Formal analysis techniques for gossiping protocols

We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them

Quantitative Verification: Formal Guarantees for Timeliness, Reliability and Performance

Computerised systems appear in almost all aspects of our daily lives, often in safety-critical scenarios such as embedded control systems in cars and aircraft or medical devices such as pacemakers and sensors. We are thus increasingly reliant on these systems working correctly, despite often operating in unpredictable or unreliable environments. Designers of such devices need ways to guarantee that they will operate in a reliable and efficient manner. Quantitative verification is a technique for analysing quantitative aspects of a system's design, such as timeliness, reliability or performance. It applies formal methods, based on a rigorous analysis of a mathematical model of the system, to automatically prove certain precisely specified properties, e.g. ``the airbag will always deploy within 20 milliseconds after a crash'' or ``the probability of both sensors failing simultaneously is less than 0.001''. The ability to formally guarantee quantitative properties of this kind is beneficial across a wide range of application domains. For example, in safety-critical systems, it may be essential to establish credible bounds on the probability with which certain failures or combinations of failures can occur. In embedded control systems, it is often important to comply with strict constraints on timing or resources. More generally, being able to derive guarantees on precisely specified levels of performance or efficiency is a valuable tool in the design of, for example, wireless networking protocols, robotic systems or power management algorithms, to name but a few. This report gives a short introduction to quantitative verification, focusing in particular on a widely used technique called model checking, and its generalisation to the analysis of quantitative aspects of a system such as timing, probabilistic behaviour or resource usage. The intended audience is industrial designers and developers of systems such as those highlighted above who could benefit from the application of quantitative verification,but lack expertise in formal verification or modelling

Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

Linear, integer separable and fuzzy programming problems: a united approach towards automatic reformulation

For mathematical programming (MP) to have greater impact as a decision tool, MP software systems must offer suitable support in terms of model communication and modelling techniques. In this paper modelling techniques that allow logical restrictions to be modelled in integer programming terms are described and their implications discussed. In addition it is demonstrated that many classes of non-linearities which are not variable separable may be after suitable algebraic manipulation put in a variable separable form. The methods of reformulating the fuzzy linear programming problem as a Max-Min problem is also introduced. It is shown that analysis of bounds plays a key role in the following four important contexts: model reduction, reformulation of logical restrictions as 0-1 mixed integer programs, reformulation of nonlinear programs as variable separable programs and reformulation of fuzzy linear programs. It is observed that as well as incorporating an interface between the modeller and the optimiser there is a need to make available to the modeller software facilities which support the model reformulation techniques described here

Advances in computational modelling for personalised medicine after myocardial infarction

Myocardial infarction (MI) is a leading cause of premature morbidity and mortality worldwide. Determining which patients will experience heart failure and sudden cardiac death after an acute MI is notoriously difficult for clinicians. The extent of heart damage after an acute MI is informed by cardiac imaging, typically using echocardiography or sometimes, cardiac magnetic resonance (CMR). These scans provide complex data sets that are only partially exploited by clinicians in daily practice, implying potential for improved risk assessment. Computational modelling of left ventricular (LV) function can bridge the gap towards personalised medicine using cardiac imaging in patients with post-MI. Several novel biomechanical parameters have theoretical prognostic value and may be useful to reflect the biomechanical effects of novel preventive therapy for adverse remodelling post-MI. These parameters include myocardial contractility (regional and global), stiffness and stress. Further, the parameters can be delineated spatially to correspond with infarct pathology and the remote zone. While these parameters hold promise, there are challenges for translating MI modelling into clinical practice, including model uncertainty, validation and verification, as well as time-efficient processing. More research is needed to (1) simplify imaging with CMR in patients with post-MI, while preserving diagnostic accuracy and patient tolerance (2) to assess and validate novel biomechanical parameters against established prognostic biomarkers, such as LV ejection fraction and infarct size. Accessible software packages with minimal user interaction are also needed. Translating benefits to patients will be achieved through a multidisciplinary approach including clinicians, mathematicians, statisticians and industry partners

A theoretical study of the response of vascular tumours to different types of chemotherapy

In this paper we formulate and explore a mathematical model to study continuous infusion of a vascular tumour with isolated and combined blood-borne chemotherapies. The mathematical model comprises a system of nonlinear partial differential equations that describe the evolution of the healthy (host) cells, the tumour cells and the tumour vasculature, coupled with distribution of a generic angiogenic stimulant (TAF) and blood-borne oxygen. A novel aspect of our model is the presence of blood-borne chemotherapeutic drugs which target different aspects of tumour growth (cf. proliferating cells, the angiogenic stimulant or the tumour vasculature). We run exhaustive numerical simulations in order to compare vascular tumour growth before and following therapy. Our results suggest that continuous exposure to anti-proliferative drug will result in the vascular tumour being cleared, becoming growth-arrested or growing at a reduced rate, the outcome depending on the drug’s potency and its rate of uptake. When the angiogenic stimulant or the tumour vasculature are targeted by the therapy, tumour elimination can not occur: at best vascular growth is retarded and the tumour reverts to an avascular form. Application of a combined treatment that destroys the vasculature and the TAF, yields results that resemble those achieved following successful treatment with anti-TAF or anti-vascular therapy. In contrast, combining anti-proliferative therapy with anti-TAF or antivascular therapy can eliminate the vascular tumour. In conclusion, our results suggest that tumour growth and the time of tumour clearance are highly sensitive to the specific combinations of anti-proliferative, anti-TAF and anti-vascular drugs

QoE Modelling, Measurement and Prediction: A Review

In mobile computing systems, users can access network services anywhere and anytime using mobile devices such as tablets and smart phones. These devices connect to the Internet via network or telecommunications operators. Users usually have some expectations about the services provided to them by different operators. Users' expectations along with additional factors such as cognitive and behavioural states, cost, and network quality of service (QoS) may determine their quality of experience (QoE). If users are not satisfied with their QoE, they may switch to different providers or may stop using a particular application or service. Thus, QoE measurement and prediction techniques may benefit users in availing personalized services from service providers. On the other hand, it can help service providers to achieve lower user-operator switchover. This paper presents a review of the state-the-art research in the area of QoE modelling, measurement and prediction. In particular, we investigate and discuss the strengths and shortcomings of existing techniques. Finally, we present future research directions for developing novel QoE measurement and prediction technique