Randomness and degrees of irregularity.

The fundamental question "Are sequential data random?" arises in myriad contexts, often with severe data length constraints. Furthermore, there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness--e.g., to evaluate the efficacy of therapy in medicine. We address both these issues from a computable framework via a quantification of regularity. ApEn (approximate entropy), defining maximal randomness for sequences of arbitrary length, indicating the applicability to sequences as short as N = 5 points. An infinite sequence formulation of randomness is introduced that retains the operational (and computable) features of the finite case. In the infinite sequence setting, we indicate how the "foundational" definition of independence in probability theory, and the definition of normality in number theory, reduce to limit theorems without rates of convergence, from which we utilize ApEn to address rates of convergence (of a deficit from maximal randomness), refining the aforementioned concepts in a computationally essential manner. Representative applications among many are indicated to assess (i) random number generation output; (ii) well-shuffled arrangements; and (iii) (the quality of) bootstrap replicates.

Independence of metastatic ability and extravasation: metastatic ras-transformed and control fibroblasts extravasate equally well.

Escape of cancer cells from the circulation (extravasation) is thought to be a major rate-limiting step in metastasis, with few cells being able to extravasate. Furthermore, highly metastatic cells are believed to extravasate more readily than poorly metastatic cells. We assessed in vivo the extravasation ability of highly metastatic ras-transformed NIH 3T3 cells (PAP2) versus control nontumorigenic nontransformed NIH 3T3 cells and primary mouse embryo fibroblasts. Fluorescently labeled cells were injected intravenously into chicken embryo chorioallantoic membrane and analyzed by intravital videomicroscopy. The chorioallantoic membrane is an appropriate model for studying extravasation, since, at the embryonic stage used, the microvasculature exhibits a continuous basement membrane and adult permeability properties. The kinetics of extravasation were assessed by determining whether individual cells (n = 1481) were intravascular, extravascular, or in the process of extravasation, at 3, 6, and 24 h after injection. Contrary to expectations, our results showed that all three cell types extravasated with the same kinetics. By 24 h after injection > 89% of observed cells had completed extravasation from the capillary plexus. After extravasation, individual fibroblasts of all cell types demonstrated preferential migration within the mesenchymal layer toward arterioles, not to venules or lymphatics. Thus in this model and for these cells, extravasation is independent of metastatic ability. This suggests that the ability to extravasate in vivo is not necessarily predictive of subsequent metastasis formation, and that postextravasation events may be key determinants in metastasis.