Proviola: A Tool for Proof Re-animation

To improve on existing models of interaction with a proof assistant (PA), in particular for storage and replay of proofs, we in- troduce three related concepts, those of: a proof movie, consisting of frames which record both user input and the corresponding PA response; a camera, which films a user's interactive session with a PA as a movie; and a proviola, which replays a movie frame-by-frame to a third party. In this paper we describe the movie data structure and we discuss a proto- type implementation of the camera and proviola based on the ProofWeb system. ProofWeb uncouples the interaction with a PA via a web- interface (the client) from the actual PA that resides on the server. Our camera films a movie by "listening" to the ProofWeb communication. The first reason for developing movies is to uncouple the reviewing of a formal proof from the PA used to develop it: the movie concept enables users to discuss small code fragments without the need to install the PA or to load a whole library into it. Other advantages include the possibility to develop a separate com- mentary track to discuss or explain the PA interaction. We assert that a combined camera+proviola provides a generic layer between a client (user) and a server (PA). Finally we claim that movies are the right type of data to be stored in an encyclopedia of formalized mathematics, based on our experience in filming the Coq standard library.Comment: Accepted for the 9th International Conference on Mathematical Knowledge Management (MKM 2010), 15 page

Improving the optimization solution for a semi-analytical shallow water inversion model in the presence of spectrally correlated noise

In coastal regions, shallow water semi-analytical inversion algorithms may be used to derive geophysical parameters such as inherent optical properties (IOPs), water column depth, and bottom albedo coefficients by inverting sensor-derived sub-surface remote sensing reflectance, rrs. The uncertainties of these derived geophysical parameters due to instrumental and environmental noise can be estimated numerically via the addition of spectral noise to the sensor-derived rrs before inversion. Repeating this process multiple times allows the calculation of the standard error and average for each derived parameter. Apart from spectral non-uniqueness, the optimization algorithm employed in the inversion must converge onto a single minimum to obtain a true representation of the uncertainty for a given set of noise-perturbed rrs. Failure to do so inflates the uncertainty and affects the average retrieved value (accuracy). We show that the standard approach of seeding the optimization with an arbitrary, fixed initial guess, can lead to the convergence to multiple minima, each having substantially different centroids in multi-parameter solution space. We present the Update-Repeat Levenberg-Marquardt (UR-LM) and Latin Hypercube Sampling (LHS) routines that dynamically search the solution space for an optimal initial guess, that when applied to the optimization allows convergence to the best local minimum. We apply the UR-LM and LHS methods on HICO-derived and simulated rrs and demonstrate the improved computational efficiency, precision, and accuracy afforded from these methods compared with the standard approach. Conceptually, these methods are applicable to remote sensing based, shallow water or oceanic semi-analytical inversion algorithms requiring nonlinear least squares optimization

Model for deriving benthic irradiance in the Great Barrier Reef from MODIS satellite imagery

We demonstrate a simple, spectrally resolved ocean color remote sensing model to estimate benthic photosynthetically active radiation (bPAR) for the waters of the Great Barrier Reef (GBR), Australia. For coastal marine environments and coral reefs, the underwater light field is critical to ecosystem health, but data on bPAR rarely exist at ecologically relevant spatio-temporal scales. The bPAR model presented here is based on Lambert-Beer’s Law and uses: (i) sea surface values of the downwelling solar irradiance, Es(λ); (ii) high-resolution seafloor bathymetry data; and (iii) spectral estimates of the diffuse attenuation coefficient, Kd(λ), calculated from GBR-specific spectral inherent optical properties (IOPs). We first derive estimates of instantaneous bPAR. Assuming clear skies, these instantaneous values were then used to obtain daily integrated benthic PAR values. Matchup comparisons between concurrent satellite-derived bPAR and in situ values recorded at four optically varying test sites indicated strong agreement, small bias, and low mean absolute error. Overall, the matchup results suggest that our benthic irradiance model was robust to spatial variation in optical properties, typical of complex shallow coastal waters such as the GBR. We demonstrated the bPAR model for a small test region in the central GBR, with the results revealing strong patterns of temporal variability. The model will provide baseline datasets to assess changes in bPAR and its external drivers and may form the basis for a future GBR water-quality index. This model may also be applicable to other coastal waters for which spectral IOP and high-resolution bathymetry data exist

Type-and-Scope Safe Programs and Their Proofs

We abstract the common type-and-scope safe structure fromcomputations on lambda-terms that deliver, e.g., renaming, substitution, evaluation, CPS-transformation, and printing witha name supply. By exposing this structure, we can prove generic simulation and fusion lemmas relating operations built this way. This work has been fully formalised in Agda

A Focused Sequent Calculus Framework for Proof Search in Pure Type Systems

Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the issues of defining such sequent calculi for Pure Type Systems (PTS, which were originally presented in natural deduction style) and then organizing their rules for effective proof-search. We introduce the idea of Pure Type Sequent Calculus with meta-variables (PTSCalpha), by enriching the syntax of a permutation-free sequent calculus for propositional logic due to Herbelin, which is strongly related to natural deduction and already well adapted to proof-search. The operational semantics is adapted from Herbelin's and is defined by a system of local rewrite rules as in cut-elimination, using explicit substitutions. We prove confluence for this system. Restricting our attention to PTSC, a type system for the ground terms of this system, we obtain the Subject Reduction property and show that each PTSC is logically equivalent to its corresponding PTS, and the former is strongly normalising iff the latter is. We show how to make the logical rules of PTSC into a syntax-directed system PS for proof-search, by incorporating the conversion rules as in syntax-directed presentations of the PTS rules for type-checking. Finally, we consider how to use the explicitly scoped meta-variables of PTSCalpha to represent partial proof-terms, and use them to analyse interactive proof construction. This sets up a framework PE in which we are able to study proof-search strategies, type inhabitant enumeration and (higher-order) unification

A pilot trial to evaluate the acute toxicity and feasibility of tamoxifen for prevention of breast cancer.

Epidemiological and experimental evidence indicates that oestrogens are involved in the carcinogenic promotion of human breast cancer. We have undertaken a pilot trial of tamoxifen, an anti-oestrogen, compared to placebo given to 200 women at a high risk of developing breast cancer. The results of this trial show that acute toxicity is low and that accrual and compliance are satisfactory. Furthermore, biochemical monitoring of lipids and clotting factors indicate that tamoxifen may reduce the risk of cardiovascular deaths. At this stage no untoward long-term risks have been identified, and it is therefore proposed that a large multicentre trial should be started

Lobular carcinoma in situ of the breast is not caused by constitutional mutations in the E-cadherin gene

Lobular carcinoma in situ (LCIS) is an unusual histological pattern of non-invasive neoplastic disease of the breast occurring predominantly in women aged between 40 and 50 years. LCIS is frequently multicentric and bilateral, and there is evidence that it is associated with an elevated familial risk of breast cancer. Although women with LCIS suffer an increased risk of invasive breast disease, this risk is moderate suggesting that LCIS may result from mutation of a gene or genes conferring a high risk of LCIS, but a lower risk of invasive breast cancer. The high frequency of somatic mutations in E-cadherin in LCIS, coupled with recent reports that germline mutations in this gene can predispose to diffuse gastric cancer, raised the possibility that constitutional E-cadherin mutations may confer susceptibility to LCIS. In order to explore this possibility we have examined a series of 65 LCIS patients for germline E-cadherin mutations. Four polymorphisms were detected but no pathogenic mutations were identified. The results indicate that E-cadherin is unlikely to act as a susceptibility gene for LCIS. © 2000 Cancer Research Campaig