Discrete time piecewise affine models of genetic regulatory networks

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. When compared to other models of regulatory networks, these models have an additional parameter which is identified as quantifying interaction delays. In spite of their simplicity, their dynamics presents a rich variety of behaviours. This phenomenology is not limited to piecewise affine model but extends to smooth nonlinear discrete time models of regulatory networks. In a first step, our analysis concerns general properties of networks on arbitrary graphs (characterisation of the attractor, symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc). In a second step, focus is made on simple circuits for which the attractor and its changes with parameters are described. In the negative circuit of 2 genes, a thorough study is presented which concern stable (quasi-)periodic oscillations governed by rotations on the unit circle -- with a rotation number depending continuously and monotonically on threshold parameters. These regular oscillations exist in negative circuits with arbitrary number of genes where they are most likely to be observed in genetic systems with non-negligible delay effects.Comment: 34 page

Correlation based Vergence Control Using Log-polar Images

. This paper describes a real-time vergence control mechanism based on log-polar images, developed for a robot head. We show that vergence behavior can be achieved at reduced computational cost using simple correlation measures on log-polar images. The main advantages of using a non-uniform image sampling mechanism, such as the log-polar images, are related both to perceptual and algorithm complexity issues. We show that, when using correlation measures to control vergence, log-polar images give better results than cartesian images. Additionally, as log-polar images are smaller, the computation time is reduced. Two algorithms for closed loop vergence control, using correlation measures over log-polar images, are proposed and compared. Their behavior in real situations is illustrated by test examples. 1 Introduction The research interests in Active Vision have increased in the past few years providing efficient ways of combining the control of robotic systems and advanced visual sensin..

The precision of 3D Reconstruction from Uncalibrated Views

We consider reconstruction algorithms using points tracked over a sequence of (at least three) images, to estimate the positions of the cameras (motion parameters), the 3D coordinates (structure parameters), and the calibration matrix of the cameras (calibration parameters). Many algorithms have been reported in literature, and there is a need to know how well they may perform. We show how the choice of assumptions on the camera intrinsic parameters (either fixed, or with a probabilistic prior) influences the precision of the estimator. We associate a Maximum Likelihood estimator to each type of assumptions, and derive analytically their covariance matrices, independently of any specific implementation. We verify that the obtained covariance matrices are realistic, and compare the relative performance of each type of estimator. 1 Introduction The problem of 3D reconstruction from images has drawn considerable attention. We focus on the problem of reconstruction from matched points (co..

The precision of 3D Reconstruction from Uncalibrated Views

We consider reconstruction algorithms using points tracked over a sequence of (at least three) images, to estimate the positions of the cameras (motion parameters), the 3D coordinates (structure parameters), and the calibration matrix of the cameras (calibration parameters). Many algorithms have been reported in literature, and there is a need to know how well they may perform. We show how the choice of assumptions on the camera intrinsic parameters (either fixed, or with a probabilistic prior) influences the precision of the estimator. We associate a Maximum Likelihood estimator to each type of assumptions, and derive analytically their covariance matrices, independently of any specific implementation. We verify that the obtained covariance matrices are realistic, and compare the relative performance of each type of estimator. 1 Introduction The problem of 3D reconstruction from images has drawn considerable attention. We focus on the problem of reconstruction from matched points (co..