Minimal symmetric Darlington synthesis

We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue

Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria

In engineering practice, a nonlinear system stable about several equilibria is often studied by linearizing the system over a small range of operation around each of these equilibria, and allowing the study of the system using linear system methods. Theoretically, for operations beyond a small range but still within the stable regime of an equilibrium, the system behaves nonlinearly, and can be described and investigated using the Volterra series approach. However, there is still no available approach that can systematically transform the model of a nonlinear system into a form that can be studied over the whole stable regime about an equilibrium so as to facilitate the system study using the Volterra series approach. This transformation is, in the present study, referred to as nonlinear model standardization, which is the extension of the well-known concept of linearization to the nonlinear case. In this paper, a novel approach to nonlinear model standardization is proposed for nonlinear systems that can be described by a Nonlinear AutoRegressive model with eXogeneous input (NARX) or a nonlinear differential equation (NDE) model. The proposed approach is then used in three case studies covering the applications in nonlinear system analysis, nonlinear system design, and nonlinearity compensation, respectively, demonstrating the significance of the proposed nonlinear model standardization in a wide range of engineering practices

Disorders of sex development: effect of molecular diagnostics

Disorders of sex development (DSDs) are a diverse group of conditions that can be challenging to diagnose accurately using standard phenotypic and biochemical approaches. Obtaining a specific diagnosis can be important for identifying potentially life-threatening associated disorders, as well as providing information to guide parents in deciding on the most appropriate management for their child. Within the past 5 years, advances in molecular methodologies have helped to identify several novel causes of DSDs; molecular tests to aid diagnosis and genetic counselling have now been adopted into clinical practice. Occasionally, genetic profiling of embryos prior to implantation as an adjunct to assisted reproduction, prenatal diagnosis of at-risk pregnancies and confirmatory testing of positive results found during newborn biochemical screening are performed. Of the available genetic tests, the candidate gene approach is the most popular. New high-throughput DNA analysis could enable a genetic diagnosis to be made when the aetiology is unknown or many differential diagnoses are possible. Nonetheless, concerns exist about the use of genetic tests. For instance, a diagnosis is not always possible even using new molecular approaches (which can be worrying for the parents) and incidental information obtained during the test might cause anxiety. Careful selection of the genetic test indicated for each condition remains important for good clinical practice. The purpose of this Review is to describe advances in molecular biological techniques for diagnosing DSDs

Admissible Controls and Attainable States for a Class of Nonlinear-systems With General Constraints

We consider nonlinear control systems where the control and the state variables are submitted to explicit constraints. This paper has two objectives. First, for a class of nonlinear systems with constraints, an existence result of nontrivial admissible controls and some of their interesting properties are proved. Then, we investigate the problem of local controllability in a neighbourhood of an equilibrium point, while observing state and control constraints along the whole trajectory. An iterative procedure is also given, which allows one to compute the steering admissible control function. This procedure is illustrated with a classical example