Nystrom Methods in the RKQ Algorithm for Initial-value Problems

We incorporate explicit Nystrom methods into the RKQ algorithm for stepwise global error control in numerical solutions of initial-value problems. The initial-value problem is transformed into an explicitly second-order problem, so as to be suitable for Nystrom integration. The Nystrom methods used are fourth-order, fifth-order and 10th-order. Two examples demonstrate the effectiveness of the algorithm.Comment: This is an extension of ideas published in J. Math. Res. (open access); see refs [1] and [2

An Euler-type method for Volterra integro-differential equations

We describe an algorithm, based on Euler's method, for solving Volterra integro-differential equations. The algorithm approximates the relevant integral by means of the composite Trapezium Rule, using the discrete nodes of the independent variable as the required nodes for the integration variable. We have developed an error control device, using Richardson extrapolation, and we have achieved accuracy better than 1e-12 for all numerical examples considered.Comment: 11 page

Stability analysis of an implicit and explicit numerical method for Volterra integro-differential equations with kernel K(x,y(t),t)

We present implicit and explicit versions of a numerical algorithm for solving a Volterra integro-differential equation. These algorithms are an extension of our previous work, and cater for a kernel of general form. We use an appropriate test equation to study the stability of both algorithms,, numerically deriving stability regions. The region for the implicit method appears to be unbounded, while the explicit has a bounded region close to the origin. We perform a few calculations to demonstrate our results.Comment: 10 pages, 1 Figur

Error propagation in an explicit and an implicit numerical method for Volterra integro-differential equations

We study error propagation in both an explicit and an implicit method for solving Volterra integro-differential equations. We determine the relationship between local and global errors. We derive upper bounds for the global error, and show that the global order for both methods is expected to be first-order. A few numerical examples illustrate our results.Comment: 14p, 5 fig

Emergency medical dispatch recognition, clinical intervention and outcome of patients in traumatic cardiac arrest from major trauma : an observational study

© Author(s) (or their employer(s)) 2018. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.OBJECTIVES: The aim of this study is to describe the demographics of reported traumatic cardiac arrest (TCA) victims, prehospital resuscitation and survival to hospital rate. SETTING: Helicopter Emergency Medical Service (HEMS) in south-east England, covering a resident population of 4.5 million and a transient population of up to 8 million people. PARTICIPANTS: Patients reported on the initial 999 call to be in suspected traumatic cardiac arrest between 1 July 2016 and 31 December 2016 within the trust's geographical region were identified. The inclusion criteria were all cases of reported TCA on receipt of the initial emergency call. Patients were subsequently excluded if a medical cause of cardiac arrest was suspected. OUTCOME MEASURES: Patient records were analysed for actual presence of cardiac arrest, prehospital resuscitation procedures undertaken and for survival to hospital rates. RESULTS: 112 patients were reported to be in TCA on receipt of the 999/112 call. 51 (46%) were found not to be in TCA on arrival of emergency medical services. Of the 'not in TCA cohort', 34 (67%) received at least one advanced prehospital medical intervention (defined as emergency anaesthesia, thoracostomy, blood product transfusion or resuscitative thoracotomy). Of the 61 patients in actual TCA, 10 (16%) achieved return-of-spontaneous circulation. In 45 (88%) patients, the HEMS team escorted the patient to hospital. CONCLUSION: A significant proportion of patients reported to be in TCA on receipt of the emergency call are not in actual cardiac arrest but are critically unwell requiring advanced prehospital medical intervention. Early activation of an enhanced care team to a reported TCA call allows appropriate advanced resuscitation. Further research is warranted to determine which interventions contribute to improved TCA survival.Peer reviewedFinal Published versio

Transformation of stimulus correlations by the retina

Redundancies and correlations in the responses of sensory neurons seem to waste neural resources but can carry cues about structured stimuli and may help the brain to correct for response errors. To assess how the retina negotiates this tradeoff, we measured simultaneous responses from populations of ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure. We found that pairwise correlations in the retinal output remained similar across stimuli with widely different spatio-temporal correlations including white noise and natural movies. Meanwhile, purely spatial correlations tended to increase correlations in the retinal response. Responding to more correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the similarity of pairwise correlations across stimuli where receptive field measurements were possible.Comment: author list corrected in metadat