A dynamical point of view on the set of B-free integers

We extend the study of the square-free flow, recently introduced by Sarnak, to the more general context of B-free integers, that is to say integers with no factor in a given family B of pairwise relatively prime integers, the sum of whose reciprocals is finite. Relying on dynamical arguments, we prove in particular that the distribution of patterns in the characteristic function of the B-free integers follows a shift-invariant probability measure, and gives rise to a measurable dynamical system isomorphic to a specific minimal rotation on a compact group. As a by-product, we get the abundance of twin B-free integers. Moreover, we show that the distribution of patterns in small intervals also conforms to the same measure. When elements of B are squares, we introduce a generalization of the M\"obius function, and discuss a conjecture of Chowla in this broader context

On spectral disjointness of powers for rank-one transformations and M\"obius orthogonality

We study the spectral disjointness of the powers of a rank-one transformation. For a large class of rank-one constructions, including those for which the cutting and stacking parameters are bounded, and other examples such as rigid generalized Chacon's maps and Katok's map, we prove that different positive powers of the transformation are pairwise spectrally disjoint on the continuous part of the spectrum. Our proof involves the existence, in the weak closure of {U_T^k: k in Z}, of "sufficiently many" analytic functions of the operator U_T. Then we apply these disjointness results to prove Sarnak's conjecture for the (possibly non-uniquely ergodic) symbolic models associated to these rank-one constructions: All sequences realized in these models are orthogonal to the M\"obius function

M\"obius disjointness for models of an ergodic system and beyond

Given a topological dynamical system $(X,T)$ and an arithmetic function $\boldsymbol{u}\colon\mathbb{N}\to\mathbb{C}$, we study the strong MOMO property (relatively to $\boldsymbol{u}$) which is a strong version of $\boldsymbol{u}$-disjointness with all observable sequences in $(X,T)$. It is proved that, given an ergodic measure-preserving system $(Z,\mathcal{D},\kappa,R)$, the strong MOMO property (relatively to $\boldsymbol{u}$) of a uniquely ergodic model $(X,T)$ of $R$ yields all other uniquely ergodic models of $R$ to be $\boldsymbol{u}$-disjoint. It follows that all uniquely ergodic models of: ergodic unipotent diffeomorphisms on nilmanifolds, discrete spectrum automorphisms, systems given by some substitutions of constant length (including the classical Thue-Morse and Rudin-Shapiro substitutions), systems determined by Kakutani sequences are M\"obius (and Liouville) disjoint. The validity of Sarnak's conjecture implies the strong MOMO property relatively to $\boldsymbol{\mu}$ in all zero entropy systems, in particular, it makes $\boldsymbol{\mu}$-disjointness uniform. The absence of strong MOMO property in positive entropy systems is discussed and, it is proved that, under the Chowla conjecture, a topological system has the strong MOMO property relatively to the Liouville function if and only if its topological entropy is zero.Comment: 35 page

A review of size and geometrical factors influencing resonant frequencies in metamaterials

Although metamaterials and so-called left-handed media have originated from theoretical considerations, it is only by their practical fabrication and the measurement of their properties that they have gained credibility and can fulfil the potential of their predicted properties. In this review we consider some of the more generally applicable fabrication methods and changes in geometry as they have progressed, exhibiting resonant frequencies ranging from radio waves to the visible optical region

HCV-induced miR146a Controls SOCS1/STAT3 and Cytokine Expression in Monocytes to Promote Regulatory T-cell Development

Host innate and adaptive immune responses must be tightly regulated by an intricate balance between positive and negative signals to ensure their appropriate onset and termination while fighting pathogens and avoiding autoimmunity; persistent pathogens may usurp these regulatory machineries to dampen host immune responses for their persistence in vivo. Here, we demonstrate that miR146a is up‐regulated in monocytes from hepatitis C virus (HCV )‐infected individuals compared to control subjects. Interestingly, miR146a expression in monocytes without HCV infection increased, whereas its level in monocytes with HCV infection decreased, following Toll‐like receptor (TLR ) stimulation. This miR146a induction by HCV infection and differential response to TLR stimulation were recapitulated in vitro in monocytes co‐cultured with hepatocytes with or without HCV infection. Importantly, inhibition of miR146a in monocytes from HCV ‐infected patients led to a decrease in IL ‐23, IL ‐10 and TGF ‐β expressions through the induction of suppressor of cytokine signalling 1 (SOCS 1) and the inhibition of signal transducer and activator transcription 3 (STAT 3), and this subsequently resulted in a decrease in regulatory T cells (Tregs) accumulated during HCV infection. These results suggest that miR146a may regulate SOCS 1/STAT 3 and cytokine signalling in monocytes, directing T‐cell differentiation and balancing immune clearance and immune injury during chronic viral infection

A Bayesian Approach for Analysis of Whole-Genome Bisulfite Sequencing Data Identifies Disease-Associated Changes in DNA Methylation

DNA methylation is a key epigenetic modification involved in gene regulation whose contribution to disease susceptibility remains to be fully understood. Here, we present a novel Bayesian smoothing approach (called ABBA) to detect differentially methylated regions (DMRs) from whole-genome bisulfite sequencing (WGBS). We also show how this approach can be leveraged to identify disease-associated changes in DNA methylation, suggesting mechanisms through which these alterations might affect disease. From a data modeling perspective, ABBA has the distinctive feature of automatically adapting to different correlation structures in CpG methylation levels across the genome while taking into account the distance between CpG sites as a covariate. Our simulation study shows that ABBA has greater power to detect DMRs than existing methods, providing an accurate identification of DMRs in the large majority of simulated cases. To empirically demonstrate the method’s efficacy in generating biological hypotheses, we performed WGBS of primary macrophages derived from an experimental rat system of glomerulonephritis and used ABBA to identify >1000 disease-associated DMRs. Investigation of these DMRs revealed differential DNA methylation localized to a 600 bp region in the promoter of the Ifitm3 gene. This was confirmed by ChIP-seq and RNA-seq analyses, showing differential transcription factor binding at the Ifitm3 promoter by JunD (an established determinant of glomerulonephritis), and a consistent change in Ifitm3 expression. Our ABBA analysis allowed us to propose a new role for Ifitm3 in the pathogenesis of glomerulonephritis via a mechanism involving promoter hypermethylation that is associated with Ifitm3 repression in the rat strain susceptible to glomerulonephritis

Metal–organic complexation in the marine environment

We discuss the voltammetric methods that are used to assess metal–organic complexation in seawater. These consist of titration methods using anodic stripping voltammetry (ASV) and cathodic stripping voltammetry competitive ligand experiments (CSV-CLE). These approaches and a kinetic approach using CSV-CLE give similar information on the amount of excess ligand to metal in a sample and the conditional metal ligand stability constant for the excess ligand bound to the metal. CSV-CLE data using different ligands to measure Fe(III) organic complexes are similar. All these methods give conditional stability constants for which the side reaction coefficient for the metal can be corrected but not that for the ligand. Another approach, pseudovoltammetry, provides information on the actual metal–ligand complex(es) in a sample by doing ASV experiments where the deposition potential is varied more negatively in order to destroy the metal–ligand complex. This latter approach gives concentration information on each actual ligand bound to the metal as well as the thermodynamic stability constant of each complex in solution when compared to known metal–ligand complexes. In this case the side reaction coefficients for the metal and ligand are corrected. Thus, this method may not give identical information to the titration methods because the excess ligand in the sample may not be identical to some of the actual ligands binding the metal in the sample

Vitamin status and cognitive function in a long-term care population

BACKGROUND: Ageing can be associated with poor dietary intake, reduced nutrient absorption, and less efficient utilization of nutrients. Loss of memory and related cognitive function are also common among older persons. This study aimed to measure the prevalence of inadequate vitamin status among long-term care patients and determine if an association exists between vitamin status and each of three variables; cognitive function, vitamin supplementation, and medications which alter gastric acid levels. METHODS: Seventy-five patients in a long-term care hospital in Guelph, Ontario were recruited to a cross-sectional study. 47 were female and the mean age was 80.7 (+/-11.5) years, ranging from 48 to 100 years. Blood was used to measure levels of vitamins B12 (cobalamin), B6 (pyridoxal-5'-phosphate/PLP), erythrocyte folate, vitamin B3 (niacin) and homocysteine (Hcy). The Standardized Mini-Mental State Examination (SMMSE) was administered to measure cognitive function. A list of medications and vitamin supplementation for each patient was provided by the pharmacy. RESULTS: The prevalence of low vitamin (B12, B6, erythrocyte folate, niacin) or high metabolite (homocysteine) levels among 75 patients were as follows: B12 <148 pmol/L in 5/75 (6.7%); B12 between 148 and 221 pmol/L in 26/75 (34.7%); B6 ≤30 nmol/L in 4/75 (5.3%); erythrocyte folate <370 nmol/L in 1/75 (1.3%); niacin ratio ≤1 in 20/75 (26.7%); homocysteine >13.3 μmol/L in 31/75 (41.3%). There was no significant difference among residents grouped into marked (n = 44), mild (n = 14), or normal (n = 9) cognitive function when evaluating the effect of vitamin status. There were no significant differences in mean B12 and homocysteine levels between users and non-users of drug therapy (Losec, Zantac, or Axid). Compared to vitamin supplement non-users, supplemented residents had significantly higher mean B12 (p < 0.0001) and erythrocyte folate (p < 0.05) concentrations and significantly lower mean homocysteine (p < 0.01) levels; 229.1 versus 423.6 pmol/L for B12, 882.9 versus 1043.6 nmol/L for erythrocyte folate and 14.4 versus 12.0 μmol/L for homocysteine. CONCLUSION: Given the prevalence data on vitamin status in this sample population, the possible benefits of vitamin supplementation should be considered in clinical intervention studies using these populations of elderly