Exact error estimates and optimal randomized algorithms for integration

Exact error estimates for evaluating multi-dimensional integrals are considered. An estimate is called exact if the rates of convergence for the low- and upper-bound estimate coincide. The algorithm with such an exact rate is called optimal. Such an algorithm has an unimprovable rate of convergence. The problem of existing exact estimates and optimal algorithms is discussed for some functional spaces that define the regularity of the integrand. Important for practical computations data classes are considered: classes of functions with bounded derivatives and Holder type conditions. The aim of the paper is to analyze the performance of two optimal classes of algorithms: deterministic and randomized for computing multidimensional integrals. It is also shown how the smoothness of the integrand can be exploited to construct better randomized algorithms.

Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

OFDM joint data detection and phase noise cancellation based on minimum mean square prediction error

This paper proposes a new iterative algorithm for orthogonal frequency division multiplexing (OFDM) joint data detection and phase noise (PHN) cancellation based on minimum mean square prediction error. We particularly highlight the relatively less studied problem of "overfitting" such that the iterative approach may converge to a trivial solution. Specifically, we apply a hard-decision procedure at every iterative step to overcome the overfitting. Moreover, compared with existing algorithms, a more accurate Pade approximation is used to represent the PHN, and finally a more robust and compact fast process based on Givens rotation is proposed to reduce the complexity to a practical level. Numerical Simulations are also given to verify the proposed algorithm. (C) 2008 Elsevier B.V. All rights reserved.

A general model of error-prone PCR

In this paper, we generalise a previously-described model of the error-prone polymerase chain reaction (PCR) reaction to conditions of arbitrarily variable amplification efficiency and initial population size. Generalisation of the model to these conditions improves the correspondence to observed and expected behaviours of PCR, and restricts the extent to which the model may explore sequence space for a prescribed set of parameters. Error-prone PCR in realistic reaction conditions is predicted to be less effective at generating grossly divergent sequences than the original model. The estimate of mutation rate per cycle by sampling sequences from an in vitro PCR experiment is correspondingly affected by the choice of model and parameters. (c) 2005 Elsevier Ltd. All rights reserved.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

Localization to the nucleolus is a common feature of coronavirus nucleoproteins and the protein may disrupt host cell division

The subcellular localization of transmissible gastroenteritis virus (TGEV) and mouse hepatitis virus (MHV) (group I and group II coronaviruses, respectively) nucleoproteins (N proteins) were examined by confocal microscopy. The proteins were shown to localize either to the cytoplasm alone or to the cytoplasm and a structure in the nucleus. This feature was confirmed to be the nucleolus by using specific antibodies to nucleolin, a major component of the nucleolus, and by confocal microscopy to image sections through a cell expressing N protein. These findings are consistent with our previous report for infectious bronchitis virus (group III coronavirus) (J. A. Hiscox et al., J. Virol. 75:506-512, 2001), indicating that nucleolar localization of the N protein is a common feature of the coronavirus family and is possibly of functional significance. Nucleolar localization signals were identified in the domain III region of the N protein from all three coronavirus groups, and this suggested that transport of N protein to the nucleus might be an active process. In addition, our results suggest that the N protein might function to disrupt cell division. Thus, we observed that approximately 30% of cells transfected with the N protein appeared to be undergoing cell division. The most likely explanation for this is that the N protein induced a cell cycle delay or arrest, most likely in the G2/M phase. In a fraction of transfected cells expressing coronavirus N proteins, we observed multinucleate cells and dividing cells with nucleoli (which are only present during interphase). These findings are consistent with the possible inhibition of cytokinesis in these cells.

A note on the analysis error associated with 3D-FGAT

The analysis-error variance of a 3D-FGAT assimilation is examined analytically using a simple scalar equation. It is shown that the analysis-error variance may be greater than the error variances of the inputs. The results are illustrated numerically with a scalar example and a shallow-water model.

Synchronisation error resistant CDMA detection

A bit-level linear CDMA detector is presented which is based on the minimum variance distortionless response (MVDR) principle. Owing to the interference suppression capability made possible by basing the detector on the MVDR principle and the fact that no inversion of the user correlation matrix is involved, the influence of synchronisation errors is greatly suppressed.

Synchronisation error resistant multiuser detection for asynchronous CDMA

Linear CDMA detectors have emerged as a promising solution to multiple access interference (MAI) suppression. Unfortunately, most existing linear detectors suffer from high sensitivity to synchronisation errors (also termed parameter estimation error), and synchronisation error resistant detectors have so far not been as widely investigated as they should have. This paper extends the minimum variance distortionless response (MVDR) detector, proposed previously by this author (Zheng 2000) for synchronous systems, to asynchronous systems. It has been shown that the MVDR structure is equally effective for asynchronous systems, especially for the weaker users.

Forecast impact of targeted observations: sensitivity to observation error and proximity to steep orography

For a targeted observations case, the dependence of the size of the forecast impact on the targeted dropsonde observation error in the data assimilation is assessed. The targeted observations were made in the lee of Greenland; the dependence of the impact on the proximity of the observations to the Greenland coast is also investigated. Experiments were conducted using the Met Office Unified Model (MetUM), over a limited-area domain at 24-km grid spacing, with a four-dimensional variational data assimilation (4D-Var) scheme. Reducing the operational dropsonde observation errors by one-half increases the maximum forecast improvement from 5% to 7%–10%, measured in terms of total energy. However, the largest impact is seen by replacing two dropsondes on the Greenland coast with two farther from the steep orography; this increases the maximum forecast improvement from 5% to 18% for an 18-h forecast (using operational observation errors). Forecast degradation caused by two dropsonde observations on the Greenland coast is shown to arise from spreading of data by the background errors up the steep slope of Greenland. Removing boundary layer data from these dropsondes reduces the forecast degradation, but it is only a partial solution to this problem. Although only from one case study, these results suggest that observations positioned within a correlation length scale of steep orography may degrade the forecast through the anomalous upslope spreading of analysis increments along terrain-following model levels.

Electrophysiological correlates of spatial orienting towards angry faces: a source localization study

The goal of this study was to examine behavioral and electrophysiological correlates of involuntary orienting toward rapidly presented angry faces in non-anxious, healthy adults using a dot-probe task in conjunction with high-density event-related potentials and a distributed source localization technique. Consistent with previous studies, participants showed hypervigilance toward angry faces, as indexed by facilitated response time for validly cued probes following angry faces and an enhanced P1 component. An opposite pattern was found for happy faces suggesting that attention was directed toward the relatively more threatening stimuli within the visual field (neutral faces). Source localization of the P1 effect for angry faces indicated increased activity within the anterior cingulate cortex, possibly reflecting conflict experienced during invalidly cued trials. No modulation of the early C1 component was found for affect or spatial attention. Furthermore, the face-sensitive N170 was not modulated by emotional expression. Results suggest that the earliest modulation of spatial attention by face stimuli is manifested in the P1 component, and provide insights about mechanisms underlying attentional orienting toward cues of threat and social disapproval.

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.