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.

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.

Accuracy of frozen section for the operative management of endometrial cancer

Objective To assess the accuracy of intra-operative frozen section reports at identifying the features of high risk uterine disease compared with final histopathology. Design Retrospective study. Methods The records, of 460 patients with uterine cancer registered with the Queensland Centre for Gynaecological Cancer between January 1, 1996 and December 31, 1998 were reviewed. Intra-operative frozen section was undertaken in 260 patients with endometrial adenocarcinoma. Frozen section pathology was compared with the final histopathology reports. Inter-observer reliability was assessed using percentage agreement and kappa statistics. Clinical notes were also reviewed to determine if errors resulted in sub-optimal patient care. Results Respectively, tumour grade and depth of myometrial invasion were accurately reported in 88.6% of cases (expected 61.5%, Kappa 0.70) and 94.7% (expected 53.8%, Kappa 0.89). Errors were predominantly attributable to difficulties with respect to the interpretation of tumour grade. The error resulted in the patient receiving sub-optimal surgical management in only I I cases (5.3%) Conclusion Frozen section is accurate at identifying the features of high risk uterine disease in the setting of endometrial cancer and can play an important role in directing primary operative management.

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.

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.

Comparisons between bone and cementum compositions and the possible basis for their layered appearances

In humans, age estimation from the adult skeleton represents an attempt to determine chronological age based on growth and maturational events. In teeth, such events can be characterized by appositional growth layers in midroot cementum. The purpose of this study was to determine the underlying cause of the layered microstructure of human midroot cementum. Whether cementum growth layers are caused by changes in relative mineralization, collagen packing and/or orientation, or by variations in organic matrix apposition was investigated by subjecting midroot sections of human canine teeth to analysis using polarized light and scanning electron microscopy (SEM). Polarized light was used to examine transverse midroot sections in both mineralized and demineralized states. Mineralized sections were also reexamined following subsequent decollagenization. Polarized light was additionally used in the examination of mineralized sections taken transversely, longitudinally, and obliquely from the same tooth root. From the birefringence patterns it was concluded that collagen orientation does not change with varying section plane. Instead, the mineral phase was most responsible for the birefringence of the cementum. SEM studies suggested that neither collagen packing nor collagen orientation change across the width of the cementum, confirming and validating the results of the polarized light examination. Also, SEM analysis using electron backscatter and the electron probe suggested no changes in the mean atomic number density, calcium, phosphate, and sulfur levels across the width of the cementum. Therefore, we conclude that crystalline orientation and/or size is responsible for the layered appearance of cementum. (Bone 30:386-392; 2002) (C) 2002 by Elsevier Science Inc. All rights reserved.