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We demonstrate the importance of graph theory for understanding boards of directors. Specifically, we focus on the ‘small world’ phenomenon. Our empirical results show that a random graph model is remarkably good at explaining board structure and connectedness in the United States, the United Kingdom and Germany. Although there are small-world traits such as ‘clustering’ and ‘short-paths’ in the corporate world, they are no more pronounced than would be expected by chance in a statistically similar, but randomly assembled corporate universe. In short, boards of directors, especially in the United States, are no more ‘clubby’ than expected. Finally, our results show the existence of positive degree correlation: directors who sit on many boards do so in the company of other directors who sit on many boards. Board members whose services are in high demand, serve on boards with similar directors.

Purpose: To introduce and describe two methods of grading the severity of infantile cataracts, and thereby propose a useful clinical guide for early surgical intervention. Methods: Thirty-three subjects, aged 1 week to 8 years, participated in the study. Twenty-two were evaluated soon after birth (1 week), and 11 in childhood (3–8 years). All had isolated infantile cataracts, of which 16 were bilateral and 17 unilateral. Nine cataract types were examined; nuclear (n ¼ 9), lamellar (n ¼ 9), posterior lenticonus (n ¼ 4), persistent hyperplastic primary vitreous (n ¼ 4), posterior polar (n ¼ 3) and single cases of total, cortical, sutural and anterior polar. Grading the infantile cataracts was performed subjectively based on the cataract morphology, density and position using an 11-point (0–10) ordinal scale. Objective measures of the cataracts were performed by scanning and then digitising photo-slit lamp images to provide cataract intensity profiles. Subjects without cataracts acted as controls. Results: Subjective gradings of 0 and 10 were assigned to the clear, cataract-free lens and the total cataract, respectively. Fixed grades of 1 (anterior polar, sutural) and 6 (posterior polar) were assigned to the three remaining cataracts with static morphologies. The five cataracts which were all progressive were given grading ranges, reflecting the initial and likely final morphological states. Objective measures were found to be valuable in indicating the exact position and relative density of the cataract, as well as accurately defining boundaries. Conclusions: The magnitude and severity of infantile cataracts can be usefully characterised by an 11-point ordinal subjective grading scale. Although subjective grading alone is satisfactory, it can be greatly assisted by objective measures, particularly in the documentation of cataract progression. Cataracts assigned grades 1–4 were considered minor obstructions to vision and therefore not candidates for early surgery. Cataracts graded 5 and above were considered major visual defects, and ideally should be removed early in life.

The eukaryotic 40S ribosomal subunit locates the translation initiation codon on an mRNA via the so-called scanning process that follows 40S binding to the capped 5' end. This key step in translation is required for the expression of almost all eukaryotic genes, yet the mechanism and dynamics of scanning are unknown. We have performed quantitative studies in vivo and in vitro of the movement of yeast 40S ribosomes along 5' untranslated regions (UTRs) of different lengths. 40S subunits perform cap-dependent scanning with high processivity for more than 1700 nucleotides in cells of Saccharomyces cerevisiae. Moreover, the observed rates of expression indicate that scanning is performed by an untethered 40S subunit that has been released from the 5' cap complex. Unexpectedly, the capability to maintain scanning competence on a long 5' UTR is more dependent on the Ded1/Dbp1 type of helicase than on eIF4A or eIF4B. In a yeast cell-free extract, scanning shows reduced processivity, with an estimated net 5'-->3' rate of approximately 10 nucleotides per second at 26 degrees C. We have developed a biased bidirectional walking model of ribosomal scanning that provides a framework for understanding the above observations as well as other known quantitative and qualitative features of this process.

It has been asserted in the literature that the low pass filtering of time series data may lead to erroneous results when calculating attractor dimensions. Here we prove that finite order, non-recursive filters do not have this effect. In fact, a generic, finite order, non-recursive filter leaves invariant all the quantities that can be estimated by using embedding techniques such as the method of delays.