Atiyah, Singer in The Boston Globe. "MIT professor wins major international math prize" was the heading on a March 30 2004 "White Coat Notes" item by Scott Allen in the Globe. The story is the award of the 2004 Abel Prize to Isadore Singer (MIT) and Michael Atiyah (now at Edinburgh) for their 40-year-old discovery of the Index Theorem. "The Atiyah-Singer index theorem calculates the number of solutions to complex formulas about nature based on the geometry of surrounding space, an idea that is difficult to explain but amazingly useful in both math and physics." The wide applicability of the index theorem in physics was referred to by the Norwegian Academy of Science and Letters in their citation, where, as quoted by Allen, they described the work as "instrumental in repairing a rift between the worlds of pure mathematics and theoretical particle physics." King Harald will present the prize on May 25.
Math Ed in Britain. Two separate pieces were posted by Gary Eason on the BBC News World Edition website, both on February 24, 2004. The first one, "Action plan to rescue maths," refers to Making Mathematics Count, a report published that day, in which Adrian Smith (Queen Mary College, London) blasted the "Curriculum 2000" reforms of secondary education, in particular of the GCSE (General certificate of secondary education) as "an utter and complete disaster for mathematics." Eason gives the following synopsis of the report's recommendations. (The A-levels cover the most advanced material).
"Mathematicians call for action" gives some reactions to the report, coming from the profession. Sir Chris Llwellyn Smith, head of the UK Advisory Committee on Mathematics Education: "We are less and less numerate as a nation, just at the time we need mathematical skills to stay competitive in the global market." TV presenter and mathematician Carol Vorderman: "... You need only look to India to see how the love and skill of mathematics is providing a new wave of wealth through computing and financial services. Britain needs the same."
Statistical Topology of Networks. "Superfamilies of Evolved and Designed Networks" appears in Science for March 5, 2004. The authors are a team of 8 scientists in various departments of the Weizmann Institute. The idea is to classify networks by the statistical properties of their local topology, in the case of oriented networks by the statistical significance of each of the 13 possible "direct connected triads". These correspond to the exactly thirteen ways (up to symmetries of the triangle) of placing forward (F), backward (B) and double-headed (D) arrows on the three edges of a triangle so that all three vertices are touched:
The statistical significance of a triad compares its frequency of appearance with the way it appears in an ensemble of randomized networks with the same degree sequence as the network under examination. (The degree sequence is the distribution of the variable "number of edges per node"). The authors number the triads from 1 to 13, as listed; the sequence of 13 statistical significances is the significance profile of the network.
The authors examine a collection of networks arising in nature ("evolved") or artificially ("designed") and find four "superfamilies" of networks with very similar significance profiles. For example word-adjacency networks from various languages (English, French, Spanish, Japanese) all fall in the same superfamily. WWW Hyperlinks between pages on the Notre Dame website, and interpersonal social networks from a variety of contexts, fall in another one. Biological systems involving direct transcription interactions and those involving signal transduction interactions fall in two other, distinct superfamilies; the paper justifies this difference in biological terms.
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