24,777 research outputs found
Higher-order expansions of powered extremes of normal samples
In this paper, higher-order expansions for distributions and densities of
powered extremes of standard normal random sequences are established under an
optimal choice of normalized constants. Our findings refine the related results
in Hall (1980). Furthermore, it is shown that the rate of convergence of
distributions/densities of normalized extremes depends in principle on the
power index
Tensor train-Karhunen-Lo\`eve expansion for continuous-indexed random fields using higher-order cumulant functions
The goals of this work are two-fold: firstly, to propose a new theoretical
framework for representing random fields on a large class of multidimensional
geometrical domain in the tensor train format; secondly, to develop a new
algorithm framework for accurately computing the modes and the second and
third-order cumulant tensors within moderate time. The core of the new
theoretical framework is the tensor train decomposition of cumulant functions.
This decomposition is accurately computed with a novel rank-revealing
algorithm. Compared with existing Galerkin-type and collocation-type methods,
the proposed computational procedure totally removes the need of selecting the
basis functions or collocation points and the quadrature points, which not only
greatly enhances adaptivity, but also avoids solving large-scale eigenvalue
problems. Moreover, by computing with third-order cumulant functions, the new
theoretical and algorithm frameworks show great potential for representing
general non-Gaussian non-homogeneous random fields. Three numerical examples,
including a three-dimensional random field discretization problem, illustrate
the efficiency and accuracy of the proposed algorithm framework
A Queuing Model for CPU Functional Unit and Issue Queue Configuration
In a superscalar processor, instructions of various types flow through an
execution pipeline, traversing hardware resources which are mostly shared among
many different instruction types. A notable exception to shared pipeline
resources is the collection of functional units, the hardware that performs
specific computations. In a trade-off of cost versus performance, a pipeline
designer must decide how many of each type of functional unit to place in a
processor's pipeline. In this paper, we model a superscalar processor's issue
queue and functional units as a novel queuing network. We treat the issue queue
as a finite-sized waiting area and the functional units as servers. In addition
to common queuing problems, customers of the network share the queue but wait
for specific servers to become ready (e.g., addition instructions wait for
adders). Furthermore, the customers in this queue are not necessary ready for
service, since instructions may be waiting for operands. In this paper we model
a novel queuing network that provides a solution to the expected queue length
of each type of instruction. This network and its solution can also be
generalized to other problems, notably other resource-allocation issues that
arise in superscalar pipelines
The Buchdahl Stability Bound in Eddington-inspired Born-Infeld Gravity
We give the Buchdahl stability bound in Eddington-inspired Born-Infeld (EiBI)
gravity. We show that this bound depends on an energy condition controlled by
the model parameter . From this bound, we can constrain if a neutron star with a mass around is observed
in the future. In addition, to avoid the potential pathologies in EiBI, a
\emph{Hagedorn-like} equation of state associated with at the center
of a compact star is inevitable, which is similar to the Hagedorn temperature
in string theory.Comment: 13 pages, 2 figures, 1 table; references and a table added, typos
corrected, \kappa-energy condition defined; version published in Chinese
Physics
The description of Nd Nucleus by a new alternative scheme
A new scheme was recently proposed in which the usual SU(3)
quadrupole-quadrupole interaction was replaced by an O(6) cubic interaction in
the Interacting Boson Model, and also successfully applied to the description
of Sm for the N = 90 rare earth isotones with X(5) symmetry. By using
this new scheme, in the present work, we further explore the properties of
another candidate of Nd for the N=90 with X(5) symmetry. The low-lying
energy levels and E2 transition rates are calculated and compared with the
experimental data. The results show that the new scheme can also reasonably
describe the experimental low-lying spectrum and the intraband and the
interband E2 transitions for Nd. However, for the low-lying spectrum,
the O(6) cubic interaction seems better in describing the energy levels,
especially in higher excited states and band, yet the
level within the band is lower than the corresponding experimental
value and, the U(5)-SU(3) scheme seems better to describe the low-lying levels
of band; and for the B(E2) transition, for the intraband transitions
within the ground band and some interband transitions between the band
and the ground band, the results from O(6) cubic interaction are better than
those from SU(3) quadrupole-quadrupole interaction, yet of which seems better
to describe the intraband E2 transitions within band. The present work
is very meaningful in helping us to deeply understand the new characteristics
of symmetry by the higher order O(6) cubic interaction.Comment: Submitted to Chinese Physics
Spreading in a shifting environment modeled by the diffusive logistic equation with a free boundary
We investigate the influence of a shifting environment on the spreading of an
invasive species through a model given by the diffusive logistic equation with
a free boundary. When the environment is homogeneous and favourable, this model
was first studied in Du and Lin \cite{DL}, where a spreading-vanishing
dichotomy was established for the long-time dynamics of the species, and when
spreading happens, it was shown that the species invades the new territory at
some uniquely determined asymptotic speed . Here we consider the
situation that part of such an environment becomes unfavourable, and the
unfavourable range of the environment moves into the favourable part with speed
. We prove that when , the species always dies out in the
long-run, but when , the long-time behavior of the species is
determined by a trichotomy described by
(a) {\it vanishing}, (b) {\it borderline spreading}, or (c) {\it spreading}.
If the initial population is writen in the form with
fixed and a parameter, then there exists such
that vanishing happens when , borderline spreading
happens when , and spreading happens when
A new SSO-based Algorithm for the Bi-Objective Time-constrained task Scheduling Problem in Cloud Computing Services
Cloud computing distributes computing tasks across numerous distributed
resources for large-scale calculation. The task scheduling problem is a
long-standing problem in cloud-computing services with the purpose of
determining the quality, availability, reliability, and ability of the cloud
computing. This paper is an extension and a correction to our previous
conference paper entitled Multi Objective Scheduling in Cloud Computing Using
MOSSO published in 2018 IEEE Congress on Evolutionary Computation. More new
algorithms, testing, and comparisons have been implemented to solve the
bi-objective time-constrained task scheduling problem in a more efficient
manner. Furthermore, this paper developed a new SSO-based algorithm called the
bi-objective simplified swarm optimization to fix the error in previous
SSO-based algorithm to address the task-scheduling problem. From the results
obtained from the new experiments conducted, the proposed BSSO outperforms
existing famous algorithms, e.g., NSGA-II, MOPSO, and MOSSO in the convergence,
diversity, number of obtained temporary nondominated solutions, and the number
of obtained real nondominated solutions. The results propound that the proposed
BSSO can successfully achieve the aim of this work
Multilevel Fast Multipole Algorithm for Characteristic Mode Analysis
Characteristic mode (CM) analysis poses challenges in computational
electromagnetics (CEM) as it calls for efficient solutions of dense generalized
eigenvalue problems (GEP). Multilevel fast multipole algorithm (MLFMA) can
greatly reduce the computational complexity and memory cost for matrix-vector
product operations, which is powerful in iteratively solving large scattering
problems. In this article, we demonstrate that MLFMA can be easily incorporated
into the implicit restarted Arnoldi (IRA) method for the calculation of CMs,
where MLFMA with the sparse approximate inverse (SAI) preconditioning technique
is employed to accelerate the construction of Arnoldi vectors. This work paves
the way of CM analysis for large-scale and complicated three-dimensional
(-D) objects with limited computational resources
ORVB Mean-Field Calculation in the Tight-Binding Model with Anti-Ferromagnetic Exchange
We give a mean-field calculation for the odd-resonating-valence-bond ORVB
pairing scheme. We obtain interesting quasi-particle excitation energy as a function of momentum . It is distinctively different from
those of the -wave, the anisotropic-s-wave, and the p-wave. It is
a gapless theory for superconductivity with well defined Fermi surface. The
ground state of the ORVB scheme is not an eigenstate of the parity or the
time-reversal transformation, thus both symmetries are violated. Some of them
are already manifested in . It is interesting to
find out if such pairing order-parameter scheme exits in some materials in
nature.Comment: 12 pages, uses phyzz
Doppler-free resolution near-infrared spectroscopy at 1.28~m with the noise-immune cavity-enhanced optical heterodyne molecular spectroscopy method
We report on the Doppler-free saturation spectroscopy of the nitrous oxide
(NO) overtone transition at 1.28~m. This measurement is performed by
the noise-immune cavity-enhanced optical heterodyne molecular spectroscopy
(NICE-OHMS) technique based on the quantum-dot (QD) laser. A high intra-cavity
power, up to 10~W, reaches the saturation limit of the overtone line using an
optical cavity with a high finesse of 113,500. At a pressure of several mTorr,
the saturation dip is observed with a full width at half-maximum of about 2~MHz
and a signal-to-noise ratio of 71. To the best of our knowledge, this is the
first saturation spectroscopy of molecular overtone transitions in 1.3~m
region. The QD laser is then locked to this dispersion signal with a stability
of 15 kHz at 1 sec integration time. We demonstrate the potential of the NO
as markers because of its particularly rich spectrum at the vicinity of
1.28-1.30 m where lies several important forbidden transitions of atomic
parity violation measurements and the 1.3 m O-band of optical
communication
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