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

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

Parametric coupling between macroscopic quantum resonators

Time-dependent linear coupling between macroscopic quantum resonator modes generates both a parametric amplification also known as a {}"squeezing operation" and a beam splitter operation, analogous to quantum optical systems. These operations, when applied properly, can robustly generate entanglement and squeezing for the quantum resonator modes. Here, we present such coupling schemes between a nanomechanical resonator and a superconducting electrical resonator using applied microwave voltages as well as between two superconducting lumped-element electrical resonators using a r.f. SQUID-mediated tunable coupler. By calculating the logarithmic negativity of the partially transposed density matrix, we quantitatively study the entanglement generated at finite temperatures. We also show that characterization of the nanomechanical resonator state after the quantum operations can be achieved by detecting the electrical resonator only. Thus, one of the electrical resonator modes can act as a probe to measure the entanglement of the coupled systems and the degree of squeezing for the other resonator mode.Comment: 15 pages, 4 figures, submitte

Intraoperative measurement of parathyroid hormone: A Copernican revolution in the surgical treatment of hyperparathyroidism

Intraoperative parathyroid hormone (PTH) monitoring in the setting of the operating room represents a valuable example of the rationale use of the laboratory diagnostic in a patient-oriented approach. Rapid intraoperative PTH (ioPTH) assay is a valid tool for an accurate evaluation of the success of parathyroid surgery. The reliability of the user-friendly portable systems as well as the collaboration between operators and surgical staff allow the one-site monitoring of the ioPTH decrements on the course of the surgical management of hyperparathyroidism.The rapid answer provided by an effective decrement of PTH during parathyroidectomy contributes dramatically to the efficacy of parathyroid surgery and the reduction of the number of re-operations. Therefore the dose of ioPTH is a valid and reliable support for the success of the intervention of parathyroidectomy at controlled costs

Tunneling spectroscopy using a probe qubit

We describe a quantum tunneling spectroscopy technique that requires only low bandwidth control. The method involves coupling a probe qubit to the system under study to create a localized probe state. The energy of the probe state is then scanned with respect to the unperturbed energy levels of the probed system. Incoherent tunneling transitions that flip the state of the probe qubit occur when the energy bias of the probe is close to an eigenenergy of the probed system. Monitoring these transitions allows the reconstruction of the probed system eigenspectrum. We demonstrate this method on an rf SQUID flux qubit