The ergodic hierarchy, randomness and Hamiltonian chaos

Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called ‘ergodic hierarchy’ (EH), which is commonly assumed to provide a hierarchy of increasing degrees of randomness. However, that notion of randomness requires clarification. The mathematical definition of EH does not make explicit appeal to randomness; nor does the usual way of presenting EH involve a specification of the notion of randomness that is supposed to underlie the hierarchy. In this paper we argue that EH is best understood as a hierarchy of random behaviour if randomness is explicated in terms of unpredictability. We then show that, contrary to common wisdom, EH is useful in characterising the behaviour of Hamiltonian dynamical systems.     

Actin dynamics in the contractile ring during cytokinesis in fission yeast

Cytokinesis in many eukaryotes requires a contractile ring of actin and myosin that cleaves the cell in two. Little is known about how actin filaments and other components assemble into this ring structure and generate force. Here we show that the contractile ring in the fission yeast Schizosaccharomyces pombe is an active site of actin assembly. This actin polymerization activity requires Arp3, the formin Cdc12, profilin and WASP, but not myosin II or IQGAP proteins. Both newly polymerized actin filaments and pre-existing actin cables can contribute to the initial assembly of the ring. Once formed, the ring remains a dynamic structure in which actin and other ring components continuously assemble and disassemble from the ring every minute. The rate of actin polymerization can influence the rate of cleavage. Thus, actin polymerization driven by the Arp2/3 complex and formins is a central process in cytokinesis. Our studies show that cytokinesis is a more dynamic process than previously thought and provide a perspective on the mechanism of cell division.     

Identification of asymmetric prediction intervals through causal forces

When causal forces are specified, the expected direction of the trend can be compared with the trend based on extrapolation. Series in which the expected trend conflicts with the extrapolated trend are called contrary series. We hypothesized that contrary series would have asymmetric forecast errors, with larger errors in the direction of the expected trend. Using annual series that contained minimal information about causality, we examined 671 contrary forecasts. As expected, most (81%) of the errors were in the direction of the causal forces. Also as expected, the asymmetries were more likely for longer forecast horizons; for six‐year‐ahead forecasts, 89% of the forecasts were in the expected direction. The asymmetries were often substantial. Contrary series should be flagged and treated separately when prediction intervals are estimated, perhaps by shifting the interval in the direction of the causal forces. Copyright © 2001 John Wiley & Sons, Ltd.     

Genome-wide association and linkage identify modifier loci of lung disease severity in cystic fibrosis at 11p13 and 20q13.2

A combined genome-wide association and linkage study was used to identify loci causing variation in cystic fibrosis lung disease severity. We identified a significant association (P = 3.34 × 10(-8)) near EHF and APIP (chr11p13) in p.Phe508del homozygotes (n = 1,978). The association replicated in p.Phe508del homozygotes (P = 0.006) from a separate family based study (n = 557), with P = 1.49 × 10(-9) for the three-study joint meta-analysis. Linkage analysis of 486 sibling pairs from the family based study identified a significant quantitative trait locus on chromosome 20q13.2 (log(10) odds = 5.03). Our findings provide insight into the causes of variation in lung disease severity in cystic fibrosis and suggest new therapeutic targets for this life-limiting disorder.     

Inhibition of Dll4 signalling inhibits tumour growth by deregulating angiogenesis

Haploinsufficiency of Dll4, a vascular-specific Notch ligand, has shown that it is essential for embryonic vascular development and arteriogenesis. Mechanistically, it is unclear how the Dll4-mediated Notch pathway contributes to complex vascular processes that demand meticulous coordination of multiple signalling pathways. Here we show that Dll4-mediated Notch signalling has a unique role in regulating endothelial cell proliferation and differentiation. Neutralizing Dll4 with a Dll4-selective antibody rendered endothelial cells hyperproliferative, and caused defective cell fate specification or differentiation both in vitro and in vivo. In addition, blocking Dll4 inhibited tumour growth in several tumour models. Remarkably, antibodies against Dll4 and antibodies against vascular endothelial growth factor (VEGF) had paradoxically distinct effects on tumour vasculature. Our data also indicate that Dll4-mediated Notch signalling is crucial during active vascularization, but less important for normal vessel maintenance. Furthermore, unlike blocking Notch signalling globally, neutralizing Dll4 had no discernable impact on intestinal goblet cell differentiation, supporting the idea that Dll4-mediated Notch signalling is largely restricted to the vascular compartment. Therefore, targeting Dll4 might represent a broadly efficacious and well-tolerated approach for the treatment of solid tumours.     

A Characterization of Majority Rule for Hierarchies

The majority rule has been a popular method for producing a consensus classification from several different classifications, when the classifications are all on the same set of objects and are structured as hierarchies. In this note, a new axiomatic characterization is proved for this consensus method on hierarchies.