Relations between a typical scale and averages in the breaking of fractal distribution

We study distributions which have both fractal and non-fractal scale regions by introducing a typical scale into a scale invariant system. As one of models in which distributions follow power law in the large scale region and deviate further from the power law in the smaller scale region, we employ 2-dim quantum gravity modified by the $R^2$ term. As examples of distributions in the real world which have similar property to this model, we consider those of personal income in Japan over latest twenty fiscal years. We find relations between the typical scale and several kinds of averages in this model, and observe that these relations are also valid in recent personal income distributions in Japan with sufficient accuracy. We show the existence of the fiscal years so called bubble term in which the gap has arisen in power law, by observing that the data are away from one of these relations. We confirm, therefore, that the distribution of this model has close similarity to those of personal income. In addition, we can estimate the value of Pareto index and whether a big gap exists in power law by using only these relations. As a result, we point out that the typical scale is an useful concept different from average value and that the distribution function derived in this model is an effective tool to investigate these kinds of distributions.Comment: 17 pages, latex, 13 eps figure

Relations between a typical scale and averages in the breaking of fractal distribution

We study distributions which have both fractal and non-fractal scale regions by introducing a typical scale into a scale invariant system. As one of models in which distributions follow power law in the large scale region and deviate further from the power law in the smaller scale region, we employ 2-dim quantum gravity modified by the $R^2$ term. As examples of distributions in the real world which have similar property to this model, we consider those of personal income in Japan over latest twenty fiscal years. We find relations between the typical scale and several kinds of averages in this model, and observe that these relations are also valid in recent personal income distributions in Japan with sufficient accuracy. We show the existence of the fiscal years so called bubble term in which the gap has arisen in power law, by observing that the data are away from one of these relations. We confirm, therefore, that the distribution of this model has close similarity to those of personal income. In addition, we can estimate the value of Pareto index and whether a big gap exists in power law by using only these relations. As a result, we point out that the typical scale is an useful concept different from average value and that the distribution function derived in this model is an effective tool to investigate these kinds of distributions.

A Genetic Linkage Map for the Tiger Pufferfish, Takifugu rubripes

The compact genome of the tiger pufferfish, Takifugu rubripes (fugu), has been sequenced to the “draft” level and annotated to identify all the genes. However, the assembly of the draft genome sequence is highly fragmented due to the lack of a genetic or a physical map. To determine the long-range linkage relationship of the sequences, we have constructed the first genetic linkage map for fugu. The maps for the male and female spanning 697.1 and 1213.5 cM, respectively, were arranged into 22 linkage groups by markers heterozygous in both parents. The resulting map consists of 200 microsatellite loci physically linked to genome sequences spanning ∼39 Mb in total. Comparisons of the genome maps of fugu, other teleosts, and mammals suggest that syntenic relationship is more conserved in the teleost lineage than in the mammalian lineage. Map comparisons also show a pufferfish lineage-specific rearrangement of the genome resulting in colocalization of two Hox gene clusters in one linkage group. This map provides a foundation for development of a complete physical map, a basis for comparison of long-range linkage of genes with other vertebrates, and a resource for mapping loci responsible for phenotypic differences among Takifugu species