Optimal input states and feedback for interferometric phase estimation

We derive optimal N-photon two-mode input states for interferometric phase measurements. Under canonical measurements the phase variance scales as N-2 for these states, as compared to N-1 or N-1/2 for states considered bq previous authors. We prove, that it is not possible to realize the canonical measurement by counting photons in the outputs of the interferometer, even if an adjustable auxiliary phase shift is allowed in the interferometer. However. we introduce a feedback algorithm based on Bayesian inference to control this auxiliary phase shift. This makes the measurement close to a canonical one, with a phase variance scaling slightly above N-2. With no feedback, the best result (given that the phase to be measured is completely unknown) is a scaling of N-1. For optimal input states having up to four photons, our feedback scheme is the best possible one, but for higher photon numbers more complicated schemes perform marginally better.

The effect of channel geometry and wall boundary conditions on the formation of extrusion surface instabilities for LLDPE

It is believed that surface instabilities can occur during the extrusion of linear low density polyethylene due to high extensional stresses at the exit of the die. Local crack development can occur at a critical stress level when melt rupture is reached. This high extensional stress results from the rearrangement of the flow at the boundary transition between the wall exit and the free surface. The stress is highest at the extrudate surface and decreases into the bulk of the material. The location of the region where the critical level is reached can determine the amplitude of the extrudate surface distortion, This paper studies the effect of wall slip on the numerically simulated extensional stress level at the die exit and correlates this to the experimentally determined amplitude of the surface instability. The effect of die exit radius and die wall roughness on extrusion surface instabilities is also correlated to the exit stress level in the same way. Whereas full slip may completely suppress the surface instability, a reduction in the exit stress level and instability amplitude is also shown for a rounded die exit and a slight increase in instability is shown to result from a rough die wall. A surface instability map demonstrates how the shear rate for onset of extrusion surface instabilities can be predicted on the basis of melt strength measurements and simulated stress peaks at the exit of the die. (C) 2001 Elsevier Science B.V. All rights reserved.

Sonographic estimation of fetal weight in macrosomic fetuses: diabetic versus non-diabetic pregnancies

The objective of this study is to compare the accuracy of sonographic estimation of fetal weight of macrosomic babies in diabetic vs non-diabetic pregnancies. Ali babies weighing 4000 g or more at birth, and who had ultrasound scans performed within one week of delivery were included in this retrospective study. Pregnancies with diabetes mellitus were compared to those without diabetes mellitus. The mean simple error (actual birthweight - estimated fetal weight); mean standardised absolute error (absolute value of simple error (g)/actual birthweight (kg)); and the percentage of estimated birthweight falling within 15% of the actual birthweight between the two groups were compared. There were 9516 deliveries during the study period. Of this total 1211 (12.7 %) babies weighed 4000 g or more. A total of 56 non-diabetic pregnancies and 19 diabetic pregnancies were compared. The average sonographic estimation of fetal weight in diabetic pregnancies was 8 % less than the actual birthweight, compared to 0.2 % in the non-diabetic group (p < 0.01). The estimated fetal weight was within 15% of the birthweight in 74 % of the diabetic pregnancies, compared to 93 % of the non-diabetic pregnancies (p < 0.05). In the diabetic group, 26.3 % of the birthweights were underestimated by more than 15 %, compared to 5.4 % in the non-diabetic group (p < 0.05). In conclusion, the prediction accuracy of fetal weight estimation using standard formulae in macrosomic fetuses is significantly worse in diabetic pregnancies compared to non-diabetic pregnancies. When sonographic fetal weight estimation is used to influence the mode of delivery for diabetic women, a more conservative cut-off needs to be considered.

Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data

Binning and truncation of data are common in data analysis and machine learning. This paper addresses the problem of fitting mixture densities to multivariate binned and truncated data. The EM approach proposed by McLachlan and Jones (Biometrics, 44: 2, 571-578, 1988) for the univariate case is generalized to multivariate measurements. The multivariate solution requires the evaluation of multidimensional integrals over each bin at each iteration of the EM procedure. Naive implementation of the procedure can lead to computationally inefficient results. To reduce the computational cost a number of straightforward numerical techniques are proposed. Results on simulated data indicate that the proposed methods can achieve significant computational gains with no loss in the accuracy of the final parameter estimates. Furthermore, experimental results suggest that with a sufficient number of bins and data points it is possible to estimate the true underlying density almost as well as if the data were not binned. The paper concludes with a brief description of an application of this approach to diagnosis of iron deficiency anemia, in the context of binned and truncated bivariate measurements of volume and hemoglobin concentration from an individual's red blood cells.

Atom lasers, coherent states, and coherence II. Maximally robust ensembles of pure states

As discussed in the preceding paper [Wiseman and Vaccaro, preceding paper, Phys. Rev. A 65, 043605 (2002)], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of rho(ss) as a stationary ensemble of pure states, is more natural. In the preceding paper we concentrated upon the question of whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy chi of the bosons in the laser mode, and the excess phase noise nu. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit (nu=chi=0), the most robust states are coherent states. As the phase noise or phase dispersion is increased through nu or the self-interaction of the bosons chi, respectively, the most robust states become more and more amplitude squeezed. We find scaling laws for these states, and give analytical derivations for them. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR ensemble being an ensemble of states with a well-defined coherent amplitude. This lends support to our approach of regarding robust PR ensembles as the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.

Influence of wall stress and left ventricular geometry on the accuracy of Dobutamine stress Echocardiography

OBJECTIVES The goal of this study was to determine whether wall stress at rest and during stress could explain the influence of left ventricular (LV) morphology on the accuracy of dobutamine stress echocardiography (DSE). BACKGROUND The sensitivity of DSE appears to be reduced in patients with concentric remodeling, but the cause of this finding is unclear. METHODS We studied 161 patients without resting wall motion abnormalities who underwent DSE and coronary angiography. Patients were classified into four groups according to relative wan thickness (normal

The impact of genotyping error on haplotype reconstruction and frequency estimation

The choice of genotyping families vs unrelated individuals is a critical factor in any large-scale linkage disequilibrium (LD) study. The use of unrelated individuals for such studies is promising, but in contrast to family designs, unrelated samples do not facilitate detection of genotyping errors, which have been shown to be of great importance for LD and linkage studies and may be even more important in genotyping collaborations across laboratories. Here we employ some of the most commonly-used analysis methods to examine the relative accuracy of haplotype estimation using families vs unrelateds in the presence of genotyping error. The results suggest that even slight amounts of genotyping error can significantly decrease haplotype frequency and reconstruction accuracy, that the ability to detect such errors in large families is essential when the number/complexity of haplotypes is high (low LD/common alleles). In contrast, in situations of low haplotype complexity (high LD and/or many rare alleles) unrelated individuals offer such a high degree of accuracy that there is little reason for less efficient family designs. Moreover, parent-child trios, which comprise the most popular family design and the most efficient in terms of the number of founder chromosomes per genotype but which contain little information for error detection, offer little or no gain over unrelated samples in nearly all cases, and thus do not seem a useful sampling compromise between unrelated individuals and large families. The implications of these results are discussed in the context of large-scale LD mapping projects such as the proposed genome-wide haplotype map.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

Estimation of total body water from bioelectrical impedance analysis in patients with pancreatic cancer - agreement between three methods of prediction

Introduction Bioelectrical impedance analysis (BIA) is a useful field measure to estimate total body water (TBW). No prediction formulae have been developed or validated against a reference method in patients with pancreatic cancer. The aim of this study was to assess the agreement between three prediction equations for the estimation of TBW in cachectic patients with pancreatic cancer. Methods Resistance was measured at frequencies of 50 and 200 kHz in 18 outpatients (10 males and eight females, age 70.2 +/- 11.8 years) with pancreatic cancer from two tertiary Australian hospitals. Three published prediction formulae were used to calculate TBW - TBWs developed in surgical patients, TBWca-uw and TBWca-nw developed in underweight and normal weight patients with end-stage cancer. Results There was no significant difference in the TBW estimated by the three prediction equations - TBWs 32.9 +/- 8.3 L, TBWca-nw 36.3 +/- 7.4 L, TBWca-uw 34.6 +/- 7.6 L. At a population level, there is agreement between prediction of TBW in patients with pancreatic cancer estimated from the three equations. The best combination of low bias and narrow limits of agreement was observed when TBW was estimated from the equation developed in the underweight cancer patients relative to the normal weight cancer patients. When no established BIA prediction equation exists, practitioners should utilize an equation developed in a population with similar critical characteristics such as diagnosis, weight loss, body mass index and/or age. Conclusions Further research is required to determine the accuracy of the BIA prediction technique against a reference method in patients with pancreatic cancer.

On the robustness of short-term interest rate models

This paper investigates the robustness of a range of short–term interest rate models. We examine the robustness of these models over different data sets, time periods, sampling frequencies, and estimation techniques. We examine a range of popular one–factor models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find that parameter estimates are highly sensitive to all of these factors in the eight countries that we examine. Since parameter estimates are not robust, these models should be used with caution in practice.

Critical comparison of Julius Kruttschnitt Mineral Research Centre (JKMRC) blast fragmentation models

Blast fragmentation can have a significant impact on the profitability of a mine. An optimum run of mine (ROM) size distribution is required to maximise the performance of downstream processes. If this fragmentation size distribution can be modelled and controlled, the operation will have made a significant advancement towards improving its performance. Blast fragmentation modelling is an important step in Mine to Mill™ optimisation. It allows the estimation of blast fragmentation distributions for a number of different rock mass, blast geometry, and explosive parameters. These distributions can then be modelled in downstream mining and milling processes to determine the optimum blast design. When a blast hole is detonated rock breakage occurs in two different stress regions - compressive and tensile. In the-first region, compressive stress waves form a 'crushed zone' directly adjacent to the blast hole. The second region, termed the 'cracked zone', occurs outside the crush one. The widely used Kuz-Ram model does not recognise these two blast regions. In the Kuz-Ram model the mean fragment size from the blast is approximated and is then used to estimate the remaining size distribution. Experience has shown that this model predicts the coarse end reasonably accurately, but it can significantly underestimate the amount of fines generated. As part of the Australian Mineral Industries Research Association (AMIRA) P483A Mine to Mill™ project, the Two-Component Model (TCM) and Crush Zone Model (CZM), developed by the Julius Kruttschnitt Mineral Research Centre (JKMRC), were compared and evaluated to measured ROM fragmentation distributions. An important criteria for this comparison was the variation of model results from measured ROM in the-fine to intermediate section (1-100 mm) of the fragmentation curve. This region of the distribution is important for Mine to Mill™ optimisation. The comparison of modelled and Split ROM fragmentation distributions has been conducted in harder ores (UCS greater than 80 MPa). Further work involves modelling softer ores. The comparisons will be continued with future site surveys to increase confidence in the comparison of the CZM and TCM to Split results. Stochastic fragmentation modelling will then be conducted to take into account variation of input parameters. A window of possible fragmentation distributions can be compared to those obtained by Split . Following this work, an improved fragmentation model will be developed in response to these findings.