Fractional order Taylor's series and the neo-classical inequality

We prove the neo-classical inequality with the optimal constant, which was conjectured by T. J. Lyons [Rev. Mat. Iberoamericana 14 (1998) 215-310]. For the proof, we introduce the fractional order Taylor's series with residual terms. Their application to a particular function provides an identity that deduces the optimal neo-classical inequality.Comment: 11 pages, 1 figur

p53 gene mutation in N-butyl-N-(4-hydroxybutyl)nitrosamine-induced urinary bladder tumors and N-methyl-N-nitrosourea-induced colon tumors of rats

We analyzed p53 mutations in 17 N-butyl-N-(4-hydroxybutyl) nitrosamine-induced bladder transitional cell carcinomas (TCCs) with or without areas of squamous cell carcinoma (SCC) of Long–Evans Cinnamon (LEC) and F344 rats, and in 7 N-methyl-N-nitrosourea-induced colon adenocarcinomas of LEC rats by polymerase chain reaction-single strand conformation polymorphism analysis and DNA sequencing. Of these bladder tumors, one TCC with moderately differentiated SCC had a T to G transversion mutation at codon 141, leading to a Val to Gly amino acid change. No p53 mutation was found in colon adenocarcinomas. Thus a p53 gene mutation seems infrequent in these rat bladder and colon carcinogenesis models even in the late stage

Calcium sparks enhance the tissue fluidity within epithelial layers and promote apical extrusion of transformed cells

In vertebrates, newly emerging transformed cells are often apically extruded from epithelial layers through cell competition with surrounding normal epithelial cells. However, the underlying molecular mechanism remains elusive. Here, using phospho-SILAC screening, we show that phosphorylation of AHNAK2 is elevated in normal cells neighboring RasV12 cells soon after the induction of RasV12 expression, which is mediated by calcium-dependent protein kinase C. In addition, transient upsurges of intracellular calcium, which we call calcium sparks, frequently occur in normal cells neighboring RasV12 cells, which are mediated by mechanosensitive calcium channel TRPC1 upon membrane stretching. Calcium sparks then enhance cell movements of both normal and RasV12 cells through phosphorylation of AHNAK2 and promote apical extrusion. Moreover, comparable calcium sparks positively regulate apical extrusion of RasV12-transformed cells in zebrafish larvae as well. Hence, calcium sparks play a crucial role in the elimination of transformed cells at the early phase of cell competition

Prevalence and Outcomes of Acute Hepatitis B in Okayama, Japan, 2006-2010

Hepatitis B virus (HBV) is one of the major viruses causing acute hepatitis. Recently, the incidence of acute hepatitis with genotype A has been increasing in Japan. The aim of this study was to investigate acute hepatitis B (AHB) in Okayama prefecture, with special attention to HBV genotype A. AHB patients who visited one of 12 general hospitals in Okayama prefecture between 2006 and 2010 were retrospectively analyzed. Over the course of the study period, 128 patients were diagnosed with AHB. Sexual transmission was supposed in the majority of patients (78 patients, 61%), including 59 (76%) having sex with heterosexual partners. The genotypes of HBV were assessed in 90 patients (70%), of whom 27 patients were infected with genotype A, 5 with genotype B, and 58 with genotype C. The prevalence of genotype A was significantly higher among male patients (28.7%), aged 20-29 (35.6%, p＜0.01), among men who had sex with men (100%, p＜0.005), and among patients having sex with unspecified partners (44.8%, p＜0.005). Genotype A was not a significant factor associated with delayed HBsAg disappearance. Caution should be exercised with regard to sexually transmissible diseases in order to slow the pandemic spread of AHB due to genotype A

Randomised, multicentre prospective trial of transarterial chemoembolisation (TACE) plus sorafenib as compared with TACE alone in patients with hepatocellular carcinoma: TACTICS trial.

OBJECTIVE:This trial compared the efficacy and safety of transarterial chemoembolisation (TACE) plus sorafenib with TACE alone using a newly established TACE-specific endpoint and pre-treatment of sorafenib before initial TACE. DESIGN:Patients with unresectable hepatocellular carcinoma (HCC) were randomised to TACE plus sorafenib (n=80) or TACE alone (n=76). Patients in the combination group received sorafenib 400 mg once daily for 2-3 weeks before TACE, followed by 800 mg once daily during on-demand conventional TACE sessions until time to untreatable (unTACEable) progression (TTUP), defined as untreatable tumour progression, transient deterioration to Child-Pugh C or appearance of vascular invasion/extrahepatic spread. Co-primary endpoints were progression-free survival (PFS), which is not a conventional one but defined as TTUP, or time to any cause of death plus overall survival (OS). Multiplicity was adjusted by gatekeeping hierarchical testing. RESULTS:Median PFS was significantly longer in the TACE plus sorafenib than in the TACE alone group (25.2 vs 13.5 months; p=0.006). OS was not analysed because only 73.6% of OS events were reached. Median TTUP (26.7 vs 20.6 months; p=0.02) was also significantly longer in the TACE plus sorafenib group. OS at 1 year and 2 years in TACE plus sorafenib group and TACE alone group were 96.2% and 82.7% and 77.2% and 64.6%, respectively. There were no unexpected toxicities. CONCLUSION:TACE plus sorafenib significantly improved PFS over TACE alone in patients with unresectable HCC. Adverse events were consistent with those of previous TACE combination trials. TRIAL REGISTRATION NUMBER:NCT01217034