Overfitting Bayesian mixture models with an unknown number of components

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.

Pole placement in multi-input systems via elementary transformations

This paper is concerned with the development of an algorithm for pole placement in multi-input dynamic systems. The algorithm which uses a series of elementary transformations is believed to be simpler, computationally more efficient and numerically stable when compared with earlier methods. In this paper two methods have been presented.

A systems evaluation of high-input management using fortified molasses for beef production in Australia's dry tropics

The potential of beef producers to profitably produce 500-kg steers at 2.5 years of age in northern Australia's dry tropics to meet specifications of high-value markets, using a high-input management (HIM) system was examined. HIM included targeted high levels of fortified molasses supplementation, short seasonal mating and the use of growth promotants. Using herds of 300-400 females plus steer progeny at three sites, HIM was compared at a business level to prevailing best-practice, strategic low-input management (SLIM) in which there is a relatively low usage of energy concentrates to supplement pasture intake. The data presented for each breeding-age cohort within management system at each site includes: annual pregnancy rates (range: 14-99%), time of conception, mortalities (range: 0-10%), progeny losses between confirmed pregnancy and weaning (range: 0-29%), and weaning rates (range: 14-92%) over the 2-year observation. Annual changes in weight and relative net worth were calculated for all breeding and non-breeding cohorts. Reasons for outcomes are discussed. Compared with SLIM herds, both weaning weights and annual growth were >= 30 kg higher, enabling 86-100% of HIM steers to exceed 500 kg at 2.5 years of age. Very few contemporary SLIM steers reached this target. HIM was most profitably applied to steers. Where HIM was able to achieve high pregnancy rates in yearlings, its application was recommended in females. Well managed, appropriate HIM systems increased profits by around $15/adult equivalent at prevailing beef and supplement prices. However, a 20% supplement price rise without a commensurate increase in values for young slaughter steers would generally eliminate this advantage. This study demonstrated the complexity of pro. table application of research outcomes to commercial business, even when component research suggests that specific strategies may increase growth and reproductive efficiency and/or be more pro. table. Because of the higher level of management required, higher costs and returns, and higher susceptibility to market changes and disease, HIM systems should only be applied after SLIM systems are well developed. To increase profitability, any strategy must ultimately either increase steer growth and sale values and/or enable a shift to high pregnancy rates in yearling heifers.

Pole placement in multi-input systems via elementary transformations

This paper is concerned with the development of an algorithm for pole placement in multi-input dynamic systems. The algorithm which uses a series of elementary transformations is believed to be simpler, computationally more efficient and numerically stable when compared with earlier methods. In this paper two methods have been presented.

Adolf and Henny Molling nee Meyerhof with Benno Molling's wife Sophie Molling nee Reuben and an unknown woman; Bad Nauheim, Germany.

Postcard written to Therese Gottschalk nee Molling at Norderney

Elizabeth Krakauer nee Gottschalk in an unknown early Krakauer apartment.

Digital Image

Portrait of Unknown Woman 1029884

Digital Image

Fisheries Queensland Long Term Monitoring Program Underwater Visual Census of twenty-four reefs on the Great Barrier Reef between 1999 and 2004.

In 1999, the Department of Employment, Economic Development and Innovation (DEEDI), Fisheries Queensland undertook a new initiative to collect long term monitoring data of various important stocks including reef fish. This data and monitoring manual for the reef fish component of that program which was based on Underwater Visual Census methodology of 24 reefs on the Great Barrier Reef between 1999 and 2004. Data was collected using six 50m x 5m transects at 4 sites on 24 reefs. Benthic cover type was also recorded for 10m of each transect. The attached Access Database contains 5 tables being: SITE DETAILS TABLE Survey year Data entry complete REF survey site ID Site # (1-4) Location (reef name) Site Date (date surveyed) Observer 1 (3 initials to identify who estimated fish lengths and recorded benthic cover) TRANSECT DETAILS Survey ID Transect Number (1-6) Time (the transect was surveyed) Visibility (in metres) Minimum Depth surveyed (m) Maximum Depth surveyed (m) Percent of survey completed (%) Comments SUBSTRATE Survey ID Transect Number (1-6) then % cover of each of eth following categories of benthic cover types Dead Coral Live Coral Soft Coral Rubble Sand Sponge Algae Sea Grass Other COORDINATES (over survey sites) from -14 38.792 to -19 44.233 and from 145 21.507 to 149 55.515 SIGHTINGS ID Survey ID Transect Number (1-6) CAAB Code Scientific Name Reef Fish Length (estimated Fork Length of fish; -1 = unknown or not recorded) Outside Transect (if a fish was observed outside a transect -1 was recorded) Morph Code (F = footballer morph for Plectropomus laevis, S = Spawning colour morph displayed)

Enhancing economic input to the CQSS2 Project report. Commissioned by the Fitzroy Basin Association.

The Fitzroy Basin is the second largest catchment area in Australia covering 143,00 km² and is the largest catchment for the Great Barrier Reef lagoon (Karfs et al., 2009). The Great Barrier Reef is the largest reef system in the world; it covers an area of approximately 225,000 km² in the northern Queensland continental shelf. There are approximately 750 reefs that exist within 40 km of the Queensland Coast (Haynes et al., 2007). The prime determinant for the changes in water quality have been attributed to grazing, with beef production the largest single land use industry comprising 90% of the land area (Karfs et al., 2009). In response to the depletion of water quality in the reef, in 2003 a Reef Water Quality plan was developed by the Australian and Queensland governments. The plan targets as a priority sediment contributions from grazing cattle in high risk catchments (The State of Queensland and Commonwealth of Australia, 2003). The economic incentive strategy designed includes analysing the costs and benefits of best management practice that will lead to improved water quality (The State of Queensland and Commonwealth of Australia, 2003).

Adolf and Henny Molling nee Meyerhof with Benno Molling's wife Sophie Molling nee Reuben and an unknown woman; Bad Nauheim, Germany.

Postcard written to Therese Gottschalk nee Molling at Norderney

Elizabeth Krakauer nee Gottschalk in an unknown early Krakauer apartment.

Digital Image

The Significance of Wild Plants in the Evolutionary Ecology of Three Major Viruses Infecting Cultivated Sweetpotato in Uganda

The studies presented in this thesis contribute to the understanding of evolutionary ecology of three major viruses threatening cultivated sweetpotato (Ipomoea batatas Lam) in East Africa: Sweet potato feathery mottle virus (SPFMV; genus Potyvirus; Potyviridae), Sweet potato chlorotic stunt virus (SPCSV; genus Crinivirus; Closteroviridae) and Sweet potato mild mottle virus (SPMMV; genus Ipomovirus; Potyviridae). The viruses were serologically detected and the positive results confirmed by RT-PCR and sequencing. SPFMV was detected in 24 wild plant species of family Convolvulacea (genera Ipomoea, Lepistemon and Hewittia), of which 19 species were new natural hosts for SPFMV. SPMMV and SPCSV were detected in wild plants belonging to 21 and 12 species (genera Ipomoea, Lepistemon and Hewittia), respectively, all of which were previously unknown to be natural hosts of these viruses. SPFMV was the most abundant virus being detected in 17% of the plants, while SPMMV and SPCSV were detected in 9.8% and 5.4% of the assessed plants, respectively. Wild plants in Uganda were infected with the East African (EA), common (C), and the ordinary (O) strains, or co-infected with the EA and the C strain of SPFMV. The viruses and virus-like diseases were more frequent in the eastern agro-ecological zone than the western and central zones, which contrasted with known incidences of these viruses in sweetpotato crops, except for northern zone where incidences were lowest in wild plants as in sweetpotato. The NIb/CP junction in SPMMV was determined experimentally which facilitated CP-based phylogenetic and evolutionary analyses of SPMMV. Isolates of all the three viruses from wild plants were genetically similar to those found in cultivated sweetpotatoes in East Africa. There was no evidence of host-driven population genetic structures suggesting frequent transmission of these viruses between their wild and cultivated hosts. The p22 RNA silencing suppressor-encoding sequence was absent in a few SPCSV isolates, but regardless of this, SPCSV isolates incited sweet potato virus disease (SPVD) in sweetpotato plants co-infected with SPFMV, indicating that p22 is redundant for synergism between SCSV and SPFMV. Molecular evolutionary analysis revealed that isolates of strain EA of SPFMV that is largely restricted geographically in East Africa experience frequent recombination in comparison to isolates of strain C that is globally distributed. Moreover, non-homologous recombination events between strains EA and C were rare, despite frequent co-infections of these strains in wild plants, suggesting purifying selection against non-homologous recombinants between these strains or that such recombinants are mostly not infectious. Recombination was detected also in the 5 - and 3 -proximal regions of the SPMMV genome providing the first evidence of recombination in genus Ipomovirus, but no recombination events were detected in the characterized genomic regions of SPCSV. Strong purifying selection was implicated on evolution of majority of amino acids of the proteins encoded by the analyzed genomic regions of SPFMV, SPMMV and SPCSV. However, positive selection was predicted on 17 amino acids distributed over the whole the coat protein (CP) in the globally distributed strain C, as compared to only 4 amino acids in the multifunctional CP N-terminus (CP-NT) of strain EA largely restricted geographically to East Africa. A few amino acid sites in the N-terminus of SPMMV P1, the p7 protein and RNA silencing suppressor proteins p22 and RNase3 of SPCSV were also submitted to positive selection. Positively selected amino acids may constitute ligand-binding domains that determine interactions with plant host and/or insect vector factors. The P1 proteinase of SPMMV (genus Ipomovirus) seems to respond to needs of adaptation, which was not observed with the helper component proteinase (HC-Pro) of SPMMV, although the HC-Pro is responsible for many important molecular interactions in genus Potyvirus. Because the centre of origin of cultivated sweetpotato is in the Americas from where the crop was dispersed to other continents in recent history (except for the Australasia and South Pacific region), it would be expected that identical viruses and their strains occur worldwide, presuming virus dispersal with the host. Apparently, this seems not to be the case with SPMMV, the strain EA of SPFMV and the strain EA of SPCSV that are largely geographically confined in East Africa where they are predominant and occur both in natural and agro-ecosystems. The geographical distribution of plant viruses is constrained more by virus-vector relations than by virus-host interactions, which in accordance of the wide range of natural host species and the geographical confinement to East Africa suggest that these viruses existed in East African wild plants before the introduction of sweetpotato. Subsequently, these studies provide compelling evidence that East Africa constitutes a cradle of SPFMV strain EA, SPCSV strain EA, and SPMMV. Therefore, sweet potato virus disease (SPVD) in East Africa may be one of the examples of damaging virus diseases resulting from exchange of viruses between introduced crops and indigenous wild plant species. Keywords: Convolvulaceae, East Africa, epidemiology, evolution, genetic variability, Ipomoea, recombination, SPCSV, SPFMV, SPMMV, selection pressure, sweetpotato, wild plant species Author s Address: Arthur K. Tugume, Department of Agricultural Sciences, Faculty of Agriculture and Forestry, University of Helsinki, Latokartanonkaari 7, P.O Box 27, FIN-00014, Helsinki, Finland. Email: tugume.arthur@helsinki.fi Author s Present Address: Arthur K. Tugume, Department of Botany, Faculty of Science, Makerere University, P.O. Box 7062, Kampala, Uganda. Email: aktugume@botany.mak.ac.ug, tugumeka@yahoo.com

On the Fourier refinement of protein structures

The situation normally encountered in the high-resolution refinement of protein structures is one in which the inaccurate positions of P out of a total of N atoms are known whereas those of the remaining atoms are unknown. Fourier maps with coefficients (FN -- F'P) × exp (i[alpha]'P) and (mFN -- nF'P) exp (i[alpha]'P), where FN is the observed structure factor and F'P and [alpha]'P are the magnitude and the phase angle of the calculated structure factor corresponding to the inaccurate atomic positions, are often used to correct the positions of the P atoms and to determine those of the Q unknown atoms. A general theoretical approach is presented to elucidate the effect of errors in the positions of the known atoms on the corrected positions of the known atoms and the positions of the unknown atoms derived from such maps. The theory also leads to the optimal choice of parameters used in the different syntheses. When the errors in the positions of the input atoms are systematic, their effects are not taken care of automatically by the syntheses.

Stabilization of linear and nonlinear dynamical systems using an observer-controller configuration

In this paper the problem of stabilization of systems by means of stable compensations is considered, and results are derived for systems using observer�controller structures, for systems using a cascade structure, and for nonlinear systems

Non-linear response of a gyrostabilized platform to transient input

In this paper the response of a gyrostabilized platform subjected to a transient torque has been analyzed by deliberately introducing non-linearity into the command of the servomotor. The resulting third-order non-linear differential equation has been solved by using a transformation technique involving the displacement variable. The condition under which platform oscillations may grow with time or die with time are important from the point of view of platform stabilization. The effect of deliberate addition of non-linearity with a view to achieving the ideal response—that is, to bring the platform back to its equilibrium position with as few oscillations as possible—has been investigated. The conditions under which instability may set in on account of the small transient input and small non-linearity has also been discussed. The analysis is illustrated by means of a numerical example. The results of analysis are compared with numerical solutions obtained on a digital computer.