Can polylogarithms at algebraic points be linearly independent?

Let $r,m$ be positive integers. Let $0\le x <1$ be a rational number. Let $\Phi_s(x,z)$ be the $s$-th Lerch function $\sum_{k=0}^{\infty}\tfrac{z^{k+1}}{(k+x+1)^s}$ with $s=1,2,\ldots ,r$. When $x=0$, this is the polylogarithmic function. Let $\alpha_1,\ldots ,\alpha_m$ be pairwise distinct algebraic numbers with $0<|\alpha_j|<1$ $(1 \le j \le m)$. In this article, we state a linear independence criterion over algebraic number fields of all the $rm+1$ numbers $:$ $\Phi_1(x,\alpha_1),\Phi_2(x,\alpha_1),\ldots, \Phi_r(x,\alpha_1),\Phi_1(x,\alpha_2),\Phi_2(x,\alpha_2),\ldots, \Phi_r(x,\alpha_2),\ldots,\Phi_1(x,\alpha_m),\Phi_2(x,\alpha_m),\ldots, \Phi_r(x,\alpha_m)$ and $1$. This is the first result that gives a sufficient condition for the linear independence of values of the $r$ Lerch functions $\Phi_1(x,z),\Phi_2(x,z),\ldots, \Phi_r(x,z)$ at $m$ distinct algebraic points without any assumption for $r$ and $m$, even for the case $x=0$, the polylogarithms. We give an outline of our proof and explain basic idea

The Molecular Pathogenesis and Clinical Implications of Hepatocellular Carcinoma

The prognosis of hepatocellular carcinoma (HCC) is affected by tumoral factors and liver functions; therefore it is often difficult to select the appropriate therapeutic methods for HCC. Recently, two global phase III trials showed that sorafenib, which is a tyrosine kinase inhibitor, improved the prognosis of patients with advanced HCC. As a new therapeutic strategy for HCC, sorafenib is expected to expand the indication for HCC in the future. However, it alone is insufficient for the molecular-targeted treatment of HCC because the signaling pathway exists not only in cancer cells but also in normal cells. Recently, cancer stem cells (CSCs) have attracted attention as a novel therapeutic target for HCC. There is now much evidence that stem cell properties such as self-renewal, unlimited proliferation, and differentiation are highly relevant to cancer recurrence and the drug resistance of HCC. In this review, we describe the molecular pathogenesis and the current state and future development of molecular- and CSC-therapeutic targeted agents for HCC, citing various reports

Limnological aspect of mires: background and a case study

Article信州大学理学部附属諏訪臨湖実験所報告 9: 47-52(1995)departmental bulletin pape

SS-unit equation in two variables and Pad\'{e} approximations

In this article, we use Pad\'{e} approximations constructed for binomial functions, to give a new upper bound for the number of the solutions of the $S$-unit equation. Combining explicit formulae of these Pad\'{e} approximants with a simple argument relying on Mahler measure and on the local height, we refine the bound due to J.-H. Evertse.Comment: 13 page

Endoscopic and Histological Features of the Large Intestine in Patients with Atopic Dermatitis

Although atopic dermatitis is known to be closely associated with food antigens, the actual changes in the gastrointestinal tract have not been clarified. The aim of this study was to investigate the macroscopic and histological features of the large intestine in patients with atopic dermatitis. We studied 15 outpatients who had generalized atopic dermatitis. Eight non-dermatitis subjects of a similar age without inflammatory bowel disease were also enrolled as controls. Total colonoscopy, pathological evaluation of biopsy specimens, and detection of Candida albicans were performed in all subjects. Four patients were re-examined after 6 months of treatment with an antifungal drug. Among the 15 patients with atopic dermatitis, 4 patients had melanosis coli. On pathological examinations, prominent infiltration of eosinophils and fragmentation of granulocyte nuclei were observed. There were no changes after an antifungal therapy. In the patients with melanosis coli, lipofuscin deposits were observed in the lamina propria. Candida albicans was not detected in any of the subjects. In conclusion, patients with atopic dermatitis may have a predisposition to develop chronic inflammation of the large intestine

Development of an integrative database with 499 novel microsatellite markers for Macaca fascicularis

<p>Abstract</p> <p>Background</p> <p>Cynomolgus macaques (<it>Macaca fascicularis</it>) are a valuable resource for linkage studies of genetic disorders, but their microsatellite markers are not sufficient. In genetic studies, a prerequisite for mapping genes is development of a genome-wide set of microsatellite markers in target organisms. A whole genome sequence and its annotation also facilitate identification of markers for causative mutations. The aim of this study is to establish hundreds of microsatellite markers and to develop an integrative cynomolgus macaque genome database with a variety of datasets including marker and gene information that will be useful for further genetic analyses in this species.</p> <p>Results</p> <p>We investigated the level of polymorphisms in cynomolgus monkeys for 671 microsatellite markers that are covered by our established Bacterial Artificial Chromosome (BAC) clones. Four hundred and ninety-nine (74.4%) of the markers were found to be polymorphic using standard PCR analysis. The average number of alleles and average expected heterozygosity at these polymorphic loci in ten cynomolgus macaques were 8.20 and 0.75, respectively.</p> <p>Conclusion</p> <p>BAC clones and novel microsatellite markers were assigned to the rhesus genome sequence and linked with our cynomolgus macaque cDNA database (QFbase). Our novel microsatellite marker set and genomic database will be valuable integrative resources in analyzing genetic disorders in cynomolgus macaques.</p

Activation of XBP1 but not ATF6α rescues heart failure induced by persistent ER stress in medaka fish

The unfolded protein response is triggered in vertebrates by ubiquitously expressed IRE1α/β (although IRE1β is gut-specific in mice), PERK, and ATF6α/β, transmembrane-type sensor proteins in the ER, to cope with ER stress, the accumulation of unfolded and misfolded proteins in the ER. Here, we burdened medaka fish, a vertebrate model organism, with ER stress persistently from fertilization by knocking out the AXER gene encoding an ATP/ADP exchanger in the ER membrane, leading to decreased ATP concentration–mediated impairment of the activity of Hsp70- and Hsp90-type molecular chaperones in the ER lumen. ER stress and apoptosis were evoked from 4 and 6 dpf, respectively, leading to the death of all AXER-KO medaka by 12 dpf because of heart failure (medaka hatch at 7 dpf). Importantly, constitutive activation of IRE1α signaling --but not ATF6α signaling-- rescued this heart failure and allowed AXER-KO medaka to survive 3 d longer, likely because of XBP1-mediated transcriptional induction of ER-associated degradation components. Thus, activation of a specific pathway of the unfolded protein response can cure defects in a particular organ

Newly proposed landform division in the Kibi Plateau area: Application for a hazard map of landslides

The Kibi Plateau is characterized by horizontal skylines and they are considered to be an uplifted peneplain. Landform of the plateaus in central part of Okayama Prefecture is divided into "Kibi plateau landform" and "Recent dissecting landform". The Kibi plateau landform is composed of low relief surface and relict mountain. The altitude of the low relief surface varies from 300 to 450m in Kayo area, and 200 to 350m in Kanayama area. The Recent dissecting landform is characterized by escarpment and cuts the Kibi plateau landform. Knick-point is formed at the boundary between two landforms and steep slope is distributed just below the knick-point. The steep slope of the recent dissecting landform is unstable and a potential of landslide is high