Integrated circuits have to be robust to manufacturing variations. This paper presents a new statistical methodology to determine the worst-case corners for a set of circuit performances. Our methodology first estimates response surfaces for circuit performances as quadratic functions of the process parameters with known statistical distributions. These response surface models are then used to extract the worst-case corners in the process parameter space as the points where the circuit performances are at their min/max values corresponding to a specified statistical level. Corners in the process parameter space close to each other are clustered to reduce their number, which reduces the number of simulations required for design verification. We introduce the novel concept of relaxation coefficient to ensure that the corners capture the min/max values of all the circuit performances at the desired statistical level. The corners are realistic since they track the multivariate statistical distribution of the process parameters. Expected worstcase circuit performances can thus be extracted with a small number of simulations suitable for subsequent design verifications. The methodology is demonstrated with examples showing extraction of corners from digital standard cells and also the corners for analog/RF blocks found in typical communication ICs.
BackgroundIt is widely recognised that significant discrepancies exist between the health of indigenous and non-indigenous populations. Whilst the reasons are incompletely defined, one potential cause is that indigenous communities do not access healthcare to the same extent. We investigated healthcare utilisation rates in the Canadian Aboriginal population to elucidate the contribution of this fundamental social determinant for health to such disparities.MethodsHealthcare utilisation data over a nine-year period were analysed for a cohort of nearly two million individuals to determine the rates at which Aboriginal and non-Aboriginal populations utilised two specialties (Cardiology and Ophthalmology) in Alberta, Canada. Unadjusted and adjusted healthcare utilisation rates obtained by mixed linear and Poisson regressions, respectively, were compared amongst three population groups - federally registered Aboriginals, individuals receiving welfare, and other Albertans.ResultsHealthcare utilisation rates for Aboriginals were substantially lower than those of non-Aboriginals and welfare recipients at each time point and subspecialty studied [e.g. During 2005/06, unadjusted Cardiology utilisation rates were 0.28% (Aboriginal, n = 97,080), 0.93% (non-Aboriginal, n = 1,720,041) and 1.37% (Welfare, n = 52,514), p = <0.001]. The age distribution of the Aboriginal population was markedly different [2.7%≥65 years of age, non-Aboriginal 10.7%], and comparable utilisation rates were obtained after adjustment for fiscal year and estimated life expectancy [Cardiology: Incidence Rate Ratio 0.66, Ophthalmology: IRR 0.85].DiscussionThe analysis revealed that Aboriginal people utilised subspecialty healthcare at a consistently lower rate than either comparatively economically disadvantaged groups or the general population. Notably, the differences were relatively invariant between the major provincial centres and over a nine year period. Addressing the causes of these discrepancies is essential for reducing marked health disparities, and so improving the health of Aboriginal people.
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