Error Spectrum Research Articles

Somatic mutation hotspots correlate with DNA polymerase eta error spectrum.

Mutational spectra analysis of 15 immunoglobulin genes suggested that consensus motifs RGYW and WA were universal descriptors of somatic hypermutation. Highly mutable sites, "hotspots", that matched WA were preferentially found in one DNA strand and RGYW hotspots were found in both strands. Analysis of base-substitution hotspots in DNA polymerase error spectra showed that 33 of 36 hotspots in the human polymerase eta spectrum conformed to the WA consensus. This and four other characteristics of polymerase eta substitution specificity suggest that errors introduced by this enzyme during synthesis of the nontranscribed DNA strand in variable regions may contribute to strand-specific somatic hypermutagenesis of immunoglobulin genes at A-T base pairs.

Error spectrum for the global M2 ocean tide

The most accurate determinations of the global ocean tides are currently based on altimeter measurements made by the Topex/Poseidon satellite. The error spectrum corresponding to the M2 tidal solution is here estimated, primarily by inverse methods and secondarily by simple differencing of several of the best tidal models. The tidal error spectrum is flatter than the tidal signal spectrum, and it exceeds 10% of the signal at spherical harmonic degree 15 and above. The tide errors also exceed the anticipated sensitivity of the upcoming Grace satellite gravity mission for all degrees below 40, and possibly below 50.

High-throughput high-density mapping and spectrum analysis of transistor gate length variations in SRAM circuits

High-throughput high-density mapping of gate length variations using static random-access memory (SRAM) as electronic test structures is reported. In the experiments, direct measurements of bit-line currents revealed the individual transistor gate length variations within every memory cell. With SRAM and its fast addressing circuits we can measure CD variations with measurement time as fast as 5 /spl mu/s per data point and spatial periodicities down to 6 /spl mu/m. Layout-dependent periodic errors were found to take up 30% to 90% of the total observed error variance, depending on the spatial frequency range and specific measurement grid used. Peaks in the error spectrum were found to be related to the periodicities existing in the circuit layout. Lithography simulations were done as efforts to identify the periodic error sources. It was found that proximity effects and pattern-dependent coma effects contributed to a large percentage of the high spatial frequency errors observed. By independent optical measurements of the poly mask, it was found that the CD error contributions from the mask are very small, and are negligible when compared to the stepper-lens-induced CD errors.

Quantization error analysis of second order bandpass Delta-Sigma modulator with sinusoidal inputs

The exact analysis of second order bandpass Delta-Sigma modulator with sinusoidal inputs is performed. The results indicate that quantization error is neither uniformly distributed nor white. The quantization error spectrum is purely discrete and symmetric with one forth of sampling frequency, and the locations of these discrete frequency components are strongly dependent on input amplitudes. Similar results are also observed for passband communication signals, such as quadrature amplitude modulation. From the analysis, crosscorrelation between quantization error and sinusoidal input was shown to exist but can be cancelled out by proper design of the noise shaping function. Crosscorrelation can degrade the performance of the delta-sigma system. Hence, the exact analysis is another method to enable design for high performance.

状態推定フィードバック閉ループシステムにおける誤差スペクトル整形

状態推定フィードバック閉ループシステムにおける誤差スペクトル整形

Thermus aquaticus DNA Polymerase I Mutants with Altered Fidelity: INTERACTING MUTATIONS IN THE O-HELIX

Phe(667) in the conserved O-helix of Thermus aquaticus (Taq) DNA polymerase I (pol I) is known to be important for discrimination against dideoxy-NTPs. We show here that Phe(667) is also important for base selection fidelity. In a forward mutation assay at high polymerase concentration, wild type pol I catalyzed frequent A --> T and G --> T transversions and -1 frameshifts at nonreiterated sites involving loss of a purine immediately downstream of a pyrimidine. The mutants F667L and A661E,I665T,F667L exhibited large decreases in A --> T and G --> T transversions, and the triple mutant displayed reduction in the aforementioned -1 frameshifts as well. Kinetic analysis showed that the F667L and A661E,I665T,F667L polymerases discriminated against synthesis of A:A mispairs more effectively and catalyzed less extension of A:A mispairs than the wild type enzyme. These data indicate that Phe(667) functions in maintaining the error frequency and spectrum, and the catalytic efficiency, of wild type pol I. We also found that the strong general mutator activity conferred by the single A661E substitution was entirely suppressed in the A661E, I665T,F667L polymerase, exemplifying how interactions among O-helix residues can contribute to fidelity. We discuss the mutator and anti-mutator mutations in light of recently obtained three-dimensional structures of T. aquaticus pol I.

Algebraic multi-grid method in two-dimension electrically large problems

In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is analyzed, and the reason why conjugate gradient iteration is not a good relaxation scheme for multi-grid algorithm is explored. The numerical results show that our algebraic block Gauss Seidel multi-grid algorithm is very effective.

Efficiency analysis of multihypothesis motion-compensated prediction for video coding

Overlapped block motion compensation or B-frames are examples of multihypothesis motion compensation where several motion-compensated signals are superimposed to reduce the bit-rate of a video codec. This paper extends the wide-sense stationary theory of motion-compensated prediction (MCP) for hybrid video codecs to multihypothesis motion compensation. The power spectrum of the prediction error is related to the displacement error probability density functions (pdfs) of an arbitrary number of hypotheses in a closed-form expression. We then study the influence of motion compensation accuracy on the efficiency of multihypothesis motion compensation as well as the influence of the residual noise level and the gain from optimal combination of N hypotheses. For the noise-free limiting case, doubling the number of (equally good) hypotheses can yield a gain of up to 1/2 bits/sample, while doubling the accuracy of motion compensation can additionally reduce the bit-rate by up to 1 bit/sample independent of N. For realistic noise levels, it is shown that the introduction of B-frames or overlapped block motion compensation can provide larger gains than doubling motion compensation accuracy. Spatial filtering of the motion-compensated candidate signals becomes less important if more hypotheses are combined. The critical accuracy beyond which the gain due to more accurate motion compensation is small moves to larger displacement error variances with increasing noise and increasing number of hypotheses N. Hence, sub-pel accurate motion compensation becomes less important with multihypothesis MCP. The theoretical insights are confirmed by experimental results for overlapped block motion compensation, B-frames, and multiframe motion-compensated prediction with up to eight hypotheses from ten previous frames.

Using a Broadband ADCP in a Tidal Channel. Part II: Turbulence

Abstract A four-transducer, 600-kHz, broadband acoustic Dopple current profiler (ADCP) was rigidly mounted to the bottom of a fully turbulent tidal channel with peak flows of 1 m s−1. Rapid samples of velocity data are used to estimate various parameters of turbulence with the covariance technique. The questions of bias and error sources, statistical uncertainty, and spectra are addressed. Estimates of the Reynolds stress are biased by the misalignment of the instrument axis with respect to vertical. This bias can be eliminated by a fifth transducer directed along the instrument axis. The estimates of turbulent kinetic energy (TKE) density have a systematic bias of 5 × 10−4 m2 s−2 due to Doppler noise, and the relative statistical uncertainty of the 20-min averages is usually less than 20%–95% confidence. The bias in the Reynolds stress due to Doppler noise is less than ±4 × 10−5 m2. The band of zero significance is never less than 1.5 × 10−5 m2 s−2 due to Doppler noise, and this band increases with incre...

Disturbance decoupled observer design for descriptor systems

In this paper we study the observer design problem for descriptor systems with partly unknown inputs. We give necessary and sufficient conditions for the existence of a solution to the disturbance decoupled estimation problem with or without stable error spectrum requiring at the same time that the resulting combined system is regular and of index at most one. All results are proved based on a condensed form that can be computed using orthogonal matrix transformations, i.e., transformations that can be implemented in a numerically stable way.

Spectral accuracy of Jgm3 from satellite crossover altimetry

A detailed accuracy assessment of the geopotential model Jgm3 is made based on independent single- and dual-satellite sea-height differences at crossovers from altimetry with Jgm3-based orbits. These differences, averaged over long time spans and in latitude bands, are converted to spectra (latitude-lumped coefficients) by least-squares estimation. The observed error spectra so obtained are then compared directly to error projections for them from the Jgm3 variance–covariance matrix. It is found from these comparisons that Jgm3 is generally well calibrated with respect to the crossover altimetry of and between Geosat, TOPEX/Poseidon (T/P), and Ers 1. Some significant discrepancies at a few lower orders (namely m=1 and 3) indicate a need for further improvement of Jgm3. A companion calibration (by order) of the geopotential model Jgm2 shows its variance–covariance matrix also to be generally well calibrated for the same single- and dual-satellite altimeter data sets (but based on Jgm2 orbits), except that the error projections for Geosat are too pessimistic. The analysis of the dual-satellite crossovers reveals possible relative coordinate system offsets (particularly for Geosat with respect to T/P) which have been discussed previously. The long-term detailed seasonally averaged Geosat sea level with respect to T/P (covering 1985–1996) should be useful in gauging the relative change in sea level between different parts of the ocean over the single 4-year gap between these missions (1988–1992).

Error spectrum shaping in two-dimensional recursive digital filters

This paper treats error spectrum shaping for two-dimensional recursive digital filters, described by a rational transfer function as well as the Roesser local state-space model. For each description of the filter, a technique is developed for obtaining the optimal error-feedback (EF) coefficients that minimize the noise variance at the filter output. The optimal solution can be characterized in a closed form which minimizes a quadratic form subject to constraints such as symmetry, antisymmetry, quadrantal symmetry, or quadrantal antisymmetry of the EF coefficients. In an unconstrained case, the optimal EF corresponds to a special case of the above optimal solution. Finally, two numerical examples are given to illustrate the utility of the proposed technique. In the numerical examples, the discrete sub-optimal coefficients of the EF are obtained by applying an existing procedure for the least-squares discrete-space optimization.

Efficient algebraic multigrid solvers with elementary restriction and prolongation

An algebraic multigrid (AMG) scheme is presented for the efficient solution of large systems of coupled algebraic equations involving second-order discrete differentials. It is based on elementary (zero-order) intergrid transfer operators but exhibits convergence rates that are independent of the system bandwidth. Inconsistencies in the coarse-grid approximation are minimised using a global scaling approximation which requires no explicit geometrical information. Residual components of the error spectrum that remain poorly represented in the coarse-grid approximations are reduced by exploiting Krylof subspace methods. The scheme represents a robust, simple and cost-effective approach to the problem of slowly converging eigenmodes when low-order prolongation and restriction operators are used in multigrid algorithms. The algorithm investigated here uses a generalised conjugate residual (GCR) accelerator; it might also be described as an AMG preconditioned GCR method. It is applied to two test problems, one based on a solution of a discrete Poisson-type equation for nodal pressures in a pipe network, the other based on coupled solutions to the discrete Navier-Stokes equations for flows and pressures in a driven cavity

Error spectrum shaping in 2D state‐space digital filters using error diagonal feedback

This paper discusses error spectrum shaping for 2D state-space digital filters. In order to reduce cost by reducing the total number of parameters, a method of analytic design is proposed in which the error feedback coefficient is specified by a diagonal matrix. The proposed algorithm has the feature that the optimal error feedback coefficient can be designed analytically in closed form by minimizing a quadratic form. The validity of the proposed algorithm is demonstrated with a numerical example. The noise reduction effect where the subdecimal part of the optimal coefficient is rounded by the power of 2 is also demonstrated. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 79–90, 1998

Reduction of quantization noise in the Notch Fourier transform

The paper considers the problem of quantization noise in the Notch Fourier transform (NFT). Quantization noise analysis is performed and a mixed configuration error spectrum shaping (ESS) technique is applied in order to reduce the quantization noise. The ESS structures are kept simple and efficient while effectively reducing the quantization noise.

Error spectrum shaping in 2D state-space digital filters using error diagonal feedback

This paper discusses error spectrum shaping for 2D state-space digital filters. In order to reduce cost by reducing the total number of parameters, a method of analytic design is proposed in which the error feedback coefficient is specified by a diagonal matrix. The proposed algorithm has the feature that the optimal error feedback coefficient can be designed analytically in closed form by minimizing a quadratic form. The validity of the proposed algorithm is demonstrated with a numerical example. The noise reduction effect where the subdecimal part of the optimal coefficient is rounded by the power of 2 is also demonstrated. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 79–90, 1998

The spatio-temporal structure of GPS water-vapor determinations

GPS can be used to determine the integrated precipitable water vapor (IPWV) on temporal and spatial scales that before GPS were unattainable. We investigate the spatial coherence of IPWV estimates for a trial 5-day period using estimates acquired from the Swedish permanent GPS network. We perform a modified Empirical Orthogonal Function analysis and find that over 90% of the water vapor variability is explained using the first temporal eigenvector only. Using the first eigenvectors, we calculate residual time series. We find that the error spectrum of the IPWV estimates contains no observable white noise component, possibly as a result of the stochastic filtering technique employed to obtain the estimates. These results indicate that GPS estimates of IPWV could be extremely useful for following the spatial progress of airmasses, but more work is required to be able to use these estimates for studying the detailed dynamics of turbulence in the atmosphere.

H∞ inferential filtering, prediction and smoothing problems

A new type of H ∞ optimal linear estimation problem is considered where no direct measurement of the output to be estimated is available. The optimal filter, predictor and smoother are derived for this case where outputs must be inferred from available measurements. The results cover the usual discrete time filtering problems and also optimal deconvolution estimation problems. They also apply to the situation, often found in industry, where estimates of signals are required which can only be determined from secondary measurements. An equalizing solution to the H ∞ problem is obtained, ensuring that the estimation error spectrum is determined directly by the choice of the dynamic cost-weighting function.

Generalized Polynomial H ∞ Predictive Control Utilizing Minimax Prediction

This paper presents a predictor which minimizes the cost function of the prediction error in a minimax sense, yielding minimization of the peaks of the prediction error spectrum, rather than its integral on the unit circle. This predictor is then used for the derivation of a predictive minimax control law. This one degree of freedom control law minimizes the peaks of a generalized cost function in the frequency domain. The predictor and control algorithms are derived via embedding of the minimax problem within an LQ problem using polynomial methods.

Discretization error and signal/error correlation in atmospheric data assimilation : (I). All scales resolved

Both the numerical models used in atmospheric data assimilation and the forward interpolation from the analysis mesh to the observations are subject to discretization errors. To examine the effect of these errors, a generalized Kalman filter, in which both model and observation errors are functions of the signal, is formulated. Far from the red model error spectrum assumed in many studies, the formulation yields a model error spectrum which increases with wavenumber to reach a maximum at the truncation limit. The resulting second-moment equations are studied in the context of the one-dimensional linear advection equation and, even for this simple equation, found to be quite complex. For example, it is found that signal/error correlations, not normally considered in standard Kalman filter theory, can play an important rale. Two types of (semi-Lagrangian) model discretization and two types of forward interpolation are examined in this paper. The first type uses Fourier interpolation (and has no error), while the second type uses cubic spline interpolation (and has amplitude and phase errors). To facilitate understanding of the general case, various simpler cases are considered first, e.g., the case of a uniform observation network with the same number of observations as analysis meshpoints reveals important analogies between the forward interpolation error and the model discretization error. It is found that the perfect-model assumption can result in degeneracy for any observation network when the signal/error correlation is properly accounted for. The case of a single observation (coinciding with an analysis gridpoint) strikingly illustrates the importance of the signal/error correlations and suggests that simple model error parametrization based purely on the model discretization error, and neglecting these correlations, would seriously underestimate the forecast and analysis errors. In this paper, it is assumed that the analysis mesh can resolve all scales in the signal. The effect of unresolved scales is considered in a companion paper.