On the inference about the spectra of high-dimensional covariance matrix based on noisy observations-with applications to integrated covolatility matrix inference in the presence of microstructure noise

In practice, observations are often contaminated by noise, making the resulting sample covariance matrix to be an information-plus-noise-type covariance matrix. Aiming to make inferences about the spectra of the underlying true covariance matrix under such a situation, we establish an asymptotic relationship that describes how the limiting spectral distribution of (true) sample covariance matrices depends on that of information-plus-noise-type sample covariance matrices. As an application, we consider the inference about the spectra of integrated covolatility (ICV) matrices of high-dimensional diffusion processes based on high-frequency data with microstructure noise. The (slightly modified) pre-averaging estimator is an information-plus-noise-type covariance matrix, and the aforementioned result, together with a (generalized) connection between the spectral distribution of true sample covariance matrices and that of the population covariance matrix, enables us to propose a two-step procedure to estimate the spectral distribution of ICV for a class of diffusion processes. An alternative estimator is further proposed, which possesses two desirable properties: it eliminates the impact of microstructure noise, and its limiting spectral distribution depends only on that of the ICV through the standard Mar\v{c}enko-Pastur equation. Numerical studies demonstrate that our proposed methods can be used to estimate the spectra of the underlying covariance matrix based on noisy observations

Exploring Mixed Integer Programming Reformulations for Virtual Machine Placement with Disk Anti-Colocation Constraints

One of the important problems for datacenter resource management is to place virtual machines (VMs) to physical machines (PMs) such that certain cost, profit or performance objective is optimized, subject to various constraints. In this paper, we consider an interesting and difficult VM placement problem with disk anti-colocation constraints: a VM's virtual disks should be spread out across the physical disks of its assigned PM. For solutions, we use the mixed integer programming (MIP) formulations and algorithms. However, a challenge is the potentially long computation time of the MIP algorithms. In this paper, we explore how reformulation of the problem can help to reduce the computation time. We develop two reformulations, by redefining the variables, for our VM placement problem and evaluate the computation time of all three formulations. We show that they have vastly different computation time. All three formulations can be useful, but for different problem instances. They all should be kept in the toolbox for tackling the problem. Out of the three, formulation COMB is especially flexible and versatile, and it can solve large problem instances

Left-Center-Right Separated Neural Network for Aspect-based Sentiment Analysis with Rotatory Attention

Deep learning techniques have achieved success in aspect-based sentiment analysis in recent years. However, there are two important issues that still remain to be further studied, i.e., 1) how to efficiently represent the target especially when the target contains multiple words; 2) how to utilize the interaction between target and left/right contexts to capture the most important words in them. In this paper, we propose an approach, called left-center-right separated neural network with rotatory attention (LCR-Rot), to better address the two problems. Our approach has two characteristics: 1) it has three separated LSTMs, i.e., left, center and right LSTMs, corresponding to three parts of a review (left context, target phrase and right context); 2) it has a rotatory attention mechanism which models the relation between target and left/right contexts. The target2context attention is used to capture the most indicative sentiment words in left/right contexts. Subsequently, the context2target attention is used to capture the most important word in the target. This leads to a two-side representation of the target: left-aware target and right-aware target. We compare our approach on three benchmark datasets with ten related methods proposed recently. The results show that our approach significantly outperforms the state-of-the-art techniques

Partial linearization for nonautonomous differential equations

In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum

On the inference about the spectral distribution of high-dimensional covariance matrix based on high-frequency noisy observations

In practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance matrix under such a situation, we establish an asymptotic relationship that describes how the limiting spectral distribution of (signal) sample covariance matrices depends on that of signal-plus-noise-type sample covariance matrices. As an application, we consider inferences about the spectral distribution of integrated covolatility (ICV) matrices of high-dimensional diffusion processes based on high-frequency data with microstructure noise. The (slightly modified) pre-averaging estimator is a signal-plus-noise sample covariance matrix, and the aforementioned result, together with a (generalized) connection between the spectral distribution of signal sample covariance matrices and that of the population covariance matrix, enables us to propose a two-step procedure to consistently estimate the spectral distribution of ICV for a class of diffusion processes. An alternative approach is further proposed, which possesses several desirable properties: it is more robust, it eliminates the effects of microstructure noise, and the asymptotic relationship that enables consistent estimation of the spectral distribution of ICV is the standard Marcenko-Pastur equation. The performance of the two approaches is examined via simulation studies under both synchronous and asynchronous observation settings.Comment: arXiv admin note: text overlap with arXiv:1409.212

The Deconfinement Phase Transition in the Interior of Neutron Stars

The deconfinement phase transition which happens in the interior of neutron stars are investigated. Coupled with the spin evolution of the stars, the effect of entropy production and deconfinement heat generation during the deconfinement phase transition in the mixed phase of the neutron stars are discussed. The entropy production of deconfinement phase transition can be act as a signature of phase transition, but less important and does not significantly change the thermal evolution of neutron stars. The deconfinement heat can change the thermal evolution of neutron star distinctly.Comment: 5 pages. To appear in Proceedings for "Compact stars in the QCD phase diagram II (CSQCD II), May 20-24, 2009, KIAA at Peking University, Beijing - P. R. China [http://vega.bac.pku.edu.cn/rxxu/csqcd.htm

A simple regression equivalence of Pillai's trace statistic

Derived here is a single regression coefficient equivalent to Pillai's trace statistic in multivariate analysis of variance.Comment: 3 page

Non-leptonic Weak Interaction in Magnetized Quark matter

We investigated the non-leptonic weak interaction in magnetic field. We discussed an improvement of previous method to analytical work out the rate for weak field case.Our result easily goes over to field-free limit.Then we calculated the reaction rate in strong magnetic field where the charged particles are confined to the lowest Landau level. A strong magnetic field strongly suppressed the rate,which will be foreseen to affect viscous dynamics in SQM .We also derived a few approximation formulae under given conditions that can be conveniently applied.Comment: 14pages, 5figure

Ergodic behaviour of nonconventional ergodic averages for commuting transformations

Based on T.Tao's result of norm convergence of multiple ergodic averages for commut-ing transformation, we obtain there is a subsequence which converges almost everywhere. Meanwhile, the ergodic behaviour, which the time average is equal to the space average, of diagonal measures is obtained and we give different result according to the classification of transformations. Additionally, on the torus with special rotation. we can not only get the convergence in T.Tao's paper for every point in Td, but also get a beautiful result for ergodic behaviour

Constructing Riemann-Hilbert problem and multi-soliton solutions for the N-coupled Hirota equations in an optical fiber

This paper focuses on investigation of the N-coupled Hirota equations arising in an optical fiber. Starting from analyzing the spectral problem, a kind of matrix Riemann-Hilbert problem is formulated strictly on the real axis. Then based on the resulting matrix Riemann-Hilbert problem under the constraint of no reflection, multi-soliton solutions to the N-coupled Hirota equations are presented explicitly.Comment: 9 page