Equity under the knife: Justice and evidence in surgery

Surgery is an increasingly common and expensive mode of medical intervention. The ethical dimensions of the surgeon-patient relationship, including respect for personal autonomy and informed consent, are much discussed; but broader equity issues have not received the same attention. This paper extends the understanding of surgical ethics by considering the nature of evidence in surgery and its relationship to a just provision of healthcare for individuals and their populations. 2012 John Wiley & Sons Ltd

The converging-input converging-state property for Lur'e systems

Using methods from classical absolute stability theory, combined with recent results on input-to-state stability (ISS) of Lur’e systems, we derive necessary and sufficient conditions for a class of Lur’e systems to have the converging-input converging-state (CICS) property. In particular, we provide sufficient conditions for CICS which are reminiscent of the complex Aizerman conjecture and the circle criterion and connections are also made with small gain ISS theorems. The penultimate section of the paper is devoted to non-negative Lur’e systems which arise naturally in, for example, ecological and biochemical applications: the main result in this context is a sufficient criterion for a so-called “quasi CICS” property for Lur’e systems which, when uncontrolled, admit two equilibria. The theory is illustrated with numerous examples

Controllability for positive discrete–time linear systems with p ositive state

Controllability of componentwise nonnegative discrete-time linear systems is considered. The key difference here from the well-established positive systems theory is that we permit the case where the input takes negative values, provided that the state remains nonnegative. Such a framework is very natural, moreover necessary, in situations such as population ecology to describe the control actions of harvesting or culling. The present contribution summarises recently published material by the authors and considers a novel application in low-gain PI contro

A necessary condition for dispersal driven growth of populations with discrete patch dynamics

We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populations to persist across discrete, spatially heterogeneous, environments even when individual patches are adverse or unfavourable. For two classes of mathematical models, one linear and one non-linear, we provide necessary conditions for dispersal driven growth in terms of the non-existence of a common linear Lyapunov function, which we describe. Our approach draws heavily upon the underlying positive dynamical systems structure. Our results apply to both discrete- and continuous-time models. The theory is illustrated with examples and both biological and mathematical conclusions are drawn

Low-gain Integral Control for Multi-Input, Multi-Output Linear Systems with Input Nonlinearities

We consider the inclusion of a static anti-windup component in a continuous-time low-gain integral controller in feedback with a multi-input multi-output stable linear system subject to an input nonlinearity (from a class of functions that includes componentwise diagonal saturation). We demonstrate that the output of the closed- loop system asymptotically tracks every constant reference vector which is “feasible” in a natural sense, provided that the integrator gain is sufficiently small. Robustness properties of the proposed control scheme are investigated and three examples are discussed in detail

Stability of Non-Negative Lur'e Systems

A stability/instability trichotomy for a class of nonnegative continuous-time Lur'e systems is derived. Asymptotic, exponential, and input-to-state stability concepts are considered. The presented trichotomy rests on Perron–Frobenius theory, absolute stability theory, and recent input-to-state stability results for Lur'e systems. Applications of the results derived arise in various fields, including density-dependent population dynamics, and two examples are discussed in detail

A stability/instability trichotomy for non-negative Lur’e systems

We identify a stability/instability trichotomy for a class of non-negative continuous-time Lur’e systems. Asymptotic as well as input-to-state stability concepts (ISS) are considered. The presented trichotomy rests on Perron-Frobenius theory, absolute stability theory and recent ISS results forLur’e systems

A functional genomic and proteomic perspective of sea urchin calcium signaling and egg activation

AbstractThe sea urchin egg has a rich history of contributions to our understanding of fundamental questions of egg activation at fertilization. Within seconds of sperm–egg interaction, calcium is released from the egg endoplasmic reticulum, launching the zygote into the mitotic cell cycle and the developmental program. The sequence of the Strongylocentrotus purpuratus genome offers unique opportunities to apply functional genomic and proteomic approaches to investigate the repertoire and regulation of Ca2+ signaling and homeostasis modules present in the egg and zygote. The sea urchin “calcium toolkit” as predicted by the genome is described. Emphasis is on the Ca2+ signaling modules operating during egg activation, but the Ca2+ signaling repertoire has ramifications for later developmental events and adult physiology as well. Presented here are the mechanisms that control the initial release of Ca2+ at fertilization and additional signaling components predicted by the genome and found to be expressed and operating in eggs at fertilization. The initial release of Ca2+ serves to coordinate egg activation, which is largely a phenomenon of post-translational modifications, especially dynamic protein phosphorylation. Functional proteomics can now be used to identify the phosphoproteome in general and specific kinase targets in particular. This approach is described along with findings to date. Key outstanding questions regarding the activation of the developmental program are framed in the context of what has been learned from the genome and how this knowledge can be applied to functional studies