»Kom til at rive Benet af en Ædderkop - stod mig herligt i Mathematik!«

I anledning af 200-året for H.C. Andersen bringes en brevveksling mellem Christian Dorph og Mads Eslund

Vort Landbrugs Forsyning med Sædefrø til det kommende Foraar.

Vort Landbrugs Forsyning med Sædefrø til det kommende Foraar

Den internationale Frøkontrolkongres i Hamborg.

Den internationale Frøkontrolkongres i Hamborg

Systematic sampling with errors in sample locations

Systematic sampling of points in continuous space is widely used in microscopy and spatial surveys. Classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases. However, the classical theory assumes that the sample grid is exactly periodic; real physical sampling procedures may introduce errors in the placement of the sample points. This paper studies the effect of errors in sample positioning on the variance of estimators in the case of one-dimensional systematic sampling. First we sketch a general approach to variance analysis using point process methods. We then analyze three different models for the error process, calculate exact expressions for the variances, and derive asymptotic variances. Errors in the placement of sample points can lead to substantial inflation of the variance, dampening of zitterbewegung, that is fluctuation effects, and a slower order of convergence. This suggests that the current practice in some areas of microscopy may be based on over-optimistic predictions of estimator accurac

Modelling ignition probability for human- and lightning-caused wildfires in Victoria, Australia

Wildfires pose a significant risk to people and property, which is expected to grow with urban expansion into fire-prone landscapes and climate change causing increases in fire extent, severity and frequency. Identifying spatial patterns associated with wildfire activity is important for assessing the potential impacts of wildfires on human life, property and other values. Here, we model the probability of fire ignitions in vegetation across Victoria, Australia, to determine the key drivers of human- and lightning-caused wildfire ignitions. In particular, we extend previous research to consider the role that fuel moisture has in predicting ignition probability while accounting for environmental and local conditions previously identified as important. We used Random Forests to test the effect of variables measuring infrastructure, topography, climate, fuel and soil moisture, fire history, and local weather conditions to investigate what factors drove ignition probability for human- and lightning-caused ignitions. Human-caused ignitions were predominantly influenced by measures of infrastructure and local weather. Lightning-sourced ignitions were driven by fuel moisture, average annual rainfall and local weather. Both human- and lightning-caused ignitions were influenced by dead fuel moisture with ignitions more likely to occur when dead fuel moisture dropped below 20 %. In future, these models of ignition probability may be used to produce spatial likelihood maps, which will improve our models of future wildfire risk and enable land managers to better allocate resources to areas of increased fire risk during the fire season