  Recent developments in extracting and processing biological and clinical data
are allowing quantitative approaches to studying living systems.
High-throughput sequencing, expression profiles, proteomics, and electronic
health records are some examples of such technologies. Extracting meaningful
information from those technologies requires careful analysis of the large
volumes of data they produce. In this note, we present a set of distributions
that commonly appear in the analysis of such data. These distributions present
some interesting features: they are discontinuous in the rational numbers, but
continuous in the irrational numbers, and possess a certain self-similar
(fractal-like) structure. The first set of examples which we present here are
drawn from a high-throughput sequencing experiment. Here, the self-similar
distributions appear as part of the evaluation of the error rate of the
sequencing technology and the identification of tumorogenic genomic
alterations. The other examples are obtained from risk factor evaluation and
analysis of relative disease prevalence and co-mordbidity as these appear in
electronic clinical data. The distributions are also relevant to identification
of subclonal populations in tumors and the study of the evolution of infectious
diseases, and more precisely the study of quasi-species and intrahost diversity
of viral populations.
