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 $\kappa$. From this bound, we can constrain $\kappa\lesssim 10^{8}\text{m}^2$ if a neutron star with a mass around $3M_{\odot}$ is observed in the future. In addition, to avoid the potential pathologies in EiBI, a \emph{Hagedorn-like} equation of state associated with $\kappa$ 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 150^{150}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 $^{152}$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 $^{150}$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 $^{150}$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 $\gamma$ band, yet the $0^{+}_{2}$ level within the $\beta$ band is lower than the corresponding experimental value and, the U(5)-SU(3) scheme seems better to describe the low-lying levels of $\beta$ band; and for the B(E2) transition, for the intraband transitions within the ground band and some interband transitions between the $\beta$ 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 $\beta$ 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 $c_0>0$. 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 $c>0$. We prove that when $c\geq c_0$, the species always dies out in the long-run, but when $0<c<c_0$, 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 $u_0(x)=\sigma \phi(x)$ with $\phi$ fixed and $\sigma>0$ a parameter, then there exists $\sigma_0>0$ such that vanishing happens when $\sigma\in (0,\sigma_0)$, borderline spreading happens when $\sigma=\sigma_0$, and spreading happens when $\sigma>\sigma_0$

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

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 $E_{\bf k}$ as a function of momentum ${\bf k}$. It is distinctively different from those of the $d_{x^2-y^2}$-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 $E_{\bf k}\neq E_{-{\bf k}}$. 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~μ\mum with the noise-immune cavity-enhanced optical heterodyne molecular spectroscopy method

We report on the Doppler-free saturation spectroscopy of the nitrous oxide (N$_2$O) overtone transition at 1.28~$\mu$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~$\mu$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 N$_2$O as markers because of its particularly rich spectrum at the vicinity of 1.28-1.30 $\mu$m where lies several important forbidden transitions of atomic parity violation measurements and the 1.3 $\mu$m O-band of optical communication

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 ($3$-D) objects with limited computational resources