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

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

Multiple novel prostate cancer susceptibility signals identified by fine-mapping of known risk loci among Europeans

Genome-wide association studies (GWAS) have identified numerous common prostate cancer (PrCa) susceptibility loci. We have fine-mapped 64 GWAS regions known at the conclusion of the iCOGS study using large-scale genotyping and imputation in 25 723 PrCa cases and 26 274 controls of European ancestry. We detected evidence for multiple independent signals at 16 regions, 12 of which contained additional newly identified significant associations. A single signal comprising a spectrum of correlated variation was observed at 39 regions; 35 of which are now described by a novel more significantly associated lead SNP, while the originally reported variant remained as the lead SNP only in 4 regions. We also confirmed two association signals in Europeans that had been previously reported only in East-Asian GWAS. Based on statistical evidence and linkage disequilibrium (LD) structure, we have curated and narrowed down the list of the most likely candidate causal variants for each region. Functional annotation using data from ENCODE filtered for PrCa cell lines and eQTL analysis demonstrated significant enrichment for overlap with bio-features within this set. By incorporating the novel risk variants identified here alongside the refined data for existing association signals, we estimate that these loci now explain ∼38.9% of the familial relative risk of PrCa, an 8.9% improvement over the previously reported GWAS tag SNPs. This suggests that a significant fraction of the heritability of PrCa may have been hidden during the discovery phase of GWAS, in particular due to the presence of multiple independent signals within the same regio

Abstracting Extensible Data Types: Or, Rows by Any Other Name

We present a novel typed language for extensible data types, generalizing and abstracting existing systems of row types and row polymorphism. Extensible data types are a powerful addition to traditional functional programming languages, capturing ideas from OOP-like record extension and polymorphism to modular compositional interpreters. We introduce row theories, a monoidal generalization of row types, giving a general account of record concatenation and projection (dually, variant injection and branching). We realize them via qualified types, abstracting the interpretation of records and variants over different row theories. Our approach naturally types terms untypable in other systems of extensible data types, while maintaining strong metatheoretic properties, such as coherence and principal types. Evidence for type qualifiers has computational content, determining the implementation of record and variant operations; we demonstrate this in giving a modular translation from our calculus, instantiated with various row theories, to polymorphic λ -calculus

Digitise This! A Quick and Easy Remote Sensing Method to Monitor the Daily Extent of Dredge Plumes

Technological advancements in remote sensing and GIS have improved natural resource managers’ abilities to monitor large-scale disturbances. In a time where many processes are heading towards automation, this study has regressed to simple techniques to bridge a gap found in the advancement of technology. The near-daily monitoring of dredge plume extent is common practice using Moderate Resolution Imaging Spectroradiometer (MODIS) imagery and associated algorithms to predict the total suspended solids (TSS) concentration in the surface waters originating from floods and dredge plumes. Unfortunately, these methods cannot determine the difference between dredge plume and benthic features in shallow, clear water. This case study at Barrow Island, Western Australia, uses hand digitising to demonstrate the ability of human interpretation to determine this difference with a level of confidence and compares the method to contemporary TSS methods. Hand digitising was quick, cheap and required very little training of staff to complete. Results of ANOSIM R statistics show remote sensing derived TSS provided similar spatial results if they were thresholded to at least 3 mg L-1. However, remote sensing derived TSS consistently provided false-positive readings of shallow benthic features as Plume with a threshold up to TSS of 6 mg L-1, and began providing false-negatives (excluding actual plume) at a threshold as low as 4 mg L-1. Semi-automated processes that estimate plume concentration and distinguish between plumes and shallow benthic features without the arbitrary nature of human interpretation would be preferred as a plume monitoring method. However, at this stage, the hand digitising method is very useful and is more accurate at determining plume boundaries over shallow benthic features and is accessible to all levels of management with basic training

Patients’ experiences of a suppoRted self-manAGeMent pAThway In breast Cancer (PRAGMATIC): quality of life and service use results

PurposeTo describe trends and explore factors associated with quality of life (QoL) and psychological morbidity and assess breast cancer (BC) health service use over a 12-month period for patients joining the supported self-management (SSM)/patient-initiated follow-up (PIFU) pathway.MethodsParticipants completed questionnaires at baseline, 3, 6, 9 and 12 months that measured QoL (FACT-B, EQ 5D-5L), self-efficacy (GSE), psychological morbidity (GHQ-12), roles and responsibilities (PRRS) and service use (cost diary).Results99/110 patients completed all timepoints; 32% (35/110) had received chemotherapy. The chemotherapy group had poorer QoL; FACT-B total score mean differences were 8.53 (95% CI: 3.42 to 13.64), 5.38 (95% CI: 0.17 to 10.58) and 8.00 (95% CI: 2.76 to 13.24) at 6, 9 and 12 months, respectively. The odds of psychological morbidity (GHQ12 >4) were 5.5-fold greater for those treated with chemotherapy. Financial and caring burdens (PRRS) were worse for this group (mean difference in change at 9 months 3.25 (95% CI: 0.42 to 6.07)). GSE and GHQ-12 scores impacted FACT-B total scores, indicating QoL decline for those with high baseline psychological morbidity. Chemotherapy patients or those with high psychological morbidity or were unable to carry out normal activities had the highest service costs. Over the 12 months, 68.2% participants phoned/emailed breast care nurses, and 53.3% visited a hospital breast clinician.ConclusionThe data suggest that chemotherapy patients and/or those with heightened psychological morbidity might benefit from closer monitoring and/or supportive interventions whilst on the SSM/PIFU pathway. Reduced access due to COVID-19 could have affected service use

Abiraterone for Prostate Cancer Not Previously Treated with Hormone Therapy

BACKGROUND Abiraterone acetate plus prednisolone improves survival in men with relapsed prostate cancer. We assessed the effect of this combination in men starting long-term androgen-deprivation therapy (ADT), using a multigroup, multistage trial design. METHODS We randomly assigned patients in a 1:1 ratio to receive ADT alone or ADT plus abiraterone acetate (1000 mg daily) and prednisolone (5 mg daily) (combination therapy). Local radiotherapy was mandated for patients with node-negative, nonmetastatic disease and encouraged for those with positive nodes. For patients with nonmetastatic disease with no radiotherapy planned and for patients with metastatic disease, treatment continued until radiologic, clinical, or prostate-specific antigen (PSA) progression; otherwise, treatment was to continue for 2 years or until any type of progression, whichever came first. The primary outcome measure was overall survival. The intermediate primary outcome was failure-free survival (treatment failure was defined as radiologic, clinical, or PSA progression or death from prostate cancer). RESULTS A total of 1917 patients underwent randomization from November 2011 through January 2014. The median age was 67 years, and the median PSA level was 53 ng per milliliter. A total of 52% of the patients had metastatic disease, 20% had node-positive or node-indeterminate nonmetastatic disease, and 28% had node-negative, nonmetastatic disease; 95% had newly diagnosed disease. The median follow-up was 40 months. There were 184 deaths in the combination group as compared with 262 in the ADT-alone group (hazard ratio, 0.63; 95% confidence interval [CI], 0.52 to 0.76; P<0.001); the hazard ratio was 0.75 in patients with nonmetastatic disease and 0.61 in those with metastatic disease. There were 248 treatment-failure events in the combination group as compared with 535 in the ADT-alone group (hazard ratio, 0.29; 95% CI, 0.25 to 0.34; P<0.001); the hazard ratio was 0.21 in patients with nonmetastatic disease and 0.31 in those with metastatic disease. Grade 3 to 5 adverse events occurred in 47% of the patients in the combination group (with nine grade 5 events) and in 33% of the patients in the ADT-alone group (with three grade 5 events). CONCLUSIONS Among men with locally advanced or metastatic prostate cancer, ADT plus abiraterone and prednisolone was associated with significantly higher rates of overall and failure-free survival than ADT alone. (Funded by Cancer Research U.K. and others; STAMPEDE ClinicalTrials.gov number, NCT00268476, and Current Controlled Trials number, ISRCTN78818544.

A Real Semantic Web for Mathematics Deserves a Real Semantics

Contains fulltext : 72735.pdf (author's version ) (Open Access)SemWiki 2008, 2 juni 200