A smooth approximation p(x;) to the plus function: maxfx; 0g, is obtained by integrating the sigmoid function 1=(1 + e ?x), commonly used in neural networks. By means of this approximation, linear and convex inequalities are converted into smooth, convex unconstrained minimization problems, the solution of which approximates the solution of the original problem to a high degree of accuracy for ...

We have used statistical methods for the analysis of two-dimensional point patterns to derive quantitative descriptions of the distributions of caveolae on freeze-fractured muscle fibre membranes. One method was based on a quadrat analysis while the second was a new procedure that we have called the interpoint distance analysis. We show that the latter analysis can unambiguously distinguish ran...

We studied all traffic accidents to pedestrians under age 15 which occurred on the Island of Montreal during an eighteen months period. Data were collected from eleven hospitals and completed with accident police records. A spatial quadrat analysis, a Comparative Accident Index, and a comparative analysis of the means of different socio-ecological variables between high and low risk accident ar...

19 20 The census of vascular plants across a ten-year interval (1995-2005) at the fringe of a 21 neotropical rainforest (Nouragues inselberg, French Guiana, South America) revealed that 22 species richness decreased, both at quadrat scale (2 m 2 ) and at the scale of the inselberg (three 23 transects, embracing the whole variation in community composition). Juvenile stages of all 24 tree and sh...

The inspection of residuals is a fundamental step to investigate the quality of adjustment of a parametric model to data. For spatial point processes, the concept of residuals has been recently proposed by Baddeley et al. Baddeley et al. (2005) as an empirical counterpart of the Campbell equilibrium equation for marked Gibbs point processes. The present paper focuses on stationary marked Gibbs ...

The vegetation pattern of Borland Mire, a 250 ha lowland raised mire near Monowai, in the rainshadow of the Fiordland mountains, is described using several numerical analyses of quadrat data collected at regular intervals along parallel transects across 430 m of a typical segment. A weak zonation pattern of both flora and vegetation is revealed amolng the 24 vascular species and the more abunda...

Many different sciences have developed many different tests to describe and characterise spatial point data. For example, all the trees in a given area may be mapped such that their x, y co-ordinates and other variables, or ‘marks’, (e.g. species, size) might be recorded. Statistical techniques can be used to explore interactions between events at different length scales and interactions betwee...

We define residuals for point process models fitted to spatial point pattern data, and propose diagnostic plots based on them. The residuals apply to any point process model that has a conditional intensity; the model may exhibit spatial heterogeneity, interpoint interaction and dependence on spatial covariates. Some existing ad hoc methods for model checking (quadrat counts, scan statistic, ke...

The mean crown diameters of stand-grown trees 5.0-in. dbh and larger were modeled as a function of stem diameter, live-crown ratio, stund-level basal area, latitude, longitude, elevation, and Hopkins bioclimatic index for 53 tree species in the western United States. Stem diameter was statistically signi@ant in al l models , and a quadrat ic term for s tem diameter was requiredfor some species ...