On the counting function of the lattice profile of periodic sequences

The lattice profile analyzes the intrinsic structure of pseudorandom number sequences with applications in Monte Carlo methods and cryptology. In this paper, using the discrete Fourier transform for periodic sequences and the relation between the lattice profile and the linear complexity, we give general formulas for the expected value, variance, and counting function of the lattice profile of periodic sequences with fixed period. Moreover, we determine in a more explicit form the expected value, variance, and counting function of the lattice profile of periodic sequences for special values of the period.     

A mathematical analysis of a fish school model

A model proposed in the literature for fish schools of relatively large size is studied for mathematical and qualitative properties. Existence, uniqueness and positivity of solutions are established and bifurcation properties relative to diffusion and alignment parameters are studied.     

Tests of ordered hypotheses in linkage in heredity

The asymptotic null distribution of the likelihood ratio test for two cases of ordered hypotheses in a particular genetic model is considered. A simple iterative process is proposed in order to get the restricted estimates. It is shown that both tests have asymptotically a chi-bar squared distribution and the same size. A simulation study is also conducted in order to compare the usual unrestricted test with the corresponding one of ordered hypotheses. Finally, the results are extended to some special cases.     

Quality evaluation of fingerprints of herbal medicine with chromatographic data

In this study, local least squares (LLS) and principal component analysis (PCA) were applied to deal with the disturbances in a data set of chromatographic fingerprints after necessary data transformations. It has been demonstrated that PCA with standard normal variate (SNV) transformation of data led to meaningful classification of 33 different Erigeron breviscapus herbal samples. The result was also corroborated by variance squares discriminant method. The quality of herbal objects was further evaluated, and the causes of this fact have been explained from a chemical point of view. At the same time, it implied an idea for qualitative evaluation of the herbal objects with a common class pattern of chromatographic fingerprints.     

Influence of two grinding methods on the uncertainty of determinations of heavy metals in atomic absorption spectrometry/electrothermal atomisation of plant samples

 Chemical analyses of trace elements are affected by relatively high analytical errors due to the different steps of the laboratory procedures: samples grinding, mineralisation and instrumental measurements. In the present communication, the influence of the grinding phase on the global uncertainty of Pb, Cd, Ni and Cr determinations in plant samples by the classical method of atomic absorption spectrometry/electrothermal atomisation (AAS-ETA) after dry ashing is quantified. Two grinding machines, a planetary mill with balls and jars of agate versus a stainless steel grinder were compared by analysing leaf samples of cucumber, strawberry, kiwivines, apple trees and grapevines from agricultural experimental plots under controlled conditions. Variance components due to the difference between grinding methods and experimental plots were estimated. Further, the simultaneous effects of the grinding methods on all considered metals have been evaluated by analysis of variance. With the stainless steel grinder, on average, higher levels of the considered heavy metals were obtained (up to 67% of the mean values). On average, the increments were similar for metals contained in steel (Ni and Cr) and those not contained (Pb and Cd). The true causes of these differences need further investigation to determine whether the higher metal detection is due to possible contamination, to a different grinding quality or to other reasons. Finally, the grinding methods did not seem to affect the combined uncertainty of the analyses. Received: 3 November 1997 · Accepted: 29 November 1997     

On the statistical independence of various column contributions to band broadening. Part 1: Second moment contributions from statistically independent,longitudinal diffusion in both phases

The total length-based second moment contribution from longitudinal sample diffusion in both phases on a column, σD , is derived by adding individual partial differential contributions to a partial differential equation accounting for the longitudinal diffusion processes only. Although each diffusion-dispersed sample part is equilibrated between two phases, the resulting σ,D (= 2D _mt _m + 2D _st _s) can be interpreted as the sum of two independent contributions in accordance with the variance addition rule. (D _m and D _s are the mean diffusion coefficients and t _mand t _s the mean residence times of the sample in the mobile and stationary phases, respectively.) The same σD expression is derived from the random walk model of Giddings by treating the diffusional process in each phase as statistically independent of the other processes. Under these conditions the broadening contribution from longitudinal diffusion in the mobile phase is shown to be independent of the velocity profile.     

Maximum likelihood estimation for second level fMRI data analysis with expectation trust region algorithm

The trust region method which originated from the Levenberg–Marquardt (LM) algorithm for mixed effect model estimation are considered in the context of second level functional magnetic resonance imaging (fMRI) data analysis. We first present the mathematical and optimization details of the method for the mixed effect model analysis, then we compare the proposed methods with the conventional expectation-maximization (EM) algorithm based on a series of datasets (synthetic and real human fMRI datasets). From simulation studies, we found a higher damping factor for the LM algorithm is better than lower damping factor for the fMRI data analysis. More importantly, in most cases, the expectation trust region algorithm is superior to the EM algorithm in terms of accuracy if the random effect variance is large. We also compare these algorithms on real human datasets which comprise repeated measures of fMRI in phased-encoded and random block experiment designs. We observed that the proposed method is faster in computation and robust to Gaussian noise for the fMRI analysis. The advantages and limitations of the suggested methods are discussed.     

Large sample prediction intervals for future geometric mean a comparative study

This paper provides simulation comparisons among the performance of 11 possible prediction intervals for the geometric.mean of a Pareto distribution with parameters (αB, ). Six different procedures were used to obtain these intervals , namely; true inter -val , pivotal interval , maximum likelihood estimation interval, centrallimit teorem interval, variance stabilizing interval and a mixture of the above intervals . Some of these intervals are valid if the observed sample size m,are large , others are valid if both, n and the future sample size m, are large. Some of these intervals require a knowledge of α or B, while others do not. The simulation validation and efficiency study shows that intervals depending on the MLE's are the best. The second best intervalsare those obtained through pivotal methods or variance stabilization transformation. The third group of intervals is that which depends on the central limit theorem when λ is known. There are two intervals which proved to be unacceptable under any criterion.     

Efficient unbiased variance reduction techniques for Monte Carlo simulations of radiative transfer in cloudy atmospheres: The solution

We present five new variance reduction techniques applicable to Monte Carlo simulations of radiative transfer in the atmosphere: detector directional importance sampling, n-tuple local estimate, prediction-based splitting and Russian roulette, and circum-solar virtual importance sampling. With this set of methods it is possible to simulate remote sensing instruments accurately and quickly. In contrast to all other known techniques used to accelerate Monte Carlo simulations in cloudy atmospheres - except for two methods limited to narrow angle lidars - the presented methods do not make any approximations, and hence do not bias the result. Nevertheless, these methods converge as quickly as any of the biasing acceleration techniques, and the probability distribution of the simulation results is almost perfectly normal. The presented variance reduction techniques have been implemented into the Monte Carlo code MYSTIC (“Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres”) in order to validate the techniques.     

Noise Stability of SIS Receivers

There is a strong interest in the submillimeter astronomy community to increase the IF bandwidth of SIS receivers in order to better facilitate broad spectral linewidth and continuum observations of extragalactic sources. However, with an increase in receiver IF bandwidth there is a decrease in the mixer stability. This in turn effects the integration efficiency and quality of the measurement. In order to better understand the noise mechanisms responsible for reducing the receiver stability, we employed a technique first described by D.W. Allan and later elaborated upon by Schieder et al. In this paper we address a variety of factors that degrade the noise stability of SIS receivers. The goal of this exercise is to make recommendations aimed at maximizing SIS receiver stability.