Suboptimal Data Research Articles

Estimating time to detect time trends in continuous cropping

Summary In long-term field trials comparing different sequences of crops and husbandry practices, the identification and understanding of trends in productivity over time is an important issue of sustainable crop production. This paper presents a statistical technique for the estimation of time trends in yield variables of a seasonal annual crop under continuous cropping. The estimation procedure incorporates the correlation structure, which is assumed to follow first-order autocorrelation in the errors that arise over time on the same plot. Because large differences in annual rainfall have a major effect on crop performance, rainfall has been allowed for in the estimation of the time trends. Expressions for the number of years (time) required to detect statistically significant time trends have been obtained. Illustrations are based on a 7-year data set of grain and straw yields from a trial in northern Syria. Although agronomic interpretation is not intended in this paper, the barley yield data indicated that a significant time trend can apparently be detected even in a suboptimal data set of 7 years' duration.

A suboptimal lossy data compression based on approximate pattern matching

A practical suboptimal (variable source coding) algorithm for lossy data compression is presented. This scheme is based on approximate string matching, and it naturally extends the lossless Lempel-Ziv (1977) data compression scheme. Among others we consider the typical length of an approximately repeated pattern within the first n positions of a stationary mixing sequence where D percent of mismatches is allowed. We prove that there exists a constant r/sub 0/(D) such that the length of such an approximately repeated pattern converges in probability to 1/r/sub 0/(D) log n (pr.) but it almost surely oscillates between 1/r/sub -/spl infin//(D) log n and 2/r/sub 1/(D) log n, where r/sub -/spl infin//(D)>r/sub 0/(D)>r/sub 1/(D)/2 are some constants. These constants are natural generalizations of Renyi entropies to the lossy environment. More importantly, we show that the compression ratio of a lossy data compression scheme based on such an approximate pattern matching is asymptotically equal to r/sub 0/(D). We also establish the asymptotic behavior of the so-called approximate waiting time N/sub l/ which is defined as the time until a pattern of length C repeats approximately for the first time. We prove that log N/sub l//l/spl rarr/r/sub 0/(D) (pr.) as l/spl rarr//spl infin/. In general, r/sub 0/(D)>R(D) where R(D) is the rate distortion function. Thus for stationary mixing sequences we settle in the negative the problem investigated by Steinberg and Gutman by showing that a lossy extension of the Wyner-Ziv (1989) scheme cannot be optimal.

安定及び不安定な力学のための近似的なデータ同化スキーム

Two suboptimal data assimilation schemes for stable and unstable dynamics are introduced. The first scheme, the partial singular value decomposition filter, is based on the most dominant singular modes of the tangent linear propagator. The second scheme, the partial eigendecomposition filter, is based on the most dominant eigenmodes of the propagated analysis error covariance matrix. Both schemes rely on iterative procedures like the Lanczos algorithm to compute the relevant modes. The performance of these schemes is evaluated for a shallow-water model linearized about an unstable Bickley jet. The results are contrasted against those of a reduced resolution filter, in which the gains used to update the state vector are calculated from a lower-dimensional dynamics than the dynamics that evolve the state itself. The results are also contrasted against the exact results given by the Kalman filter. These schemes are validated for the case of stable dynamics as well. The two new approximate assimilation schemes are shown to perform well with relatively few modes computed. Adaptive tuning of a modeled trailing error covariance for all three of these low-rank approximate schemes enhances performance and compensates for the approximation employed.

Class of fast methods for processing irregularly sampled or otherwise inhomogeneous one-dimensional data.

With the ansatz that a data set's correlation matrix has a certain parametrized from (one general enough, however, to allow the arbitrary specification of a slowly varying decorrelation distance and population variance), the general machinery of Wiener or optimal filtering can be reduced from $O({n}^{3})$ to $O(n)$ operations, where $n$ is the size of the data set. The implied vast increase in computational speed can allow many common suboptimal or heuristic data analysis methods to be replaced by fast, relatively sophisticated, statistical algorithms. Three examples are given: data rectification, high- or low-pass filtering, and linear least-squares fitting to a model with unaligned data points.

Towards Atomic Interpretation of F-Actin Filament Three-dimensional Reconstructions

We have recorded dark field images of negatively stained F-actin filaments polymerized with 2 mM MgCl2 and 50 mM KCl with a scanning transmission electron microscope and computed 3-D reconstructions using a helical parameter scarch to optimize simultaneously the helical repeat length, the radial position of the filament axis, and the helical selection rule. The resulting optimized averaged filament 3-D reconstruction at 2·5 nm resolution is remarkably similar to an atomic model of the F-actin filament. By comparison, several structural features of the reconstruction can be interpreted at the level of distinct secondary structure elements, and predictions made by the atomic model could be verified: for instance, the density connecting the two long-pitch helical strands in our reconstruction co-localizes with an extended β-hairpin, the "hydrophobic loop" (i.e. residues 262 to 274), which according to the atomic model establishes the major intersubunit contact between the two long-pitch helical strands. The most pronounced structural variations among individual filament 3-D reconstructions were observed in (1) the details of the intersubunit contact pattern between the two long-pitch helical strands, and (2) the exact size and shape of subdomain 2 of the F-actin molecule, which appears rather flexible and easily deformed. In addition, we found that all phenotypes of F-actin filament 3-D reconstructions that arise from small deviations from the optimal helical parameters or from lowering the nominal resolution exhibited stronger intersubunit contacts between than along the two-pitch helical strands, a structural feature that has been emphasized for a number of F-actin filament 3-D reconstructions in the past. Since this is clearly at variance with the relative strength of the intersubunit contacts as predicted by the atomic model, it may represent an artifactual structural feature arising from low-resolution data or suboptimal helical data processing, and should therefore be interpreted with caution in terms of indicating chemical, mechanical or conformational states of the F-actin filament.

Suboptimal joint probabilistic data association

A significant problem in multiple target tracking is the hit-to-track data association. A hit is a received signal from a target or background clutter which provides positional information. If an incorrect hit is associated with a track, that track could diverge and terminate. Prior methods for this data association problem include various optimal and suboptimal two-dimensional assignment algorithms which make hit-to-track associations. Another method is to assign a weight for the reasonable hits and use a weighted centroid of those hits to update the track. The method of weighting the hits is known as joint probabilistic data association (JPDA). The authors review the JPDA approach and a simple ad hoc approximation and then introduce a new suboptimal JPDA algorithm. Examples which compare an optimal two-dimensional assignment algorithm with the ad hoc and the new suboptimal JPDA formulation are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Remote sensing in land-use planning: an application in west central Scotland using SPOT-simulation data

Abstract The urban fringe area is often characterized by a conflict between competing demands for land from many types of development; thus it requires active planning to achieve a landscape compatible with green-belt designation. Data were obtained from the NRSC SPOT-simulation campaign for an area near eastern Glasgow in an exercise to assess the value of remotely sensed data for surveying the structure of this urban fringe area. Digital enhancement and classification methods were applied to the data, identifying eight rural and six urban land-cover classes. Cloud and cloud shadow prevented a statistical accuracy assessment being performed. The most useful results were obtained by first stratifying the area into urban and rural subdivisions, followed by an interactive classification approach to the training and classification of desired fringe classes involving an analyst with local knowledge. Results showed that important urbanfringe classes of land cover can be readily identified from SPOT data, but the 20 m resolution is insufficient to discriminate inner city detail. These interim conclusions using suboptimal simulation data imply that high-resolution satellite data, rectified to a map base, classified and accuracy assessed, can be used as a survey tool to aid the physical planning of urban-fringe areas.

Improving the Reliability of Catchment Mass Input: Output Estimations from Sub-Optimal Data in Areas of Urban Growth

A new mass input:output formula is presented which makes full use of available data which are commonly sub-optimal for mass input:output analysis. Results indicate that some useful information on wet and dry fallout may be obtained from bulk precipitation data only, and that the new formula provides generally more reliable results for catchment chemical mass export under various conditions than other simpler formulae. Care is taken not to assume rates of natural denudation from the results in the light of an inability clearly to separate non-denudational from denudational components of mass export, and natural from man-induced components of denudation.