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 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

Beliefs About Medication and Uptake of Preventive Therapy in Women at Increased Risk of Breast Cancer: Results From a Multicenter Prospective Study

Introduction Uptake of preventive therapies for breast cancer is low. We examined whether women at increased risk of breast cancer can be categorized into groups with similar medication beliefs, and whether belief group membership was prospectively associated with uptake of preventive therapy. Patients and Methods Women (n = 732) attending an appointment to discuss breast cancer risk were approached; 408 (55.7%) completed the Beliefs About Medicines and the Perceived Sensitivity to Medicines questionnaires. Uptake of tamoxifen at 3 months was reported in 258 (63.2%). The optimal number of belief groups were identified using latent profile analysis. Results Uptake of tamoxifen was 14.7% (38/258). One in 5 women (19.4%; 78/402) reported a strong need for tamoxifen. The model fit statistics supported a 2-group model. Both groups held weak beliefs about their need for tamoxifen for current and future health. Group 2 (38%; 154/406 of the sample) reported stronger concerns about tamoxifen and medicines in general, and stronger perceived sensitivity to the negative effects of medicines compared with group 1 (62%; 252/406). Women with low necessity and lower concerns (group 1) were more likely to initiate tamoxifen (18.3%; 33/180) than those with low necessity and higher concerns (group 2) (6.4%; 5/78). After adjusting for demographic and clinical factors, the odds ratio was 3.37 (95% confidence interval, 1.08-10.51; P = .036). Conclusion Uptake of breast cancer preventive therapy was low. A subgroup of women reported low need for preventive therapy and strong medication concerns. These women were less likely to initiate tamoxifen. Medication beliefs are targets for supporting informed decision-making

Ten-year mortality, disease progression, and treatment-related side effects in men with localised prostate cancer from the ProtecT randomised controlled trial according to treatment received

Background The ProtecT trial reported intention-to-treat analysis of men with localised prostate cancer randomly allocated to active monitoring (AM), radical prostatectomy, and external beam radiotherapy. Objective To report outcomes according to treatment received in men in randomised and treatment choice cohorts. Design, setting, and participants This study focuses on secondary care. Men with clinically localised prostate cancer at one of nine UK centres were invited to participate in the treatment trial comparing AM, radical prostatectomy, and radiotherapy. Intervention Two cohorts included 1643 men who agreed to be randomised and 997 who declined randomisation and chose treatment. Outcome measurements and statistical analysis Analysis was carried out to assess mortality, metastasis and progression and health-related quality of life impacts on urinary, bowel, and sexual function using patient-reported outcome measures. Analysis was based on comparisons between groups defined by treatment received for both randomised and treatment choice cohorts in turn, with pooled estimates of intervention effect obtained using meta-analysis. Differences were estimated with adjustment for known prognostic factors using propensity scores. Results and limitations According to treatment received, more men receiving AM died of PCa (AM 1.85%, surgery 0.67%, radiotherapy 0.73%), whilst this difference remained consistent with chance in the randomised cohort (p = 0.08); stronger evidence was found in the exploratory analyses (randomised plus choice cohort) when AM was compared with the combined radical treatment group (p = 0.003). There was also strong evidence that metastasis (AM 5.6%, surgery 2.4%, radiotherapy 2.7%) and disease progression (AM 20.35%, surgery 5.87%, radiotherapy 6.62%) were more common in the AM group. Compared with AM, there were higher risks of sexual dysfunction (95% at 6 mo) and urinary incontinence (55% at 6 mo) after surgery, and of sexual dysfunction (88% at 6 mo) and bowel dysfunction (5% at 6 mo) after radiotherapy. The key limitations are the potential for bias when comparing groups defined by treatment received and changes in the protocol for AM during the lengthy follow-up required in trials of screen-detected PCa. Conclusions Analyses according to treatment received showed increased rates of disease-related events and lower rates of patient-reported harms in men managed by AM compared with men managed by radical treatment, and stronger evidence of greater PCa mortality in the AM group. Patient summary More than 95 out of every 100 men with low or intermediate risk localised prostate cancer do not die of prostate cancer within 10 yr, irrespective of whether treatment is by means of monitoring, surgery, or radiotherapy. Side effects on sexual and bladder function are better after active monitoring, but the risks of spreading of prostate cancer are more common