A Formalization of the Theorem of Existence of First-Order Most General Unifiers

This work presents a formalization of the theorem of existence of most general unifiers in first-order signatures in the higher-order proof assistant PVS. The distinguishing feature of this formalization is that it remains close to the textbook proofs that are based on proving the correctness of the well-known Robinson's first-order unification algorithm. The formalization was applied inside a PVS development for term rewriting systems that provides a complete formalization of the Knuth-Bendix Critical Pair theorem, among other relevant theorems of the theory of rewriting. In addition, the formalization methodology has been proved of practical use in order to verify the correctness of unification algorithms in the style of the original Robinson's unification algorithm.Comment: In Proceedings LSFA 2011, arXiv:1203.542

Several types of types in programming languages

Types are an important part of any modern programming language, but we often forget that the concept of type we understand nowadays is not the same it was perceived in the sixties. Moreover, we conflate the concept of "type" in programming languages with the concept of the same name in mathematical logic, an identification that is only the result of the convergence of two different paths, which started apart with different aims. The paper will present several remarks (some historical, some of more conceptual character) on the subject, as a basis for a further investigation. The thesis we will argue is that there are three different characters at play in programming languages, all of them now called types: the technical concept used in language design to guide implementation; the general abstraction mechanism used as a modelling tool; the classifying tool inherited from mathematical logic. We will suggest three possible dates ad quem for their presence in the programming language literature, suggesting that the emergence of the concept of type in computer science is relatively independent from the logical tradition, until the Curry-Howard isomorphism will make an explicit bridge between them.Comment: History and Philosophy of Computing, HAPOC 2015. To appear in LNC

An evaluation of a nurse led unit: an action research study

This study is an exemplar of working in a participatory way with members of the public and health and social care practitioners as co-researchers. A Nurse Consultant Older People working in a nurse-led bed, intermediate care facility in a community hospital acted as joint project lead with an academic researcher. From the outset, members of the public were part of a team of 16 individuals who agreed an evaluation focus and were involved in all stages of the research process from design through to dissemination. An extensive evaluation reflecting all these stakeholders’ preferences was undertaken. Methods included research and audit including: patient and carer satisfaction questionnaire surveys, individual interviews with patients, carers and staff, staff surveys, graffiti board, suggestion box, first impressions questionnaire, patient tracking and a bed census. A key aim of the study has been capacity building of the research team members which has also been evaluated. In terms of impact, the co-researchers have developed research skills and knowledge, grown in confidence, developed in ways that have impacted elsewhere in their lives, developed posters, presented at conferences and gained a better understanding of the NHS. The evaluation itself has provided useful information on the processes and outcomes of intermediate care on the ward which was used to further improve the service

Outcome of ATP-based tumor chemosensitivity assay directed chemotherapy in heavily pre-treated recurrent ovarian carcinoma

BACKGROUND: We wished to evaluate the clinical response following ATP-Tumor Chemosensitivity Assay (ATP-TCA) directed salvage chemotherapy in a series of UK patients with advanced ovarian cancer. The results are compared with that of a similar assay used in a different country in terms of evaluability and clinical endpoints. METHODS: From November 1998 to November 2001, 46 patients with pre-treated, advanced ovarian cancer were given a total of 56 courses of chemotherapy based on in-vitro ATP-TCA responses obtained from fresh tumor samples or ascites. Forty-four patients were evaluable for results. Of these, 18 patients had clinically platinum resistant disease (relapse < 6 months after first course of chemotherapy). There was evidence of cisplatin resistance in 31 patients from their first ATP-TCA. Response to treatment was assessed by radiology, clinical assessment and tumor marker level (CA 125). RESULTS: The overall response rate was 59% (33/56) per course of chemotherapy, including 12 complete responses, 21 partial responses, 6 with stable disease, and 15 with progressive disease. Two patients were not evaluable for response having received just one cycle of chemotherapy: if these were excluded the response rate is 61%. Fifteen patients are still alive. Median progression free survival (PFS) was 6.6 months per course of chemotherapy; median overall survival (OAS) for each patient following the start of TCA-directed therapy was 10.4 months (95% confidence interval 7.9-12.8 months). CONCLUSION: The results show similar response rates to previous studies using ATP-TCA directed therapy in recurrent ovarian cancer. The assay shows high evaluability and this study adds weight to the reproducibility of results from different centre

Physics, Topology, Logic and Computation: A Rosetta Stone

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.Comment: 73 pages, 8 encapsulated postscript figure

MRI-targeted or standard biopsy for prostate-cancer diagnosis

Background Multiparametric magnetic resonance imaging (MRI), with or without targeted biopsy, is an alternative to standard transrectal ultrasonography-guided biopsy for prostate-cancer detection in men with a raised prostate-specific antigen level who have not undergone biopsy. However, comparative evidence is limited. Methods In a multicenter, randomized, noninferiority trial, we assigned men with a clinical suspicion of prostate cancer who had not undergone biopsy previously to undergo MRI, with or without targeted biopsy, or standard transrectal ultrasonography-guided biopsy. Men in the MRI-targeted biopsy group underwent a targeted biopsy (without standard biopsy cores) if the MRI was suggestive of prostate cancer; men whose MRI results were not suggestive of prostate cancer were not offered biopsy. Standard biopsy was a 10-to-12-core, transrectal ultrasonography-guided biopsy. The primary outcome was the proportion of men who received a diagnosis of clinically significant cancer. Secondary outcomes included the proportion of men who received a diagnosis of clinically insignificant cancer. Results A total of 500 men underwent randomization. In the MRI-targeted biopsy group, 71 of 252 men (28%) had MRI results that were not suggestive of prostate cancer, so they did not undergo biopsy. Clinically significant cancer was detected in 95 men (38%) in the MRI-targeted biopsy group, as compared with 64 of 248 (26%) in the standard-biopsy group (adjusted difference, 12 percentage points; 95% confidence interval [CI], 4 to 20; P=0.005). MRI, with or without targeted biopsy, was noninferior to standard biopsy, and the 95% confidence interval indicated the superiority of this strategy over standard biopsy. Fewer men in the MRI-targeted biopsy group than in the standard-biopsy group received a diagnosis of clinically insignificant cancer (adjusted difference, -13 percentage points; 95% CI, -19 to -7; P&lt;0.001). Conclusions The use of risk assessment with MRI before biopsy and MRI-targeted biopsy was superior to standard transrectal ultrasonography-guided biopsy in men at clinical risk for prostate cancer who had not undergone biopsy previously. (Funded by the National Institute for Health Research and the European Association of Urology Research Foundation; PRECISION ClinicalTrials.gov number, NCT02380027 .)

The concordance between the volume hotspot and the grade hotspot: a 3-D reconstructive model using the pathology outputs from the PROMIS trial.

The rationale for directing targeted biopsy towards the centre of lesions has been questioned in light of prostate cancer grade heterogeneity. In this study, we assess the assumption that the maximum cancer Gleason grade (Gleason grade hotspot) lies within the maximum dimension (volume hotspot) of a prostate cancer lesion. 3-D histopathological models were reconstructed using the outputs of the 5-mm transperineal mapping (TPM) biopsies used as the reference test in the pilot phase of Prostate Mri Imaging Study (PROMIS), a paired validating cohort study investigating the performance of multi-parametric magnetic resonance imaging (MRI) against transrectal ultrasound (TRUS) biopsies. The prostate was fully sampled with 5 mm intervals; each core was separately labelled, inked and orientated in space to register 3-D cancer lesions location. The data from the histopathology results were used to create a 3-D interpolated reconstruction of each lesion and identify the spatial coordinates of the largest dimension (volume hot spot) and highest Gleason grade (Gleason grade hotspot) and assess their concordance. Ninety-four men, with median age 62 years (interquartile range, IQR= 58-68) and median PSA 6.5 ng ml(-1) (4.6-8.8), had a median of 80 (I69-89) cores each with a median of 4.5 positive cores (0-12). In the primary analysis, the prevalence of homogeneous lesions was 148 (76%; 95% confidence interval (CI) ±6.0%). In all, 184 (94±3.2%) lesions showed concordant hotspots and 11/47 (23±12.1%) of heterogeneous lesions showed discordant hotspots. The median 3-D distance between discordant hotspots was 12.8 mm (9.9-15.5). These figures remained stable on secondary analyses using alternative reconstructive assumptions. Limitations include a certain degree of error within reconstructed models. Guiding one biopsy needle to the maximum cancer diameter would lead to correct Gleason grade attribution in 94% of all lesions and 79% of heterogeneous ones if a true hit was obtained. Further correlation of histological lesions, their MRI appearance and the detectability of these hotspots on MRI will be undertaken once PROMIS results are released