1. A distributed computing system for optimizing stable gene analysis of transcriptome sequencing data across a plurality of information processing systems within the distributed computing system, the distributed computing system comprising: a plurality of information processing systems, wherein the information processing systems of the plurality of information processing systems are external to each other, and wherein each of the information processing systems of the plurality of information processing system comprises a memory and a processor communicatively coupled to the memory, wherein a first information processing system of the plurality of information processing systems comprises a first transcriptome sequencing data analyzer circuit in communication with at least the first processor, where the first transcriptome sequencing data analyzer circuit is a separate hardware component, wherein the first processor is configured to perform a plurality of operations comprising, communicating with at least a second of the plurality of information processing systems, the second of the plurality of information processing systems performing transcriptome sequencing operations and generating a plurality of datasets each comprising transcriptome sequencing data based on performing the transcriptome sequencing operations; obtaining based on the communicating, the plurality of datasets, wherein each of the plurality of datasets comprises a plurality of genes and expression levels for each gene of the plurality of genes; and storing the plurality of datasets in memory of the first information processing system; wherein the first transcriptome sequencing data analyzer circuit is configured to perform a plurality of operations comprising performing one or more simulation operations on the plurality of datasets in the memory of the first information processing system, wherein the one or more simulation operations generate one or more replicate datasets for each dataset of the plurality of datasets, where the one or more replicate datasets increase a robustness for subsequent stable gene analysis operations; adding the one or more replicate datasets to the plurality of datasets as separate datasets; and after the one or more replicate datasets have been added to the plurality of datasets, assigning, a rank to each of the plurality of genes, wherein the assigning comprises generating a plurality of bins, each bin comprising a range of values of the ranking value, and assigning each gene to a bin of the plurality of bins based on the gene's respective ranking value, wherein genes that are assigned to the same bin have been assigned the same rank; obtaining a plurality of rank normalized input datasets based on the assigning, each rank normalized input dataset of the plurality of rank normalized input datasets comprising a sequence of normalized values; transmitting the plurality of rank normalized input datasets to at least a second transcriptome sequencing data analyzer circuit in communication with a second processor of at least a third information processing system of the plurality of information processing systems, where the second transcriptome sequencing data analyzer circuit is a separate hardware component; wherein the second transcriptome sequencing data analyzer circuit is configured to operating on the plurality of rank normalized input datasets utilizing a dynamic programming process, the dynamic programming process optimizing at least the third information processing system by reducing computation time required for performing the stable gene analysis of transcriptome sequencing data, wherein reducing the computation time comprises traversing each position in the sequence of normalized values for each rank normalized input dataset of the plurality of rank normalized input datasets; identifying, based on the traversal and for each position in the sequence of normalized values, a longest increasing subsequence of ranks; storing, for each traversal, a maximum size of the longest increasing subsequence of ranks and a position within the sequence of normalized values associated with the maximum size in a sorted data structure residing within a memory of the third information processing system, wherein for each traversal that is subsequent to an initial traversal, the longest increasing subsequence of ranks is identified based on searching the sorted data structure for all maximum sizes associated with positions of the sequence of normalized values that precede a current position of the sequence of normalized values, and extending the longest increasing subsequence of ranks for the preceding positions with the normalized value of the current position; storing the longest increasing subsequence of ranks in the memory of the third information processing system; identifying, based on each of the longest increasing subsequence of ranks stored in the memory, a set of stable genes from the plurality of genes that does not change across the plurality of rank normalized input datasets; and presenting the set of stable genes that has been identified on a display.