SUMMARYA new variant ' P M F of factor analysis is described. It is assumed that X is a matrix of observed data and u is the known matrix of standard deviations of elements of X. Both X and u are of dimensions n x m. The method solves the bilinear matrix problem X = GF + E where G is the unknown left hand factor matrix (scores) of dimensions n x p , F is the unknown right hand factor matrix (loadings) of dimensions p x m, and E is the matrix of residuals. The problem is solved in the weighted least squares sense: G and F are determined so that the Frobenius norm of E divided (element-by-element) by u is minimized. Furthermore, the solution is constrained so that all the elements of G and F are required to be non-negative. It is shown that the solutions by PMF are usually different from any solutions produced by the customary factor analysis (FA, i.e. principal component analysis (PCA) followed by rotations). Usually PMF produces a better fit to the data than FA. Also, the result of P F is guaranteed to be non-negative, while the result of FA often cannot be rotated so that all negative entries would be eliminated. Different possible application areas of the new method are briefly discussed. In environmental data, the error estimates of data can be widely varying and non-negativity is often an essential feature of the underlying models. Thus it is concluded that PMF is better suited than FA or PCA in many environmental applications. Examples of successful applications of PMF are shown in companion papers.

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Microfibrillated cellulose (MFC), also referred to as nanocellulose, is one of the most promising innovations for forest sector. MFC is produced by fibrillating the fibres under high compression and shear forces. In this study we evaluated the worker exposures to particles in air during grinding and spray drying of birch cellulose. Processing of MFC with either a friction grinder or a spray dryer did not cause significant exposure to particles during normal operation. Grinding generated small amount of particles, which were mostly removed by fume hood. Spray dryer leaked particles when duct valve was closed, but when correctly operated the exposure to particles was low or nonexistent. To assess the health effects of the produced MFC, mouse macrophages and human monocyte derived macrophages were exposed to MFC and the viability and cytokine profile of the cells were studied thereafter. No evidence of inflammatory effects or cytotoxicity on mouse and human macrophages was observed after 6 and 24 h exposure to the materials studied. The results of toxicity studies suggest that the friction ground MFC is not cytotoxic and does not cause any effects on inflammatory system in macrophages. In addition, environmental safety of MFC was studied with ecotoxicity test. Acute environmental toxicity assessed with kinetic luminescent bacteria test showed high NOEC values ([100 mg/l) for studied MFC. However, MFC disturbed Daphnia magna mobility mechanically when the test was performed according to the standard procedure.

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