Any-order propagation of the nonlinear Schroedinger equation

We derive an exact propagation scheme for nonlinear Schroedinger equations. This scheme is entirely analogous to the propagation of linear Schroedinger equations. We accomplish this by defining a special operator whose algebraic properties ensure the correct propagation. As applications, we provide a simple proof of a recent conjecture regarding higher-order integrators for the Gross-Pitaevskii equation, extend it to multi-component equations, and to a new class of integrators.Comment: 10 pages, no figures, submitted to Phys. Rev.

A conserved gene regulatory network subcircuit drives different developmental fates in the vegetal pole of highly divergent echinoderm embryos

AbstractComparisons of orthologous developmental gene regulatory networks (GRNs) from different organisms explain how transcriptional regulation can, or cannot, change over time to cause morphological evolution and stasis. Here, we examine a subset of the GRN connections in the central vegetal pole mesoderm of the late sea star blastula and compare them to the GRN for the same embryonic territory of sea urchins. In modern sea urchins, this territory gives rise to skeletogenic mesoderm; in sea stars, it develops into other mesodermal derivatives. Orthologs of many transcription factors that function in the sea urchin skeletogenic mesoderm are co-expressed in the sea star vegetal pole, although this territory does not form a larval skeleton. Systematic perturbation of erg, hex, tbr, and tgif gene function was used to construct a snapshot of the sea star mesoderm GRN. A comparison of this network to the sea urchin skeletogenic mesoderm GRN revealed a conserved, recursively wired subcircuit operating in both organisms. We propose that, while these territories have evolved different functions in sea urchins and sea stars, this subcircuit is part of an ancestral GRN governing echinoderm vegetal pole mesoderm development. The positive regulatory feedback between these transcription factors may explain the conservation of this subcircuit

Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution

We analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed. The dynamics of this system has been the subject of long-standing interest. In 1984 Kuramoto proposed several conjectures about its behavior; ten years later, Crawford obtained the first analytical results by means of a local center manifold calculation. Nevertheless, many questions have remained open, especially about the possibility of global bifurcations. Here we derive the system's complete stability diagram for the special case where the bimodal distribution consists of two equally weighted Lorentzians. Using an ansatz recently discovered by Ott and Antonsen, we show that in this case the infinite-dimensional problem reduces exactly to a flow in four dimensions. Depending on the parameters and initial conditions, the long-term dynamics evolves to one of three states: incoherence, where all the oscillators are desynchronized; partial synchrony, where a macroscopic group of phase-locked oscillators coexists with a sea of desynchronized ones; and a standing wave state, where two counter-rotating groups of phase-locked oscillators emerge. Analytical results are presented for the bifurcation boundaries between these states. Similar results are also obtained for the case in which the bimodal distribution is given by the sum of two Gaussians.Comment: 28 pages, 7 figures; submitted to Phys. Rev. E Added comment

The interrelationships between customer satisfaction, brand loyalty and relationship intentions of Generation Y consumers towards smart phone brands

Smart phone marketers are finding it difficult to maintain market share in a market characterised by fierce competition and continued new product development. Generation Y consumers generally have a good command of technology and engage in technology-related behaviour such as texting, tweeting and web-surfing. When it comes to the adoption of smart phone applications, it is believed that Generation Y is leading the way. To retain Generation Y consumers, it is critical for organisations to ensure that customer satisfaction is achieved, brand loyalty has to be generated and meaningful long-term relationships with these consumers should be established. In this regard, this study aims to determine the interrelationships between customer satisfaction, brand loyalty and the relationship intentions of Generation Y smart phone users. Self-administered questionnaires were fielded among 395 Generation Y smart phone users living in Gauteng, South Africa. Results indicate significant and positive interrelationships between customer satisfaction, brand loyalty and relationship intention

An expanded population of CD8dim T cells with features of mitochondrial dysfunction and senescence is associated with persistent HIV-associated Kaposi’s sarcoma under ART

HIV-associated Kaposi’s sarcoma (KS), which is caused by Kaposi’s sarcoma-associated herpesvirus, usually arises in the context of uncontrolled HIV replication and immunosuppression. However, disease occasionally occurs in individuals with durable HIV viral suppression and CD4 T cell recovery under antiretroviral therapy (ART). The underlying mechanisms associated with this phenomenon are unclear. Suppression of viral infections can be mediated by CD8 T cells, which detect infected cells via their T cell receptor and the CD8 coreceptor. However, CD8 T cells exhibit signs of functional exhaustion in untreated HIV infection that may not be fully reversed under ART. To investigate whether KS under ART was associated with phenotypic and functional perturbations of CD8 T cells, we performed a cross-sectional study comparing HIV-infected individuals with persistent KS under effective ART (HIV+ KS+) to HIV-infected individuals receiving effective ART with no documented history of KS (HIV+ KSneg). A subset of T cells with low cell surface expression of CD8 (“CD8dim T cells”) was expanded in HIV+ KS+ compared with HIV+ KSneg participants. Relative to CD8bright T cells, CD8dim T cells exhibited signs of senescence (CD57) and mitochondrial alterations (PGC-1α, MitoTracker) ex vivo. Mitochondrial activity (MitoTracker) was also reduced in proliferating CD8dim T cells. These findings indicate that an expanded CD8dim T cell population displaying features of senescence and mitochondrial dysfunction is associated with KS disease under ART. CD8 coreceptor down-modulation may be symptomatic of ongoing disease

Chemical Abundances of Planetary Nebulae in the Sagittarius Dwarf Elliptical Galaxy

Spectrophotometry and imaging of the two planetary nebulae He2-436 and Wray16-423, recently discovered to be in the Sagittarius dwarf elliptical galaxy, are presented. Wray16-423 is a high excitation planetary nebula (PN) with a hot central star. In contrast He2-436 is a high density PN with a cooler central star and evidence of local dust, the extinction exceeding that for Wray16-423 by E(B-V)=0.28. The extinction to Wray16-423, (E(B-V)=0.14), is consistent with the extinction to the Sagittarius (Sgr) Dwarf. Both PN show Wolf-Rayet features in their spectra, although the lines are weak in Wray16-423. Images in [O III] and H-alpha+[N II], although affected by poor seeing, yield a diameter of 1.2'' for Wray16-423 after deconvolution; He~2-436 was unresolved. He2-436 has a luminosity about twice that of Wray16-423 and its size and high density suggest a younger PN. In order to reconcile the differing luminosity and nebular properties of the two PN with similar age progenitor stars, it is suggested that they are on He burning tracks The abundance pattern is very similar in both nebulae and shows an oxygen depletion of -0.4 dex with respect to the mean O abundance of Galactic PN and [O/H] = -0.6. The Sgr PN progenitor stars are representative of the higher metallicity tail of the Sgr population. The pattern of abundance depletion is similar to that in the only other PN in a dwarf galaxy companion of the Milky Way, that in Fornax, for which new spectra are presented. However the abundances are larger than for Galactic halo PN suggesting a later formation age. The O abundance of the Sgr galaxy deduced from its PN, shows similarities with that of dwarf ellipticals around M31, suggesting that this galaxy was a dwarf elliptical before its interaction with the Milky Way.Comment: 24 pages, Latex (aas2pp4.sty) including 5 postscript figures. To appear in Ap

The causal relationship between natural gas consumption and economic growth : evidence from the G7 countries

This article re-examines the nature of the causality between natural gas consumption and economic growth in G7 countries over the period from 1965 to 2011. We employ the Granger causality procedure proposed by Emirmahmutoglu and Kose (2011) which takes into account cross-sectional dependency and heterogeneity across countries. Our overall empirical results support the neutrality hypothesis for the panel while the individual country results confirm the same result with the exception of the case of UK, where the conservation hypothesis is confirmed, showing that GDP causes natural gas consumption in the country. These results make policies that promote the consumption of natural gas risk-free with regard to their effects to the economic growth and development levels.http://www.tandfonline.com/loi/rael202017-06-30hb201