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

新機能性物質設計の基礎的研究 : 熱力学量と構造の関係について

博士（理学）神戸大

Current Work on Mathematical Truth

The overall aim of this paper is to serve as an introduction to the work currently being done on the topic of mathematical truth. It provides an overview of the major developments concerning mathematical truth and also evaluates those developments as potential contributions to mathematician’s understanding of the subject

Proof and Intuition

This paper aims to give a clear exposition of two critiques of logicism. The intuitionist, Brouwer, is best known for rejecting the law of the excluded middle (his special critique. ) The paper argues that Brouwer\u27s general critique is deeper and more extensive than this. That is, Brouwer is arguing that mathematical knowledge requires a kind of direct mathematical experience, analogous to sensory experience and this cannot be attained simply by linguistic operations independently of experience. It also discusses Poincare\u27s critiques - that there is a huge difference between genuine mathematical insight and an ability to logically manipulate mathematical truths and that different areas of mathematics have distinctive forms of reasoning

Proof and Intution

This paper discusses various perspectives on proof and intuition by examing two epistemic systems, Intuition Intensive and Logic Intensive, and Jules Henri Poincaré\u27s objections to the latter

Typing of pancreatic cancer-associated fibroblasts identifies different subpopulations

AIM To determine whether it is possible to identify different immune phenotypic subpopulations of cancer-associated fibroblasts (CAFs) in pancreatic cancer (PC). METHODS We defined four different stromal compartments in surgical specimens with PC: The juxtatumoural, peripheral, lobular and septal stroma. Tissue microarrays were produced containing all pre-defined PC compartments, and the expression of 37 fibroblast (FB) and 8 extracellular matrix (ECM) markers was evaluated by immunohistochemistry, immunofluorescence (IF), double-IF, and/or in situ hybridization. The compartment-specific mean labelling score was determined for each marker using a four-tiered scoring system. DOG1 gene expression was examined by quantitative reverse transcription PCR (qPCR). RESULTS CD10, CD271, cytoglobin, DOG1, miR-21, nestin, and tenascin C exhibited significant differences in expression profiles between the juxtatumoural and peripheral compartments. The expression of CD10, cytoglobin, DOG1, nestin, and miR-21 was moderate/strong in juxtatumoural CAFs (j-CAFs) and barely perceptible/weak in peripheral CAFs (p-CAFs). The upregulation of DOG1 gene expression in PC compared to normal pancreas was verified by qPCR. Tenascin C expression was strong in the juxtatumoural ECM and barely perceptible/weak in the peripheral ECM. CD271 expression was barely perceptible in j-CAFs but moderate in the other compartments. Galectin-1 was stronger expressed in j-CAFs vs septal fibroblasts, PDGFRß, tissue transglutaminase 2, and hyaluronic acid were stronger expressed in lobular fibroblasts vs p-CAFs, and plectin-1 was stronger expressed in j-CAFs vs l-FBs. The expression of the remaining 33 markers did not differ significantly when related to the quantity of CAFs/FBs or the amount of ECM in the respective compartments. CONCLUSION Different immune phenotypic CAF subpopulations can be identified in PC, using markers such as cytoglobin, CD271, and miR-21. Future studies should determine whether CAF subpopulations have different functional properties.</p

Frequency of Mismatch Repair Deficiency in Pancreatic Ductal Adenocarcinoma

Pancreatic ductal adenocarcinoma (PDAC) has an ominous prognosis and there are only few treatment options. It is therefore crucial to investigate possible predictive markers that may improve the treatment of this disease. Mismatch repair (MMR) deficiency (d-MMR), meaning MMR protein loss (l-MMR) and/or microsatellite instability (MSI), is predictive of response to immunotherapy, but its frequency has to our knowledge not been elucidated in Scandinavian PDACs. Our aims were to examine the frequency of d-MMR in a Danish cohort of PDACs. We constructed multi-punch tissue microarrays (TMAs) using primary tumor tissue. Immunohistochemistry (IHC) for the DNA MMR proteins MLH1, MSH2, MSH6 and PMS2 was performed, and their expression was evaluated using a scoring system from 0 to 4. If the overall score was between 0–2 or if IHC was inconclusive for technical reasons, IHC on whole-tissue sections and MSI using PCR was performed. A final score of 0, 1–2 or 3–4 defined the tumor as l-MMR, MMR reduced (r-MMR) or MMR proficient. In total, 4/164 (2.4 %), 2/164 (1.2 %) and 3/164 (1.8 %) were l-MMR, r-MMR, or inconclusive based on IHC. MSI testing of these specimens showed that two of the four l-MMR tumors were MSI-high, while the remaining cases were microsatellite stable (MSS). In conclusion, in this study of Danish PDACss, d-MMR was found in a small proportion of the tumors. For these patients, individualized treatment using immunotherapy could be considered.</p

Review on treatment of pleural metastasis and malignant pleural effusion with Pressurized IntraThoracic Aerosol Chemotherapy (PITAC)

Background: Malignant pleural effusion (MPE) is a common and debilitating condition seen in advanced cancer disease, and life-expectancy is short. Symptoms include pain and severe shortness of breath. Current first-line treatment options include pleural drainage using catheters as well as pleurodesis. However, these treatment modalities are often inefficient and patients need repeated procedures. Pressurized IntraThoracic Aerosol Chemotherapy (PITAC) is a minimally invasive procedure, where antineoplastic agents are nebulized under pressure into the pleural space. Content: We present the preliminary safety, feasibility, and response assessment data for PITAC based on a comprehensive literature review. Summary: Five retrospective studies reported data on 38 PITACs in 21 patients. Data were heterogeneous and incomplete on several important aspects such as procedure, safety, local effect and long-term outcomes. PITAC seems technically feasible with a low risk of complications and may provide some reduction in MPE in selected cases. Outlook: PITAC seems feasible, but prospective phase I and II studies are needed to define safety, indications, and efficacy.</p

Adjuvant Pressurized IntraPeritoneal Aerosol Chemotherapy (PIPAC) in resected high-risk colon cancer patients - study protocol for the PIPAC-OPC3 Trial. A prospective, controlled phase 2 Study

Background: Peritoneal metastasis (PM) is the second most common site of recurrence in colon cancer (CC) patients and accounts for approximately one-third of all recurrences. Patients with T4 or intraperitoneal perforated colon cancers have an increased risk of developing PM, and since manifest PM is difficult to treat, high-risk patients should be offered prophylactic treatment. Here, we propose a study of adjuvant oxaliplatin administered as pressurized intraperitoneal aerosol chemotherapy (PIPAC OX) in patients with high-risk colon cancer (T4, perforated tumors, ovarian metastasis).Methods: PIPAC-OPC3 CC is a non-randomized, non-blinded phase 2 cohort study designed to treat high-risk colon cancer patients with adjuvant PIPAC-directed therapy. Based on an expected 90 % peritoneal recurrence-free survival with adjuvant PIPAC against the estimated 75 % without, 60 patients are needed (α: 0.05, power: 0.8). Eligible patients will receive two PIPAC treatments with oxaliplatin (92 mg/m 2) at 4-6 week intervals. During laparoscopy, the peritoneum is biopsied at two locations, and peritoneal lavage with 500 mL of saline and laparoscopic ultrasound is performed. The patients are screened for adverse medical events and surgery-related complications after each PIPAC procedure. After the second PIPAC procedure, the patients will be examined in the outpatient clinic and followed with CT scans 12, 24 and 36 months after resection. The primary outcome of the PIPAC-OPC3 CC trial is to evaluate if PIPAC-directed adjuvant therapy can reduce the risk of PM. Secondary outcomes include the number of conversions from positive to negative peritoneal lavage cytology after one PIPAC procedure, completion rate of two adjuvant PIPAC treatments, toxicity and complication rate and recurrence-free and overall survival rates after 1, 3 and 5 years. Results: It is expected that PIPAC-directed adjuvant therapy can provide an absolute risk reduction of 15 % regarding the development of PM in high-risk colon cancer patients, and that this may result in increased survival rates. We expect that free intraperitoneal tumor cells (FITC) may be detected by peritoneal lavage performed just prior to the administration of PIPAC-directed therapy, and that this treatment may convert FITC-positive patients to a FITC-negative status.Conclusions: This study may provide important knowledge to be used in designing additional studies on PIPAC in the adjuvant setting of other primary cancers.Trial registration: ClinicalTrials.gov Identifier NCT03280511 (2017-09-12). European Clinical Trials Database (EudraCT) 2017-002637-37.</p

Mutational profiling of 103 unresectable pancreatic ductal adenocarcinomas using EUS-guided fine-needle biopsy

BACKGROUND AND OBJECTIVE: Pancreatic ductal adenocarcinoma (PDAC) is among the most lethal cancers, with a 5-year survival rate of around 9%. Only 20% are candidates for surgery. Most unresectable patients undergo EUS-guided fine-needle biopsy (EUS-FNB) for diagnosis. Identification of targetable mutations using next-generation sequencing (NGS) is increasingly requested. Data on feasibility of EUS-FNB for NGS and knowledge regarding mutational profile of unresectable PDAC are scarce. We evaluated the "technical yield" of EUS-FNB for NGS in unresectable PDAC: relative fraction of diagnostic EUS-FNBs meeting technical criteria. We also investigated the "molecular yield": relative fraction of EUS-FNBs included in NGS containing sufficient DNA for detection of at least one mutation. Furthermore, we determined the relative frequency of cancer-associated mutations in unresectable PDAC.PATIENTS AND METHODS: Formalin-fixed and paraffin-embedded EUS-FNBs diagnostic of unresectable PDAC and fulfilling these criteria were included (n = 105): minimum 3-mm2 tissue, minimum of 2-mm2 tumor area, and minimum 20% relative tumor area. NGS was performed using Ion GeneStudio S5 Prime System and Oncomine™ Comprehensive Assay v.3 including 161 cancer-related genes.RESULTS: Technical yield was 48% (105/219) and molecular yield was 98% (103/105). Most frequently mutated genes were KRAS (89.3%) and TP53 (69.9%), followed by CDKN2A (24.3%), ARID1A (9.7%), SMAD4 (7.8%), TSC2 (7.8%), and CCND3 (6.8%).CONCLUSION: EUS-FNB for NGS of unresectable PDAC is feasible. Our technical criteria for NGS, using leftovers in formalin-fixed and paraffin-embedded blocks after routine pathology diagnosis, were met by around half of EUS-FNBs. Almost all EUS-FNBs fulfilling the technical criteria yielded a successful NGS analysis.</p