We recorded the association between the planthopper Tettigometra laetus Herrich-Schäffer, 1835 (Hemiptera: Fulgoromorpha: Tettigometridae) and three ant species belonging to the subfamilies Myrmicinae and Formicinae in a coastal dune area of Flanders (Belgium). Lasius psammophilus Seifert, Tetramorium caespitum L. and Formica cunicularia Latreille were observed attending and palpating the dorsal glandular area of this planthopper, taking honeydew directly from its anus, herding them and carrying them into their nests when disturbed. The planthopper was rarely found in the absence of ants and probably develops within ant nests, which may provide protection against predation and adverse weather conditions. The natural history of temperate ant-hemipteran relationships is discussed.
In a series of articles, we have been developing a theory of \emph{tropical diagrams of probability spaces}, expecting it to be useful for information optimization problems in information theory and artificial intelligence. In this article, we give a summary of our work so far and apply the theory to derive a dimension-reduction statement about the shape of the entropic cone.