Linearized Asymptotic Stability for Fractional Differential Equations

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector \{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\} where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable

An evaluation of processing methods for HumanMethylation450 BeadChip data

BackgroundIllumina's HumanMethylation450 arrays provide the most cost-effective means of high-throughput DNA methylation analysis. As with other types of microarray platforms, technical artifacts are a concern, including background fluorescence, dye-bias from the use of two color channels, bias caused by type I/II probe design, and batch effects. Several approaches and pipelines have been developed, either targeting a single issue or designed to address multiple biases through a combination of methods. We evaluate the effect of combining separate approaches to improve signal processing.ResultsIn this study nine processing methods, including both within- and between- array methods, are applied and compared in four datasets. For technical replicates, we found both within- and between-array methods did a comparable job in reducing variance across replicates. For evaluating biological differences, within-array processing always improved differential DNA methylation signal detection over no processing, and always benefitted from performing background correction first. Combinations of within-array procedures were always among the best performing methods, with a slight advantage appearing for the between-array method Funnorm when batch effects explained more variation in the data than the methylation alterations between cases and controls. However, when this occurred, RUVm, a new batch correction method noticeably improved reproducibility of differential methylation results over any of the signal-processing methods alone.ConclusionsThe comparisons in our study provide valuable insights in preprocessing HumanMethylation450 BeadChip data. We found the within-array combination of Noob + BMIQ always improved signal sensitivity, and when combined with the RUVm batch-correction method, outperformed all other approaches in performing differential DNA methylation analysis. The effect of the data processing method, in any given data set, was a function of both the signal and noise

A total production index for Washington, D.C.

A heavy concentration of services characterizes the economy of the District of Columbia. Growth in the D.C. economy, although usually heavily insulated from the swings of the U.S. business cycle, varies in intensity and, sometimes, in direction. Now, a new monthly index of total production provides a timely measure of services and goods production in Washington, D.C.Industrial production index ; Federal Reserve District, 5th

The ARGUS Vertex Trigger

A fast second level trigger has been developed for the ARGUS experiment which recognizes tracks originating from the interaction region. The processor compares the hits in the ARGUS Micro Vertex Drift Chamber to 245760 masks stored in random access memories. The masks which are fully defined in three dimensions are able to reject tracks originating in the wall of the narrow beampipe of 10.5\,mm radius.Comment: gzipped Postscript, 27 page

Celiac Disease: Role of the Epithelial Barrier

In celiac disease (CD) a T-cell–mediated response to gluten is mounted in genetically predisposed individuals, resulting in a malabsorptive enteropathy histologically highlighted by villous atrophy and crypt hyperplasia. Recent data point to the epithelial layer as an under-rated hot spot in celiac pathophysiology to date. This overview summarizes current functional and genetic evidence on the role of the epithelial barrier in CD, consisting of the cell membranes and the apical junctional complex comprising sealing as well as ion and water channel-forming tight junction proteins and the adherens junction. Moreover, the underlying mechanisms are discussed, including apoptosis of intestinal epithelial cells, biology of intestinal stem cells, alterations in the apical junctional complex, transcytotic uptake of gluten peptides, and possible implications of a defective epithelial polarity. Current research is directed toward new treatment options for CD that are alternatives or complementary therapeutics to a gluten-free diet. Thus, strategies to target an altered epithelial barrier therapeutically also are discussed

Optimal sequential fingerprinting: Wald vs. Tardos

We study sequential collusion-resistant fingerprinting, where the fingerprinting code is generated in advance but accusations may be made between rounds, and show that in this setting both the dynamic Tardos scheme and schemes building upon Wald's sequential probability ratio test (SPRT) are asymptotically optimal. We further compare these two approaches to sequential fingerprinting, highlighting differences between the two schemes. Based on these differences, we argue that Wald's scheme should in general be preferred over the dynamic Tardos scheme, even though both schemes have their merits. As a side result, we derive an optimal sequential group testing method for the classical model, which can easily be generalized to different group testing models.Comment: 12 pages, 10 figure

Using DNA Methylation Patterns to Infer Tumor Ancestry

Background: Exactly how human tumors grow is uncertain because serial observations are impractical. One approach to reconstruct the histories of individual human cancers is to analyze the current genomic variation between its cells. The greater the variations, on average, the greater the time since the last clonal evolution cycle (‘‘a molecular clock hypothesis’’). Here we analyze passenger DNA methylation patterns from opposite sides of 12 primary human colorectal cancers (CRCs) to evaluate whether the variation (pairwise distances between epialleles) is consistent with a single clonal expansion after transformation. Methodology/Principal Findings: Data from 12 primary CRCs are compared to epigenomic data simulated under a single clonal expansion for a variety of possible growth scenarios. We find that for many different growth rates, a single clonal expansion can explain the population variation in 11 out of 12 CRCs. In eight CRCs, the cells from different glands are all equally distantly related, and cells sampled from the same tumor half appear no more closely related than cells sampled from opposite tumor halves. In these tumors, growth appears consistent with a single ‘‘symmetric’ ’ clonal expansion. In three CRCs, the variation in epigenetic distances was different between sides, but this asymmetry could be explained by a single clonal expansion with one region of a tumor having undergone more cell division than the other. The variation in one CRC was complex and inconsistent with a simple single clonal expansion