First Passage Times of Long Transient Dynamics in Ecology.

Long transient dynamics in ecological models are characterized by extended periods in one state or regime before an eventual, and often abrupt, transition. One mechanism leading to long transient dynamics is the presence of ghost attractors, states where system dynamics slow down and the system lingers before eventually transitioning to the true attractor. This transition results solely from system dynamics rather than external factors. This paper investigates the dynamics of a classical herbivore-grazer model with the potential for ghost attractors or alternative stable states. We propose an intuitive threshold for first passage time analysis applicable to both bistable and ghost attractor regimes. By formulating the first passage time problem as a backward Kolmogorov equation, we examine how the mean first passage time changes as parameters are varied from the ghost attractor regime to the bistable one, through a saddle-node bifurcation. Our results reveal that the mean and variance of first passage times vary smoothly across the bifurcation threshold, eliminating the deterministic distinction between ghost attractors and bistable regimes. This work suggests that first passage time analysis can be an informative way to classify the length of a long transient. A better understanding of the duration of long transients may contribute to greater ecological understanding and more effective environmental management.

Boundary homogenization for patchy surfaces trapping patchy particles.

Trapping diffusive particles at surfaces is a key step in many systems in chemical and biological physics. Trapping often occurs via reactive patches on the surface and/or the particle. The theory of boundary homogenization has been used in many prior works to estimate the effective trapping rate for such a system in the case that either (i) the surface is patchy and the particle is uniformly reactive or (ii) the particle is patchy and the surface is uniformly reactive. In this paper, we estimate the trapping rate for the case that the surface and the particle are both patchy. In particular, the particle diffuses translationally and rotationally and reacts with the surface when a patch on the particle contacts a patch on the surface. We first formulate a stochastic model and derive a five-dimensional partial differential equation describing the reaction time. We then use matched asymptotic analysis to derive the effective trapping rate, assuming that the patches are roughly evenly distributed and occupy a small fraction of the surface and the particle. This trapping rate involves the electrostatic capacitance of a four-dimensional duocylinder, which we compute using a kinetic Monte Carlo algorithm. We further use Brownian local time theory to derive a simple heuristic estimate of the trapping rate and show that it is remarkably close to the asymptotic estimate. Finally, we develop a kinetic Monte Carlo algorithm to simulate the full stochastic system and then use these simulations to confirm the accuracy of our trapping rate estimates and homogenization theory.

Sialorrhoea treated with inhaled glycopyrronium.

Sialorrhoea or drooling is a distressing and often socially isolating symptom seen in palliative care. Evidence to support efficacy and safety of drug therapy in sialorrhoea is limited. Most drugs, in an adult population, are unlicensed for this indication in the UK including glycopyrronium. A 73-year-old Caucasian man, diagnosed with a right-sided sarcomatoid malignant pleural mesothelioma, presented with difficulty in swallowing and sialorrhoea. A glycopyrronium inhaler (administering 55 µg of glycopyrronium bromide/puff) was initiated in the mornings, increasing up to three times per day as tolerated. He reported a significant decrease in his symptoms 2 days after initiation using a numerical rating scale. A regular dose of one puff two times per day completely resolved the patient's symptoms within 5 days. This case supports the use of inhaled glycopyrronium as a possible therapy for sialorrhoea in palliative care patients. In addition, doses required for resolution of symptoms were significantly lower when compared with systemic dosages.

Temporal stability vs. community matrix measures of stability and the role of weak interactions.

Relationships between different measures of stability are not well understood in part because empiricists and theoreticians tend to measure different aspects and most studies only explore a single form of stability. Using time-series data from experimental plankton communities, we compared temporal stability typically measured by empiricists (coefficient of variation in biomass) to stability measures typically measured by theoreticians derived from the community matrix (asymptotic resilience, initial resilience and intrinsic stochastic invariability) using first-order multivariate autoregressive models (MAR). Community matrices were also used to derive estimates of interaction strengths between plankton groups. We found no relationship between temporal stability and stability measures derived from the community matrix. Weaker interaction strengths were generally associated with higher stability for community matrix measures of stability, but were not consistently associated with higher temporal stability. Temporal stability and stability measures derived from the community matrix stability appear to represent different aspects of stability reflecting the multi-dimensionality of stability.

Early specialist palliative care on quality of life for malignant pleural mesothelioma: a randomised controlled trial.

PURPOSE: Malignant pleural mesothelioma (MPM) has a high symptom burden and poor survival. Evidence from other cancer types suggests some benefit in health-related quality of life (HRQoL) with early specialist palliative care (SPC) integrated with oncological services, but the certainty of evidence is low. METHODS: We performed a multicentre, randomised, parallel group controlled trial comparing early referral to SPC versus standard care across 19 hospital sites in the UK and one large site in Western Australia. Participants had newly diagnosed MPM; main carers were additionally recruited. INTERVENTION: review by SPC within 3 weeks of allocation and every 4 weeks throughout the study. HRQoL was assessed at baseline and every 4 weeks with the European Organization for Research and Treatment of Cancer (EORTC) Quality of Life Questionnaire Core 30. PRIMARY OUTCOME: change in EORTC C30 Global Health Status 12 weeks after randomisation. RESULTS: Between April 2014 and October 2016, 174 participants were randomised. There was no significant between group difference in HRQoL score at 12 weeks (mean difference 1.8 (95% CI -4.9 to 8.5; p=0.59)). HRQoL did not differ at 24 weeks (mean difference -2.0 (95% CI -8.6 to 4.6; p=0.54)). There was no difference in depression/anxiety scores at 12 weeks or 24 weeks. In carers, there was no difference in HRQoL or mood at 12 weeks or 24 weeks, although there was a consistent preference for care, favouring the intervention arm. CONCLUSION: There is no role for routine referral to SPC soon after diagnosis of MPM for patients who are cared for in centres with good access to SPC when required. TRIAL REGISTRATION NUMBER: ISRCTN18955704.