Powers of sets in free groups

We prove that |A^n| > c_n |A|^{[\frac{n+1}{2}]} for any finite subset A of a free group if A contains at least two noncommuting elements, where c_n>0 are constants not depending on A. Simple examples show that the order of these estimates are the best possible for each n>0.Comment: 3 page

Comment on "Peierls Gap in Mesoscopic Ring Threated by a Magnetic Flux"

In a recent letter, Yi et al. PRL 78, 3523 (1997), have considered the stability of a Charge Density Wave in a one-dimensional ring, in the presence of an Aharonov-Bohm flux. This comment shows that, in one dimension, the stability of the Charge Density Wave depends on the parity of the number of electrons in the ring. This effect is similar to the parity effect known for the persistent current in one-dimensional rings.Comment: Latex, 1 page, 2 figure

Pauli Diagonal Channels Constant on Axes

We define and study the properties of channels which are analogous to unital qubit channels in several ways. A full treatment can be given only when the dimension d is a prime power, in which case each of the (d+1) mutually unbiased bases (MUB) defines an axis. Along each axis the channel looks like a depolarizing channel, but the degree of depolarization depends on the axis. When d is not a prime power, some of our results still hold, particularly in the case of channels with one symmetry axis. We describe the convex structure of this class of channels and the subclass of entanglement breaking channels. We find new bound entangled states for d = 3. For these channels, we show that the multiplicativity conjecture for maximal output p-norm holds for p=2. We also find channels with behavior not exhibited by unital qubit channels, including two pairs of orthogonal bases with equal output entropy in the absence of symmetry. This provides new numerical evidence for the additivity of minimal output entropy

Extending additivity from symmetric to asymmetric channels

We prove a lemma which allows one to extend results about the additivity of the minimal output entropy from highly symmetric channels to a much larger class. A similar result holds for the maximal output $p$-norm. Examples are given showing its use in a variety of situations. In particular, we prove the additivity and the multiplicativity for the shifted depolarising channel.Comment: 8 pages. This is the latest version of the first half of the original paper. The other half will appear in another pape

Utility of Parental Mediation Model on Youth’s Problematic Online Gaming

The Parental Mediation Model PMM) was initially designed to regulate children’s attitudes towards the traditional media. In the present era, because of prevalent online media there is a need for similar regulative measures. Spending long hours on social media and playing online games increase the risks of exposure to the negative outcomes of online gaming. This paper initially applied the PMM developed by European Kids Online to (i) test the reliability and validity of this model and (ii) identify the effectiveness of this model in controlling problematic online gaming (POG). The data were collected from 592 participants comprising 296 parents and 296 students of four foreign universities, aged 16 to 22 years in Kuala Lumpur (Malaysia). The study found that the modified model of the five-factor PMM (Technical mediation, Monitoring mediation, Restrictive mediation, Active Mediation of Internet Safety, and Active mediation of Internet Use) functions as a predictor for mitigating POG. The findings suggest the existence of a positive relation between ‘monitoring’ and ‘restrictive’ mediation strategies and exposure to POG while Active Mediation of Internet Safety and Active mediation of Internet use were insignificant predictors. Results showed a higher utility of ‘technical’ strategies by the parents led to less POG. The findings of this study do not support the literature suggesting active mediation is more effective for reducing youth’s risky behaviour. Instead, parents need to apply more technical mediations with their children and adolescents’ Internet use to minimize the negative effects of online gaming

Validation of vessel size imaging (VSI) in high-grade human gliomas using magnetic resonance imaging, image-guided biopsies, and quantitative immunohistochemistry.

To evaluate the association between a vessel size index (VSIMRI) derived from dynamic susceptibility contrast (DSC) perfusion imaging using a custom spin-and-gradient echo echoplanar imaging (SAGE-EPI) sequence and quantitative estimates of vessel morphometry based on immunohistochemistry from image-guided biopsy samples. The current study evaluated both relative cerebral blood volume (rCBV) and VSIMRI in eleven patients with high-grade glioma (7 WHO grade III and 4 WHO grade IV). Following 26 MRI-guided glioma biopsies in these 11 patients, we evaluated tissue morphometry, including vessel density and average radius, using an automated procedure based on the endothelial cell marker CD31 to highlight tumor vasculature. Measures of rCBV and VSIMRI were then compared to histological measures. We demonstrate good agreement between VSI measured by MRI and histology; VSIMRI = 13.67 μm and VSIHistology = 12.60 μm, with slight overestimation of VSIMRI in grade III patients compared to histology. rCBV showed a moderate but significant correlation with vessel density (r = 0.42, p = 0.03), and a correlation was also observed between VSIMRI and VSIHistology (r = 0.49, p = 0.01). The current study supports the hypothesis that vessel size measures using MRI accurately reflect vessel caliber within high-grade gliomas, while traditional measures of rCBV are correlated with vessel density and not vessel caliber

Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu

Using Gene Expression Signatures to Identify Novel Treatment Strategies in Gulf War Illness

Background Gulf War Illness (GWI) is a complex multi-symptom disorder that affects up to one in three veterans of this 1991 conflict and for which no effective treatment has been found. Discovering novel treatment strategies for such a complex chronic illness is extremely expensive, carries a high probability of failure and a lengthy cycle time. Repurposing Food and Drug Administration approved drugs offers a cost-effective solution with a significantly abbreviated timeline. Methods Here, we explore drug re-purposing opportunities in GWI by combining systems biology and bioinformatics techniques with pharmacogenomic information to find overlapping elements in gene expression linking GWI to successfully treated diseases. Gene modules were defined based on cellular function and their activation estimated from the differential expression of each module’s constituent genes. These gene modules were then cross-referenced with drug atlas and pharmacogenomic databases to identify agents currently used successfully for treatment in other diseases. To explore the clinical use of these drugs in illnesses similar to GWI we compared gene expression patterns in modules that were significantly expressed in GWI with expression patterns in those same modules in other illnesses. Results We found 19 functional modules with significantly altered gene expression patterns in GWI. Within these modules, 45 genes were documented drug targets. Illnesses with highly correlated gene expression patterns overlapping considerably with GWI were found in 18 of the disease conditions studied. Brain, muscular and autoimmune disorders composed the bulk of these. Conclusion Of the associated drugs, immunosuppressants currently used in treating rheumatoid arthritis, and hormone based therapies were identified as the best available candidates for treating GWI symptoms

Aharonov-Anandan Effect Induced by Spin-Orbit Interaction and Charge-Density-Waves in Mesoscopic Rings

We study the spin-dependent geometric phase effect in mesoscopic rings of charge-density-wave(CDW) materials. When electron spin is explicitly taken into account, we show that the spin-dependent Aharonov-Casher phase can have a pronounced frustration effects on such CDW materials with appropriate electron filling. We show that this frustration has observable consequences for transport experiment. We identify a phase transition from a Peierls insulator to metal, which is induced by spin-dependent phase interference effects. Mesoscopic CDW materials and spin-dependent geometric phase effects, and their interplay, are becoming attractive opportunities for exploitation with the rapid development of modern fabrication technology.Comment: 5 pages, 6 figures, to appear in Phys.Rev.B(Aug.15, 1998

Integrated whole transcriptome and DNA methylation analysis identifies gene networks specific to late-onset Alzheimer’s disease

Previous transcriptome studies observed disrupted cellular processes in late-onset Alzheimer\u27s disease (LOAD), yet it is unclear whether these changes are specific to LOAD, or are common to general neurodegeneration. In this study, we address this question by examining transcription in LOAD and comparing it to cognitively normal controls and a cohort of disease controls. Differential transcription was examined using RNA-seq, which allows for the examination of protein coding genes, non-coding RNAs, and splicing. Significant transcription differences specific to LOAD were observed in five genes: C10orf105, DIO2, a lincRNA, RARRES3, and WIF1. These findings were replicated in two independent publicly available microarray data sets. Network analyses, performed on 2,504 genes with moderate transcription differences in LOAD, reveal that these genes aggregate into seven networks. Two networks involved in myelination and innate immune response specifically correlated to LOAD. FRMD4B and ST18, hub genes within the myelination network, were previously implicated in LOAD. Of the five significant genes, WIF1 and RARRES3 are directly implicated in the myelination process; the other three genes are located within the network. LOAD specific changes in DNA methylation were located throughout the genome and substantial changes in methylation were identified within the myelination network. Splicing differences specific to LOAD were observed across the genome and were decreased in all seven networks. DNA methylation had reduced influence on transcription within LOAD in the myelination network when compared to both controls. These results hint at the molecular underpinnings of LOAD and indicate several key processes, genes, and networks specific to the disease