Integrating a Global Induction Mechanism into a Sequent Calculus

Most interesting proofs in mathematics contain an inductive argument which requires an extension of the LK-calculus to formalize. The most commonly used calculi for induction contain a separate rule or axiom which reduces the valid proof theoretic properties of the calculus. To the best of our knowledge, there are no such calculi which allow cut-elimination to a normal form with the subformula property, i.e. every formula occurring in the proof is a subformula of the end sequent. Proof schemata are a variant of LK-proofs able to simulate induction by linking proofs together. There exists a schematic normal form which has comparable proof theoretic behaviour to normal forms with the subformula property. However, a calculus for the construction of proof schemata does not exist. In this paper, we introduce a calculus for proof schemata and prove soundness and completeness with respect to a fragment of the inductive arguments formalizable in Peano arithmetic.Comment: 16 page

HER2 and TOP2A in high-risk early breast cancer patients treated with adjuvant epirubicin-based dose-dense sequential chemotherapy

<p>Abstract</p> <p>Background</p> <p>HER2 and TOP2A parameters (gene status, mRNA and protein expression) have individually been associated with the outcome of patients treated with anthracyclines. The aim of this study was to comprehensively evaluate the prognostic/predictive significance of the above parameters in early, high-risk breast cancer patients treated with epirubicin-based, dose-dense sequential adjuvant chemotherapy.</p> <p>Methods</p> <p>In a series of 352 breast carcinoma tissues from patients that had been post-operatively treated with epirubicin-CMF with or without paclitaxel, we assessed HER2 and TOP2A gene status (chromogenic in situ hybridization), mRNA expression (quantitative reverse transcription PCR), as well as HER2 and TopoIIa protein expression (immunohistochemistry).</p> <p>Results</p> <p>HER2 and TOP2A amplification did not share the same effects on their downstream molecules, with consistent patterns observed in HER2 mRNA and protein expression according to HER2 amplification (all parameters strongly inter-related, p values < 0.001), but inconsistent patterns in the case of TOP2A. TOP2A gene amplification (7% of all cases) was not related to TOP2A mRNA and TopoIIa protein expression, while TOP2A mRNA and TopoIIa protein were strongly related to each other (p < 0.001). Hence, TOP2A amplified tumors did not correspond to tumors with high TOP2A mRNA or TopoIIa protein expression, while the latter were characterized by high Ki67 scores (p = 0.003 and p < 0.001, respectively). Multivariate analysis adjusted for nodal involvement, hormone receptor status, Ki67 score and HER2/TOP2A parameters revealed HER2/TOP2A co-amplification (21.2% of HER2 amplified tumors) as an independent favorable prognostic factor for DFS (HR = 0.13, 95% CI: 0.02-0.96, p = 0.046); in contrast, increased HER2/TOP2A mRNA co-expression was identified as an independent adverse prognostic factor for both DFS (HR = 2.41, 95% CI: 1.31-4.42, p = 0.005) and OS (HR = 2.83, 95% CI: 1.42-5.63, p = 0.003), while high TOP2A mRNA expression was an independent adverse prognostic factor for OS (HR = 2.06, 95% CI: 1.23-3.46, p = 0.006). None of the parameters tested was associated with response to paclitaxel.</p> <p>Conclusions</p> <p>This study confirms the favorable prognostic value of HER2/TOP2A co-amplification and the adverse prognostic value of high TOP2A mRNA expression extending it to the adjuvant treatment setting in early high-risk breast cancer. The strong adverse prognostic impact of high HER2/TOP2A mRNA co-expression needs further validation in studies designed to evaluate markers predictive for anthracyclines.</p> <p>Trial registration</p> <p>Australian New Zealand Clinical Trials Registry <a href="http://www.anzctr.org.au/ACTRN12611000506998">ACTRN12611000506998</a>.</p

Four cycles of paclitaxel and carboplatin as adjuvant treatment in early-stage ovarian cancer: a six-year experience of the Hellenic Cooperative Oncology Group

BACKGROUND: Surgery can cure a significant percentage of ovarian carcinoma confined to the pelvis. Nevertheless, there is still a 10–50% recurrence rate. We administered paclitaxel/carboplatin as adjuvant treatment in early-stage ovarian carcinoma. METHODS: Patients with stages Ia or Ib, Grade 2 or 3 and Ic to IIb (any grade) were included. Patients were treated with 4 cycles of Paclitaxel 175 mg/m(2 )and Carboplatin [area under the curve (AUC) 6 (Calvert Formula)] every 3 weeks. RESULTS: Sixty-nine patients with no residual disease following cytoreductive surgery and minimal or modified surgical staging were included in this analysis. Grade 3 or 4 neutropenia occured in 29.9% of patients, while neutropenic fever was reported in 4.5%. Neurotoxicity (all Grade 1 or 2) was reported in 50% of cases. Median follow-up was 62 months. 5-year overall survival (OS) and relapse-free survival (RFS) were: 87% (95% confidence intervals [CI]: 78–96) and 79% (95% CI: 69–89), respectively. Significantly fewer patients with stages Ic-IIb and tumor grade 2 or 3 achieved a 5-year RFS than patients with only one of these two factors (73% vs 92%, p = 0.03). CONCLUSION: Paclitaxel/Carboplatin chemotherapy is a safe and effective adjuvant treatment in early-stage ovarian carcinoma. Patients with stages Ic-IIb and tumor grade 2 or 3 may benefit from more extensive treatment

A multicenter phase III trial comparing irinotecan-gemcitabine (IG) with gemcitabine (G) monotherapy as first-line treatment in patients with locally advanced or metastatic pancreatic cancer

Our purpose was to determine the response rate and median and overall survival of gemcitabine as monotherapy versus gemcitabine plus irinotecan in advanced or metastatic pancreatic cancer. Patients with histologically or cytologically confirmed adenocarcinoma who were chemotherapy and radiotherapy naive were enrolled. Patients were centrally randomised at a one-to-one ratio to receive either gemcitabine monotherapy (900 mg m−2 on days 1, 8 and 15 every 4 weeks (arm G), or gemcitabine (days 1 and 8) plus irinotecan (300 mg m−2 on day 8) (arm IG), repeated every 3 weeks. The total number of cycles administered was 255 in the IG arm and 245 in the G arm; the median number of cycles was 3. In all, 145 patients (71 in arm IG and 74 in arm G) were enrolled; 60 and 70 patients from arms IG and G, respectively, were evaluable. A complete clinical response was achieved in three (4.3%) arm G patients; nine (15%) patients in arm IG and four (5.7%) in arm G achieved a partial response. The overall response rate was: arm IG 15% and arm G 10% (95% CI 5.96–24.04 and 95% CI 2.97–17.03, respectively; P=0.387). The median time to tumour progression was 2.8 months and 2.9 months and median survival time was 6.4 and 6.5 months for the IG and G arms, respectively. One-year survival was 24.3% for the IG arm and 21.8% for the G arm. No statistically significant difference was observed comparing gemcitabine monotherapy versus gemcitabine plus irinotecan in the treatment of advanced pancreatic cancer, with respect to overall and 1-year survival

Association between adolescent idiopathic scoliosis prevalence and age at menarche in different geographic latitudes

BACKGROUND: Age at menarche is considered a reliable prognostic factor for idiopathic scoliosis and varies in different geographic latitudes. Adolescent idiopathic scoliosis prevalence has also been reported to be different in various latitudes and demonstrates higher values in northern countries. A study on epidemiological reports from the literature was conducted to investigate a possible association between prevalence of adolescent idiopathic scoliosis and age at menarche among normal girls in various geographic latitudes. An attempt is also made to implicate a possible role of melatonin in the above association. MATERIAL-METHODS: 20 peer-reviewed published papers reporting adolescent idiopathic scoliosis prevalence and 33 peer-reviewed papers reporting age at menarche in normal girls from most geographic areas of the northern hemisphere were retrieved from the literature. The geographic latitude of each centre where a particular study was originated was documented. The statistical analysis included regression of the adolescent idiopathic scoliosis prevalence and age at menarche by latitude. RESULTS: The regression of prevalence of adolescent idiopathic scoliosis and age at menarche by latitude is statistically significant (p < 0.001) and are following a parallel declining course of their regression curves, especially in latitudes northern than 25 degrees. CONCLUSION: Late age at menarche is parallel with higher prevalence of adolescent idiopathic scoliosis. Pubarche appears later in girls that live in northern latitudes and thus prolongs the period of spine vulnerability while other pre-existing or aetiological factors are contributing to the development of adolescent idiopathic scoliosis. A possible role of geography in the pathogenesis of idiopathic scoliosis is discussed, as it appears that latitude which differentiates the sunlight influences melatonin secretion and modifies age at menarche, which is associated to the prevalence of idiopathic scoliosis

Design concepts for the Cherenkov Telescope Array CTA: an advanced facility for ground-based high-energy gamma-ray astronomy

Ground-based gamma-ray astronomy has had a major breakthrough with the impressive results obtained using systems of imaging atmospheric Cherenkov telescopes. Ground-based gamma-ray astronomy has a huge potential in astrophysics, particle physics and cosmology. CTA is an international initiative to build the next generation instrument, with a factor of 5-10 improvement in sensitivity in the 100 GeV-10 TeV range and the extension to energies well below 100 GeV and above 100 TeV. CTA will consist of two arrays (one in the north, one in the south) for full sky coverage and will be operated as open observatory. The design of CTA is based on currently available technology. This document reports on the status and presents the major design concepts of CTA