Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.

A HIDDEN MARKOV MODEL FOR JOINT ESTIMATION OF GENOTYPE AND COPY NUMBER IN HIGH-THROUGHPUT SNP CHIPS

Amplifications and deletions of chromosomal DNA, as well as copy-neutral loss of heterozygosity have been associated with diseases processes. High-throughput single nucleotide polymorphism (SNP) arrays are useful for making genome-wide estimates of copy number and genotype calls. Because neighboring SNPs in high throughput SNP arrays are likely to have dependent copy number and genotype due to the underlying haplotype structure and linkage disequilibrium, hidden Markov models (HMM) may be useful for improving genotype calls and copy number estimates that do not incorporate information from nearby SNPs. We improve previous approaches that utilize a HMM framework for inference in high throughput SNP arrays by integrating copy number, genotype calls, and the corresponding confidence scores when available. Using simulated data, we demonstrate how confidence scores control smoothing in a probabilistic framework. Software for fitting HMMs to SNP array data is available in the R package ICE.

NONLINEAR TUBE-FITTING FOR THE ANALYSIS OF ANATOMICAL AND FUNCTIONAL STRUCTURES

We are concerned with the estimation of the exterior surface of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distribution in three dimensions from a sample from that distribution, possibly measured with error. We propose a novel tube-fitting algorithm to construct such estimators. Further, we conduct a simulation study to aid in the choice of a key parameter of the algorithm, and we test our algorithm with validation study tailored to the motivating data sets. Finally, we apply the tube-fitting algorithm to a colon image produced by single photon emission computed tomography (SPECT)and to a white-matter tract image produced using diffusion tensor `imaging (DTI).

Electrolysis of Molten Mixtures of Galena and Lead Chloride.

Electrolysis of molten mixtures of lead chloride and galena was carried out under various conditions of temperature, time, composition, and current densities; without a diaphram, and with various diaphrams. Continuous runs, with necessary additions of lead sulfide and lead chloride to maintain a melt of the proper composition, were attempted on a small scale.

Laboratory Model Shaking Table; An Investigation of Defects and Suggested Improvements

The laboratory model is considered in this thesis. Information gained from this investigation has not been trans­ferred to the larger industrial machines. Some of the factors noted concerning the efficiency of the laboratory shaking table are inherent in this small scale model only.

“Sweating meteorites”-Water-soluble salts and temperature variation in ordinary chondrites and soil from the hot desert of Oman

The common appearance of hygroscopic brine (“sweating”) on ordinary chondrites (OCs) from Oman during storage under room conditions initiated a study on the role of water-soluble salts on the weathering of OCs. Analyses of leachates from OCs and soils, combined with petrography of alteration features and a 11-month record of in situ meteorite and soil temperatures, are used to evaluate the role of salts in OC weathering. Main soluble ions in soils are Ca2+, SO42−, HCO3−, Na+, and Cl−, while OC leachates are dominated by Mg2+ (from meteoritic olivine), Ca2+ (from soil), Cl− (from soil), SO42− (from meteoritic troilite and soil), and iron (meteoritic). “Sweating meteorites” mainly contain Mg2+ and Cl−. The median Na/Cl mass ratio of leachates changes from 0.65 in soils to 0.07 in meteorites, indicating the precipitation of a Na-rich phase or loss of an efflorescent Na-salt. The total concentrations of water-soluble ions in bulk OCs ranges from 600 to 9000 μg g−1 (median 2500 μg g−1) as compared to 187–14140 μg g−1 in soils (median 1148 μg g−1). Soil salts dissolved by rain water are soaked up by meteorites by capillary forces. Daily heating (up to 66.3 °C) and cooling of the meteorites cause a pumping effect, resulting in a strong concentration of soluble ions in meteorites over time. The concentrations of water-soluble ions in meteorites, which are complex mixtures of ions from the soil and from oxidation and hydrolysis of meteoritic material, depend on the degree of weathering and are highest at W3. Input of soil contaminants generally dominates over the ions mobilized from meteorites. Silicate hydrolysis preferentially affects olivine and is enhanced by sulfide oxidation, producing local acidic conditions as evidenced by jarosite. Plagioclase weathering is negligible. After completion of troilite oxidation, the rate of chemical weathering slows down with continuing Ca-sulfate contamination.

Calibration of cosmogenic noble gas production in ordinary chondrites based on 36 Cl- 36 Ar ages. Part 1: Refined produced rates for cosmogenic 21 Ne and 38 Ar

We measured the concentrations and isotopic compositions of He, Ne, and Ar in bulk samples and metal separates of 14 ordinary chondrite falls with long exposure ages and high metamorphic grades. In addition, we measured concentrations of the cosmogenic radionuclides 10Be, 26Al, and 36Cl in metal separates and in the nonmagnetic fractions of the selected meteorites. Using cosmogenic 36Cl and 36Ar measured in the metal separates, we determined 36Cl-36Ar cosmic-ray exposure (CRE) ages, which are shielding-independent and therefore particularly reliable. Using the cosmogenic noble gases and radionuclides, we are able to decipher the CRE history for the studied objects. Based on the correlation 3He/21Ne versus 22Ne/21Ne, we demonstrate that, among the meteorites studied, only one suffered significant diffusive losses (about 35%). The data confirm that the linear correlation 3He/21Ne versus 22Ne/21Ne breaks down at high shielding. Using 36Cl-36Ar exposure ages and measured noble gas concentrations, we determine 21Ne and 38Ar production rates as a function of 22Ne/21Ne. The new data agree with recent model calculations for the relationship between 21Ne and 38Ar production rates and the 22Ne/21Ne ratio, which does not always provide unique shielding information. Based on the model calculations, we determine a new correlation line for 21Ne and 38Ar production rates as a function of the shielding indicator 22Ne/21Ne for H, L, and LL chondrites with preatmospheric radii less than about 65 cm. We also calculated the 10Be/21Ne and 26Al/21Ne production rate ratios for the investigated samples, which show good agreement with recent model calculations.

The abundance and isotopic composition of Cd in iron meteorites

Cadmium is a highly volatile element and its abundance in meteorites may help better understand volatility-controlled processes in the solar nebula and on meteorite parent bodies. The large thermal neutron capture cross section of 113Cd suggests that Cd isotopes might be well suited to quantify neutron fluences in extraterrestrial materials. The aims of this study were (1) to evaluate the range and magnitude of Cd concentrations in magmatic iron meteorites, and (2) to assess the potential of Cd isotopes as a neutron dosimeter for iron meteorites. Our new Cd concentration data determined by isotope dilution demonstrate that Cd concentrations in iron meteorites are significantly lower than in some previous studies. In contrast to large systematic variations in the concentration of moderately volatile elements like Ga and Ge, there is neither systematic variation in Cd concentration amongst troilites, nor amongst metal phases of different iron meteorite groups. Instead, Cd is strongly depleted in all iron meteorite groups, implying that the parent bodies accreted well above the condensation temperature of Cd (i.e., ≈650 K) and thus incorporated only minimal amounts of highly volatile elements. No Cd isotope anomalies were found, whereas Pt and W isotope anomalies for the same iron meteorite samples indicate a significant fluence of epithermal and higher energetic neutrons. This observation demonstrates that owing to the high Fe concentrations in iron meteorites, neutron capture mainly occurs at epithermal and higher energies. The combined Cd-Pt-W isotope results from this study thus demonstrate that the relative magnitude of neutron capture-induced isotope anomalies is strongly affected by the chemical composition of the irradiated material. The resulting low fluence of thermal neutrons in iron meteorites and their very low Cd concentrations make Cd isotopes unsuitable as a neutron dosimeter for iron meteorites.

OXA-48 carbapenemase-producing Salmonella enterica serovar Kentucky isolate of sequence type 198 in a patient transferred from Libya to Switzerland

Here, we report a case of OXA-48-producing Salmonella enterica serovar Kentucky of sequence type 198 (ST198) from perianal screening cultures of a patient transferred from Libya to Switzerland. The blaOXA-48 gene was carried by Tn1999.2 and located on an ∼60-kb IncL/M plasmid. This Salmonella strain also possessed the blaVEB-8, aac(6)-Ib, tet(A), sul1, and mphA resistance genes and substitutions in GyrA (Ser83Phe and Asp87Asn) and ParC (Ser80Ile). This finding emphasizes that prompt screening strategies are essential to prevent the dissemination of carbapenemase producers imported from countries where they are endemic.