A symmetric quantum calculus

We introduce the $\alpha,\beta$-symmetric difference derivative and the $\alpha,\beta$-symmetric N\"orlund sum. The associated symmetric quantum calculus is developed, which can be seen as a generalization of the forward and backward $h$-calculus.Comment: Submitted 26/Sept/2011; accepted in revised form 28/Dec/2011; to Proceedings of International Conference on Differential & Difference Equations and Applications, in honour of Professor Ravi P. Agarwal, to be published by Springer in the series Proceedings in Mathematics (PROM

The CountEm software: simple, efficient and unbiased population size estimation

Population size estimation is essential in ecology and conservation studies. Aerial photography can facilitate this laborious task with high resolution images. However, in images with thousands of individuals exhaustive manual counting is tedious, slow and difficult to verify. Computer vision software may work under some particular conditions but they are generally biased and known to fail in several situations. The CountEm software is a simple alternative based on geometric sampling. It provides a fast and unbiased size estimation for all sorts of populations. The only requirement is that the discrete objects (e.g. animals) in the target population are unambiguously distinguishable for counting in a still image. Typical relative standard errors in the 5?10% range are obtained after counting ~200 properly sampled animals in about 5?min irrespective of population size. The CountEm ver. 1.4.1 is presented here, which includes a guided mode with a simple software interface.MC acknowledges financial support from the AYA-2015-66357-R (MINECO/FEDER) project