On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

A situational analysis of health information library needs in Tanzania

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Reproducibility of the peritoneal regression grading score for assessment of response to therapy in peritoneal metastasis.

The four-tiered peritoneal regression grading score (PRGS) assesses the response to chemotherapy in peritoneal metastasis (PM). The PRGS is used, for example, to assess the response to pressurised intraperitoneal aerosol chemotherapy (PIPAC). However, the reproducibility of the PRGS is currently unknown. We aimed to evaluate the inter- and intraobserver variability of the PRGS. Thirty-three patients who underwent at least three PIPAC treatments as part of the PIPAC-OPC1 or PIPAC-OPC2 clinical trials at Odense University Hospital, Denmark, were included. Prior to each therapy cycle, peritoneal quadrant biopsies were obtained and three haematoxylin and eosin (H&E)-stained step sections were scanned and uploaded to a pseudonymised web library. For determining interobserver variability, eight pathologists assessed the PRGS for each quadrant biopsy, and Krippendorff's alpha and intraclass correlation coefficients (ICCs) were calculated. For determining intraobserver variability, three pathologists repeated their own assessments and Cohen's kappa and ICCs were calculated. A total of 331 peritoneal biopsies were analysed. Interobserver variability for PRGS of each biopsy and for the mean and maximum PRGS per biopsy set was moderate to good/substantial. The intraobserver variability for PRGS of each biopsy and for the mean and maximum PRGS per biopsy set was good to excellent/almost perfect. Our data support the PRGS as a reproducible and useful tool to assess response to intraperitoneal chemotherapy in PM. Future studies should evaluate the prognostic and predictive role of the PRGS

The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer

From Euclidean Geometry to Knots and Nets

This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.Peer reviewe

Recent progress in random metric theory and its applications to conditional risk measures

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a brief introduction to random metric theory, risk measures and conditional risk measures. Section 2 gives the central framework in random metric theory, topological structures, important examples, the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals. Section 3 gives several important representation theorems for random conjugate spaces. Section 4 gives characterizations for a complete random normed module to be random reflexive. Section 5 gives hyperplane separation theorems currently available in random locally convex modules. Section 6 gives the theory of random duality with respect to the locally $L^{0}-$convex topology and in particular a characterization for a locally $L^{0}-$convex module to be $L^{0}-$pre$-$barreled. Section 7 gives some basic results on $L^{0}-$convex analysis together with some applications to conditional risk measures. Finally, Section 8 is devoted to extensions of conditional convex risk measures, which shows that every representable $L^{\infty}-$type of conditional convex risk measure and every continuous $L^{p}-$type of convex conditional risk measure ($1\leq p<+\infty$) can be extended to an $L^{\infty}_{\cal F}({\cal E})-$type of $\sigma_{\epsilon,\lambda}(L^{\infty}_{\cal F}({\cal E}), L^{1}_{\cal F}({\cal E}))-$lower semicontinuous conditional convex risk measure and an $L^{p}_{\cal F}({\cal E})-$type of ${\cal T}_{\epsilon,\lambda}-$continuous conditional convex risk measure ($1\leq p<+\infty$), respectively.Comment: 37 page

Representation of the penalty term of dynamic concave utilities

In this paper we will provide a representation of the penalty term of general dynamic concave utilities (hence of dynamic convex risk measures) by applying the theory of g-expectations.Comment: An updated version is published in Finance & Stochastics. The final publication is available at http://www.springerlink.co

European guideline on IgG4-related digestive disease – UEG and SGF evidence-based recommendations

The overall objective of these guidelines is to provide evidence-based recommendations for the diagnosis and management of immunoglobulin G4 (IgG4)-related digestive disease in adults and children. IgG4-related digestive disease can be diagnosed only with a comprehensive work-up that includes histology, organ morphology at imaging, serology, search for other organ involvement, and response to glucocorticoid treatment. Indications for treatment are symptomatic patients with obstructive jaundice, abdominal pain, posterior pancreatic pain, and involvement of extra-pancreatic digestive organs, including IgG4-related cholangitis. Treatment with glucocorticoids should be weight-based and initiated at a dose of 0.6–0.8 mg/kg body weight/day orally (typical starting dose 30-40 mg/day prednisone equivalent) for 1 month to induce remission and then be tapered within two additional months. Response to initial treatment should be assessed at week 2–4 with clinical, biochemical and morphological markers. Maintenance treatment with glucocorticoids should be considered in multi-organ disease or history of relapse. If there is no change in disease activity and burden within 3 months, the diagnosis should be reconsidered. If the disease relapsed during the 3 months of treatment, immunosuppressive drugs should be added