We describe DDE-BIFTOOL, a Matlab package for numerical bifurcation analysis of systems of delay differential equations with several fixed, discrete delays. The package implements continuation of steady state solutions and periodic solutions and their stability analysis. It also computes and continues steady state fold and Hopf bifurcations and, from the latter, it can switch to the emanating branch of periodic solutions. We describe the numerical methods upon which the package is based and illustrate its usage and capabilities through analysing three examples: two models of coupled neurons with delayed feedback and a model of two oscillators coupled with delay.

This paper describes a new method for the suppression of noise in images via the wavelet transform. The method relies on two measures. The first is a classic measure of smoothness of the image and is based on an approximation of the local Holder exponent via the wavelet coefficients. The second, novel measure takes into account geometrical constraints, which are generally valid for natural images. The smoothness measure and the constraints are combined in a Bayesian probabilistic formulation, and are implemented as a Markov random field (MRF) image model. The manipulation of the wavelet coefficients is consequently based on the obtained probabilities. A comparison of quantitative and qualitative results for test images demonstrates the improved noise suppression performance with respect to previous wavelet-based image denoising methods.

Advances in fluorescent labeling of cells as measured by flow cytometry have allowed for quantitative studies of proliferating populations of cells. The investigations (Luzyanina et al. in J. Math. Biol. 54:57–89, 2007; J. Math. Biol., 2009; Theor. Biol. Med. Model. 4:1–26, 2007) contain a mathematical model with fluorescence intensity as a structure variable to describe the evolution in time of proliferating cells labeled by carboxyfluorescein succinimidyl ester (CFSE). Here, this model and several extensions/modifications are discussed. Suggestions for improvements are presented and analyzed with respect to statistical significance for better agreement between model solutions and experimental data. These investigations suggest that the new decay/label loss and time dependent effective proliferation and death rates do indeed provide improved fits of the model to data. Statistical models for the observed variability/noise in the data are discussed with implications for uncertainty quantification. The resulting new cell dynamics model should prove useful in proliferation assay tracking and modeling, with numerous applications in the biomedical sciences.

International audienceThis paper is concerned with the efficient computation of periodic orbits in large-scale dynamical systems that arise after spatial discretization of partial differential equations (PDEs). A hybrid Newton–Picard scheme based on the shooting method is derived, which in its simplest form is the recursive projection method (RPM) of Shroff and Keller [SIAM J. Numer. Anal., 30 (1993), pp. 1099–1120] and is used to compute and determine the stability of both stable and unstable periodic orbits. The number of time integrations needed to obtain a solution is shown to be determined only by the system's dynamics. This contrasts with traditional approaches based on Newton's method, for which the number of time integrations grows with the order of the spatial discretiza-tion. Two test examples are given to show the performance of the methods and to illustrate various theoretical points

In this paper, we describe a stabilization method for linear time-delay systems which extends the classical pole placement method for ordinary di erential equations. Unlike methods based on ÿnite spectrum assignment, our method does not render the closed loop system, ÿnite dimensional but consists of controlling the rightmost eigenvalues. Because these are moved to the left half plane in a (quasi-)continuous way, we refer to our method as continuous pole placement. We explain the method by means of the stabilization of a linear ÿnite dimensional system in the presence of an input delay and illustrate its applicability to more general stabilization problems.

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Background: The flow cytometry analysis of CFSE-labelled cells is currently one of the most informative experimental techniques for studying cell proliferation in immunology. The quantitative interpretation and understanding of such heterogenous cell population data requires the development of distributed parameter mathematical models and computational techniques for data assimilation.