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Mozell Gentges

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Jul 4, 2024, 1:57:34 PM7/4/24
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Visualization of general relativity illustrates aspects of Einstein's insights into the curved nature of space and time to the expert as well as the layperson. One of the most interesting models which came up with Einstein's theory was developed by Kurt Gödel in 1949. The Gödel universe is a valid solution of Einstein's field equations, making it a possible physical description of our universe. It offers remarkable features like the existence of an optical horizon beyond which time travel is possible. Although we know that our universe is not a Gödel universe, it is interesting to visualize physical aspects of a world model resulting from a theory which is highly confirmed in scientific history. Standard techniques to adopt an egocentric point of view in a relativistic world model have shortcomings with respect to the time needed to render an image as well as difficulties in applying a direct illumination model. In this paper we want to face both issues to reduce the gap between common visualization standards and relativistic visualization. We will introduce two techniques to speed up recalculation of images by means of preprocessing and lookup tables and to increase image quality through a special optimization applicable to the Gödel universe. The first technique allows the physicist to understand the different effects of general relativity faster and better by generating images from existing datasets interactively. By using the intrinsic symmetries of Gödel's spacetime which are expressed by the Killing vector field, we are able to reduce the necessary calculations to simple cases using the second technique. This even makes it feasible to account for a direct illumination model during the rendering process. Although the presented methods are applied to Gödel's universe, they can also be extended to other manifolds, for example light propagation in moving dielectric media. Therefore, other areas of research can benefit from these generic improvements.

The characteristics of the D antigen are important as they influence the immunogenicity of D variant cells. Several studies on antigenic sites have been reported in normal D positive, weak D and partial D cases, including a comprehensive analysis of DEL types in Caucasians. The aim of this study was to assess D antigen density and epitopes on the erythrocyte surface of Asian type DEL phenotypic individuals carrying the RHD1227A allele in the Chinese population. A total of 154 DEL phenotypic individuals carrying the RHD1227A allele were identified through adsorption and elution tests and polymerase chain reaction analysis with sequence-specific primers in the Chinese population. D antigen density on the erythrocyte surface of these individuals was detected using a flow cytometric method. An erythrocyte sample with known D antigen density was used as a standard. Blood samples from D-negative and D-positive individuals were used as controls. In addition, D antigen epitopes on the erythrocyte surface of DEL individuals carrying the RHD1227A allele were investigated with 18 monoclonal anti-D antibodies specific for different D antigen epitopes. The means of the median fluorescence intensity of D antigen on the erythrocyte membrane surface of D-negative, D-positive and DEL individuals were 2.140.25, 193.6111.43 and 2.450.82, respectively. The DEL samples were estimated to have approximately 22 D antigens per cell. The samples from all 154 DEL individuals reacted positively with 18 monoclonal anti-D antibodies specific for different D antigen epitopes. In this study, D antigen density on the erythrocyte surface of DEL individuals carrying the RHD1227A allele was extremely low, there being only very few antigenic molecules per cell, but the D antigen epitopes were grossly complete.

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