Finding polynomial loop invariants for probabilistic programs

Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an alternative approach. First, we fix a polynomial template as a candidate of a loop invariant. Using Stengle's Positivstellensatz and a transformation to a sum-of-squares problem, we find sufficient conditions on the coefficients. Then, we solve a semidefinite programming feasibility problem to synthesize the loop invariants. If the semidefinite program is unfeasible, we backtrack after increasing the degree of the template. Our approach is semi-complete in the sense that it will always lead us to a feasible solution if one exists and numerical errors are small. Experimental results show the efficiency of our approach.Comment: accompanies an ATVA 2017 submissio

Computational modelling of cancerous mutations in the EGFR/ERK signalling pathway

This article has been made available through the Brunel Open Access Publishing Fund - Copyright @ 2009 Orton et al.BACKGROUND: The Epidermal Growth Factor Receptor (EGFR) activated Extracellular-signal Regulated Kinase (ERK) pathway is a critical cell signalling pathway that relays the signal for a cell to proliferate from the plasma membrane to the nucleus. Deregulation of the EGFR/ERK pathway due to alterations affecting the expression or function of a number of pathway components has long been associated with numerous forms of cancer. Under normal conditions, Epidermal Growth Factor (EGF) stimulates a rapid but transient activation of ERK as the signal is rapidly shutdown. Whereas, under cancerous mutation conditions the ERK signal cannot be shutdown and is sustained resulting in the constitutive activation of ERK and continual cell proliferation. In this study, we have used computational modelling techniques to investigate what effects various cancerous alterations have on the signalling flow through the ERK pathway. RESULTS: We have generated a new model of the EGFR activated ERK pathway, which was verified by our own experimental data. We then altered our model to represent various cancerous situations such as Ras, B-Raf and EGFR mutations, as well as EGFR overexpression. Analysis of the models showed that different cancerous situations resulted in different signalling patterns through the ERK pathway, especially when compared to the normal EGF signal pattern. Our model predicts that cancerous EGFR mutation and overexpression signals almost exclusively via the Rap1 pathway, predicting that this pathway is the best target for drugs. Furthermore, our model also highlights the importance of receptor degradation in normal and cancerous EGFR signalling, and suggests that receptor degradation is a key difference between the signalling from the EGF and Nerve Growth Factor (NGF) receptors. CONCLUSION: Our results suggest that different routes to ERK activation are being utilised in different cancerous situations which therefore has interesting implications for drug selection strategies. We also conducted a comparison of the critical differences between signalling from different growth factor receptors (namely EGFR, mutated EGFR, NGF, and Insulin) with our results suggesting the difference between the systems are large scale and can be attributed to the presence/absence of entire pathways rather than subtle difference in individual rate constants between the systems.This work was funded by the Department of Trade and Industry (DTI), under their Bioscience Beacon project programme. AG was funded by an industrial PhD studentship from Scottish Enterprise and Cyclacel

Brownian bridges to submanifolds

We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete Riemannian manifold. We use the formula to derive lower bounds, an asymptotic relation and derivative estimates. We also see a connection to hypersurface local time. This work is motivated by the desire to extend the analysis of path and loop spaces to measures on paths which terminate on a submanifold

Is gynaecological surgical training a cause for concern? A questionnaire survey of trainees and trainers

<p>Astract</p> <p>Background</p> <p>Concerns have been raised as to whether the current postgraduate training programme for gynaecological surgery is being detrimentally affected by changes in working practices, in particular the European Working Time Directive (EWTD). The purpose of this study was to investigate the surgical activity of obstetrics and gynaecology trainees and to explore trainees' and trainers' opinions on the current barriers and potential solutions to surgical training.</p> <p>Methods</p> <p>Two questionnaire surveys were conducted, one to obstetrics and gynaecology trainees working within the West Midlands Deanery and a second to consultant gynaecologists in the West Midlands region.</p> <p>Results</p> <p>One hundred and four trainees (64.3%) and 66 consultant gynaecologists (55.0%) responded. Sixty-six trainees (66.7%) reported attending up to one operating list per week. However, 28.1% reported attending up to one list every two weeks or less and 5 trainees stated that they had not attended a list at all over the preceding 8 weeks. Trainees working in a unit with less than 3999 deliveries attended significantly more theatre sessions compared to trainees in units with over 4000 deliveries (p = 0.007), as did senior trainees (p = 0.032) and trainees attached to consultants performing major gynaecological surgery (p = 0.022). In the previous 8 weeks, only 6 trainees reported performing a total abdominal hysterectomy independently, all were senior trainees (ST6 and above). In the trainers' survey, only two respondents (3.0%) agreed that the current program produces doctors competent in general gynaecological surgery by the end of training, compared to 48 (73.8%) respondents who disagreed.</p> <p>Conclusions</p> <p>Trainees' concerns over a lack of surgical training appear to be justified. The main barriers to training are perceived to be a lack of team structure and a lack of theatre time.</p

Role of MC1R variants in uveal melanoma

Variants of the melanocortin-1 receptor (MC1R) gene have been linked to sun-sensitive skin types and hair colour, and may independently play a role in susceptibility to cutaneous melanoma. To assess the role of MC1R variants in uveal melanoma, we have analysed a cohort of 350 patients for the changes within the major region of the gene displaying sequence variation. Eight variants were detected – V60L, D84E, V92M, R151C, I155T, R160W, R163Q and D294H – 63% of these patients being hetero- or homozygous for at least one variant. Standard melanoma risk factor data were available on 119 of the patients. MC1R variants were significantly associated with hair colour (P¼0.03) but not skin or eye colour. The frequency of the variants detected in the 350 patients was comparable with those in the general population, and comparison of the cumulative tumour distribution by age at diagnosis in carriers and noncarriers provided no evidence that MC1R variants confer an increased risk of uveal melanoma. We interpret the data as indicating that MC1R variants do not appear to be major determinants of susceptibility to uveal melanoma. © 2003 Cancer Research U

Regionalisation of trauma care in England

Aims We aimed to determine whether there is evidence of improved patient outcomes in Major Trauma Centres following the regionalisation of trauma care in England. Patients and Methods An observational study was undertaken using the Trauma Audit and Research Network (TARN), Hospital Episode Statistics (HES) and national death registrations. The outcome measures were indicators of the quality of trauma care, such as treatment by a senior doctor and clinical outcomes, such as mortality in hospital. Results and Conclusion A total of 20 181 major trauma cases were reported to TARN during the study period, which was 270 days before and after each hospital became a Major Trauma Centre. Following regionalisation of trauma services, all indicators of the quality of care improved, fewer patients required secondary transfer between hospitals and a greater proportion were discharged with a Glasgow Outcome Score of “good recovery”. In this early post-implementation analysis, there were a number of apparent process improvements (e.g. time to CT) but no differences in either crude or adjusted mortality. The overall number of deaths following trauma in England did not change following the national reconfiguration of trauma services. Evidence from other countries that have regionalised trauma services suggests that further benefits may become apparent after a period of maturing of the trauma system

Pharmaceutical cost control in primary care: opinion and contributions by healthcare professionals

<p>Abstract</p> <p>Background</p> <p>Strategies adopted by health administrations and directed towards drug cost control in primary care (PC) can, according to earlier studies, generate tension between health administrators and healthcare professionals. This study collects and analyzes the opinions of general practitioners (GPs) regarding current cost control measures as well as their proposals for improving the effectiveness of these measures.</p> <p>Methods</p> <p>A qualitative exploratory study was carried out using 11 focus groups composed of GPs from the Spanish regions of Aragon, Catalonia and the Balearic Islands. A semi-structured guide was applied in obtaining the GPs' opinions. The transcripts of the dialogues were analyzed by two investigators who independently considered categorical and thematic content. The results were supervised by other members of the team, with overall responsibility assigned to the team leader.</p> <p>Results</p> <p>GPs are conscious of their public responsibility with respect to pharmaceutical cost, but highlight the need to spread responsibility for cost control among the different actors of the health system. They insist on implementing measures to improve the quality of prescriptions, avoiding mere quantitative evaluations of prescription costs. They also suggest moving towards the self-management of the pharmaceutical budget by each health centre itself, as a means to design personalized incentives to improve their outcomes. These proposals need to be considered by the health administration in order to pre-empt the feelings of injustice, impotence, frustration and lack of motivation that currently exist among GPs as a result of the implemented measures.</p> <p>Conclusion</p> <p>Future investigations should be oriented toward strategies that involve GPs in the planning and management of drug cost control mechanisms. The proposals in this study may be considered by the health administration as a means to move toward the rational use of drugs while avoiding concerns about injustice and feelings of impotence on the part of the GPs, which can lead to lack of interest in and disaffection with the current measures.</p