Computing Slow Manifolds of Saddle Type

Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories on slow manifolds that are normally hyperbolic with both stable and unstable fast manifolds. We present two examples of bifurcation problems where these manifolds play a key role and a third example in which saddle-type slow manifolds are part of a traveling wave profile of a partial differential equation. Initial value solvers are incapable of computing trajectories on saddle-type slow manifolds, so the slow manifold of saddle type (SMST) algorithm presented here is formulated as a boundary value method. We take an empirical approach here to assessing the accuracy and effectiveness of the algorithm.Comment: preprint version - for final version see journal referenc

Computation of saddle type slow manifolds using iterative methods

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $\epsilon$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System

The stroke oxygen pilot study: a randomized control trial of the effects of routine oxygen supplementation early after acute stroke--effect on key outcomes at six months

Introduction: Post-stroke hypoxia is common, and may adversely affect outcome. We have recently shown that oxygen supplementation may improve early neurological recovery. Here, we report the six-month outcomes of this pilot study. Methods: Patients with a clinical diagnosis of acute stroke were randomized within 24 h of admission to oxygen supplementation at 2 or 3 L/min for 72 h or to control treatment (room air). Outcomes (see below) were assessed by postal questionnaire at 6 months. Analysis was by intention-to-treat, and statistical significance was set at p#0.05. Results: Out of 301 patients randomized two refused/withdrew consent and 289 (148 in the oxygen and 141 in the control group) were included in the analysis: males 44%, 51%; mean (SD) age 73 (12), 71 (12); median (IQR) National Institutes of Health Stroke Scale score 6 (3, 10), 5 (3, 10) for the two groups respectively. At six months 22 (15%) patients in the oxygen group and 20 (14%) in the control group had died; mean survival in both groups was 162 days (p= 0.99). Median (IQR) scores for the primary outcome, the modified Rankin Scale, were 3 (1, 5) and 3 (1, 4) for the oxygen and control groups respectively. The covariate-adjusted odds ratio was 1.04 (95% CI 0.67, 1.60), indicating that the odds of a lower (i.e. better) score were non-significantly higher in the oxygen group (p= 0.86). The mean differences in the ability to perform basic (Barthel Index) and extended activities of daily living (NEADL), and quality of life (EuroQol) were also non-significant. Conclusions: None of the key outcomes differed at 6 months between the groups. Although not statistically significant and generally of small magnitude, the effects were predominantly in favour of the oxygen group; a larger trial, powered to show differences in longer-term functional outcomes, is now on-going. Trial Registration: Controlled-Trials.com ISRCTN12362720; Eudract.ema.europa.eu 2004-001866-4

Adaptive and Phase Selective Spike Timing Dependent Plasticity in Synaptically Coupled Neuronal Oscillators

We consider and analyze the influence of spike-timing dependent plasticity (STDP) on homeostatic states in synaptically coupled neuronal oscillators. In contrast to conventional models of STDP in which spike-timing affects weights of synaptic connections, we consider a model of STDP in which the time lags between pre- and/or post-synaptic spikes change internal state of pre- and/or post-synaptic neurons respectively. The analysis reveals that STDP processes of this type, modeled by a single ordinary differential equation, may ensure efficient, yet coarse, phase-locking of spikes in the system to a given reference phase. Precision of the phase locking, i.e. the amplitude of relative phase deviations from the reference, depends on the values of natural frequencies of oscillators and, additionally, on parameters of the STDP law. These deviations can be optimized by appropriate tuning of gains (i.e. sensitivity to spike-timing mismatches) of the STDP mechanism. However, as we demonstrate, such deviations can not be made arbitrarily small neither by mere tuning of STDP gains nor by adjusting synaptic weights. Thus if accurate phase-locking in the system is required then an additional tuning mechanism is generally needed. We found that adding a very simple adaptation dynamics in the form of slow fluctuations of the base line in the STDP mechanism enables accurate phase tuning in the system with arbitrary high precision. Adaptation operating at a slow time scale may be associated with extracellular matter such as matrix and glia. Thus the findings may suggest a possible role of the latter in regulating synaptic transmission in neuronal circuits

Cyclic stretch increases splicing noise rate in cultured human fibroblasts

BACKGROUND: Mechanical forces are known to alter the expression of genes, but it has so far not been reported whether they may influence the fidelity of nucleus-based processes. One experimental approach permitting to address this question is the application of cyclic stretch to cultured human fibroblasts. As a marker for the precision of nucleus-based processes, the number of errors that occur during co-transcriptional splicing can then be measured. This so-called splicing noise is found at low frequency in pre-mRNA splicing. FINDINGS: The amount of splicing noise was measured by RT-qPCR of seven exon skips from the test genes AATF, MAP3K11, NF1, PCGF2, POLR2A and RABAC1. In cells treated by altered uniaxial cyclic stretching for 18 h, a uniform and significant increase of splicing noise was found for all detectable exon skips. CONCLUSION: Our data demonstrate that application of cyclic stretch to cultured fibroblasts correlates with a reduced transcriptional fidelity caused by increasing splicing noise

Farnesylated Nuclear Proteins Kugelkern and Lamin Dm0 Affect Nuclear Morphology by Directly Interacting with the Nuclear Membrane

Nuclear shape changes are observed during a variety of developmental processes, pathological conditions and ageing. Here, the molecular mechanism is analyzed how the farnesylated nuclear proteins interact with the nuclear envelope and deform the phospholipid bilayer

From sea monsters to charismatic megafauna: changes in perception and use of large marine animals

Marine megafauna has always elicited contrasting feelings. In the past, large marine animals were often depicted as fantastic mythological creatures and dangerous monsters, while also arousing human curiosity. Marine megafauna has been a valuable resource to exploit, leading to the collapse of populations and local extinctions. In addition, some species have been perceived as competitors of fishers for marine resources and were often actively culled. Since the 1970s, there has been a change in the perception and use of megafauna. The growth of marine tourism, increasingly oriented towards the observation of wildlife, has driven a shift from extractive to non-extractive use, supporting the conservation of at least some species of marine megafauna. In this paper, we review and compare the changes in the perception and use of three megafaunal groups, cetaceans, elasmobranchs and groupers, with a special focus on European cultures. We highlight the main drivers and the timing of these changes, compare different taxonomic groups and species, and highlight the implications for management and conservation. One of the main drivers of the shift in perception, shared by all the three groups of megafauna, has been a general increase in curiosity towards wildlife, stimulated inter alia by documentaries (from the early 1970s onwards), and also promoted by easy access to scuba diving. At the same time, environmental campaigns have been developed to raise public awareness regarding marine wildlife, especially cetaceans, a process greatly facilitated by the rise of Internet and the World Wide Web. Currently, all the three groups (cetaceans, elasmobranchs and groupers) may represent valuable resources for ecotourism. Strikingly, the economic value of live specimens may exceed their value for human consumption. A further change in perception involving all the three groups is related to a growing understanding and appreciation of their key ecological role. The shift from extractive to non-extractive use has the potential for promoting species conservation and local economic growth. However, the change in use may not benefit the original stakeholders (e.g. fishers or whalers) and there may therefore be a case for providing compensation for disadvantaged stakeholders. Moreover, it is increasingly clear that even non-extractive use may have a negative impact on marine megafauna, therefore regulations are needed.SFRH/BPD/102494/2014, UID/MAR/04292/2019, IS1403info:eu-repo/semantics/publishedVersio

Spatial resource wars: A two region example

We develop a spatial resource model in continuous time in which two agents strategically exploit a mobile resource in a two-location setup. In order to contrast the overexploitation of the resource (the tragedy of commons) that occurs when the player are free to choose where to fish/hunt/extract/harvest, the regulator can establish a series of spatially structured policies. We compare the three situations in which the regulator: (a) leaves the player free to choose where to harvest; (b) establishes a natural reserve where nobody is allowed to harvest; (c) assigns to each player a specific exclusive location to hunt. We show that when preference parameters dictate a low harvesting intensity, the policies cannot mitigate the overexploitation and in addition they worsen the utilities of the players. Conversely, in a context of harsher harvesting intensity, the intervention can help to safeguard the resource, preventing the extinction and also improving the welfare of both players

Clinical symptoms, signs and tests for identification of impending and current water-loss dehydration in older people (Review)

BackgroundThere is evidence that water-loss dehydration is common in older people and associated with many causes of morbidity and mortality.However, it is unclear what clinical symptoms, signs and tests may be used to identify early dehydration in older people, so that support can be mobilised to improve hydration before health and well-being are compromised.ObjectivesTo determine the diagnostic accuracy of state (one time), minimally invasive clinical symptoms, signs and tests to be used as screeningtests for detecting water-loss dehydration in older people by systematically reviewing studies that have measured a reference standard and at least one index test in people aged 65 years and over. Water-loss dehydration was defined primarily as including everyone with either impending or current water-loss dehydration (including all those with serum osmolality ≥ 295 mOsm/kg as being dehydrated).Search methodsStructured search strategies were developed for MEDLINE (OvidSP), EMBASE (OvidSP), CINAHL, LILACS, DARE and HTAdatabases (The Cochrane Library), and the International Clinical Trials Registry Platform (ICTRP). Reference lists of included studiesand identified relevant reviews were checked. Authors of included studies were contacted for details of further studies.Selection criteriaTitles and abstracts were scanned and all potentially relevant studies obtained in full text. Inclusion of full text studies was assessed independently in duplicate, and disagreements resolved by a third author. We wrote to authors of all studies that appeared to have collected data on at least one reference standard and at least one index test, and in at least 10 people aged ≥ 65 years, even where no comparative analysis has been published, requesting original dataset so we could create 2 x 2 tables.Data collection and analysis.Diagnostic accuracy of each test was assessed against the best available reference standard for water-loss dehydration (serum or plasma osmolality cut-off≥295mOsm/kg, serumosmolarity or weight change) within each study. For each index test study data were presented in forest plots of sensitivity and specificity. The primary target condition was water-loss dehydration (including either impending or current water-loss dehydration). Secondary target conditions were intended as current (> 300 mOsm/kg) and impending (295 to 300 mOsm/kg) water-loss dehydration, but restricted to current dehydration in the final review.We conducted bivariate random-effects meta-analyses (Stata/IC, StataCorp) for index tests where there were at least four studies and study datasets could be pooled to construct sensitivity and specificity summary estimates. We assigned the same approach for index tests with continuous outcome data for each of three pre-specified cut-off points investigated.Pre-set minimum sensitivity of a useful test was 60%, minimum specificity 75%. As pre-specifying three cut-offs for each continuoustest may have led to missing a cut-off with useful sensitivity and specificity, we conducted post-hoc exploratory analyses to createreceiver operating characteristic (ROC) curves where there appeared some possibility of a useful cut-off missed by the original three.These analyses enabled assessment of which tests may be worth assessing in further research. A further exploratory analysis assessed the value of combining the best two index tests where each had some individual predictive ability.Main resultsThere were few published studies of the diagnostic accuracy of state (one time), minimally invasive clinical symptoms, signs or tests tobe used as screening tests for detecting water-loss dehydration in older people. Therefore, to complete this review we sought, analysed and included raw datasets that included a reference standard and an index test in people aged ≥ 65 years.We included three studies with published diagnostic accuracy data and a further 21 studies provided datasets that we analysed. Weassessed 67 tests (at three cut-offs for each continuous outcome) for diagnostic accuracy of water-loss dehydration (primary targetcondition) and of current dehydration (secondary target condition).Only three tests showed any ability to diagnose water-loss dehydration (including both impending and current water-loss dehydration) as stand-alone tests: expressing fatigue (sensitivity 0.71 (95% CI 0.29 to 0.96), specificity 0.75 (95% CI 0.63 to 0.85), in one study with 71 participants, but two additional studies had lower sensitivity); missing drinks between meals (sensitivity 1.00 (95% CI 0.59 to 1.00), specificity 0.77 (95% CI 0.64 to 0.86), in one study with 71 participants) and BIA resistance at 50 kHz (sensitivities 1.00 (95% CI 0.48 to 1.00) and 0.71 (95% CI 0.44 to 0.90) and specificities of 1.00 (95% CI 0.69 to 1.00) and 0.80 (95% CI 0.28 to 0.99) in 15 and 22 people respectively for two studies, but with sensitivities of 0.54 (95% CI 0.25 to 0.81) and 0.69 (95% CI 0.56 to 0.79) and specificities of 0.50 (95% CI 0.16 to 0.84) and 0.19 (95% CI 0.17 to 0.21) in 21 and 1947 people respectively in two other studies). In post-hoc ROC plots drinks intake, urine osmolality and axillial moisture also showed limited diagnostic accuracy. No test was consistently useful in more than one study.Combining two tests so that an individual both missed some drinks between meals and expressed fatigue was sensitive at 0.71 (95%CI 0.29 to 0.96) and specific at 0.92 (95% CI 0.83 to 0.97).There was sufficient evidence to suggest that several stand-alone tests often used to assess dehydration in older people (including fluid intake, urine specific gravity, urine colour, urine volume, heart rate, dry mouth, feeling thirsty and BIA assessment of intracellular water or extracellular water) are not useful, and should not be relied on individually as ways of assessing presence or absence of dehydration in older people.No tests were found consistently useful in diagnosing current water-loss dehydration.Authors’ conclusionsThere is limited evidence of the diagnostic utility of any individual clinical symptom, sign or test or combination of tests to indicatewater-loss dehydration in older people. Individual tests should not be used in this population to indicate dehydration; they miss a highproportion of people with dehydration, and wrongly label those who are adequately hydrated.Promising tests identified by this review need to be further assessed, as do new methods in development. Combining several tests may improve diagnostic accuracy

Protocol for the perfusion and angiography imaging sub-study of the Third International Stroke Trial (IST-3) of alteplase treatment within six-hours of acute ischemic stroke

RATIONALE: Intravenous thrombolysis with recombinant tissue Plasminogen Activator improves outcomes in patients treated early after stroke but at the risk of causing intracranial hemorrhage. Restricting recombinant tissue Plasminogen Activator use to patients with evidence of still salvageable tissue, or with definite arterial occlusion, might help reduce risk, increase benefit and identify patients for treatment at late time windows. AIMS: To determine if perfusion or angiographic imaging with computed tomography or magnetic resonance help identify patients who are more likely to benefit from recombinant tissue Plasminogen Activator in the context of a large multicenter randomized trial of recombinant tissue Plasminogen Activator given within six-hours of onset of acute ischemic stroke, the Third International Stroke Trial. DESIGN: Third International Stroke Trial is a prospective multicenter randomized controlled trial testing recombinant tissue Plasminogen Activator (0·9 mg/kg, maximum dose 90 mg) started up to six-hours after onset of acute ischemic stroke, in patients with no clear indication for or contraindication to recombinant tissue Plasminogen Activator. Brain imaging (computed tomography or magnetic resonance) was mandatory pre-randomization to exclude hemorrhage. Scans were read centrally, blinded to treatment and clinical information. In centers where perfusion and/or angiography imaging were used routinely in stroke, these images were also collected centrally, processed and assessed using validated visual scores and computational measures. STUDY OUTCOMES: The primary outcome in Third International Stroke Trial is alive and independent (Oxford Handicap Score 0-2) at 6 months; secondary outcomes are symptomatic and fatal intracranial hemorrhage, early and late death. The perfusion and angiography study additionally will examine interactions between recombinant tissue Plasminogen Activator and clinical outcomes, infarct growth and recanalization in the presence or absence of perfusion lesions and/or arterial occlusion at presentation. The study is registered ISRCTN25765518