52,114 research outputs found

    Accuracy of Numerical Solution to Dynamic Programming Models

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    Dynamic programming models with continuous state and control variables are solved approximately using numerical methods in most applications. We develop a method for measuring the accuracy of numerical solution of stochastic dynamic programming models. Using this method, we compare the accuracy of various interpolation schemes. As expected, the results show that the accuracy improves as number of nodes is increased. Comparison of Chebyshev and linear spline indicates that the linear spline may give higher maximum absolute error than Chebyshev, however, the overall performance of spline interpolation is better than Chebyshev interpolation for non-smooth functions. Two-stage grid search method of optimization is developed and examined with accuracy analysis. The results show that this method is more efficient and accurate. Accuracy is also examined by allocating a different number of nodes for each dimension. The results show that a change in node configuration may yield a more efficient and accurate solution.Research Methods/ Statistical Methods,

    Cygnus X-2, super-Eddington mass transfer, and pulsar binaries

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    We consider the unusual evolutionary state of the secondary star in Cygnus X-2. Spectroscopic data give a low mass (M_2 \simeq 0.5 - 0.7\msun) and yet a large radius (R_2 \simeq 7\rsun) and high luminosity (L_2 \simeq 150\lsun). We show that this star closely resembles a remnant of early massive Case B evolution, during which the neutron star ejected most of the \sim 3\msun transferred from the donor (initial mass M_{\rm 2i}\sim 3.6\msun) on its thermal time-scale 106\sim 10^6 yr. As the system is far too wide to result from common-envelope evolution, this strongly supports the idea that a neutron star efficiently ejects the excess inflow during super--Eddington mass transfer. Cygnus X-2 is unusual in having had an initial mass ratio qi=M2i/M1q_{\rm i} = M_{\rm 2i}/M_1 in a narrow critical range near qi2.6q_{\rm i}\simeq 2.6. Smaller qiq_{\rm i} lead to long-period systems with the former donor near the Hayashi line, and larger qiq_{\rm i} to pulsar binaries with shorter periods and relatively massive white dwarf companions. The latter naturally explain the surprisingly large companion masses in several millisecond pulsar binaries. Systems like Cygnus X-2 may thus be an important channel for forming pulsar binaries.Comment: 9 pages, 4 encapsulated figures, LaTeX, revised version with a few typos corrected and an appendix added, accepted by MNRA

    LHC Signatures of the Constrained Exceptional Supersymmetric Standard Model

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    We discuss two striking Large Hadron Collider (LHC) signatures of the constrained version of the exceptional supersymmetric standard model (cE6SSM), based on a universal high energy soft scalar mass m_0, soft trilinear coupling A_0 and soft gaugino mass M_{1/2}. The first signature we discuss is that of light exotic colour triplet charge 1/3 fermions, which we refer to as D-fermions. We calculate the LHC production cross section of D-fermions, and discuss their decay patterns. Secondly we discuss the E6 type U(1)_N spin-1 Z' gauge boson and show how it may decay into exotic states, increasing its width and modifying the line shape of the dilepton final state. We illustrate these features using two representative cE6SSM benchmark points, including an "early LHC discovery" point, giving the Feynman rules and numerical values for the relevant couplings in order to facilitate further studies.Comment: 30 pages, 5 figures, corrections to figure caption

    The molecular mechanisms of accessory cell-T lymphocyte interaction

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    By a process of negative selection, lymphoid dendritic cells were isolated to high purity from human tonsils. In comparison with other purified tonsillar accessory cell types these dendritic cells were shown to be potent inducers of T lymphocyte proliferation in the periodate oxidative mitogenesis reaction, autologous MLR and allogeneic MLR. The tonsillar dendritic cell induced oxidative mitogenesis reaction was used as a model to study the molecular mechanisms of dendritic cell induced T lymphocyte proliferation. For this, panels of antibodies were used as tools to probe different aspects of the cell-cell interaction. The results indicate that dendritic cells induce T lymphocyte proliferation by a complex two stage mechanism. One stage is an early dendritic cell-T lymphocyte clustering stage which is mediated by LFA-1, ICAM-1, the CD2 antigen and LFA-3 and in which the CD45 antigen plays an indirect role. The other stage is a signal transduction stage. LFA-1, ICAM-1, the CD2 antigen, LFA-3 and the CD45 antigen are also implicated at this stage in addition to a variety of other molecules including the CD3, CD4, CDS, CD25, CD26, CD28, CD39, CD44, CD48, CDw70, CD71 and CDw78 antigens and class I and II MHC. In quantitative assays the molecular events involved in PMA differentiated U937-T lymphocyte clustering were also investigated. This type of clustering is mediated by the same epitopes of LFA-1 and ICAM-1 as dendritic cell-T lymphocyte clustering and again the CD45 antigen is indirectly implicated. There are differences, however, in that the CD2 antigen and LFA-3 are not involved and that the CD44 antigen and class II MHC, too, play an indirect role. Along with evidence that the roles of the CD44 and CD45 antigens in U937-T clustering are distinct, these findings emphasise the heterogeneity of structures and mechanisms involved in accessory cell-T lymphocyte interaction

    Leptogenesis in the two right-handed neutrino model revisited

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    We revisit leptogenesis in the minimal non-supersymmetric type I see-saw mechanism with two right-handed (RH) neutrinos, including flavour effects and allowing both RH neutrinos N_1 and N_2 to contribute, rather than just the lightest RH neutrino N_1 that has hitherto been considered. By performing scans over parameter space in terms of the single complex angle z of the orthogonal matrix R, for a range of PMNS parameters, we find that in regions around z \sim \pm \pi/2, for the case of a normal mass hierarchy, the N_2 contribution can dominate the contribution to leptogenesis, allowing the lightest RH neutrino mass to be decreased by about an order of magnitude in these regions, down to M_1 \sim 1.3*10^11 GeV for vanishing initial N_2-abundance, with the numerical results supported by analytic estimates. We show that the regions around z \sim \pm \pi /2 correspond to light sequential dominance, so the new results in this paper may be relevant to unified model building.Comment: 41 pages, 10 figures; v2 matches published version in PR
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