Deterministic Sampling Scheme Research Articles

Faster deterministic sorting through better sampling

In this paper, a refined deterministic sampling strategy is presented. It allows to improve the performance of deterministic sample-sort algorithms to the point that they can compete with their randomized counterparts. The method is illustrated by a detailed analysis for the cases of sorting on meshes and for sorting in external memory on a single processor machine.

Fast sorting algorithms on a linear array with a reconfigurable pipelined bus system

We present two fast algorithms for sorting on a linear array with a reconfigurable pipelined bus system (LARPBS), one of the recently proposed parallel architectures based on optical buses. In our first algorithm, we sort N numbers in O(log N log log N) worst-case time using N processors. In our second algorithm, we sort N numbers in O((log log N)/sup 2/) worst-case time using N/sup 1+/spl epsi// processors, for any fixed /spl epsi/ such that 0 < /spl epsi/ < 1. Our algorithms are based on a novel deterministic sampling scheme for merging two sorted arrays of length N each in O(log log N) time on an LARPBS with N processors. To our knowledge, the previous best sorting algorithm on this architecture has a running time of O((log N)/sup 2/) using N processors.

Synthesis of digital optimal reduced-order compensators for asynchronously sampled systems

The synthesis of finite-horizon digital optimal reduced-order compensators is presented, for asynchronous and aperiodically sampled continuous-time systems. The dimensions of the compensator state are a priori fixed and may be time varying. Asynchronous and aperiodic sampling refers to a deterministic sampling scheme where an arbitrary, but a priori known, number of control variables is updated, and/or an arbitrary, but a priori known, number of outputs is sampled, at arbitrary, but a priori known, time instants. This sampling scheme generalizes most deterministic sampling schemes considered in the control literature. Through the use of an integral criterion the intersample behaviour is explicitly considered in the design. As a result, frequent, synchronous and periodic sampling is no longer necessary, which can be highly relevant in practice. Also the synthesis enables comparison of the optimal performance of reduced-order compensators as a function of their dimensions and the sampling scheme. The synthesis is illustrated with a numerical example

Synthesis of digital optimal reduced-order compensators for asynchronously sampled systems

The synthesis of finite-horizon digital optimal reduced-order compensators is presented, for asynchronous and aperiodically sampled continuous-time systems. The dimensions of the compensator state are a priori fixed and may be time varying. Asynchronous and aperiodic sampling refers to a deterministic sampling scheme where an arbitrary, but a priori known, number of control variables is updated, and/or an arbitrary, but a priori known, number of outputs is sampled, at arbitrary, but a priori known, time instants. This sampling scheme generalizes most deterministic sampling schemes considered in the control literature. Through the use of an integral criterion the intersample behaviour is explicitly considered in the design. As a result, frequent, synchronous and periodic sampling is no longer necessary, which can be highly relevant in practice. Also the synthesis enables comparison of the optimal performance of reduced-order compensators as a function of their dimensions and the sampling scheme. The synthesis is illustrated with a numerical example.

Estimating a function from ergodic samples with additive noise

We study the problem of estimating an unknown function from ergodic samples corrupted by additive noise. It is shown that one can consistently recover an unknown measurable function in this setting, if the one-dimensional (1-D) distribution of the samples is comparable to a known reference distribution, and the noise is independent of the samples and has known mixing rates. The estimates are applied to deterministic sampling schemes, in which successive samples are obtained by repeatedly applying a fixed map to a given initial vector, and it is then shown how the estimates can be used to reconstruct an ergodic transformation from one of its trajectories.

Finite sample performance of density estimators from unequally spaced data

For broad classes of deterministic and random sampling schemes { τ k }, exact mean integrated squared error (MISE) expressions for the kernel estimator of the marginal density of a first-order continuous-time autoregressive process are derived. The obtained expressions show that the effect on MISE due to both the sampling scheme and the sampling rate is significant for finite samples. The results are also extended to a case where the irregular observations are generated from a mixture of first-order continuous-time processes.

VALIDITY OF 95% t-CONFIDENCE INTERVALS UNDER SOME TRANSECT SAMPLING STRATEGIES

Soil pH data were used to assess the capture rates of 95 % t-confidence intervals based on five different transect sampling strategies. Two different sampling methods were considered, "deterministic" and "two-stage simple random sampling". The data used were pH readings at 15 and 30 centimeter depths from two local agricultural fields in the Manhattan, Kansas area. The data provided three distinct populations with three different distributions - skewed left, symmetric, and bimodal. The total number of transects randomly sampled was 2, 5, and 10. The total number of points sampled along each transect was 2, 7 and 14. The 95% t-confidence intervals were simulated 5000 times using five different transect sampling strategies, and the capture rates of the population mean were recorded. Box plots of the capture rates for the five transect sampling strategies were constructed and compared. In most cases the "deterministic" sampling method had capture rates that underestimated the 95 % confidence level, whereas the two-stage sampling strategies produced capture rates which were conservative or closer to the 95 % confidence level. The variances of the capture rates for the two-stage sampling strategies were relatively small in comparison to the deterministic sampling strategies. In conclusion, the "two-stage simple random sampling" method along with the Satterthwaite degrees of freedom are recommended when using transect sampling.

A Novel Deterministic Sampling Scheme with Applications to Broadcast-Efficient Sorting on the Reconfigurable Mesh

The main contribution of this work is to present a simple deterministic sampling strategy that, when used for bucket sorting, yields buckets that are remarkably well balanced, making costly balanci...

A Novel Deterministic Sampling Scheme with Applications to Broadcast-Efficient Sorting on the Reconfigurable Mesh

The main contribution of this work is to present a simple deterministic sampling strategy that, when used for bucket sorting, yields buckets that are remarkably well balanced, making costly balancing unnecessary. To the best of our knowledge, this is the first instance of a deterministic sampling strategy featuring this performance. Although the strategy is perfectly general, we illustrate its power by devising a VLSI-optimal,O(1) time sorting algorithm for the reconfigurable mesh. As a by-product of the inherent simplicity of our sampling and bucketing scheme, we show that our sorting algorithm can be implemented using only 35 broadcast operations, a substantial improvement over the previously best known algorithm that requires 59 broadcasts.

Probability density estimation from sampled data

For broad classes of deterministic and random sampling schemes <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{t_{k}\}</tex> we establish the consistency and asymptotic expressions for the bias and covariance of discrete-time estimates <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f̂_{n}(x)</tex> for the marginal probability density function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f(x)</tex> of continuous-time processes <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X(t)</tex> . The effect of the sampling scheme and the sampling rate on the performance of the estimates is studied. The results are established for continuous-time processes <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X(t)</tex> satisfying various asymptotic independence-uncorrelatedness conditions.

Sampling designs for the detection of signals in noise

Sampling designs for the detection of sure signals in Gaussian noise are considered. Both deterministic and random sampling schemes, using optimal and nonoptimal detectors, are presented and their performance is studied. The analytical results are supplemented by comparison of performance for small and large Sample size for some representative processes including the Gauss-Markov and Wiener processes.

Comments on "On linear sampled-data feedback systems with finite pulse width"

Certain aspects of a recent correspondence by Jury and Kan are discussed. It is pointed out that deterministic sampling schemes may be regarded as special cases of a random sampling scheme.