Demonstrating the Central Limit Theorem Using MATLAB

In this paper MATLAB is used in a demonstration of the central limit theorem (CLT). MATLAB is a powerful computer program used in educa­tion and industry. MATLAB allows us to increase the sample size and not sacrifice speed of computation while demonstrating the basic concept of the CLT as it applies to probability and statistics. We will give its history as well as a clear understanding of its power. In addition to reproducing previous work[l], we will provide the MATLAB code used to perform further dem­onstrations. Our program will select 30 integers between one and six, as in Lazari et. al. It will then compute each individual mean (L1) and store it in a list (L5) while repeating itself n times, where n is the total number of en­sembles. Upon completion, distribution plots are obtained for then means as well as a combined histogram for each individual (L5). For a very large n, the program does indeed demonstrate that the distribution of the sample means is really normal as in Lazari et al

The OmniPod Insulin Management System: the latest innovation in insulin pump therapy

This review of insulin pump therapy focuses on the OmniPod® Insulin Management System (Insulet Corp., Bedford, MA, USA). The OmniPod System is the first commercially available “patch pump.” It is a fully integrated wearable pump, controlled wirelessly through a handheld device containing a built-in blood glucose meter. This is an evaluation of the OmniPod System, with the aim of providing an educational tool for physicians who are considering recommending this product to their patients. The review includes a discussion of the traditional insulin pump configuration and its limitations, a detailed overview of the OmniPod System, references to clinical study data, planned product enhancements, its use as an insulin delivery system in the Juvenile Diabetes Research Foundation’s Artificial Pancreas Project, and its use to deliver additional compounds

Data-Driven Robust Control for Type 1 Diabetes Under Meal and Exercise Uncertainties

We present a fully closed-loop design for an artificial pancreas (AP) which regulates the delivery of insulin for the control of Type I diabetes. Our AP controller operates in a fully automated fashion, without requiring any manual interaction (e.g. in the form of meal announcements) with the patient. A major obstacle to achieving closed-loop insulin control is the uncertainty in those aspects of a patient's daily behavior that significantly affect blood glucose, especially in relation to meals and physical activity. To handle such uncertainties, we develop a data-driven robust model-predictive control framework, where we capture a wide range of individual meal and exercise patterns using uncertainty sets learned from historical data. These sets are then used in the controller and state estimator to achieve automated, precise, and personalized insulin therapy. We provide an extensive in silico evaluation of our robust AP design, demonstrating the potential of this approach, without explicit meal announcements, to support high carbohydrate disturbances and to regulate glucose levels in large clusters of virtual patients learned from population-wide survey data.Comment: Extended version of paper accepted at the 15th International Conference on Computational Methods in Systems Biolog

Regional and hemispheric influences on measured spring peroxyacetyl nitrate (PAN) mixing ratios at the Auchencorth UK EMEP supersite

AbstractThis work presents 15-min averaged measurements of peroxyacetyl nitrate (PAN) obtained during spring 2014 (24/04/2014 – 06/05/2014) at the Auchencorth UK EMEP supersite (southeast Scotland). The aim of this analysis was to investigate the conditions producing the distribution of PAN mixing ratios at the supersite in spring 2014. Air mass back trajectories showed the majority of air masses to have spent substantial time over the UK, continental Europe or Scandinavia prior to arrival at Auchencorth. The median and 95th percentile PAN mixing ratios observed were 0.46ppb and 1.03ppb, respectively. The median mixing ratio was elevated compared with previous PAN measurements during springtime (April–May) in southeast Scotland (corresponding median mixing ratios April–May 1994–1998: 0.1–0.3ppb), which is hypothesised to be due to conditions conducive to regional (European) photochemical PAN production. Additionally, PAN mixing ratios during regionally influenced conditions (0.4–1.5ppb) were substantially more elevated from hemispheric background mixing ratios (0.4–0.6ppb) than for ozone (O3, regional: 10–45ppb, hemispheric: 30–40ppb). PAN and O3 both impact upon vegetation and human health and it is necessary to understand the extent to which hemispheric and regional processes contribute to their abundances in different locations. Regional processes can both increase and decrease PAN and O3 mixing ratios compared to imported hemispheric background mixing ratios. This study concludes that during the measurement period in spring 2014 at the Auchencorth supersite, regional PAN and O3 modifying processes enhanced PAN mixing ratios more than for O3