STABILIZATION BY ADAPTIVE FEEDBACK CONTROL FOR POSITIVE DIFFERENCE EQUATIONS WITH APPLICATIONS IN PEST MANAGEMENT

An adaptive feedback control scheme is proposed for stabilizing a class of forced nonlinear positive difference equations. The adaptive scheme is based on so-called high-gain adaptive controllers and contains substantial robustness with respect to model uncertainty as well as with respect to persistent forcing signals, including measurement errors. Our results take advantage of the underlying positive systems structure and ideas from input-to-state stability from nonlinear control theory. Our motivating application is to pest or weed control, and in this context the present work substantially strengthens previous work by the authors. The theory is illustrated with examples

Exponential input-to-state stability for Lur’e systems via Integral Quadratic Constraints and Zames–Falb multipliers

Absolute stability criteria that are sufficient for global exponential stability are shown, under a Lipschitz assumption, to be sufficient for the a priori stronger exponential input-to-state stability property. Important corollaries of this result are as follows: (i) absolute stability results obtained using Zames–Falb multipliers for systems containing slope-restricted nonlinearities provide exponential input-to-state-stability under a mild detectability assumption; and (ii) more generally, many absolute stability results obtained via Integral Quadratic Constraint methods provide, with the additional Lipschitz assumption, this stronger property

Transfer Functions of Infinite-Dimensional Systems: Positive Realness and Stabilization

We consider a general class of operator-valued irrational positive-real functions with an emphasis on their frequency-domain properties and the relation with stabilization by output feedback. Such functions arise naturally as the transfer functions of numerous infinite-dimensional control systems, including examples specified by PDEs. Our results include characterizations of positive realness in terms of imaginary axis conditions, as well as characterizations in terms of stabilizing output feedback, where both static and dynamic output feedback are considered. In particular, it is shown that stabilizability by all static output feedback operators belonging to a sector can be characterized in terms of a natural positive-real condition and, furthermore, we derive a characterization of positive realness in terms of a mixture of imaginary axis and stabilization conditions. Finally, we introduce concepts of strict and strong positive realness, prove results which relate these notions and analyse the relationship between the strong positive realness property and stabilization by feedback. The theory is illustrated by examples, some arising from controlled and observed partial differential equations

Infinite-dimensional Lur'e systems with almost periodic forcing

We consider forced Lur’e systems in which the linear dynamic component is an infinite-dimensional well-posed system. Numerous physically motivated delay- and partial-differential equa-tions are known to belong to this class of infinite-dimensional systems. We present refinements ofrecent incremental input-to-state stability results [14] and use them to derive convergence results fortrajectories generated by Stepanov almost periodic inputs. In particular, we show that the incrementalstability conditions guarantee that for every Stepanov almost periodic input there exists a unique pairof state and output signals which are almost periodic and Stepanov almost periodic, respectively. Thealmost periods of the state and output signals are shown to be closely related to the almost periodsof the input, and a natural module containment result is established. All state and output signalsgenerated by the same Stepanov almost periodic input approach the almost periodic state and theStepanov almost periodic output in a suitable sense, respectively, as time goes to infinity. The sufficientconditions guaranteeing incremental input-to-state stability and the existence of almost periodic stateand Stepanov almost periodic output signals are reminiscent of the conditions featuring in well-knownabsolute stability criteria such as the complex Aizerman conjecture and the circle criterion

An equivalence framework for an age-structured multi-stage representation of the cell cycle

We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an age-structured multi-stage Markov process for approximating cell cycle time distributions. We further demonstrate that the resulting mean behaviour is equivalent, over large timescales, to the classical McKendrick-von Foerster integro-partial differential equation. We conclude by extending this framework to a spatial context, facilitating the modelling of travelling wave phenomena and cell-mediated pattern formation. More generally, this methodology may be extended to myriad reaction-diffusion processes for which the age of individuals is relevant to the dynamics

Boundedness, persistence and stability for classes of forced difference equations arising in population ecology

Boundedness, persistence and stability properties are considered for a class of nonlinear, possibly infinite-dimensional, forced difference equations which arise in a number of ecological and biological contexts. The inclusion of forcing incorporates the effects of control actions (such as harvesting or breeding programmes), disturbances induced by seasonal or environmental variation, or migration. We provide sufficient conditions under which the states of these models are bounded and persistent uniformly with respect to the forcing terms. Under mild assumptions, the models under consideration naturally admit two equilibria when unforced: the origin and a unique non-zero equilibrium. We present sufficient conditions for the non-zero equilibrium to be stable in a sense which is strongly inspired by the input-to-state stability concept well-known in mathematical control theory. In particular, our stability concept incorporates the impact of potentially persistent forcing. Since the underlying state-space may be infinite dimensional, our framework enables treatment of so-called integral projection models (IPMs). The theory is applied to a number of examples from population dynamics

The regime-conversion method: a hybrid technique for simulating well-mixed chemical reaction networks

There exist several methods for simulating biological and physical systems as represented by chemical reaction networks. Systems with low numbers of particles are frequently modelled as discrete-state Markov jump processes and are typically simulated via a stochastic simulation algorithm (SSA). An SSA, while accurate, is often unsuitable for systems with large numbers of individuals, and can become prohibitively expensive with increasing reaction frequency. Large systems are often modelled deterministically using ordinary differential equations, sacrificing accuracy and stochasticity for computational efficiency and analytical tractability. In this paper, we present a novel hybrid technique for the accurate and efficient simulation of large chemical reaction networks. This technique, which we name the regime-conversion method, couples discrete-state Markov jump process to a system of ordinary differential equations by simulating a reaction network using both techniques simultaneously. Individual molecules in the network are represented by exactly one regime at any given time, and may switch their governing regime depending on particle density. In this manner, we model high copy-number species using the cheaper continuum method and low copy-number species using the more expensive, discrete-state stochastic method to preserve the impact of stochastic fluctuations at low copy number. The motivation, as with similar methods, is to retain the advantages while mitigating the shortfalls of each method. We demonstrate the performance and accuracy of our method for several test problems that exhibit varying degrees of inter-connectivity and complexity by comparing averaged trajectories obtained from both our method and from exact stochastic simulation

The Diagnostic and Prognostic Accuracy of Five Markers of Serious Bacterial Infection in Malawian Children with Signs of Severe Infection

Early recognition and prompt and appropriate antibiotic treatment can significantly reduce mortality from serious bacterial infections (SBI). The aim of this study was to evaluate the utility of five markers of infection: C-reactive protein (CRP), procalcitonin (PCT), soluble triggering receptor expressed on myeloid cells-1 (sTREM-1), CD163 and high mobility group box-1 (HMGB1), as markers of SBI in severely ill Malawian children.Children presenting with a signs of meningitis (n = 282) or pneumonia (n = 95), were prospectively recruited. Plasma samples were taken on admission for CRP, PCT, sTREM-1 CD163 and HMGB1 and the performance characteristics of each test to diagnose SBI and to predict mortality were determined. Of 377 children, 279 (74%) had SBI and 83 (22%) died. Plasma CRP, PCT, CD163 and HMGB1 and were higher in HIV-infected children than in HIV-uninfected children (p<0.01). In HIV-infected children, CRP and PCT were higher in children with SBI compared to those with no detectable bacterial infection (p<0.0005), and PCT and CD163 were higher in non-survivors (p = 0.001, p = 0.05 respectively). In HIV-uninfected children, CRP and PCT were also higher in children with SBI compared to those with no detectable bacterial infection (p<0.0005), and CD163 was higher in non-survivors (p = 0.05). The best predictors of SBI were CRP and PCT, and areas under the curve (AUCs) were 0.81 (95% CI 0.73–0.89) and 0.86 (95% CI 0.79–0.92) respectively. The best marker for predicting death was PCT, AUC 0.61 (95% CI 0.50–0.71).Admission PCT and CRP are useful markers of invasive bacterial infection in severely ill African children. The study of these markers using rapid tests in a less selected cohort would be important in this setting

Cancer risk in 680 000 people exposed to computed tomography scans in childhood or adolescence: Data linkage study of 11 million Australians

Objective To assess the cancer risk in children and adolescents following exposure to low dose ionising radiation from diagnostic computed tomography (CT) scans. Design Population based, cohort, data linkage study in Australia. Cohort members 10.9 million people identified from Australian Medicare records, aged 0-19 years on 1 January 1985 or born between 1 January 1985 and 31 December 2005; all exposures to CT scans funded by Medicare during 1985-2005 were identified for this cohort. Cancers diagnosed in cohort members up to 31 December 2007 were obtained through linkage to national cancer records. Main outcome Cancer incidence rates in individuals exposed to a CT scan more than one year before any cancer diagnosis, compared with cancer incidence rates in unexposed individuals. Results 60 674 cancers were recorded, including 3150 in 680 211 people exposed to a CT scan at least one year before any cancer diagnosis. The mean duration of follow-up after exposure was 9.5 years. Overall cancer incidence was 24% greater for exposed than for unexposed people, after accounting for age, sex, and year of birth (incidence rate ratio (IRR) 1.24 (95% confidence interval 1.20 to 1.29); P<0.001). We saw a dose-response relation, and the IRR increased by 0.16 (0.13 to 0.19) for each additional CT scan. The IRR was greater after exposure at younger ages (P<0.001 for trend). At 1-4, 5-9, 10-14, and 15 or more years since first exposure, IRRs were 1.35 (1.25 to 1.45), 1.25 (1.17 to 1.34), 1.14 (1.06 to 1.22), and 1.24 (1.14 to 1.34), respectively. The IRR increased significantly for many types of solid cancer (digestive organs, melanoma, soft tissue, female genital, urinary tract, brain, and thyroid); leukaemia, myelodysplasia, and some other lymphoid cancers. There was an excess of 608 cancers in people exposed to CT scans (147 brain, 356 other solid, 48 leukaemia or myelodysplasia, and 57 other lymphoid). The absolute excess incidence rate for all cancers combined was 9.38 per 100 000 person years at risk, as of 31 December 2007. The average effective radiation dose per scan was estimated as 4.5 mSv. Conclusions The increased incidence of cancer after CT scan exposure in this cohort was mostly due to irradiation. Because the cancer excess was still continuing at the end of follow-up, the eventual lifetime risk from CT scans cannot yet be determined. Radiation doses from contemporary CT scans are likely to be lower than those in 1985-2005, but some increase in cancer risk is still likely from current scans. Future CT scans should be limited to situations where there is a definite clinical indication, with every scan optimised to provide a diagnostic CT image at the lowest possible radiation dose

Polymers of Intrinsic Microporosity derived from a carbocyclic analogue of Tröger's base

Tröger's base (TB) is often used as a building block for the synthesis of Polymers of Intrinsic Microporosity (PIMs) due to its rigid bicyclic V-shaped structure. In this study the TB component in the structure of a PIM is replaced by 2,3:6,7-dibenzobicyclo[3.3.1]nonane, a purely carbocyclic analogue of TB. This modification results in only a slightly reduced amount of microporosity as determined using nitrogen adsorption. Further comparisons with previously reported PIMs indicate that this building unit (and therefore TB) is significantly less effective for the generation of intrinsic microporosity than spirobisindane, a commonly used structural unit for PIM synthesis. It appears that the V-shape of the 2,3:6,7-dibenzobicyclo[3.3.1]nonane and TB units allows closer contact between polymer chains thereby enhancing packing efficiency