Divided Differences & Restriction Operator on Paley-Wiener Spaces PWtaupPW_{tau}^{p} for N−N-Carleson Sequences

For a sequence of complex numbers $\Lambda$ we consider the restriction operator $R_{\Lambda}$ defined on Paley-Wiener spaces $PW_{\tau}^{p}$ ($1<p<\infty$). Lyubarskii and Seip gave necessary and sufficient conditions on $\Lambda$ for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and a certain weighted $l^{p}$ space. The Carleson condition appears to be necessary. We extend their result to $N-$Carleson sequences (finite unions of $N$ disjoint Carleson sequences). More precisely, we give necessary and sufficient conditions for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and an appropriate sequence space involving divided differences

Experimental Designs for Binary Data in Switching Measurements on Superconducting Josephson Junctions

We study the optimal design of switching measurements of small Josephson junction circuits which operate in the macroscopic quantum tunnelling regime. Starting from the D-optimality criterion we derive the optimal design for the estimation of the unknown parameters of the underlying Gumbel type distribution. As a practical method for the measurements, we propose a sequential design that combines heuristic search for initial estimates and maximum likelihood estimation. The presented design has immediate applications in the area of superconducting electronics implying faster data acquisition. The presented experimental results confirm the usefulness of the method. KEY WORDS: optimal design, D-optimality, logistic regression, complementary log-log link, quantum physics, escape measurement

Hydrodynamics of polar liquid crystals

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local $C_{\infty v}$-symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals ($D_{\infty h}$) in that it contains terms violating the ${\bf{n}}\to -{\bf{n}}$ symmetry. First we show that these $\mathcal{Z}_2$-odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.Comment: 9 pages, corrected typos, added references, revised content, to appear in PR

Union renewal in historical perspective

This article revisits contemporary union renewal/revival debates through comparison with the late 1930s resurgence of trade unionism in the UK’s engineering industry. It is argued that the 1930s union renewal arose from more favourable contextual conditions than those currently obtaining. It was led by political activists, with better-articulated organisation and greater resonance in the working class than their contemporary counterparts, and who were assisted by state policy and pro-worker forces. Conclusions are drawn in relation to current debates

‘The longest suicide vote in history’: the Labour Party leadership election of 2015

The Labour leadership contest of 2015 resulted in the election of the veteran Left-wing backbencher, Jeremy Corbyn, who clearly defeated the early favourite, Andy Burnham. Yet Corbyn enjoyed very little support among Labour MPs, and his victory plunged the PLP into turmoil, particularly as he was widely viewed as incapable of leading the Party to victory in the 2020 general election. Given that, much of the established academic literature on Party leadership contests emphasises the ability to foster unity, and thereby render a party electable, as two of the key criteria for electing a new leader, coupled with overall competence, important questions are raised about how and why the Labour Party chose someone to lead them who clearly does not meet these criteria. We will argue that whilst these are the natural priorities of MPs when electing a new leader, in Corbyn’s case, much of the extra-parliamentary Labour Party was more concerned about ideological conviction and purity of principles, regardless of how far these diverged from public opinion. This was especially true of those who signed-up to the Labour Party following the 2015 general election defeat. Indeed, many of these only did so after Corbyn had become a candidate. This clearly suggests a serious tension between maximising intra-party democracy and ensuring the electability of the parliamentary party itself

Connexin-mimetic peptide Gap 27 decreases osteoclastic activity

BACKGROUND: Bone remodelling is dependent on the balance between bone resorbing osteoclasts and bone forming osteoblasts. We have shown previously that osteoclasts contain gap-junctional protein connexin-43 and that a commonly used gap-junctional inhibitor, heptanol, can inhibit osteoclastic bone resorption. Since heptanol may also have some unspecific effect unrelated to gap-junctional inhibition we wanted to test the importance of gap-junctional communication to osteoclasts using a more specific inhibitor. METHODS: A synthetic connexin-mimetic peptide, Gap 27, was used to evaluate the contribution of gap-junctional communication to osteoclastic bone resorption. We utilised the well-characterised pit-formation assay to study the effects of the specific gap-junctional inhibitor to the survival and activity of osteoclasts. RESULTS: Gap 27 caused a remarked decrease in the number of both TRAP-positive mononuclear and multinucleated rat osteoclasts cultured on bovine bone slices. The decrease in the cell survival seemed to be restricted to TRAP-positive cells, whereas the other cells of the culture model seemed unaffected. The activity of the remaining osteoclasts was found to be diminished by measuring the percentage of osteoclasts with actin rings of all TRAP-positive cells. In addition, the resorbed area in the treated cultures was greatly diminished. CONCLUSIONS: On the basis of these results we conclude that gap-junctional communication is essential for the action of bone resorbing osteoclasts and for proper remodelling for bone

Synchrotron x-ray fluorescence and extended x-ray absorption fine structure analysis

The advent of dedicated synchrotron radiation sources has led to a significant increase in activity in many areas of science dealing with the interaction of x-rays with matter. Synchrotron radiation provides intense, linearly polarized, naturally collimated, continuously tunable photon beams, which are used to determine not only the elemental composition of a complex, polyatomic, dilute material but also the chemical form of the elements with improved accuracy. Examples of the application of synchrotron radiation include experiments in synchrotron x-ray fluorescence (SXRF) analysis and extended x-ray absorption fine structure (EXAFS) analysis. New synchrotron radiation x-ray microprobes for elemental analysis in the parts per billion range are under construction at several laboratories. 76 references, 24 figures

Unsatisfactory gene transfer into bone-resorbing osteoclasts with liposomal transfection systems

BACKGROUND: Bone-resorbing osteoclasts are multinucleated cells that are formed via fusion of their hematopoietic stem cells. Many of the details of osteoclast formation, activation and motility remain unsolved. Therefore, there is an interest among bone biologists to transfect the terminally differentiated osteoclasts and follow their responses to the transgenes in vitro. Severe difficulties in transfecting the large, adherent osteoclasts have been encountered, however, making the use of modern cell biology tools in osteoclast research challenging. Transfection of mature osteoclasts by non-viral gene transfer systems has not been reported. RESULTS: We have systematically screened the usefulness of several commercial DNA transfection systems in human osteoclasts and their mononuclear precursor cell cultures, and compared transfection efficacy to adenoviral DNA transfection. None of the liposome-based or endosome disruption-inducing systems could induce EGFP-actin expression in terminally differentiated osteoclasts. Instead, a massive cell death by apoptosis was found with all concentrations and liposome/DNA-ratios tested. Best transfection efficiencies were obtained by adenoviral gene delivery. Marginal DNA transfection was obtained by just adding the DNA to the cell culture medium. When bone marrow-derived CD34-positive precursor cells were transfected, some GFP-expression was found at the latest 24 h after transfection. Large numbers of apoptotic cells were found and those cells that remained alive, failed to form osteoclasts when cultured in the presence of RANKL and M-CSF, key regulators of osteoclast formation. In comparison, adenoviral gene delivery resulted in the transfection of CD34-positive cells that remained GFP-positive for up to 5 days and allowed osteoclast formation. CONCLUSION: Osteoclasts and their precursors are sensitive to liposomal transfection systems, which induce osteoclast apoptosis. Gene transfer to mononuclear osteoclast precursors or differentiated osteoclasts was not possible with any of the commercial transfection systems tested. Osteoclasts are non-dividing, adherent cells that are difficult to grow as confluent cultures, which may explain problems with transfection reagents. Large numbers of α(v)β(3 )integrin on the osteoclast surface allows adenovirus endocytosis and infection proceeds in dividing and non-dividing cells efficiently. Viral gene delivery is therefore currently the method of choice for osteoclast transfection