On the Fourier spectrum of symmetric Boolean functions

We study the following questionWhat is the smallest t such that every symmetric boolean function on κ variables (which is not a constant or a parity function), has a non-zero Fourier coefficient of order at least 1 and at most t?We exclude the constant functions for which there is no such t and the parity functions for which t has to be κ. Let τ (κ) be the smallest such t. Our main result is that for large κ, τ (κ)≤4κ/logκ.The motivation for our work is to understand the complexity of learning symmetric juntas. A κ-junta is a boolean function of n variables that depends only on an unknown subset of κ variables. A symmetric κ-junta is a junta that is symmetric in the variables it depends on. Our result implies an algorithm to learn the class of symmetric κ-juntas, in the uniform PAC learning model, in time n ^o(κ) . This improves on a result of Mossel, O’Donnell and Servedio in [16], who show that symmetric κ-juntas can be learned in time n ^2κ/3.     

Post-synthetic modification of isomorphic coordination layers: exchange dynamics of metal ions in a single crystal to single crystal fashion

A diverse set of guest molecules template the consistent formation of fifteen iso-structural layered structures containing a pyridine based tripodal ligand, divalent metal ions and anions. These materials have shown a remarkable ability to interconvert from Zn(II) to Cu(II), Cd(II) to Cu(II), Cu(II) to Cd(II) complexes in a SCSC (single crystal-to-single crystal) fashion.     

Protective role of estrogen against excessive erythrocytosis in Monge’s disease

Monge’s disease (chronic mountain sickness (CMS)) is a maladaptive condition caused by chronic (years) exposure to high-altitude hypoxia. One of the defining features of CMS is excessive erythrocytosis with extremely high hematocrit levels. In the Andean population, CMS prevalence is vastly different between males and females, being rare in females. Furthermore, there is a sharp increase in CMS incidence in females after menopause. In this study, we assessed the role of sex hormones (testosterone, progesterone, and estrogen) in CMS and non-CMS cells using a well-characterized in vitro erythroid platform. While we found that there was a mild (nonsignificant) increase in RBC production with testosterone, we observed that estrogen, in physiologic concentrations, reduced sharply CD235a⁺ cells (glycophorin A; a marker of RBC), from 56% in the untreated CMS cells to 10% in the treated CMS cells, in a stage-specific and dose-responsive manner. At the molecular level, we determined that estrogen has a direct effect on GATA1, remarkably decreasing the messenger RNA (mRNA) and protein levels of GATA1 (p < 0.01) and its target genes (Alas2, BclxL, and Epor, p < 0.001). These changes result in a significant increase in apoptosis of erythroid cells. We also demonstrate that estrogen regulates erythropoiesis in CMS patients through estrogen beta signaling and that its inhibition can diminish the effects of estrogen by significantly increasing HIF1, VEGF, and GATA1 mRNA levels. Taken altogether, our results indicate that estrogen has a major impact on the regulation of erythropoiesis, particularly under chronic hypoxic conditions, and has the potential to treat blood diseases, such as high altitude severe erythrocytosis.Subject terms: Haematopoietic stem cells, Myeloproliferative disease     

Allium schoenoprasum L.: a review of phytochemistry,pharmacology and future directions

Allium schoenoprasum L. (family Amaryllidaceae), commonly known as chives has great culinary value besides being used as ethnomedicine. This review emphasises on phytochemistry and pharmacological activities of A. schoenoprasum, and discusses the future opportunities for systematic investigations. Scientific evaluation of chives validates its traditional claims and demonstrates diverse pharmacological potential including an anti-inflammatory, anticancer, antioxidant, anthelmintic and antihypertensive. Though phytochemical studies revealed the presence of sulphur and phenolic compounds, flavonoids, saponin and steroidal glycosides yet methodical research to identify bioactive compounds is required. This review confirms the medicinal importance of A. schoenoprasum and could stimulate future research on its unexplored aspects, especially identification of bioactive compounds and related mechanisms and safety, which might develop it as a drug.     

Kinetics and mechanisms of oxidations by metal ions. Part 17. Oxidation of formate ion by alkaline osmium tetroxide

Summary The oxidation of formate ion by alkaline osmium tetroxide, such that [HCO _inf2 ^p– ] [Os^VII], exhibits first-order dependence in [Os^VII], an order less than unity in [HCO _inf2 ^p– ], and zero-order in [OH^–]. HCO^2– reacts as an ion-pair formed with an alkali metal ion and [OsO₄(OH)₂]^2– is the reactive species of Os^VII. The formation of an intermediate Os^VII-HCO₂M complex is substantiated by the rapid-scan spectra of the reaction mixture. Anions (Cl^–, ClO _inf4 ^p– ) have no effect on the rate. The close agreement between the observed k _H/k _D = 7.1 and the theoretically calculated value (7.0), based on the stretching frequencies of C-H and C-D bonds in the free molecule, indicates an outer-sphere mechanism.Author to whom all correspondence should be directed.     

Pyrene absorption can be a convenient method for probing critical micellar concentration (cmc) and indexing micellar polarity

The critical micellar concentration (cmc) of both ionic and non-ionic surfactants can be conveniently determined from the measurements of UV absorption of pyrene in surfactant solution. The results on a number of surfactants have agreed with that realized from pyrene fluorescence measurements as well as that obtained following conductometric, tensiometric and calorimetric methods. The absorbance vs [surfactant] profiles for all the major UV spectral peaks of pyrene have been found to be sigmoidal in nature which were analyzed according to Sigmoidal-Boltzmann equation (SBE) to evaluate the cmcs of the studied surfactants. The difference between the initial and the final asymptotes (a(i) and a(f), respectively) of the sigmoidal profile, Delta a = (a(f)-a(i)) and the slope of the sigmoid, S(sig) have been observed to depend on the type of the surfactant. The Delta a has shown a linear correlation with the ratio of the fluorescence intensities of the first and the third vibronic peaks, I1/I3 of pyrene which is considered as a measure of the environmental polarity (herein micellar interior) of the probe (pyrene). Thus, Delta a values have the prospect for use as another index for the estimation of polarity of micellar interior.     

Terwilliger algebras of wreath products of one-class association schemes

In this paper, we study the wreath product of one-class association schemes K _n =H(1,n) for n≥2. We show that the d-class association scheme \(K_{n_{1}}\wr K_{n_{2}}\wr \cdots \wr K_{n_{d}}\) formed by taking the wreath product of \(K_{n_{i}}\) (for n _i ≥2) has the triple-regularity property. Then based on this fact, we determine the structure of the Terwilliger algebra of \(K_{n_{1}}\wr K_{n_{2}}\wr \cdots \wr K_{n_{d}}\) by studying its irreducible modules. In particular, we show that every non-primary module of this algebra is 1-dimensional.     

Structural Diversity and Magnetic Properties of Hybrid Ruthenium Halide Perovskites and Related Compounds

There has been a great deal of recent interest in extended compounds containing Ru³⁺ and Ru⁴⁺ in light of their range of unusual physical properties. Many of these properties are displayed in compounds with the perovskite and related structures. Here we report an array of structurally diverse hybrid ruthenium halide perovskites and related compounds: MA₂RuX₆ (X=Cl or Br), MA₂MRuX₆ (M=Na, K or Ag; X=Cl or Br) and MA₃Ru₂X₉ (X=Br) based upon the use of methylammonium (MA=CH₃NH₃⁺) on the perovskite A site. The compounds MA₂RuX₆ with Ru⁴⁺ crystallize in the trigonal space group and can be described as vacancy‐ordered double‐perovskites. The ordered compounds MA₂MRuX₆ with M⁺ and Ru³⁺ crystallize in a structure related to BaNiO₃ with alternating MX₆ and RuX₆ face‐shared octahedra forming linear chains in the trigonal space group. The compound MA₃Ru₂Br₉ crystallizes in the orthorhombic Cmcm space group and displays pairs of face‐sharing octahedra forming isolated Ru₂Br₉ moieties with very short Ru–Ru contacts of 2.789 Å. The structural details, including the role of hydrogen bonding and dimensionality, as well as the optical and magnetic properties of these compounds are described. The magnetic behavior of all three classes of compounds is influenced by spin–orbit coupling and their temperature‐dependent behavior has been compared with the predictions of the appropriate Kotani models.