The Szekeres Swiss Cheese model and the CMB observations

This paper presents the application of the Szekeres Swiss Cheese model to the analysis of observations of the cosmic microwave background (CMB) radiation. The impact of inhomogeneous matter distribution on the CMB observations is in most cases studied within the linear perturbations of the Friedmann model. However, since the density contrast and the Weyl curvature within the cosmic structures are large, this issue is worth studying using another approach. The Szekeres model is an inhomogeneous, non-symmetrical and exact solution of the Einstein equations. In this model, light propagation and matter evolution can be exactly calculated, without such approximations as small amplitude of the density contrast. This allows to examine in more realistic manner the contribution of the light propagation effect to the measured CMB temperature fluctuations. The results of such analysis show that small-scale, non-linear inhomogeneities induce, via Rees-Sciama effect, temperature fluctuations of amplitude 10⁻⁷–10⁻⁵ on angular scale ϑ < 0.24° (ℓ > 750). This is still much smaller than the measured temperature fluctuations on this angular scale. However, local and uncompensated inhomogeneities can induce temperature fluctuations of amplitude as large as 10⁻³, and thus can be responsible the low multipoles anomalies observed in the angular CMB power spectrum.     

Consistency of modified MLE in EV model with replicated observations

In case that replicated observations are available in some experimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved under mild conditions.     

Spectral density estimation with amplitude modulation and outlier detection

This paper studies spectral density estimation based on amplitude modulation including missing data as a specific case. A generalized periodogram is introduced and smoothed to give a consistent estimator of the spectral density by running local linear regression smoother. We explore the asymptotic properties of the proposed estimator and its application to time series data with periodic missing. A simple data-driven local bandwidth selection rule is proposed and an algorithm for computing the spectral density estimate is presented. The effectiveness of the proposed method is demonstrated using simulations. The application to outlier detection based on leave-one-out diagnostic is also considered. An illustrative example shows that the proposed diagnostic procedure succeeds in revealing outliers in time series without masking and smearing effects. Supported by Chinese NSF Grants 10001004 and 39930160, and Fellowship of City University of Hong Kong.     

Noise measurements on a tunnel junction d.c. SQUID for a gravitational radiation detector at ultralow temperature

Summary We present noise measurements made at temperatures down to 200 mK on a tunnel junction d.c. SQUID, to be used as amplifier for the gravitational-wave experiment Nautilus of the Rome group. We find that the flux noise decreases with temperature, as expected, with a best measured value of at 0.2 K. The presence of an excess noise term independent of temperature is discussed.     

Linear viscoelastic properties of electro-rheological nano-suspension confined to narrow gap between electrodes

The linear viscoelastic properties of a suspension composed of titanium dioxide nanoparticles were measured under the direct current (dc) electric field with narrow gap distances between the electrodes. The yielding behavior under no external electric fields was also discussed. The wall slip at the interface between the parallel plates and the nano-suspension was briefly discussed. Under the dc electric field, a fine chain-like microstructure was optically found within a narrow gap of 50 μm between the electrodes in the quiescent state. The nano-suspension confined to a narrow gap of 65 μm between the parallel plates was rather viscoelastic even at the highest strength of the electric field of 16 kV·mm⁻¹. Furthermore, fast and slow relaxations of the dynamic moduli were found after removal of the electric field. It was pointed out that the linear viscoelasticity was an appropriate measure of the microstructure before yielding.     

A new multivariate variability control chart based on a covariance matrix combination

In the field of multivariate quality control, there are many control charts related to the process mean but few options addressing process variability. Variability control charts have two main drawbacks: the first relates to the number of parameters to tune and the second relates to how changes in the mean affect the performance of these charts. Thus, in this paper, we propose a new multivariate variability control chart, called the multivariate exponentially weighted covariance matrix combination, which solves these two problems. The results show that this new chart performs well in the detection of changes in variance when the mean does not change and outperforms other charts when the mean does change.     

Robust asset allocation with conditional value at risk using the forward search

The well‐known Markowitz approach to portfolio allocation, based on expected returns and their covariance, seems to provide questionable results in financial management. One motivation for the pitfall is that financial returns have heavier than Gaussian tails, so the covariance of returns, used in the Markowitz model as a measure of portfolio risk, is likely to provide a loose quantification of the effective risk. Additionally, the Markowitz approach is very sensitive to small changes in either the expected returns or their correlation, often leading to irrelevant portfolio allocations. More recent allocation techniques are based on alternative risk measures, such as value at risk (VaR) and conditional VaR (CVaR), which are believed to be more accurate measures of risk for fat‐tailed distributions. Nevertheless, both VaR and CVaR estimates can be influenced by the presence of extreme returns. In this paper, we discuss sensitivity to the presence of extreme returns and outliers when optimizing the allocation, under the constraint of keeping CVaR to a minimum. A robust and efficient approach, based on the forward search, is suggested. A Monte Carlo simulation study shows the advantages of the proposed approach, which outperforms both robust and nonrobust alternatives under a variety of specifications. The performance of the method is also thoroughly evaluated with an application to a set of US stocks.     

Luminosity-peak energy relation in the decay phases of gamma-ray burst pulses

Using time-resolved spectral data for a sample of 30 pulses in 27 bright GRBs detected with CGRO/BATSE, we investigate the luminosity-peak energy relation (L-E p relation) in the decay phases of these pulses. A tight L-E p relation is found for most of the pulses, but its power law index is various among pulses, which is normally distributed at 1.84±0.60(1σ) for the pulses in our sample, roughly consistent with the L-E p relation within a GRB and the isotropic gamma-ray energy-E p relation among GRBs. The large scatter of the power law index cannot be explained with both the statistical or observational effects and it may be an intrinsic feature, indicating that no universal L-E p relation would be expected among GRBs/pulses. This may strongly weaken the cosmological use of this relation.     

在不确定观测下离散状态时滞系统的最优滤波

研究了在不确定观测下离散状态时滞系统的最优滤波问题,观测值的不确定性则通过一个满足Bernoulli分布且统计特性已知的随机变量来描述. 一般采用状态增广方法将时滞系统转换为无时滞随机系统, 再利用Kalman滤波器的设计方法解决最优状态估计问题, 但是当系统时滞较大时,转换后的系统状态维数很高, 这样增加了计算负担. 为此,基于最小方差估计准则, 利用射影性质和递归射影公式得到了一个新的滤波器设计方法, 而且保证了滤波器的维数与原系统相同.最后, 给出一个仿真例子说明所提方法的有效性.     

Partially Observed Analytic Systems with Fully Unbounded Actuators and Sensors-FEM Algorithms

Partially observed control systems described by analytic semigroup are considered. Finite-dimensional feedback control based on FEM approximations and accounting for incomplete observations is constructed. It is shown that this feedback control provides uniform stability (in time) of the originally unstable system. The main novel feature of the problem is that both—control and observation operators—are modeled by fully unbounded operators as they frequently arise in modeling of smart sensors and actuators. This contributes to technical difficulties at the level of perturbation theory for analytic semigroups. It is shown that a careful and rather special approximation in the area of support of the unbounded control/observation operators allows to obtain the right stability estimates. Theoretical results are illustrated with several examples of control problems governed by heat and plate equations.