Dimensions of fractals related to languages defined by tagged strings in complete genomes

A representation of frequency of strings of length K in complete genomes of many organisms in a square has led to seemingly self-similar patterns when K increases. These patterns are caused by under-represented strings with a certain "tag"-string and they define some fractals when K tends to infinite. The Box and Hausdorff dimensions of the limit set are discussed. Although the method proposed by Mauldin and Williams to calculate Box and Hausdorff dimension is valid in our case, a different and simpler method is proposed in this paper.Comment: 9 pages with two figure

Transcriptomic comparison of the self-pollinated and cross-pollinated flowers of Erigeron breviscapus to analyze candidate self-incompatibility-associated genes

Table S1. Functional annotation of E.breviscapus transcriptome. (XLSX 4281 kb

Experimental measurement-device-independent quantum digital signatures over a metropolitan network

Quantum digital signatures (QDS) provide a means for signing electronic communications with informationtheoretic security. However, all previous demonstrations of quantum digital signatures assume trusted measurement devices. This renders them vulnerable against detector side-channel attacks, just like quantum key distribution. Here, we exploit a measurement-device-independent (MDI) quantum network, over a 200-square-kilometer metropolitan area, to perform a field test of a three-party measurement-device-independent quantum digital signature (MDI-QDS) scheme that is secure against any detector side-channel attack. In so doing, we are able to successfully sign a binary message with a security level of about 1E-7. Remarkably, our work demonstrates the feasibility of MDI-QDS for practical applications.Comment: 5 pages, 1 figure, 2 tables, supplemental materials included as ancillary fil