12,649 research outputs found
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
Nuclear quantum shape-phase transitions in odd-mass systems
Microscopic signatures of nuclear ground-state shape phase transitions in
odd-mass Eu isotopes are explored starting from excitation spectra and
collective wave functions obtained by diagonalization of a core-quasiparticle
coupling Hamiltonian based on energy density functionals. As functions of the
physical control parameter -- the number of nucleons -- theoretical low-energy
spectra, two-neutron separation energies, charge isotope shifts, spectroscopic
quadrupole moments, and reduced transition matrix elements accurately
reproduce available data, and exhibit more pronounced discontinuities at
neutron number , compared to the adjacent even-even Sm and Gd isotopes.
The enhancement of the first-order quantum phase transition in odd-mass systems
can be attributed to a shape polarization effect of the unpaired proton which,
at the critical neutron number, starts predominantly coupling to Gd core nuclei
that are characterized by larger quadrupole deformation and weaker proton
pairing correlations compared to the corresponding Sm isotopes.Comment: 6 pages, 4 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 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: ,
, , , , as well as the
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.
STG2Seq: Spatial-temporal Graph to Sequence Model for Multi-step Passenger Demand Forecasting
Multi-step passenger demand forecasting is a crucial task in on-demand
vehicle sharing services. However, predicting passenger demand over multiple
time horizons is generally challenging due to the nonlinear and dynamic
spatial-temporal dependencies. In this work, we propose to model multi-step
citywide passenger demand prediction based on a graph and use a hierarchical
graph convolutional structure to capture both spatial and temporal correlations
simultaneously. Our model consists of three parts: 1) a long-term encoder to
encode historical passenger demands; 2) a short-term encoder to derive the
next-step prediction for generating multi-step prediction; 3) an
attention-based output module to model the dynamic temporal and channel-wise
information. Experiments on three real-world datasets show that our model
consistently outperforms many baseline methods and state-of-the-art models.Comment: 7 page
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
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