Observable Optimal State Points of Sub-additive Potentials

For a sequence of sub-additive potentials, Dai [Optimal state points of the sub-additive ergodic theorem, Nonlinearity, 24 (2011), 1565-1573] gave a method of choosing state points with negative growth rates for an ergodic dynamical system. This paper generalizes Dai's result to the non-ergodic case, and proves that under some mild additional hypothesis, one can choose points with negative growth rates from a positive Lebesgue measure set, even if the system does not preserve any measure that is absolutely continuous with respect to Lebesgue measure.Comment: 16 pages. This work was reported in the summer school in Nanjing University. In this second version we have included some changes suggested by the referee. The final version will appear in Discrete and Continuous Dynamical Systems- Series A - A.I.M. Sciences and will be available at http://aimsciences.org/journals/homeAllIssue.jsp?journalID=

SDiff(2) Toda equation -- hierarchy, τ\tau function, and symmetries

A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum Einstein equation and its hyper-K\"ahler version, however now based upon a symplectic structure and the group SDiff(2) of area preserving diffeomorphisms on a cylinder $S^1 \times \R$. An analogue of the Toda lattice tau function is introduced. The existence of hidden SDiff(2) symmetries are derived from a Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function turn out to have commutator anomalies, hence give a representation of a central extension of the SDiff(2) algebra.Comment: 16 pages (``vanilla.sty" is attatched to the end of this file after ``\bye" command

Asthma families show transmission disequilibrium of gene variants in the vitamin D metabolism and signalling pathway

The vitamin D prophylaxis of rickets in pregnant women and newborns may play a role in early allergic sensitization. We now asked if an already diseased population may have inherited genetic variants in the vitamin D turnover or signalling pathway. Serum levels of calcidiol (25-OH-D(3)) and calcitriol (1,25-(OH)(2)-D(3)) were retrospectively assessed in 872 partipants of the German Asthma Family Study. 96 DNA single base variants in 13 different genes were genotyped with MALDI-TOF and a bead array system. At least one positive SNP with a TDT of p < 0.05 for asthma or total IgE and calcidiol or calcitriol was seen in IL10, GC, IL12B, CYP2R1, IL4R, and CYP24A1. Consistent strong genotypic association could not be observed. Haplotype association were found only for CYP24A1, the main calcidiol degrading enzyme, where a frequent 5-point-haplotype was associated with asthma (p = 0,00063), total IgE (p = 0,0014), calcidiol (p = 0,0043) and calcitriol (p = 0,0046). Genetic analysis of biological pathways seem to be a promising approach where this may be a first entry point into effects of a polygenic inherited vitamin D sensitivity that may affect also other metabolic, immunological and cancerous diseases

Circulating 25-Hydroxyvitamin D and Risk of Esophageal and Gastric Cancer: Cohort Consortium Vitamin D Pooling Project of Rarer Cancers

Upper gastrointestinal (GI) cancers of the stomach and esophagus have high incidence and mortality worldwide, but they are uncommon in Western countries. Little information exists on the association between vitamin D and risk of upper GI cancers. This study examined the association between circulating 25-hydroxyvitamin D (25(OH)D) and upper GI cancer risk in the Cohort Consortium Vitamin D Pooling Project of Rarer Cancers. Concentrations of 25(OH)D were measured from 1,065 upper GI cancer cases and 1,066 age-, sex-, race-, and season-of blood draw–matched controls from 8 prospective cohort studies. In multivariate-adjusted models, circulating 25(OH)D concentration was not significantly associated with upper GI cancer risk. Subgroup analysis by race showed that among Asians, but not Caucasians, lower concentrations of 25(OH)D (<25 nmol/L) were associated with a statistically significant decreased risk of upper GI cancer (reference: 50–<75 nmol/L) (odds ratio = 0.53, 95% confidence interval: 0.31, 0.91; P trend = 0.003). Never smokers with concentrations of <25 nmol/L showed a lower risk of upper GI cancers (odds ratio = 0.55, 95% confidence interval: 0.31, 0.96). Subgroup analyses by alcohol consumption produced opposing trends. Results do not support the hypothesis that interventions aimed at increasing vitamin D status would lead to a lower risk of these highly fatal cancers

Prospective study of serum 25(OH)-vitamin D concentration and risk of oesophageal and gastric cancers

We prospectively examined the relation between pretrial serum vitamin D status and risk of oesophageal and gastric cancers among subjects who developed cancer over 5.25 years of follow-up, including 545 oesophageal squamous cell carcinomas (ESCC), 353 gastric cardia adenocarcinomas, 81 gastric noncardia adenocarcinomas, and an age- and sex-stratified random sample of 1105 subjects. The distribution of serum 25(OH)D was calculated using the known sampling weights. For the cohort as a whole, the 25th, 50th, and 75th percentile concentrations of 25(OH)-vitamin D were 19.6, 31.9, and 48.7 nmol l−1, respectively, and we found that higher serum 25(OH)D concentrations were associated with monotonically increasing risk of ESCC in men, but not in women. Comparing men in the fourth quartile of serum 25(OH)D concentrations to those in the first, we found a hazard ratio (HR) (95% confidence interval (CI)) of 1.77 (1.16–2.70), P trend=0.0033. The same comparison in women had a HR (95% CI) of 1.06 (0.71–1.59), P trend=0.70. We found no associations for gastric cardia or noncardia adenocarcinoma. Among subjects with low vitamin D status, higher serum 25(OH)D concentrations were associated with significantly increased risk of ESCC in men, but not in women. Further refinements of the analysis did not suggest any factors, which could explain this unexpected result

Hierarchical structure of cascade of primary and secondary periodicities in Fourier power spectrum of alphoid higher order repeats

<p>Abstract</p> <p>Background</p> <p>Identification of approximate tandem repeats is an important task of broad significance and still remains a challenging problem of computational genomics. Often there is no single best approach to periodicity detection and a combination of different methods may improve the prediction accuracy. Discrete Fourier transform (DFT) has been extensively used to study primary periodicities in DNA sequences. Here we investigate the application of DFT method to identify and study alphoid higher order repeats.</p> <p>Results</p> <p>We used method based on DFT with mapping of symbolic into numerical sequence to identify and study alphoid higher order repeats (HOR). For HORs the power spectrum shows equidistant frequency pattern, with characteristic two-level hierarchical organization as signature of HOR. Our case study was the 16 mer HOR tandem in AC017075.8 from human chromosome 7. Very long array of equidistant peaks at multiple frequencies (more than a thousand higher harmonics) is based on fundamental frequency of 16 mer HOR. Pronounced subset of equidistant peaks is based on multiples of the fundamental HOR frequency (multiplication factor <it>n </it>for <it>n</it>mer) and higher harmonics. In general, <it>n</it>mer HOR-pattern contains equidistant secondary periodicity peaks, having a pronounced subset of equidistant primary periodicity peaks. This hierarchical pattern as signature for HOR detection is robust with respect to monomer insertions and deletions, random sequence insertions etc. For a monomeric alphoid sequence only primary periodicity peaks are present. The 1/<it>f</it>^{<it>β </it>}– noise and periodicity three pattern are missing from power spectra in alphoid regions, in accordance with expectations.</p> <p>Conclusion</p> <p>DFT provides a robust detection method for higher order periodicity. Easily recognizable HOR power spectrum is characterized by hierarchical two-level equidistant pattern: higher harmonics of the fundamental HOR-frequency (secondary periodicity) and a subset of pronounced peaks corresponding to constituent monomers (primary periodicity). The number of lower frequency peaks (secondary periodicity) below the frequency of the first primary periodicity peak reveals the size of <it>n</it>mer HOR, i.e., the number <it>n </it>of monomers contained in consensus HOR.</p

The Genetic Signatures of Noncoding RNAs

The majority of the genome in animals and plants is transcribed in a developmentally regulated manner to produce large numbers of non–protein-coding RNAs (ncRNAs), whose incidence increases with developmental complexity. There is growing evidence that these transcripts are functional, particularly in the regulation of epigenetic processes, leading to the suggestion that they compose a hitherto hidden layer of genomic programming in humans and other complex organisms. However, to date, very few have been identified in genetic screens. Here I show that this is explicable by an historic emphasis, both phenotypically and technically, on mutations in protein-coding sequences, and by presumptions about the nature of regulatory mutations. Most variations in regulatory sequences produce relatively subtle phenotypic changes, in contrast to mutations in protein-coding sequences that frequently cause catastrophic component failure. Until recently, most mapping projects have focused on protein-coding sequences, and the limited number of identified regulatory mutations have been interpreted as affecting conventional cis-acting promoter and enhancer elements, although these regions are often themselves transcribed. Moreover, ncRNA-directed regulatory circuits underpin most, if not all, complex genetic phenomena in eukaryotes, including RNA interference-related processes such as transcriptional and post-transcriptional gene silencing, position effect variegation, hybrid dysgenesis, chromosome dosage compensation, parental imprinting and allelic exclusion, paramutation, and possibly transvection and transinduction. The next frontier is the identification and functional characterization of the myriad sequence variations that influence quantitative traits, disease susceptibility, and other complex characteristics, which are being shown by genome-wide association studies to lie mostly in noncoding, presumably regulatory, regions. There is every possibility that many of these variations will alter the interactions between regulatory RNAs and their targets, a prospect that should be borne in mind in future functional analyses