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With the multiplicity of genomes sequenced today, it has been shown that significant percentages of genes in any given taxon do not possess orthologous sequences in other taxa. These sequences are typically designated as orphans/ORFans when found as singletons in one species only or taxonomically restricted genes (TRGs) when found at higher taxonomic ranks. Therefore, quantitative and collective studies of these genes are necessary for understanding their biological origins. Currently, orphan gene identifying software is limited, and those previously available are either not functional, are limited in their database search range, or are too complex algorithmically. Thus, an interested researcher studying orphan genes must harvest their data from many disparate sources. ORFanID is a graphical web-based search engine that efficiently finds orphan genes and TRGs at all taxonomic levels, from DNA or amino acid sequences in the entire NCBI database cluster and other large bioinformatics repositories. To our knowledge, this is the first program that allows the identification of orphan genes using both nucleotide and protein sequences in any species of interest. ORFanID identifies genes unique to any taxonomic rank, from species to a domain, using standard NCBI systematic classifiers. The software allows for user control of the NCBI database search parameters. The results of the search are provided in a spreadsheet as well as a graphical display. All the tables in the software are sortable by column, and results can be easily filtered with fuzzy search functionality. In addition, the visual presentation is expandable and collapsible by taxonomy.

In this work a conjecture to draw the bifurcation diagram of a map with multiple critical points is enunciated. The conjecture is checked by using two quartic maps in order to verify that the bifurcation diagrams obtained according to the conjecture contain all the periodic orbits previously counted by Xie and Hao for maps with four laps. We show that a map with split bifurcation contains more periodic orbits than those counted by these authors for a map with the same number of laps.

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