We study the transition between laminar and turbulent states in a Galerkin representation of a parallel shear flow, where a stable laminar flow and a transient turbulent flow state coexist. The regions of initial conditions where the lifetimes show strong fluctuations and a sensitive dependence on initial conditions are separated from the ones with a smooth variation of lifetimes by an object in phase space which we call the "edge of chaos." We describe techniques to identify and follow the edge, and our results indicate that the edge is a surface. For low Reynolds numbers we find that the surface coincides with the stable manifold of a periodic orbit, whereas at higher Reynolds numbers it is the stable set of a higher-dimensional chaotic object.

A large number of papers are appearing in the biomedical engineering literature that describe the use of machine learning techniques to develop classifiers for detection or diagnosis of disease. However, the usefulness of this approach in developing clinically validated diagnostic techniques so far has been limited and the methods are prone to overfitting and other problems which may not be immediately apparent to the investigators. This commentary is intended to help sensitize investigators as well as readers and reviewers of papers to some potential pitfalls in the development of classifiers, and suggests steps that researchers can take to help avoid these problems. Building classifiers should be viewed not simply as an add-on statistical analysis, but as part and parcel of the experimental process. Validation of classifiers for diagnostic applications should be considered as part of a much larger process of establishing the clinical validity of the diagnostic technique.

The collection of microbes that live in and on the human bodythe human microbiomecan impact on cancer initiation, progression, and response to therapy, including cancer immunotherapy. The mechanisms by which microbiomes impact on cancers can yield new diagnostics and treatments, but much remains unknown. The interactions between microbes, diet, host factors, drugs, and cellcell interactions within the cancer itself likely involve intricate feedbacks, and no single component can explain all the behavior of the system. Understanding the role of host-associated microbial communities in cancer systems will require a multidisciplinary approach combining microbial ecology, immunology, cancer cell biology, and computational biologya systems biology approach.

No abstract

A centerpiece of dynamical systems is comparison by an equivalence relationship called topological conjugacy. We present details of how a method to produce conjugacy functions based on a functional fixed point iteration scheme can be generalized to compare dynamical systems that are not conjugate. When applied to nonconjugate dynamical systems, we show that the fixed-point iteration scheme still has a limit point, which is a function we now call a "commuter"-a nonhomeomorphic change of coordinates translating between dissimilar systems. This translation is natural to the concepts of dynamical systems in that it matches the systems within the language of their orbit structures, meaning that orbits must be matched to orbits by some commuter function. We introduce methods to compare nonequivalent systems by quantifying how much the commuter function fails to be a homeomorphism, an approach that gives more respect to the dynamics than the traditional comparisons based on normed linear spaces, such as L(2). Our discussion addresses a fundamental issue-how does one make principled statements of the degree to which a "toy model" might be representative of a more complicated system?