The entropy distance between the Wiener and stationary Gaussian measures

Investigating the entropy distance between the Wiener measure, W-t0,W- (tau) and stationary Gaussian measures, Q(t0, tau) on the space of continuous functions C[t(0) - tau, t(0) + tau], we show that in some cases this distance can essentially be computed. This is done by explicitly computing a related quantity which in effect is a valid approximation of the entropy distance, provided it is sufficiently small; this will be the case if tau/t(0) is small. We prove that H(Wt(0, tau), Q(t0, tau)) > tau/2(t0), and then show that tau/2t(0) is essentially the typical case of such entropy distance, provided the mean and the variance of the stationary measures are set "appropriately". Utilizing a similar technique, we estimate the entropy distance between the Ornstein-Uhlenbeck measure and other stationary Gaussian measures on C[1 - tau, 1 + tau]. Using this result combined with a variant of the triangle inequality for the entropy distance, which we devise, yields an upper bound on the entropy distance between stationary Gaussian measures which are absolutely continuous with respect to the Wiener measure

Absolute continuity between the Wiener and stationary Gaussian measures

It is known that the entropy distance between two Gaussian measures is finite if, and only if, they are absolutely continuous with respect to one another. Shepp (1966) characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to the Wiener measure. By analyzing the entropy distance, we show that one of his conditions, involving the spectrum of an associated operator, is essentially extraneous, providing a simple criterion for finite entropy distance in this case

On L^p Bounds for Kakeya Maximal Functions and the Minkowski Dimension in R^2

We prove that the bound on the L^p norms of the Kakeya type maximal functions studied by Cordoba [2] and Bourgain [1] are sharp for p > 2. The proof is based on a construction originally due to Schoenberg [5], for which we provide an alternative derivation. We also show that r^2 log (1/r) is the exact Minkowski dimension of the class of Kakeya sets in R^2, and prove that the exact Hausdorff dimension of these sets is between r^2 log (1/r) and r^2 log (1/r) [log log (1/r)]^(2+ε)

The Effect of Dosage Regimen on Medication Compliance

According to recent data, between 25% and 50% of patients are noncompliant in their therapy regimen in some manner. The fourth report of the Joint National Committee on the Detection, Evaluation, and Treatment of High Blood Pressure (Neal, 1989) states that noncompliance is the major problem in hypertension control. It was hypothesized there would be a difference in the compliance of hypertensive patients whose medication regimen consisted of single daily dosing as opposed to those patients whose regimen consisted of two or more times a day dosing. Potential subjects for the study were hypertensive patients selected from a rural, southeastern Georgia setting who patronized a local pharmacy. The pharmacy\u27s records from January 1, 1989 through October 15, 1991 were accessed to identify patients prescribed only antihypertensive therapy and whose therapy had been consistent for at least fourteen months. Fifty-five subjects met this criteria. A data collection form was developed so that information from pharmaceutical records (computerized and printed patient profiles) could be obtained in a standardized manner. The form consisted of twelve questions which addressed demographics, types of medication, physician information, payor type, and medication therapy. From the information obtained, the relationship between ten variables (age, gender, town of residence, race, marital status, payor type, whether subject had children, class of medication, physician setting, medication regimen) and compliance percentage was analyzed. Analysis of data was accomplished by univariate and multivariate analysis of variance (ANOVA) to test for significant differences between compliance percentage and the factors of interest for the study. Dosage regimen (once a day versus two or more times a day) was the only statistically significant factor related to compliance percentage

Designing seeds for similarity search in genomic DNA

AbstractLarge-scale comparison of genomic DNA is of fundamental importance in annotating functional elements of genomes. To perform large comparisons efficiently, BLAST (Methods: Companion Methods Enzymol 266 (1996) 460, J. Mol. Biol. 215 (1990) 403, Nucleic Acids Res. 25(17) (1997) 3389) and other widely used tools use seeded alignment, which compares only sequences that can be shown to share a common pattern or “seed’’ of matching bases. The literature suggests that the choice of seed substantially affects the sensitivity of seeded alignment, but designing and evaluating seeds is computationally challenging.This work addresses the problem of designing a seed to optimize performance of seeded alignment. We give a fast, simple algorithm based on finite automata for evaluating the sensitivity of a seed in a Markov model of ungapped alignments, along with extensions to mixtures and inhomogeneous Markov models. We give intuition and theoretical results on which seeds are good choices. Finally, we describe Mandala, a software tool for seed design, and show that it can be used to improve the sensitivity of alignment in practice

Deep RNA sequencing of L. monocytogenes reveals overlapping and extensive stationary phase and sigma B-dependent transcriptomes, including multiple highly transcribed noncoding RNAs

BACKGROUND: Identification of specific genes and gene expression patterns important for bacterial survival, transmission and pathogenesis is critically needed to enable development of more effective pathogen control strategies. The stationary phase stress response transcriptome, including many σ(B)-dependent genes, was defined for the human bacterial pathogen Listeria monocytogenes using RNA sequencing (RNA-Seq) with the Illumina Genome Analyzer. Specifically, bacterial transcriptomes were compared between stationary phase cells of L. monocytogenes 10403S and an otherwise isogenic ΔsigB mutant, which does not express the alternative σ factor σ(B), a major regulator of genes contributing to stress response, including stresses encountered upon entry into stationary phase. RESULTS: Overall, 83% of all L. monocytogenes genes were transcribed in stationary phase cells; 42% of currently annotated L. monocytogenes genes showed medium to high transcript levels under these conditions. A total of 96 genes had significantly higher transcript levels in 10403S than in ΔsigB, indicating σ(B)-dependent transcription of these genes. RNA-Seq analyses indicate that a total of 67 noncoding RNA molecules (ncRNAs) are transcribed in stationary phase L. monocytogenes, including 7 previously unrecognized putative ncRNAs. Application of a dynamically trained Hidden Markov Model, in combination with RNA-Seq data, identified 65 putative σ(B )promoters upstream of 82 of the 96 σ(B)-dependent genes and upstream of the one σ(B)-dependent ncRNA. The RNA-Seq data also enabled annotation of putative operons as well as visualization of 5'- and 3'-UTR regions. CONCLUSIONS: The results from these studies provide powerful evidence that RNA-Seq data combined with appropriate bioinformatics tools allow quantitative characterization of prokaryotic transcriptomes, thus providing exciting new strategies for exploring transcriptional regulatory networks in bacteria. See minireivew http://jbiol.com/content/8/12/107

Health-related Quality of Life in Pediatric Patients With Chronic Hepatitis B Living in the United States and Canada

OBJECTIVES: The aim of the study was to determine whether selected sociodemographic and hepatitis B virus (HBV)-specific clinical factors are associated with health-related quality of life (HRQoL) among pediatric patients chronically infected with HBV. METHODS: Children with chronic HBV enrolled in the Hepatitis B Research Network completed the Child Health Questionnaire at study entry. Caregivers of children 5 to <10 years completed the parent-reported form (CHQ-Parent Report Form); youth 10 to <18 years completed the child-reported CHQ-Child Report Form. We examined univariable associations of the Child Health Questionnaire scores with selected independent variables: sex, adoption status, maternal education, alanine aminotransferase (U/L), aspartate aminotransferase-to-platelet ratio index, and HBV-specific symptom count. RESULTS: A total of 244 participants (83 young children 5-<10 years, 161 youth 10-<18 years) were included, all HBV treatment-naïve. Among young children, increased alanine aminotransferase level was negatively associated with CHQ-Parent Report Form psychosocial summary t score (r = -0.28, P = 0.01). No other subscale comparisons for young children were statistically significant. Among youth, adoption was associated with better physical functioning and general health (P < 0.01). Higher maternal education was associated with better role/functioning-physical and -emotional scores (P < 0.05). Maternal education and adoption status were linked with adoption associated with higher maternal education. Increased symptom count in youth was associated with worse HRQoL in subscales measuring bodily pain, behavior, mental health, and self-esteem (P < 0.01). CONCLUSIONS: Although overall HRQoL is preserved in children with chronic HBV, some sociodemographic and HBV-related clinical factors were associated with impaired HRQoL in our pediatric patients at baseline. Measurement of HRQoL can focus resources on education and psychosocial support in children and families most in need