Singularity and Nonnormality in the Classification of Compositional Data

Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore–Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.     

Observations of the compact group of galaxies Shahbazian 130

Byurakan Astrophysical Observatory and Special Astrophysical Observatory, Academy of Sciences. Translated fromAstrofizika, Vol. 35, No. 1, pp. 67–75, July–August, 1991.     

Computational parameter estimation for a maize crop

During a whole growing season, the evolution of the displacement height, d, and roughness length, z ₀, of a maize crop has been estimated by a measurement programme. The results have been used to check different types of existing models to calculate these parameters from canopy characteristics only; a simple geometric model and two matching models have been investigated. A geometric model is based on geometric features of the surface only. After a simple modification, the geometric model gives good results for the displacement height as well as for the roughness length.A matching model, based on gradient-diffusion theory, yields good results for the displacement height. The roughness parameter, however, is overestimated by 17%. By a simple modification, the model results could be improved considerably.A matching model, based on a second-order closure procedure, yields excellent results for the displacement height and good results for the roughness length. But it appears that, when applying this model, the plant density index and plant area density distribution as a function of height must be well known.     

Changing depositional environment revealed from sediment components,west of “Swatch of No Ground”, northern Bay of Bengal

The sediment cores of 20 cm length collected from 31 to 83 m range of water depth from the inner shelf of Bay of Bengal west of “Swatch of No Ground” were analyzed for grain size, organic carbon, total nitrogen, calcium carbonate and clay mineralogy. Grain size analysis revealed that the sediment size decreases from west to east within the study area indicating a possible direction of transport towards east parallel to the coast. The grain size also decreases with increasing water depth, i.e. north to south, indicating sediment contribution to the area of study from Hooghly and other local rivers. In the cores studied, illite was the dominant clay mineral which seems to be a product of glacial weathering under arid conditions with its source being the Himalayan region. The organic carbon content was low in the sediments and was attributed to low plankton production or intense oxidation processes. Low calcium carbonate percentage also supports the view of a low productivity in this region. Organic carbon increases gradually from west to east indicating its association with finer sediments and also indicates transport due to currents which drift the organic carbon away before it settles down within the sediments. Higher values relatively closer to the coast in the eastern side indicate additional contribution from Sunderban mangroves. The C/N ratio obtained indicates mixed source of terrestrial and marine for the organic matter in the sediments. Sedimentation rates available for deltaic plains and shelves off Bangladesh when adopted for the present area revealed that a 20 cm long sediment column was deposited in around 10 years. In most of the cores studied, a change in the trend of sediment components and organic carbon was observed at around 10 cm where grain size increases and organic carbon decreases towards the surface inferring that during the last 5 years, possible floods during NE monsoon or due to melting of ice in Himalaya are responsible for releasing additional water and material which brought a change in hydrodynamic conditions. The surface depletion of organic carbon indicates its dilution by the addition of coarser materials.     

Understanding distribution and abundance of metals with space and time in estuarine mudflat sedimentary environment

Spatial and depth-wise distribution of sediment components, organic carbon and selected metals (Fe, Mn, Al, Ni, Cr, Co, Zn and Pb) is studied across upper and middle tidal flats from lower and middle estuarine regions of Kundalika Estuary, central west coast of India. Silt and clay form the major components in lower and middle estuary, respectively. Sand, silt, clay and organic carbon showed band-type distribution along the estuary. The sediment deposition over the years took place in varying hydrodynamic conditions in lower and middle estuarine regions. Upper flats of the lower estuary represent mud while middle flats of the lower estuary facilitated the deposition of sandy mud. Correlation results indicated the importance of clay and organic carbon in removal and trapping of metals at lower and middle estuary, respectively. Factor analysis indicated that the distribution of metals is largely controlled by Fe–Mn oxyhydroxides and organic carbon. The middle flats of the lower estuary showed an anthropogenic source for Ni, Cr and Co while middle flats of the middle estuary showed a mainly lithogenic source.     

An Aerosol Model of the Marine and Coastal Atmospheric Surface Layer

We present a microphysical model for the surface layer marine and coastal atmospheric aerosols that is based on long-term observations of size distributions for 0.01–100 µm particles. The fundamental feature of the model is a parameterization of amplitudes and widths for aerosol modes of the aerosol size distribution function (ASDF) as functions of fetch and wind speed. The shape of ASDF and its dependence on meteorological parameters, height above sea level (H), fetch (X), wind speed (U) and relative humidity (RH), are investigated. At present, the model covers the ranges H = 0–25 m, U?=?3–18 km s^?1, X?≤?120 km and RH?=?40–98%.

The latest version of the Marine Aerosol Extinction Profiles model (MaexPro) is described and applied to the computation and analysis of the spectral profiles of aerosol extinction coefficients α(λ) in the wavelength band λ?=?0.2–12 µm. MaexPro is based on the aforementioned aerosol model assuming spherically shaped aerosol particles and the well-known Mie theory.

The spectral profiles of α(λ) calculated by MaexPro are in good agreement with observational data and the numerical results obtained from the Navy Aerosol Model (NAM) and the Advanced Navy Aerosol Model (ANAM). Moreover, MaexPro was found to be an accurate and reliable tool for investigating the optical properties of atmospheric aerosols.     

壳聚糖分离膜的研制

近年来,膜分离材料及膜分离技术是一个相当受重视的研究开发和应用的领域[1,2]。反渗透法是一项新型的膜分离技术。