A discrete square global grid system based on the parallels plane projection

Knowledge Innovation Project of Chinese Academy of Sciences [KZCX3-SW-347]; National Science Fund for Distinguished Young Scholar [40225004]

Parallels plane projection and its geometric features

A new equivalent map projection called the parallels plane projection is proposed in this paper. The transverse axis of the parallels plane projection is the expansion of the equator and its vertical axis equals half the length of the central meridian. On the parallels plane projection, meridians are projected as sine curves and parallels are a series of straight, parallel lines. No distortion of length occurs along the central meridian or on any parallels of this projection. Angular distortion and the proportion of length along meridians (except the central meridian) introduced by the projection transformation increase with increasing longitude and latitude. A potential application of the parallels plane projection is that it can provide an efficient projection transformation for global discrete grid systems.

A discrete square global grid system based on the parallels plane projection

We developed a direct partitioning method to construct a seamless discrete global grid system (DGGS) with any resolution based on a two-dimensional projected plane and the earth ellipsoid. This DGGS is composed of congruent square grids over the projected plane and irregular ellipsoidal quadrilaterals on the ellipsoidal surface. A new equal area projection named the parallels plane (PP) projection derived from the expansion of the central meridian and parallels has been employed to perform the transformation between the planar squares and the corresponding ellipsoidal grids. The horizontal sides of the grids are parts of the parallel circles and the vertical sides are complex ellipsoidal curves, which can be obtained by the inverse expression of the PP projection. The partition strategies, transformation equations, geometric characteristics and distortions for this DGGS have been discussed. Our analysis proves that the DGGS is area-preserving while length distortions only occur on the vertical sides off the central meridian. Angular and length distortions positively correlate to the increase in latitudes and the spanning of longitudes away from a chosen central meridian. This direct partition only generates a small number of broken grids that can be treated individually.

Peripheries of molecular projection in three-dimensional space and studies of quantitative structure-activity relationships

A new index, i.e., the periphery representation of the projection of a molecule from 3D space to a 2D plane is described. The results, correlation with toxicity of substituted nitrobenzenes, obtained by using periphery descriptors are much better than that obtained by using the areas (i.e., shadows) of projections of the compounds. Even better results were achieved by using the combination of periphery descriptors and the projections areas as well as the indicated variable K reflecting the action of group NO position on the benzene ring.

Applications of the method of three-dimensional projection of a molecule in quantitative structure-activity relationship of phenol derivatives

Five variables for phenol derivatives were calculated by molecular projection in three-dimensional space which were combined with eight quantum-chemical parameters and three Am indices. These variables were selected by using leaps-and-bounds regression analysis. Multiple linear regression analysis and artificial neural networks' were performed, and the results obtained by using. artificial neural networks are superior than that obtained by using multiple linear regression.

Feeding and growth on bivalve biodeposits by the deposit feeder Stichopus japonicus Selenka (Echinodennata : Holothuroidea) co-cultured in lantern nets

Suspension aquaculture of filter-feeding bivalves has been developing rapidly in coastal waters in the world, especially in China. Previous studies have demonstrated that dense populations of filter-feeding bivalves in shallow water can produce a large amount of faeces and pseudofaeces (biodeposits) that may lead to negative impacts on the benthic environment. To determine whether the deposit feeder Stichopus (Apostichopus) japonicus Selenka can feed on bivalve biodeposits and whether the sea cucumber can be co-cultured with bivalves in suspended lantern nets, three experiments were conducted, two in tanks in the laboratory and one in the field. In a 3-month flow-through experiment, results showed that sea cucumbers grew well with specific growth rate (SGR) reaching 1.38% d(-1), when cultured in the bottom of tanks (10 m(3) water volume) where scallops were cultured in suspension in lantern nets. Moreover, results of another laboratory experiment demonstrated that sea cucumbers could survive well on bivalve biodeposits, with a feeding rate of 1.82 +/- 0.13 g dry biodeposits ind(-1) d(-1), absorption efficiency of organic matter in biodeposits of 17.2% +/- 5.5%, and average SGR of 1.60% d(-1). Our longer-term field experiments in two coastal bays (Sishili Bay and Jiaozhou Bay, northern China) showed that S. japonicus co-cultured with bivalves also grew well at growth rates (0.09-0.31 g wet weight ind(-1) d(-1)) depending on individual size. The results suggest that bivalve lantern nets can provide a good habitat for sea cucumbers; and the co-culture of bivalve molluscs with sea cucumbers may provide an additional valuable crop with no additional inputs. (c) 2006 Elsevier B.V. All rights reserved.

3D Pose from Three Corresponding Points Under Weak-Perspective Projection

Model-based object recognition commonly involves using a minimal set of matched model and image points to compute the pose of the model in image coordinates. Furthermore, recognition systems often rely on the "weak-perspective" imaging model in place of the perspective imaging model. This paper discusses computing the pose of a model from three corresponding points under weak-perspective projection. A new solution to the problem is proposed which, like previous solutins, involves solving a biquadratic equation. Here the biquadratic is motivate geometrically and its solutions, comprised of an actual and a false solution, are interpreted graphically. The final equations take a new form, which lead to a simple expression for the image position of any unmatched model point.

Uniqueness of the polar factorisation and projection of a vector-valued mapping

G.R. BURTON and R.J. DOUGLAS, Uniqueness of the polar factorisation and projection of a vector-valued mapping. Ann. I.H. Poincare ? A.N. 20 (2003), 405-418.

To fit in or stand out? The interaction between mortality salience, dissent and self esteem on social projection

Social projection (SP) refers to our tendency to assume that others think the same as we do, but the effect can also be used to detect the extent to which participants want to see themselves as similar to others. Simon et al (1997) found that participants informed that they were deviant increased their SP but those told that they were conformist reduced theirs. This compensatory function supports Brewer’s optimal distinctiveness which states that a balance must be struck between competing desires to feel similar and unique. In line with terror management theory, the effect was particularly apparent under conditions of mortality salience (MS). So far SP has only been examined on measures that target personal identity so this experiment developed a measure to target social identity as well. Participants were provided with either minority or majority dissent feedback, in MS or control conditions, and their SP on items relevant to personal and social identity were recorded. Results showed that group feedback only impacted upon participants SP on social identity measures and interacted with MS and self-esteem; those with high self-esteem had higher SP scores following minority dissent under conditions of mortality salience, indicating an attempt to assert their individuality. On SP measures targeting personal identity, MS and self-esteem interacted; the death prime increased SP scores for those with low self-esteem but decreased it for those with high self-esteem. Findings are interpreted in terms of TMT and optimal distinctiveness theory and their applications.