Population need and geographical access to general practitioners in rural New Zealand

To use a geographical information system (GIS) approach to demonstrate the extent to which different areas in New Zealand vary in their geographical access to GPs, and to analyse the extent to which spatial access varies in relation to different population groups. Methods Three methods; population/GP ratios, least cost path analysis (LCPA), and an allocation method (which considered the capacity constraint of GPs) were used to demonstrate differences in geographic accessibility to GPs. Travel time, and distance to the closest GP, was calculated for every census enumeration district in New Zealand (n=38336)—thus enabling population-based accessibility statistics to be calculated and aggregated to the territorial local authority level. These calculations include the average travel time if everybody visited a GP once and the population more than 30 minutes from a GP. The composition of this population is analysed according to three criteria of need: the level of deprivation (NZDep2001), ethnicity (%Maori), and age (% <5 years, and %65 years and over). Results There are significant regional variations in geographical accessibility in New Zealand, and these differences are dependent upon the method to calculate accessibility. Ratio measures give a different picture of GP access than the other two indicators, reflecting the fact that TAs with similar ratios often have wide variations in travel times as well as the size and proportion of the population living more than 30 minutes from the closest GP. TAs with larger numbers and a higher proportion of their populations living in such areas tend to be more deprived and have a higher proportion of Maori, especially in the North Island. There appears to be no significant trend by age. Conclusion Given the health and service consequences of poor access, the results suggest that more attention needs to be paid to extending the spatial information base in primary care, in order to achieve more effective planning of services for disadvantaged populations

Corrigendum to "The holomorphic flow of the Riemann Zeta function"

Theorem 4.5 of [2], describing the topological type of the zeros of the flow s˙ = ζ(s) at reflected points off the critical line, claiming they were the same, contains an error. We gratefully acknowledge Professor Cevat Gokcek for pointing out the error to us

Linear law for the logarithms of the Riemann periods at simple critical zeta zeros

Each simple zero 1/2 + iγn of the Riemann zeta function on the critical line with γn > 0 is a center for the flow s˙ = ξ(s) of the Riemann xi function with an associated period Tn. It is shown that, as γn →∞, log Tn ≥ π/4 γn + O(log γn). Numerical evaluation leads to the conjecture that this inequality can be replaced by an equality. Assuming the Riemann Hypothesis and a zeta zero separation conjecture γn+1 − γn≥ γn-θ for some exponent θ > 0, we obtain the upper bound log Tn ≤ γn2 + θ Assuming a weakened form of a conjecture of Gonek, giving a bound for the reciprocal of the derivative of zeta at each zero, we obtain the expected upper bound for the periods so, conditionally, log Tn = π/ 4 γn +O(log γn). Indeed, this linear relationship is equivalent to the given weakened conjecture, which implies the zero separation conjecture, provided the exponent is sufficiently large. The frequencies corresponding to the periods relate to natural eigenvalues for the Hilbert–Polya conjecture. They may provide a goal for those seeking a self-adjoint operator related to the Riemann hypothesis

The holomorphic flow of the Riemann zeta function

The flow of the Riemann zeta function, ś = ς(s), is considered, and phase portraits are presented. Attention is given to the characterization of the flow lines in the neighborhood of the first 500 zeros on the critical line. All of these zeros are foci. The majority are sources, but in a small proportion of exceptional cases the zero is a sink. To produce these portraits, the zeta function was evaluated numerically to 12 decimal places, in the region of interest, using the Chebyshev method and using Mathematica. The phase diagrams suggest new analytic properties of zeta, of which some are proved and others are given in the form of conjectures

Design and Implementation of Interactive Tutorials for Data Structures

The Tutorial Generation Toolkit (TGT) is a set of Java classes that supports authoring of interactive tutorial applications. This paper describes extensions to the capabilities of the TGT and several new tutorials aimed at the Data Structures course which were built using the toolkit

Establishing the validity of domestication genes using DNA from ancient chickens

Peer reviewedPostprin

Gravitomagnetic Field of a Rotating Superconductor and of a Rotating Superfluid

The quantization of the extended canonical momentum in quantum materials including the effects of gravitational drag is applied successively to the case of a multiply connected rotating superconductor and superfluid. Experiments carried out on rotating superconductors, based on the quantization of the magnetic flux in rotating superconductors, lead to a disagreement with the theoretical predictions derived from the quantization of a canonical momentum without any gravitomagnetic term. To what extent can these discrepancies be attributed to the additional gravitomagnetic term of the extended canonical momentum? This is an open and important question. For the case of multiply connected rotating neutral superfluids, gravitational drag effects derived from rotating superconductor data appear to be hidden in the noise of present experiments according to a first rough analysis

The weight for random quark masses

In theories in which the parameters of the low energy theory are not unique, perhaps having different values in different domains of the universe as is possible in some inflationary models, the fermion masses would be distributed with respect to some weight. In such a situation the specifics of the fermion masses do not have a unique explanation, yet the weight provides the visible remnant of the structure of the underlying theory. This paper introduces this concept of a weight for the distribution of masses and provides a quantitative estimate of it from the observed quarks and leptons. The weight favors light quark masses and appears roughly scale invariant (rho ~ 1/m). Some relevant issues, such as the running of the weight with scale and the possible effects of anthropic constraints, are also discussed.Comment: 35pages, 19 figure