Finite mixtures of matrix-variate Poisson-log normal distributions for three-way count data

Three-way data structures, characterized by three entities, the units, the variables and the occasions, are frequent in biological studies. In RNA sequencing, three-way data structures are obtained when high-throughput transcriptome sequencing data are collected for n genes across p conditions at r occasions. Matrix-variate distributions offer a natural way to model three-way data and mixtures of matrix-variate distributions can be used to cluster three-way data. Clustering of gene expression data is carried out as means to discovering gene co-expression networks. In this work, a mixture of matrix-variate Poisson-log normal distributions is proposed for clustering read counts from RNA sequencing. By considering the matrix-variate structure, full information on the conditions and occasions of the RNA sequencing dataset is simultaneously considered, and the number of covariance parameters to be estimated is reduced. A Markov chain Monte Carlo expectation-maximization algorithm is used for parameter estimation and information criteria are used for model selection. The models are applied to both real and simulated data, giving favourable clustering results

Finite Mixtures of Multivariate Poisson-Log Normal Factor Analyzers for Clustering Count Data

A mixture of multivariate Poisson-log normal factor analyzers is introduced by imposing constraints on the covariance matrix, which resulted in flexible models for clustering purposes. In particular, a class of eight parsimonious mixture models based on the mixtures of factor analyzers model are introduced. Variational Gaussian approximation is used for parameter estimation, and information criteria are used for model selection. The proposed models are explored in the context of clustering discrete data arising from RNA sequencing studies. Using real and simulated data, the models are shown to give favourable clustering performance. The GitHub R package for this work is available at https://github.com/anjalisilva/mixMPLNFA and is released under the open-source MIT license.Comment: 29 pages, 2 figure

Geometrical shape improvement of steel moulds by robot polishing process for polymer optic replication

The quality of injection-moulded polymer optic parts depends on the surface finish of the respective mould. In order to improve the surface finish of the mould, it is important to use a tactical material removal, which allows a controlled correction of the mould’s surface geometry. The aim of this work is to use a polishing correction technique to improve and correct the flatness of hardened steel samples in order to reduce the need for manual polishing. A polishing tool function is simulated from the contact between the tool and the hardened steel sample and used to determine the material removal rate per time. A feed profile is calculated, which allows the industrial robot to tactically control the material removal. It is observed that a correction improves the surface’s flatness by up to 70%

Influence of laser polishing on the material properties of aluminium L-PBF components

In this study, the influence of laser polishing on the microstructural and mechanical properties of additively manufactured aluminium AlSi10Mg Laser Powder Bed Fusion (L-PBF) parts is analysed. The investigation is carried out on a 5-axis laser cell equipped with 1D Scanner optics driven by a solid-state disc laser at a wavelength of 1030 nm. Laser polishing is performed with pulsed or continuous laser radiation on samples in the initial L-PBF state or after stress relief treatment in a furnace. The metallurgical investigation of the remelting zone with a depth of 101–237 µm revealed an unchanged and homogeneous chemical composition, with a coarsened α-phase and a changed grain structure. The hardness within the remelting zone is reduced to 102–104 HV 0.1 compared to 146 HV 0.1 at the L-PBF initial state. Below the remelting zone, within the heat affected zone, a reduced microhardness, which can reach a thickness up to 1.5 mm, occurs. Laser polishing results in a reduction in residual stresses and resulting distortions compared to the L-PBF initial state. Nevertheless, the re-solidification shrinkage of the polished surface layer introduces additional tensions, resulting in sample distortions well above ones remaining after a stress relieve heat treatment of the initial state. The mechanical properties, analysed on laser polished flat tensile specimens, revealed an increase in the ultimate elongation from 4.5% to 5.4–10.7% and a reduction in the tensile strength from 346 N/mm2 to 247–271 N/mm2 through laser polishing. Hence, the strength resulting from this is comparable to the initial L-PBF specimens after stress relieve heat treatment