Verification of floating point programs

In this thesis we present an approach to automated verification of floating point programs. Existing techniques for automated generation of correctness theorems are extended to produce proof obligations for accuracy guarantees and absence of floating point exceptions. A prototype automated real number theorem prover is presented, demonstrating a novel application of function interval arithmetic in the context of subdivision-based numerical theorem proving. The prototype is tested on correctness theorems for two simple yet nontrivial programs, proving exception freedom and tight accuracy guarantees automatically. The prover demonstrates a novel application of function interval arithmetic in the context of subdivision-based numerical theorem proving. The experiments show how function intervals can be used to combat the information loss problems that limit the applicability of traditional interval arithmetic in the context of hard real number theorem proving.

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs. © 2014 Springer International Publishing Switzerland.

Les quantifieurs flottants sont des attributs quantitatifs totalisants

This paper considers three features of Floating Quantifiers FQ) in French. FQs comprise a larger class of items than is usually recognised; criterial distribution within the verb phrase and adjoined to a relative pronoun apply not only to the equivalents of all and each, but also to only, them both, one another and related items. This extension leads to the question of what properties may be defining the class. The semantic property is that of commenting on the relation between the individual entities and the set of the noun they belong to. Akin to focus particles in this respect, FQs are optional complements. These complements relating semantically to a nominal argument belong to the category of attributive complements. The dissociation between the QF and the noun referred to is the syntactic property of the class. An attributive function with a semantic commentary on the make-up of the nominal set in question defines Floating Quantifiers.

Drug delivery strategies for the treatment of Helicobacter pylori infections

Helicobacter pylori is one of the most common pathogenic bacterial infections, colonising an estimated half of all humans. It is associated with the development of serious gastroduodenal disease - including peptic ulcers, gastric lymphoma and acute chronic gastritis. Current recommended regimes are not wholly effective and patient compliance, side-effects and bacterial resistance can be problematic. Drug delivery to the site of residence in the gastric mucosa may improve efficacy of the current and emerging treatments. Gastric retentive delivery systems potentially allow increased penetration of the mucus layer and therefore increased drug concentration at the site of action. Proposed gastric retentive systems for the enhancement of local drug delivery include floating systems, expandable or swellable systems and bioadhesive systems. Generally, problems with these formulations are lack of specificity, limited to mucus turnover or failure to persist in the stomach. Gastric mucoadhesive systems are hailed as a promising technology to address this issue, penetrating the mucus layer and prolonging activity at the mucus-epithelial interface. This review appraises gastroretentive delivery strategies specifically with regard to their application as a delivery system to target Helicobacter. As drug-resistant strains emerge, the development of a vaccine to eradicate and prevent reinfection is an attractive proposition. Proposed prophylactic and therapeutic vaccines have been delivered using a number of mucosal routes using viral and non-viral vectors. The delivery form, inclusion of adjuvants, and delivery regime will influence the immune response generated. © 2005 Bentham Science Publishers Ltd.

Time complexity and convergence analysis of domain theoretic Picard method

We present an implementation of the domain-theoretic Picard method for solving initial value problems (IVPs) introduced by Edalat and Pattinson [1]. Compared to Edalat and Pattinson's implementation, our algorithm uses a more efficient arithmetic based on an arbitrary precision floating-point library. Despite the additional overestimations due to floating-point rounding, we obtain a similar bound on the convergence rate of the produced approximations. Moreover, our convergence analysis is detailed enough to allow a static optimisation in the growth of the precision used in successive Picard iterations. Such optimisation greatly improves the efficiency of the solving process. Although a similar optimisation could be performed dynamically without our analysis, a static one gives us a significant advantage: we are able to predict the time it will take the solver to obtain an approximation of a certain (arbitrarily high) quality.

Corporate restructuring: empirical evidence from the UK

Corporate restructuring is perceived as a challenge to research. Prior studies do not provide conclusive evidence regarding the effects of restructuring. Since there are discernible findings, this research attempts to examine the effects of restructuring events amongst the UK listed firms. The sample firms are listed in the LSE and London AIM stock exchange. Only completed restructuring transactions are included in the study. The time horizon extends from year 1999 to 2003. A three-year floating window is assigned to examine the sample firms. The key enquiry is to scrutinise the ex post effects of restructuring on performance and value measures of firms with contrast to a matched criteria non-restructured sample. A cross sectional study employing logit estimate is undertaken to examine firm characteristics of restructuring samples. Further, additional parameters, i.e. Conditional Volatility and Asymmetry are generated under the GJR-GARCH estimate and reiterated in logit models to capture time-varying heteroscedasticity of the samples. This research incorporates most forms of restructurings, while prior studies have examined certain forms of restructuring. Particularly, these studies have made limited attempts to examine different restructuring events simultaneously. In addition to logit analysis, an event study is adopted to evaluate the announcement effect of restructuring under both the OLS and GJR-GARCH estimate supplementing our prior results. By engaging a composite empirical framework, our estimation method validates a full appreciation of restructuring effect. The study provides evidence that restructurings indicate non-trivial significant positive effect. There are some evidences that the response differs because of the types of restructuring, particularly while event study is applied. The results establish that performance measures, i.e. Operating Profit Margin, Return on Equity, Return on Assets, Growth, Size, Profit Margin and Shareholders' Ownership indicate consistent and significant increase. However, Leverage and Asset Turn Over suggest reasonable influence on restructuring across the sample period. Similarly, value measures, i.e. Abnormal Returns, Return on Equity and Cash Flow Margin suggest sizeable improvement. A notable characteristic seen coherently throughout the analysis is the decreasing proportion of Systematic Risk. Consistent with these findings, Conditional Volatility and Asymmetry exhibit similar trend. The event study analysis suggests that on an average market perceives restructuring favourably and shareholders experience significant and systematic positive gain.

Dynamic behaviour of rotary mechanical seals

This thesis covers both experimental and computer investigations into the dynamic behaviour of mechanical seals. The literature survey shows no investigations on the effect of vibration on mechanical seals of the type common in the various process industries. Typical seal designs are discussed. A form of Reynolds' equation has been developed that permits the calculation of stiffnesses and damping coefficients for the fluid film. The dynamics of the mechanical seal floating ring have been investigated using approximate formulae, and it has been shown that the floating ring will behave as a rigid body. Some elements, such as the radial damping due to the fluid film, are small and may be neglected. The equations of motion of the floating ring have been developed utilising the significant elements, and a solution technique described. The stiffness and damping coefficients of nitrile rubber o-rings have been obtained. These show a wide variation, with a constant stiffness up to 60 Hz. The importance of the effect of temperature on the properties is discussed. An unsuccessful test rig is described in the appendices. The dynamic behaviour of a mechanical seal has been investigated experimentally, including the effect of changes of speed, sealed pressure and seal geometry. The results, as expected, show that high vibration levels result in both high leakage and seal temperatures. Computer programs have been developed to solve Reynolds' Equation and the equations of motion. Two solution techniques for this latter program were developed, the unsuccesful technique is described in the appendices. Some stability problems were encountered, but despite these the solution shows good agreement with some of the experimental conditions. Possible reasons for the discrepancies are discussed. Various suggestions for future work in this field are given. These include the combining of the programs and more extensive experimental and computer modelling.

Slow light optofluidics:a proposal

The resonant slow light structures created along a thin-walled optical capillary by nanoscale deformation of its surface can perform comprehensive simultaneous detection and manipulation of microfluidic components. This concept is illustrated with a model of a 0.5 mm long, 5 nm high, triangular bottle resonator created at a 50 μm radius silica capillary containing floating microparticles. The developed theory shows that the microparticle positions can be determined from the bottle resonator spectrum. In addition, the microparticles can be driven and simultaneously positioned at predetermined locations by the localized electromagnetic field created by the optimized superposition of eigenstates of this resonator, thus exhibiting a multicomponent, near-field optical tweezer.