Block-Structured Supermarket Models

Supermarket models are a class of parallel queueing networks with an adaptive control scheme that play a key role in the study of resource management of, such as, computer networks, manufacturing systems and transportation networks. When the arrival processes are non-Poisson and the service times are non-exponential, analysis of such a supermarket model is always limited, interesting, and challenging. This paper describes a supermarket model with non-Poisson inputs: Markovian Arrival Processes (MAPs) and with non-exponential service times: Phase-type (PH) distributions, and provides a generalized matrix-analytic method which is first combined with the operator semigroup and the mean-field limit. When discussing such a more general supermarket model, this paper makes some new results and advances as follows: (1) Providing a detailed probability analysis for setting up an infinite-dimensional system of differential vector equations satisfied by the expected fraction vector, where "the invariance of environment factors" is given as an important result. (2) Introducing the phase-type structure to the operator semigroup and to the mean-field limit, and a Lipschitz condition can be obtained by means of a unified matrix-differential algorithm. (3) The matrix-analytic method is used to compute the fixed point which leads to performance computation of this system. Finally, we use some numerical examples to illustrate how the performance measures of this supermarket model depend on the non-Poisson inputs and on the non-exponential service times. Thus the results of this paper give new highlight on understanding influence of non-Poisson inputs and of non-exponential service times on performance measures of more general supermarket models.Comment: 65 pages; 7 figure

A Matrix-Analytic Solution for Randomized Load Balancing Models with Phase-Type Service Times

In this paper, we provide a matrix-analytic solution for randomized load balancing models (also known as \emph{supermarket models}) with phase-type (PH) service times. Generalizing the service times to the phase-type distribution makes the analysis of the supermarket models more difficult and challenging than that of the exponential service time case which has been extensively discussed in the literature. We first describe the supermarket model as a system of differential vector equations, and provide a doubly exponential solution to the fixed point of the system of differential vector equations. Then we analyze the exponential convergence of the current location of the supermarket model to its fixed point. Finally, we present numerical examples to illustrate our approach and show its effectiveness in analyzing the randomized load balancing schemes with non-exponential service requirements.Comment: 24 page

Global analysis of quadrupole shape invariants based on covariant energy density functionals

Coexistence of different geometric shapes at low energies presents a universal structure phenomenon that occurs over the entire chart of nuclides. Studies of the shape coexistence are important for understanding the microscopic origin of collectivity and modifications of shell structure in exotic nuclei far from stability. The aim of this work is to provide a systematic analysis of characteristic signatures of coexisting nuclear shapes in different mass regions, using a global self-consistent theoretical method based on universal energy density functionals and the quadrupole collective model. The low-energy excitation spectrum and quadrupole shape invariants of the two lowest $0^{+}$ states of even-even nuclei are obtained as solutions of a five-dimensional collective Hamiltonian (5DCH) model, with parameters determined by constrained self-consistent mean-field calculations based on the relativistic energy density functional PC-PK1, and a finite-range pairing interaction. The theoretical excitation energies of the states: $2^+_1$, $4^+_1$, $0^+_2$, $2^+_2$, $2^+_3$, as well as the $B(E2; 0^+_1\to 2^+_1)$ values, are in very good agreement with the corresponding experimental values for 621 even-even nuclei. Quadrupole shape invariants have been implemented to investigate shape coexistence, and the distribution of possible shape-coexisting nuclei is consistent with results obtained in recent theoretical studies and available data. The present analysis has shown that, when based on a universal and consistent microscopic framework of nuclear density functionals, shape invariants provide distinct indicators and reliable predictions for the occurrence of low-energy coexisting shapes. This method is particularly useful for studies of shape coexistence in regions far from stability where few data are available.Comment: 13 pages, 3 figures, accepted for publication in Phys. Rev.

1I/2017 U1 (`Oumuamua) is Hot: Imaging, Spectroscopy and Search of Meteor Activity

1I/2017 U1 (`Oumuamua), a recently discovered asteroid in a hyperbolic orbit, is likely the first macroscopic object of extrasolar origin identified in the solar system. Here, we present imaging and spectroscopic observations of \textquoteleft Oumuamua using the Palomar Hale Telescope as well as a search of meteor activity potentially linked to this object using the Canadian Meteor Orbit Radar. We find that \textquoteleft Oumuamua exhibits a moderate spectral gradient of $10\%\pm6\%~(100~\mathrm{nm})^{-1}$, a value significantly lower than that of outer solar system bodies, indicative of a formation and/or previous residence in a warmer environment. Imaging observation and spectral line analysis show no evidence that \textquoteleft Oumuamua is presently active. Negative meteor observation is as expected, since ejection driven by sublimation of commonly-known cometary species such as CO requires an extreme ejection speed of $\sim40$ m s$^{-1}$ at $\sim100$ au in order to reach the Earth. No obvious candidate stars are proposed as the point of origin for \textquoteleft Oumuamua. Given a mean free path of $\sim10^9$ ly in the solar neighborhood, \textquoteleft Oumuamua has likely spent a very long time in the interstellar space before encountering the solar system.Comment: ApJL in pres

Multifunctional Bracts in the Dove Tree Davidia involucrata (Nyssaceae:Cornales)

Although there has been much experimental work on floral traits that are under selection from mutualists and antagonists, selection by abiotic environmental factors on flowers has been largely ignored. Here we test whether pollen susceptibility to rain damage could have played a role in the evolution of the reproductive architecture of Davidia involucrata, an endemic in the mountains of western China. Flowers in this tree species lack a perianth and are arranged in capitula surrounded by large (up to 10 cm#5 cm) bracts that at anthesis turn from green to white, losing their photosynthetic capability. Flowers are nectarless, and pollen grains are presented on the recurved anther walls for 5–7 days. Flower visitors, and likely pollinators, were mainly pollen-collecting bees from the genera Apis, Xylocopa, Halictus, and Lasioglossum. Capitula with natural or white paper bracts attracted significantly more bees per hour than capitula that had their bracts removed or replaced by green paper. Experimental immersion of pollen grains in water resulted in rapid loss of viability, and capitula with bracts lost less pollen to rain than did capitula that had their bracts removed, suggesting that the bracts protect the pollen from rain damage as well as attracting pollinators

Analysis of tick-borne encephalitis virus-induced host responses in human cells of neuronal origin and interferon-mediated protection

Tick-borne encephalitis virus (TBEV) is a member of the genus Flavivirus. It can cause serious infections in humans that may result in encephalitis/meningoencephalitis. Although several studies have described the involvement of specific genes in the host response to TBEV infection in the central nervous system (CNS), the overall network remains poorly characterized. Therefore, we investigated the response of DAOY cells (human medulloblastoma cells derived from cerebellar neurons) to TBEV (Neudoerfl strain, Western subtype) infection to characterize differentially expressed genes by transcriptome analysis. Our results revealed a wide panel of interferon-stimulated genes (ISGs) and pro-inflammatory cytokines, including type III but not type I (or II) interferons (IFNs), which are activated upon TBEV infection, as well as a number of non-coding RNAs, including long non-coding RNAs. To obtain a broader view of the pathways responsible for eliciting an antiviral state in DAOY cells we examined the effect of type I and III IFNs and found that only type I IFN pre-treatment inhibited TBEV production. The cellular response to TBEV showed only partial overlap with gene expression changes induced by IFN-β treatment – suggesting a virus-specific signature – and we identified a group of ISGs that were highly up-regulated following IFN-β treatment. Moreover, a high rate of down-regulation was observed for a wide panel of pro-inflammatory cytokines upon IFN-β treatment. These data can serve as the basis for further studies of host–TBEV interactions and the identification of ISGs and/or lncRNAs with potent antiviral effects in cases of TBEV infection in human neuronal cells