A novel procedure for the identification of chaos in complex biological systems.

We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility, reproduction and predation, with predation following the cyclic rules of the popular rock, paper and scissors game. The study uncovers the possibility to distinguish between time evolutions that start from slightly different initial states, guided by the Hamming distance which heuristically unveils the chaotic behavior. The finding opens up a quantitative approach that relates the correlation length to the average density of maxima of a typical species, and an ensemble of stochastic simulations is implemented to support the procedure. The main result of the work shows how a single and simple experimental realization that counts the density of maxima associated with the chaotic evolution of the species serves to infer its correlation length. We use the result to investigate others distinct complex systems, one dealing with a set of differential equations that can be used to model a diversity of natural and artificial chaotic systems, and another one, focusing on the ocean water level.

Identification of a de novo inv dup(X)(pter--> q22) by multicolor banding in a girl with Turner syndrome.

We report on a 23-year-old girl with short stature, short and wide neck, low posterior hairline, hypogonadism, underdeveloped breasts, infantile uterus, ovaries not visualized, and primary amenorrhea. Cytogenetic G-banding analysis revealed a mosaic karyotype of 46,X,dup(X)(q22)[35]/45,X[15], confirming the clinical suspicion of Turner syndrome. Molecular cytogenetics using a multicolor banding probe set for the X-chromosome characterized an inverted dup(X). The karyotype of the patient was therefore interpreted as 46,X,inv dup(X) (pter --> q22::q22 --> pter). This patient had a mosaic Turner syndrome with a cell line comprising partial trisomy Xpter to Xq22 and partial monosomy Xq22 to Xqter.