerly unsolved problems

Well known theorems on triangular systems and the D5 principle

International audienceThe theorems that we present in this paper are very important to prove the correctness of triangular decomposition algorithms. The most important of them are not new but their proofs are. We illustrate how they articulate with the D5 principle

Chemical Reaction Systems, Computer Algebra and Systems Biology

International audienceIn this invited paper, we survey some of the results obtained in the computer algebra team of Lille, in the domain of systems biology. So far, we have mostly focused on models (systems of equations) arising from generalized chemical reaction systems. Eight years ago, our team was involved in a joint project, with physicists and biologists, on the modeling problem of the circadian clock of the green algae Ostreococcus tauri. This cooperation led us to different algorithms dedicated to the reduction problem of the deterministic models of chemical reaction systems. More recently, we have been working more tightly with another team of our lab, the BioComputing group, interested by the stochastic dynamics of chemical reaction systems. This cooperation led us to efficient algorithms for building the ODE systems which define the statistical moments associated to these dynamics. Most of these algorithms were implemented in the MAPLE computer algebra software. We have chosen to present them through the corresponding MAPLE packages

Towards an automated reduction method for polynomial ODE models in cellular biology

International audienceThis paper presents the first version of an algorithmic scheme dedicated to the model reduction problem, in the context of polynomial ODE models derived from generalized chemical reaction systems. This scheme, which relies on computer algebra, is implemented within a new MAPLE package. It is applied over an example. The qualitative analysis of the reduced model is afterwards completely carried out, proving the practical relevance of our methods

In vivo evidence for quasispecies distributions in the bovine respiratory syncytial virus genome

We analyzed the genetic evolution of bovine respiratory syncytial virus (BRSV) isolate W2-00131, from its isolation in bovine turbinate (BT) cells to its inoculation in calves. Results showed that the BRSV genomic region encoding the highly variable glycoprotein G remains genetically stable after virus isolation and over 10 serial infections in BT cells, as well as following experimental inoculation in calves. This remarkable genetic stability led us to examine the mutant spectrum of several populations derived from this field isolate. Sequence analysis of molecular clones revealed an important genetic heterogeneity in G coding region of each population, with mutation frequencies ranging from 6.8 to 10.1 10-4 substitutions/nucleotide. The non-synonymous mutations of the mutant spectrum mapped preferentially within the two variable antigenic regions of the ectodomain or close to the highly conserved domain. These results suggest that RSV populations may evolve as complex and dynamic mutant swarms, despite apparent genetic stability

New diagnostics for tuberculosis: fulfilling patient needs first

An effective tuberculosis (TB) control programme requires early diagnosis and immediate initiation of treatment. Any delays in diagnosing TB not only impair a patient's prognosis, but also increase the risks of transmitting the disease within the community. Unfortunately, the most recent TB diagnostic tools still depend on high-infrastructure laboratories, making them poorly adapted for use in resource-limited settings. Additionally, existing tests show poor performance in diagnosing TB in children, people living with HIV/AIDS, and extrapulmonary forms of the disease. As a consequence, TB patients are still to date left with either fair access to poor diagnostics or poor access to fair diagnostics

Real Root Isolation of Regular Chains

We present an algorithm RealRootIsolate for isolating the real roots of a system of multivariate polynomials given by a zerodimensional squarefree regular chain. The output of the algorithm is guaranteed in the sense that all real roots are obtained and are described by boxes of arbitrary precision. Real roots are encoded with a hybrid representation, combining a symbolic object, namely a regular chain, and a numerical approximation given by intervals. Our isolation algorithm is a generalization, for regular chains, of the algorithm proposed by Collins and Akritas. We have implemented RealRootIsolate as a command of the module SemiAlgebraicSetTools of the RegularChains library in Maple. Benchmarks are reported.