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PGGA: A predictable and grouped genetic algorithm for job scheduling
This paper presents a predictable and grouped genetic algorithm (PGGA) for job scheduling. The novelty of the PGGA is twofold: (1) a job workload estimation algorithm is designed to estimate a job workload based on its historical execution records, (2) the divisible load theory (DLT) is employed to predict an optimal fitness value by which the PGGA speeds up the convergence process in searching a large scheduling space. Comparison with traditional scheduling methods such as first-come-first-serve (FCFS) and random scheduling, heuristics such as a typical genetic algorithm, Min-Min and Max-Min indicates that the PGGA is more effective and efficient in finding optimal scheduling solutions
Bounds for eigenvalue ratios of the Laplacian
For a bounded domain with a piecewise smooth boundary in an
-dimensional Euclidean space , we study eigenvalues of the
Dirichlet eigenvalue problem of the Laplacian. First we give a general
inequality for eigenvalues of the Laplacian. As an application, we study lower
order eigenvalues of the Laplacian and derive the ratios of lower order
eigenvalues of the Laplacian.Comment: 14 page
Capacities of Quantum Amplifier Channels
Quantum amplifier channels are at the core of several physical processes. Not
only do they model the optical process of spontaneous parametric
down-conversion, but the transformation corresponding to an amplifier channel
also describes the physics of the dynamical Casimir effect in superconducting
circuits, the Unruh effect, and Hawking radiation. Here we study the
communication capabilities of quantum amplifier channels. Invoking a recently
established minimum output-entropy theorem for single-mode phase-insensitive
Gaussian channels, we determine capacities of quantum-limited amplifier
channels in three different scenarios. First, we establish the capacities of
quantum-limited amplifier channels for one of the most general communication
tasks, characterized by the trade-off between classical communication, quantum
communication, and entanglement generation or consumption. Second, we establish
capacities of quantum-limited amplifier channels for the trade-off between
public classical communication, private classical communication, and secret key
generation. Third, we determine the capacity region for a broadcast channel
induced by the quantum-limited amplifier channel, and we also show that a fully
quantum strategy outperforms those achieved by classical coherent detection
strategies. In all three scenarios, we find that the capacities significantly
outperform communication rates achieved with a naive time-sharing strategy.Comment: 16 pages, 2 figures, accepted for publication in Physical Review
Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
We propose a systematical approach to construct generic fractional quantum
anomalous Hall (FQAH) states, which are generalizations of the fractional
quantum Hall states to lattice models with zero net magnetic field and full
lattice translation symmetry. Local and translationally invariant Hamiltonians
can also be constructed, for which the proposed states are unique ground
states. Our result demonstrates that generic chiral topologically ordered
states can be realized in lattice models, without requiring magnetic
translation symmetry and Landau level structure. We further generalize our
approach to the time-reversal invariant analog of fractional quantum Hall
states--fractional topological insulators, and provide the first explicit
wavefunction description of fractional topological insulators in the absence of
spin conservation.Comment: 4.5 pages, 2 figure
Galaxy growth in the concordance CDM cosmology
We use galaxy and dark halo data from the public database for the Millennium
Simulation to study the growth of galaxies in the De Lucia et al. (2006) model
for galaxy formation. Previous work has shown this model to reproduce many
aspects of the systematic properties and the clustering of real galaxies, both
in the nearby universe and at high redshift. It assumes the stellar masses of
galaxies to increase through three processes, major mergers, the accretion of
smaller satellite systems, and star formation. We show the relative importance
of these three modes to be a strong function of stellar mass and of redshift.
Galaxy growth through major mergers depends strongly on stellar mass, but only
weakly on redshift. Except for massive systems, minor mergers contribute more
to galaxy growth than major mergers at all redshifts and at all stellar masses.
For galaxies significantly less massive than the Milky Way, star formation
dominates the growth at all epochs. For galaxies significantly more massive
than the Milky Way, growth through mergers is the dominant process at all
epochs. At a stellar mass of , star formation dominates
at and mergers at later times. At every stellar mass, the growth rates
through star formation increase rapidly with increasing redshift. Specific star
formation rates are a decreasing function of stellar mass not only at but
also at all higher redshifts. For comparison, we carry out a similar analysis
of the growth of dark matter halos. In contrast to the galaxies, growth rates
depend strongly on redshift, but only weakly on mass. They agree qualitatively
with analytic predictions for halo growth.Comment: 11 pages, 6 figure
Applications of position-based coding to classical communication over quantum channels
Recently, a coding technique called position-based coding has been used to
establish achievability statements for various kinds of classical communication
protocols that use quantum channels. In the present paper, we apply this
technique in the entanglement-assisted setting in order to establish lower
bounds for error exponents, lower bounds on the second-order coding rate, and
one-shot lower bounds. We also demonstrate that position-based coding can be a
powerful tool for analyzing other communication settings. In particular, we
reduce the quantum simultaneous decoding conjecture for entanglement-assisted
or unassisted communication over a quantum multiple access channel to open
questions in multiple quantum hypothesis testing. We then determine achievable
rate regions for entanglement-assisted or unassisted classical communication
over a quantum multiple-access channel, when using a particular quantum
simultaneous decoder. The achievable rate regions given in this latter case are
generally suboptimal, involving differences of Renyi-2 entropies and
conditional quantum entropies.Comment: v4: 44 pages, v4 includes a simpler proof for an upper bound on
one-shot entanglement-assisted capacity, also found recently and
independently in arXiv:1804.0964
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