Cantor Series Constructions Contrasting Two Notions of Normality

A. R\'enyi \cite{Renyi} made a definition that gives a generalization of simple normality in the context of $Q$-Cantor series. In \cite{Mance}, a definition of $Q$-normality was given that generalizes the notion of normality in the context of $Q$-Cantor series. In this work, we examine both $Q$-normality and $Q$-distribution normality, treated in \cite{Laffer} and \cite{Salat}. Specifically, while the non-equivalence of these two notions is implicit in \cite{Laffer}, in this paper, we give an explicit construction witnessing the nontrivial direction. That is, we construct a base $Q$ as well as a real $x$ that is $Q$-normal yet not $Q$-distribution normal. We next approach the topic of simultaneous normality by constructing an explicit example of a base $Q$ as well as a real $x$ that is both $Q$-normal and $Q$-distribution normal

Tris(1,3-dichloro-2-propyl) phosphate disrupts dorsoventral patterning in zebrafish embryos.

Tris(1,3-dichloro-2-propyl) phosphate (TDCIPP) is a high-production volume organophosphate flame retardant widely used within the United States. Within zebrafish, initiation of TDCIPP exposure at 0.75 h post-fertilization (hpf) results in genome-wide alterations in methylation during cleavage (2 hpf) as well as epiboly delay or arrest (at higher concentrations) during late-blastula and early-gastrula (4-6 hpf). To determine whether these TDCIPP-induced effects were associated with impacts on the transcriptome, embryos were exposed to vehicle (0.1% DMSO) or 2 µM TDCIPP from 0.75 hpf to 6 hpf, and total RNA was extracted from triplicate embryo pools per treatment and hybridized onto duplicate Affymetrix Zebrafish Gene 1.0 ST Arrays per RNA sample. Based on transcriptome-wide profiling, TDCIPP resulted in a significant impact on biological processes involved in dorsoventral patterning and bone morphogenetic protein (BMP) signaling. Consistent with these responses, TDCIPP exposure also resulted in strongly dorsalized embryos by 24 hpf-a phenotype that mimicked the effects of dorsomorphin, a potent and selective BMP inhibitor. Moreover, the majority of dorsalized embryos were preceded by epiboly arrest at 6 hpf. Our microarray data also revealed that the expression of sizzled (szl)-a gene encoding a secreted Frizzled-related protein that limits BMP signaling-was significantly decreased by nearly 4-fold at 6 hpf. Therefore, we used a splice-blocking morpholino to test the hypothesis that knockdown of szl phenocopies TDCIPP-induced delays in epiboly progression. Interestingly, contrary to our hypothesis, injection of szl MOs did not affect epiboly progression but, similar to chordin (chd) morphants, resulted in mildly ventralized embryos by 24 hpf. Overall, our findings suggest that TDCIPP-induced epiboly delay may not be driven by decreased szl expression, and that TDCIPP-induced dorsalization may-similar to dorsomorphin-be due to interference with BMP signaling during early zebrafish development

Direct inhibition of the pacemaker (I-f) current in rabbit sinoatrial node cells by genistein

1 Genistein is a tyrosine kinase inhibitor which interferes with the activity of several ionic channels either by altering modulatory phosphorylating processes or by direct binding. In whole-cell conditions, genistein induces a partial inhibition of the pacemaker (If) current recorded in cardiac sinoatrial and ventricular myocytes. 2 We investigated the mechanism of action of genistein (50 mM) on the If current in whole-cell, cellattached, and inside-out configurations, and the measured fractional inhibitions were similar: 26.6, 27.2, and 33.6%, respectively. 3 When ATP was removed from the whole-cell pipette solution no differences were revealed in the effect of the drug when compared to metabolically active cells. Genistein fully maintained its blocking ability even when herbimycin, a tyrosine kinase inhibitor, was added to the whole-cell ATP-free pipette solution. 4 Genistein-induced block was independent of the gating state of the channel and did not display voltage or current dependence; this independence distinguishes genistein from all other f-channel blockers. 5 When inside-out experiments were performed to test for a direct interaction with the channel, genistein, superfused on the intracellular side of the membrane, decreased the maximal If conductance, and slightly shifted the current\u2013activation curve to the left. Furthermore, the effect of genistein was independent of cAMP modulation. 6 We conclude that, in addition to its tyrosine kinase-inhibitory properties, genistein also blocks If by directly interacting with the channel, and thus cannot be considered a valuable pharmacological tool to investigate phosphorylation-dependent modulatory pathways of the If current and of cardiac rhythm

Data from docking simulations to develop an efficient strategy able to evaluate the interactions between RAGE and MDA-induced albumin adducts

This data article contains the results of docking simulations performed in order to develop a suitable in silico strategy able to assess the stability of the putative complexes between RAGE and MDA induced adducts on human albumin as experimentally determined doi: 10.1016/j.redox.2016.12.017, (Degani et al., 2017) [1]. The docking simulations involved different approaches to give a simplified yet realistic representation of the protein adducts and their environment. With increasing complexity, simulations involved the corresponding albumin tripeptides and pentapeptides with the modified residue in the central position as well as pseudo-structures which were generated by collecting the albumin residues around the adducted residue within a sphere of 7.5 \uc5 and 5 \uc5 radius. The reliability of the tested approaches was assessed by monitoring the score differences between adducted and unmodified residues. The obtained results revealed the greater predictive power of the spherical pseudo-structures compared to the simple tri- or pentapeptidic sequences thus suggesting that RAGE recognition involves residues which are spatially close to the modified residue even though not necessarily adjacent in the primary sequence

Bone marrow-derived cells can acquire cardiac stem cells properties in damaged heart

Experimental data suggest that cell-based therapies may be useful for cardiac regeneration following ischaemic heart disease. Bone marrow (BM) cells have been reported to contribute to tissue repair after myocardial infarction (MI) by a variety of humoural and cellular mechanisms. However, there is no direct evidence, so far, that BM cells can generate cardiac stem cells (CSCs). To investigate whether BM cells contribute to repopulate the Kit+ CSCs pool, we transplanted BM cells from transgenic mice, expressing green fluorescent protein under the control of Kit regulatory elements, into wild-type irradiated recipients. Following haematological reconstitution and MI, CSCs were cultured from cardiac explants to generate 'cardiospheres', a microtissue normally originating in vitro from CSCs. These were all green fluorescent (i.e. BM derived) and contained cells capable of initiating differentiation into cells expressing the cardiac marker Nkx2.5. These findings indicate that, at least in conditions of local acute cardiac damage, BM cells can home into the heart and give rise to cells that share properties of resident Kit+ CSCs

4-Hydr­oxy-4,4-diphenyl­butan-2-one

The mol­ecules of the title compound, C16H16O2, display an intra­molecular O—H⋯O hydrogen bond between the hydroxyl donor and the ketone acceptor. Inter­molecular C—H⋯π inter­actions connect adjacent mol­ecules into chains that propagate parallel to the ac diagonal. The chains are arranged in sheets, and mol­ecules in adjacent sheets inter­act via inter­molecular O—H⋯O hydrogen bonds

Bone Involvement in Systemic Lupus Erythematosus

Systemic lupus erythematosus (SLE) is a chronic autoimmune disease characterized by a wide variability of clinical manifestations due to the potential involvement of several tissues and internal organs, with a relapsing and remitting course. Dysregulation of innate and adaptive immune systems, due to genetic, hormonal and environmental factors, may be responsible for a broad spectrum of clinical manifestations, affecting quality of life, morbidity and mortality. Bone involvement represents one of the most common cause of morbidity and disability in SLE. Particularly, an increased incidence of osteoporosis, avascular necrosis of bone and osteomyelitis has been observed in SLE patients compared to the general population. Moreover, due to the improvement in diagnosis and therapy, the survival of SLE patient has improved, increasing long-term morbidities, including osteoporosis and related fractures. This review aims to highlight bone manifestations in SLE patients, deepening underlying etiopathogenetic mechanisms, diagnostic tools and available treatment

C60 1,1,2,2-tetra­chloro­ethyl­ene tetra­solvate

In the title complex, C60·4C2Cl4, the C60 mol­ecule is located on an inversion centre and there are two tetra­chloro­ethyl­ene (TCE) mol­ecules in the asymmetric unit. Both TCE mol­ecules show positional disorder, with occupancy ratios of 0.75:0.25 and 0.56:0.44. Four fullerene C atoms form short contacts [3.208 (17) and 3.223 (17) Å] with the centres of the TCE double bonds, indicating that C60–solvent inter­actions are largely π–π in nature