Spectral decomposition of real circulant matrices

AbstractThis paper presents spectral decompositions, i.e., eigendecompositions and singular value decompositions of four types of real circulant matrices. Right and left circulants (whose elements topple from right to left or from left to right, respectively) as well as skew right and skew left circulants (whose elements change their sign when toppling) are analyzed.The inherent periodicity of circulant matrices means that they are closely related to Fourier analysis and group theory. This relationship is utilized in the spectral decompositions of this paper

Bayesian and frequentist analysis of an Austrian genome-wide association study of colorectal cancer and advanced adenomas

Most genome-wide association studies (GWAS) were analyzed using single marker tests in combination with stringent correction procedures for multiple testing. Thus, a substantial proportion of associated single nucleotide polymorphisms (SNPs) remained undetected and may account for missing heritability in complex traits. Model selection procedures present a powerful alternative to identify associated SNPs in high-dimensional settings. In this GWAS including 1060 colorectal cancer cases, 689 cases of advanced colorectal adenomas and 4367 controls we pursued a dual approach to investigate genome-wide associations with disease risk applying both, single marker analysis and model selection based on the modified Bayesian information criterion, mBIC2, implemented in the software package MOSGWA. For different case-control comparisons, we report models including between 1-14 candidate SNPs. A genome-wide significant association of rs17659990 (P=5.43x10(-9), DOCK3, chromosome 3p21.2) with colorectal cancer risk was observed. Furthermore, 56 SNPs known to influence susceptibility to colorectal cancer and advanced adenoma were tested in a hypothesis-driven approach and several of them were found to be relevant in our Austrian cohort. After correction for multiple testing (alpha=8.9x10(-4)), the most significant associations were observed for SNPs rs10505477 (P=6.08x10(-4)) and rs6983267 (P=7.35x10(-4)) of CASC8, rs3802842 (P=8.98x10(-5), COLCA1,2), and rs12953717 (P=4.64x10(-4), SMAD7). All previously unreported SNPs demand replication in additional samples. Reanalysis of existing GWAS datasets using model selection as tool to detect SNPs associated with a complex trait may present a promising resource to identify further genetic risk variants not only for colorectal cancer

Rectum-spacer related acute toxicity – endoscopy results of 403 prostate cancer patients after implantation of gel or balloon spacers

Abstract Background Rectal spacers are used to limit dose to the anterior rectal wall in high dose external beam radiation therapy of the prostate and have been shown to reduce radiation induced toxicity. Here we report the complication rate and toxicity of the implantation procedure in a large cohort of patients who have either received a gel- or balloon-type spacer. Methods In total, 403 patients received rectal spacing, 264 with balloon, 139 with gel. Allocation was non-randomized. Two hundred seventy-six patients were treated with normofractionated regimen, the remaining 125 patients in moderate hypofractionation. Spacer related acute and late rectal toxicity was prospectively assessed by endoscopy using a mucosa scoring system (Vienna Rectoscopy Score) as well as CTCAE V.4. For the balloon subgroup, position and rotation of balloon spacers were additionally correlated to incidence and grade of rectal reactions in a post-hoc analysis of post-implant planning MRIs. Results Overall rectal toxicity was very low with average VRS scores of 0.06 at the day after implantation, 0.10 at the end of RT, 0.31 at 6 months and 0.42 at 12 months follow up. Acute Grade 3 toxicity (rectum perforation and urethral damage) directly related to the implantation procedure occurred in 1.49% (n = 6) and was seen exclusively in patients who had received the spacer balloon. Analysis of post implant MR imaging did not identify abnormal or mal-rotated positions of this spacer to be a predictive factors for the occurrence of spacer related G3 toxicities. Conclusions Spacer technology is an effective means to minimize dose to the anterior rectal wall. However, the benefits in terms of dose sparing need to be weighed against the low, but possible risks of complications such as rectum perforation