Divergent mathematical treatments in utility theory

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper

Mathematical modeling in Medical Sciences

This article mainly concerns with mathematical modelling in medicine. There is one area in medicine namely pharmaco- kinetics which have already been mathematicized. There are large areas in medical science which are not amenable to mathematical treatment, and modelling constantly endeavour to widen the areas to which mathematical techniques can be applied for gaining a better insight, and help deepen our understanding of those areas which have already been mathematicized. The skills needed to be successful in applying mathematics are quite different from those needed to understand concepts, to prove theorems or to solve equations. The difficulty is not in learning and understanding the mathematics involved but in seeing where and how to apply it. In this paper an attempt is made to demonstrate the essentials of mathematical modelling without going deep in to the details on specialised topics

3D modelling of Ti–6Al–4V linear friction welds

Linear friction welding (LFW) is a solid-state joining process that significantly reduces manufacturing costs when fabricating Ti–6Al–4V aircraft components. This article describes the development of a novel 3D LFW process model for joining Ti–6Al–4V. Displacement histories were taken from experiments and used as modelling inputs; herein is the novelty of the approach, which resulted in decreased computational time and memory storage requirements. In general, the models captured the experimental weld phenomena and showed that the thermo-mechanically affected zone and interface temperature are reduced when the workpieces are oscillated along the shorter of the two interface contact dimensions. Moreover, the models showed that unbonded regions occur at the corners of the weld interface, which are eliminated by increasing the burn-off

Developing and testing accelerated partner therapy for partner notification for people with genital Chlamydia trachomatis diagnosed in primary care: a pilot randomised controlled trial

Background Accelerated partner therapy (APT) is a promising partner notification (PN) intervention in specialist sexual health clinic attenders. To address its applicability in primary care, we undertook a pilot randomised controlled trial (RCT) of two APT models in community settings. Methods Three-arm pilot RCT of two adjunct APT interventions: APTHotline (telephone assessment of partner(s) plus standard PN) and APTPharmacy (community pharmacist assessment of partner(s) plus routine PN), versus standard PN alone (patient referral). Index patients were women diagnosed with genital chlamydia in 12 general practices and three community contraception and sexual health (CASH) services in London and south coast of England, randomised between 1 September 2011 and 31 July 2013. Results 199 women described 339 male partners, of whom 313 were reported by the index as contactable. The proportions of contactable partners considered treated within 6 weeks of index diagnosis were APTHotline 39/111 (35%), APTPharmacy 46/100 (46%), standard patient referral 46/102 (45%). Among treated partners, 8/39 (21%) in APTHotline arm were treated via hotline and 14/46 (30%) in APTPharmacy arm were treated via pharmacy. Conclusions The two novel primary care APT models were acceptable, feasible, compliant with regulations and capable of achieving acceptable outcomes within a pilot RCT but intervention uptake was low. Although addition of these interventions to standard PN did not result in a difference between arms, overall PN uptake was higher than previously reported in similar settings, probably as a result of introducing a formal evaluation. Recruitment to an individually randomised trial proved challenging and full evaluation will likely require service-level randomisation

TreeWatch.net : a water and carbon monitoring and modeling network to assess instant tree hydraulics and carbon status

TreeWatch.net is an initiative that has been developed to watch trees grow and function in real-time. It is a water- and carbon-monitoring and modeling network, in which high quality measurements of sap flow and stem diameter variation are collected on individual trees. Automated data processing using a cloud service enables instant visualization of water movement and radial stem growth. This can be used to demonstrate the sensitivity of trees to changing weather conditions, such as drought, heat waves, or heavy rain showers. But TreeWatch.net's true innovation lies in its use of these high precision harmonized data to also parameterize process-based tree models in real-time, which makes displaying the much needed mechanisms underlying tree responses to climate change possible. Continuous simulation of turgor to describe growth processes and long-term time series of hydraulic resistance to assess drought-vulnerability in real-time are only a few of the opportunities our approach offers. TreeWatch.net has been developed with the view to be complementary to existing forest monitoring networks and with the aim to contribute to existing dynamic global vegetation models. It provides high-quality data and real-time simulations in order to advance research on the impact of climate change on the biological response of trees and forests. Besides its application in natural forests to answer climate-change related scientific and political questions, we also envision a broader societal application of TreeWatch.net by selecting trees in nature reserves, public areas, cities, university areas, schoolyards, and parks to teach youngsters and create public awareness on the effects of changing weather conditions on trees and forests in this era of climate change

Timing of progression from Chlamydia trachomatis infection to pelvic inflammatory disease: a mathematical modelling study

PMCID: PMC3505463The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2334/12/187. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Computation of transient viscous flows using indirect radial basis function networks

In this paper, an indirect/integrated radial-basis-function network (IRBFN) method is further developed to solve transient partial differential equations (PDEs) governing fluid flow problems. Spatial derivatives are discretized using one- and two-dimensional IRBFN interpolation schemes, whereas temporal derivatives are approximated using a method of lines and a finite-difference technique. In the case of moving interface problems, the IRBFN method is combined with the level set method to capture the evolution of the interface. The accuracy of the method is investigated by considering several benchmark test problems, including the classical lid-driven cavity flow. Very accurate results are achieved using relatively low numbers of data points

Evaluation of innovative sprayed-concrete-lined tunnelling

The front-shunt tunnel was the first tunnel of the Terminal 5 project at Heathrow to be constructed, and was the first section of sprayed-concrete-lined (SCL) tunnel to be constructed using the method known as LaserShell. This innovation represented a significant deviation from the methods previously used in SCL construction. Therefore it was subjected to a careful examination before and during construction using sophisticated 3D numerical modelling and monitoring during construction. The paper presents typical results from surface settlement levelling, inclinometers and extensometers, pressure cells and tunnel lining displacement measurements, and comments on the performance of the methods and instruments used. The paper then presents the methodology and typical results of the numerical modelling, and shows that the predictions of displacements and stresses compared well with the field measurements. In terms of the control of ground deformations and structural safety the tunnel performed well