Linear independence of Gamma values in positive characteristic

We investigate the arithmetic nature of special values of Thakur's function field Gamma function at rational points. Our main result is that all linear independence relations over the field of algebraic functions are consequences of the known relations of Anderson and Thakur arising from the functional equations of the Gamma function.Comment: 51 page

Future observational and modelling needs identified on the basis of the existing shelf data

NOWESP has compiled a vast quantity of existing data from the North-West European Shelf. Such a focused task is without precedence. It is now highly recommended that one, or a few national and international data centres or agencies should be chosen and properly supported by the EU, where all available observational data, including the NOWESP data, are collected, stored, regularly updated by the providers of the data, and made available to the researchers. International agreement must be reached on the quality control procedures and quality standards for data to be stored in these data bases. Proper arrangements should be made to preserve the economic value of the data for their "owners" without compromising use of the data by researchers or duplicating data collecting efforts. The continental shelf data needed are concentration fields of temperature, salinity, nutrients, suspended matter and chlorophyll, which can be called "climatological" fields. For this purpose at least one monthly survey on the whole European shelf is needed at least during five years, with a proper spatial resolution e.g. 1 degree by 1 degree, and at least in those areas where climatological data are now totally lacking. From the modelling point of view an alternative would be the availability of data from sufficiently representative fixed stations on the shelf, with weekly sampling for several years

Modular symbols in Iwasawa theory

This survey paper is focused on a connection between the geometry of $\mathrm{GL}_d$ and the arithmetic of $\mathrm{GL}_{d-1}$ over global fields, for integers $d \ge 2$. For $d = 2$ over $\mathbb{Q}$, there is an explicit conjecture of the third author relating the geometry of modular curves and the arithmetic of cyclotomic fields, and it is proven in many instances by the work of the first two authors. The paper is divided into three parts: in the first, we explain the conjecture of the third author and the main result of the first two authors on it. In the second, we explain an analogous conjecture and result for $d = 2$ over $\mathbb{F}_q(t)$. In the third, we pose questions for general $d$ over the rationals, imaginary quadratic fields, and global function fields.Comment: 43 page

Class I histone deacetylases 1, 2 and 3 are highly expressed in renal cell cancer

Background Enhanced activity of histone deacetylases (HDAC) is associated with more aggressive tumour behaviour and tumour progression in various solid tumours. The over-expression of these proteins and their known functions in malignant neoplasms has led to the development of HDAC inhibitors (HDI) as new anti-neoplastic drugs. However, little is known about HDAC expression in renal cell cancer. Methods We investigated the expression of HDAC 1, 2 and 3 in 106 renal cell carcinomas and corresponding normal renal tissue by immunohistochemistry on tissue micro arrays and correlated expression data with clinico-pathological parameters including patient survival. Results Almost 60% of renal cell carcinomas expressed the HDAC isoforms 1 and 2. In contrast, HDAC 3 was only detected in 13% of all renal tumours, with particular low expression rates in the clear cell subtype. HDAC 3 was significantly higher expressed in pT1/2 tumours in comparison to pT3/4 tumours. Expression of class I HDAC isoforms correlated with each other and with the proliferative activity of the tumours. We found no prognostic value of the expression of any of the HDAC isoforms in this tumour entity. Conclusion Class I HDAC isoforms 1 and 2 are highly expressed in renal cell cancer, while HDAC 3 shows low, histology dependent expression rates. These unexpected differences in the expression patterns suggests alternative regulatory mechanisms of class I HDACs in renal cell cancer and should be taken into account when trials with isoform selective HDI are being planned. Whether HDAC expression in renal cancers is predictive of responsiveness for HDI will have to be tested in further studies

High expression of RelA/p65 is associated with activation of nuclear factor-κB-dependent signaling in pancreatic cancer and marks a patient population with poor prognosis

Activation of nuclear factor-κB (NF-κB) signaling was observed in pancreatic adenocarcinoma cell lines and tumours. However, information on the expression of RelA/p65, the major transcription activating NF-κB subunit, in these carcinomas and possible correlations thereof with NF-κB activation and patient survival is not available. To provide this missing translational link, we analysed expression of RelA/p65 in 82 pancreatic adenocarcinomas by immunohistochemistry. Moreover, we measured activation of the NF-κB pathway in 11 tumours by quantitative PCR for NF-κB target genes. We observed strong cytoplasmic or nuclear expression of RelA/p65 in 42 and 37 carcinomas, respectively. High cytoplasmic and nuclear expression of RelA/p65 had negative prognostic impact with 2-year survival rates for patients without cytoplasmic or nuclear RelA/p65 positivity of 41 and 40% and rates for patients with strong cytoplasmic or nuclear RelA/p65 expression of 22 and 20%, respectively. High RelA/p65 expression was correlated to increased expression of NF-κB target genes. The observation that high expression of RelA/p65 is correlated to an activation of the NF-κB pathway and indicates poor patient survival identifies a patient subgroup that might particularly benefit from NF-κB-inhibiting agents in the treatment of pancreatic cancer. Based on our findings, this subgroup could be identified by applying simple immunohistochemical techniques

Histone deacetylases 1, 2 and 3 are highly expressed in prostate cancer and HDAC2 expression is associated with shorter PSA relapse time after radical prostatectomy

High activity of histone deacetylases (HDACs) causes epigenetic alterations associated with malignant cell behaviour. Consequently, HDAC inhibitors have entered late-phase clinical trials as new antineoplastic drugs. However, little is known about expression and function of specific HDAC isoforms in human tumours including prostate cancer. We investigated the expression of class I HDACs in 192 prostate carcinomas by immunohistochemistry and correlated our findings to clinicopathological parameters including follow-up data. Class I HDAC isoforms were strongly expressed in the majority of the cases (HDAC1: 69.8%, HDAC2: 74%, HDAC3: 94.8%). High rates of HDAC1 and HDAC2 expression were significantly associated with tumour dedifferentiation. Strong expression of all HDACs was accompanied by enhanced tumour cell proliferation. In addition, HDAC2 was an independent prognostic marker in our prostate cancer cohort. In conclusion, we showed that the known effects of HDACs on differentiation and proliferation of cancer cells observed in vitro can also be confirmed in vivo. The class I HDAC isoforms 1, 2 and 3 are differentially expressed in prostate cancer, which might be important for upcoming studies on HDAC inhibitors in this tumour entity. Also, the highly significant prognostic value of HDAC2 clearly deserves further study

Oleanolic Acid Initiates Apoptosis in Non-Small Cell Lung Cancer Cell Lines and Reduces Metastasis of a B16F10 Melanoma Model In Vivo

Drug resistance, a process mediated by multiple mechanisms, is a critical determinant for treating lung cancer. The aim of this study is to determine if oleanolic acid (OA), a pentacyclic triterpene present in several plants, is able to circumvent the mechanisms of drug resistance present in non-small cell lung cancer (NSCLC) cell lines and to induce their death.OA decreased the cell viability of the NSCLC cell lines A459 and H460 despite the presence of active, multidrug-resistant (MDR) MRP1/ABCC1 proteins and the anti-apoptotic proteins Bcl-2 and survivin. These effects are due to apoptosis, as evidenced by the capacity of OA to induce fragmentation of DNA and activate caspase 3. Induction of NSCLC cell death by OA cannot be explained by inhibition of the MDR proteins, since treatment with triterpene had little or no effect on the activity or expression of MRP1. Moreover, treatment with OA had no effect on the expression of the anti-apoptotic protein Bcl-2, but increased the expression of the pro-apoptotic protein Bax, altering the Bcl-2/Bax balance towards a pro-apoptotic profile. OA also decreased the expression of the anti-apoptotic protein survivin. Furthermore, OA decreased the expression of the angiogenic vascular endothelial growth factor (VEGF) and decreased the development of melanoma-induced lung metastasis.Our data provide a significant insight into the antitumoral and antimetastatic activity of OA in NSCLC and suggest that including OA in the NSCLC regimens may help to decrease the number of relapses and reduce the development of metastases

Mathematical methods for mechanics: a handbook with Matlab experiments

This book introduces all the mathematical tools necessary for solving complex problems in the field of mechanics. It also contains various applications of mathematical and numerical methods for modeling comprehensive mechanical-technical practical problems