In many living trees, much of the interior of the trunk can be rotten or even hollowed out. Previously, this has been suggested to be adaptive, with microbial or animal consumption of interior wood producing a rain of nutrients to the soil beneath the tree that allows recycling of those nutrients into new growth via the trees roots. Here I propose an alternative (non-exclusive) explanation: suc...

A number n > 1 is harmonic if σ(n) | nτ(n), where τ(n) and σ(n) are the number of positive divisors of n and their sum, respectively. It is known that there are no odd harmonic numbers up to 1015. We show here that, for any odd number n > 106, τ(n) ≤ n1/3. It follows readily that if n is odd and harmonic, then n > p3a/2 for any prime power divisor pa of n, and we have used this in showing that ...

William Nicholson was an English chemist as well a journalist, publisher, inventor, patent agent, and civil engineer (Figure 1). He wrote several important books on very different topics ranging from physics chemistry to architecture marine navigation. His contribution science in establishing 1797 the first periodic scientific journal: Journal of Natural Philosophy, Chemistry, Arts, which gener...

Artificial neural networks are becoming increasingly popular as predictive statistical tools in ecosystem ecology and as models of signal processing in behavioural and evolutionary ecology. We demonstrate here that a commonly used network in ecology, the three-layer feed-forward network, trained with the backpropagation algorithm, can be extremely sensitive to the stochastic variation in traini...