Random point sets and their diffraction

The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$. We present several systems with an effective stochastic interaction that still allow for explicit calculations of the autocorrelation and the diffraction measure. We concentrate on one-dimensional examples for illustrative purposes, and briefly indicate possible generalisations to higher dimensions. In particular, we discuss the stationary Poisson process in $\mathbb{R}^{d}$ and the renewal process on the line. The latter permits a unified approach to a rather large class of one-dimensional structures, including random tilings. Moreover, we present some stationary point processes that are derived from the classical random matrix ensembles as introduced in the pioneering work of Dyson and Ginibre. Their re-consideration from the diffraction point of view improves the intuition on systems with randomness and mixed spectra.Comment: 9 pages, 2 figures; talk presented at ICQ 11 (Sapporo

A Seven-Marker Signature and Clinical Outcome in Malignant Melanoma: A Large-Scale Tissue-Microarray Study with Two Independent Patient Cohorts

Current staging methods such as tumor thickness, ulceration and invasion of the sentinel node are known to be prognostic parameters in patients with malignant melanoma (MM). However, predictive molecular marker profiles for risk stratification and therapy optimization are not yet available for routine clinical assessment.; Using tissue microarrays, we retrospectively analyzed samples from 364 patients with primary MM. We investigated a panel of 70 immunohistochemical (IHC) antibodies for cell cycle, apoptosis, DNA mismatch repair, differentiation, proliferation, cell adhesion, signaling and metabolism. A marker selection procedure based on univariate Cox regression and multiple testing correction was employed to correlate the IHC expression data with the clinical follow-up (overall and recurrence-free survival). The model was thoroughly evaluated with two different cross validation experiments, a permutation test and a multivariate Cox regression analysis. In addition, the predictive power of the identified marker signature was validated on a second independent external test cohort (n?=?225). A signature of seven biomarkers (Bax, Bcl-X, PTEN, COX-2, loss of ?-Catenin, loss of MTAP, and presence of CD20 positive B-lymphocytes) was found to be an independent negative predictor for overall and recurrence-free survival in patients with MM. The seven-marker signature could also predict a high risk of disease recurrence in patients with localized primary MM stage pT1-2 (tumor thickness ?2.00 mm). In particular, three of these markers (MTAP, COX-2, Bcl-X) were shown to offer direct therapeutic implications.; The seven-marker signature might serve as a prognostic tool enabling physicians to selectively triage, at the time of diagnosis, the subset of high recurrence risk stage I-II patients for adjuvant therapy. Selective treatment of those patients that are more likely to develop distant metastatic disease could potentially lower the burden of untreatable metastatic melanoma and revolutionize the therapeutic management of MM

Wnt signaling pathway analysis in renal cell carcinoma in young patients

Renal cell carcinomas in young patients constitute a morphologically and genetically heterogeneous group. Twenty percent belong to the newly recognized Xp11.2 translocation-associated family and rare tumors arise from nephroblastoma. Aberrant Wnt signaling through beta-catenin mutation has been implicated in nephroblastoma pathogenesis and has been found to synergize with WT1 mutations. To characterize Wnt signaling activity in renal cell carcinomas in young patients, we gathered 34 tumors (three clear cell, ten Xp11.2 translocation associated, five papillary, two chromophobe, two collecting duct, one neuroblastoma associated, eight unclassified renal cell carcinomas, and three carcinomas combined with nephroblastoma) from patients less than 22 years. Expression of beta-catenin, its homologue gamma-catenin, and of WT1 was assessed by immunohistochemistry in 30 tumors, and sequence analysis of CTNNB1, CTNNG1, and WT1 genes was performed in 25 tumors. Cytoplasmic beta-catenin accumulation was demonstrated in two papillary carcinomas, one neuroblastoma-associated carcinoma, and two carcinomas arising from nephroblastoma. The pattern of gamma-catenin expression paralleled that of beta-catenin but its signal intensity was lower in 22, equal in 7, and stronger only in 1 tumor, respectively. Four tumors showed nuclear WT1 expression. One Xp11.2 translocation-associated carcinoma presented a rare intronic CTNNB1 single nucleotide polymorphism and cytoplasmic beta-catenin accumulation. There were no further CTNNB1 or CTNNG1 sequence alterations. A WT1 mutation was found in the nephroblastoma component of a carcinoma arising from nephroblastoma. These findings suggest Wnt signaling pathway activation only in a minority of renal cell carcinomas in young patients. CTNNB1 mutations are rare events. Cytoplasmic beta-catenin accumulation in an Xp11.2-associated carcinoma suggests potential interaction of Wnt signaling components with microphthalmia transcription factor family also in Xp11.2 translocation carcinomas. WT1 mutation in the nephroblastoma component of a mixed-type renal cell carcinoma provides direct evidence for clonal independence of nephroblastoma and carcinoma components in this exceptional tumor