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The Institute of Fundamental Sciences (IFS) is an academic unit embracing the four disciplines of chemistry, mathematics, physics and statistics. Each has its own distinctive identity within the Institute. Interdisciplinary teaching is encouraged and promoted through programmes drawing upon expertise as appropriate and required from the individual disciplines. The nanoscience major for example, draws upon chemists and physicists, as well as colleagues from other Institutes.

The fundamental sciences of necessity underpin all scientific endeavour, but more significant is the increasingly important role of these sciences as cutting edges at the forefront of science. Research within the Institute is exemplified by the latest publications.
(See Latest 5 list in right column and below.)

On the Rat Trail in Near Oceania: Applying the Commensal Model to the Question of the Lapita Colonization   Given a multi-variate probability distribution, we describe the first efficient algorithm to find, for a given sample size, the combination to each category which maximises the probability of drawing that sample.

Generalized knot groups distinguish the square and granny knots (with an appendix by David Savitt)   One of the goals of knot theory is to find mathematical methods of distinguishing knots from each other. Surprisingly, one of the most important tools for understanding knots, the fundamental group , cannot tell the difference between a reef knot and a granny knot! This is because it has trouble with mirror images, and these two knots differ only by a reflection of half of the knot (some other knot invariants, such as the famous Jones polynomial, don't suffer from this problem). This paper shows that strengthened versions of the fundamental group, so called generalised knot groups, can in fact detect the difference between a reef knot and a granny knot.

Nelson and Neumann have since shown the stronger result that the generalised knot groups can detect the difference between any two knots that are not simply reflections of each other.

Identifying Health Inequalities between Mâori and Non-Mâori using Mortality Tables   While there is a need for more detailed information on health inequality to guide public health policy, the most complete and easily available data remains that in mortality tables. We investigate, via a comparative analysis of data from New Zealand on M ori and non-M ori mortality, whether more detailed information than raw life expectancy may be extracted from the mortality tables. Given a parametric distribution for the mortality capable of fitting irregularities in mortality table data, the curvature of the survival and hazard rates can identify changes in mortality rates, such as infant and late-life adult mortality, which allows for straightforward comparisons between the two sub-populations. Our results identify an exogenous effect in earlier mortality among Māori, which correlates well with many published observations of health and health-care inequalities between Māori and non-Māori. This “proof of concept” for our method of analysis indicates that examination of bulk data such as those in mortality tables has a potential role in the design of more detailed studies involving causes of mortality.

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