Remarks on Inner Functions and Optimal Approximants

We discuss the concept of inner function in reproducing kernelHilbert spaces with an orthogonal basis of monomials and examine connections between inner functions and optimal polynomial approximants to 1/f , where f is a function in the space. We revisit some classical examples from this perspective, and show how a construction of Shapiro and Shields can be modiûed to produce inner functions

On the Bohr inequality

The Bohr inequality, first introduced by Harald Bohr in 1914, deals with finding the largest radius $r$, $0<r<1$, such that $\sum_{n=0}^\infty |a_n|r^n \leq 1$ holds whenever $|\sum_{n=0}^\infty a_nz^n|\leq 1$ in the unit disk $\mathbb{D}$ of the complex plane. The exact value of this largest radius, known as the \emph{Bohr radius}, has been established to be $1/3.$ This paper surveys recent advances and generalizations on the Bohr inequality. It discusses the Bohr radius for certain power series in $\mathbb{D},$ as well as for analytic functions from $\mathbb{D}$ into particular domains. These domains include the punctured unit disk, the exterior of the closed unit disk, and concave wedge-domains. The analogous Bohr radius is also studied for harmonic and starlike logharmonic mappings in $\mathbb{D}.$ The Bohr phenomenon which is described in terms of the Euclidean distance is further investigated using the spherical chordal metric and the hyperbolic metric. The exposition concludes with a discussion on the $n$-dimensional Bohr radius

Avicin D, a Plant Triterpenoid, Induces Cell Apoptosis by Recruitment of Fas and Downstream Signaling Molecules into Lipid Rafts

Avicins, a family of triterpene electrophiles originally identified as potent inhibitors of tumor cell growth, have been shown to be pleiotropic compounds that also possess antioxidant, anti-mutagenic, and anti-inflammatory activities. We previously showed that Jurkat cells, which express a high level of Fas, are very sensitive to treatment with avicins. Thus, we hypothesized that avicins may induce cell apoptosis by activation of the Fas pathway. By using a series of cell lines deficient in cell death receptors, we demonstrated that upon avicin D treatment, Fas translocates to the cholesterol- and sphingolipid-enriched membrane microdomains known as lipid rafts. In the lipid rafts, Fas interacts with Fas-associated death domain (FADD) and Caspase-8 to form death-inducing signaling complex (DISC) and thus mediates cell apoptosis. Interfering with lipid raft organization by using a cholesterol-depleting compound, methyl-β-cyclodextrin, not only prevents the clustering of Fas and its DISC complex but also reduces the sensitivity of the cells to avicin D. Avicin D activates Fas pathways independent of the association between extracellular Fas ligands and Fas receptors. A deficiency in Fas and its downstream signaling molecules leads to the resistance of the cells to avicin D treatment. Taken together, our results demonstrate that avicin D triggers the redistribution of Fas in the membrane lipid rafts, where Fas activates receptor-mediated cell death

Rare variants in the genetic background modulate cognitive and developmental phenotypes in individuals carrying disease-associated variants.

To assess the contribution of rare variants in the genetic background toward variability of neurodevelopmental phenotypes in individuals with rare copy-number variants (CNVs) and gene-disruptive variants. We analyzed quantitative clinical information, exome sequencing, and microarray data from 757 probands and 233 parents and siblings who carry disease-associated variants. The number of rare likely deleterious variants in functionally intolerant genes ("other hits") correlated with expression of neurodevelopmental phenotypes in probands with 16p12.1 deletion (n=23, p=0.004) and in autism probands carrying gene-disruptive variants (n=184, p=0.03) compared with their carrier family members. Probands with 16p12.1 deletion and a strong family history presented more severe clinical features (p=0.04) and higher burden of other hits compared with those with mild/no family history (p=0.001). The number of other hits also correlated with severity of cognitive impairment in probands carrying pathogenic CNVs (n=53) or de novo pathogenic variants in disease genes (n=290), and negatively correlated with head size among 80 probands with 16p11.2 deletion. These co-occurring hits involved known disease-associated genes such as SETD5, AUTS2, and NRXN1, and were enriched for cellular and developmental processes. Accurate genetic diagnosis of complex disorders will require complete evaluation of the genetic background even after a candidate disease-associated variant is identified

Radical Cyclisation of α-Halo Aluminium Acetals: A Mechanistic Study

International audienceα‐Bromo aluminium acetals are suitable substrates for Ueno–Stork‐like radical cyclisations affording γ‐lactols and acid‐sensitive methylene‐γ‐lactols in high yields. The mechanistic study herein sets the scope and limitation of this reaction. The influence of the halide (or chalcogenide) atom X (X=Cl, Br, I, SPh, SePh) in the precursors α‐haloesters, as well as influence of the solvent and temperature was studied. The structure of the aluminium acetal intermediates resulting from the reduction of the corresponding α‐haloesters has been investigated by low‐temperature 13C‐INEPT diffusion‐ordered NMR spectroscopy (DOSY) experiments and quantum calculations, providing new insights into the structures of these thermally labile intermediates. Oxygen‐bridged dimeric structures with a planar Al2O2 ring are proposed for the least hindered aluminium acetals, while monomeric structures seem to prevail for the most hindered species. A comparison against the radical cyclisation of aluminium acetals derived from allyl and propargyl alcohols with the parent Ueno–Stork has been made at the BHandHLYP/6‐311++G(d,p) level of theory, highlighting mechanistic similarities and differences