Is the List of Incomplete Open Cubes Complete?

Variations of Incomplete Open Cubes is the major project by the twentieth-century conceptual artist Sol LeWitt. In this paper we interpret the enumerative component of the project as embeddings of graphs. This formulation permits use of an algorithm to check the completeness of the list of the structures produced by the artist. Our conclusion is that the artist found the correct number of structures (that is, 122), but that his list contains a mistake in the presentation of a pair of incomplete cubes, a discovery that appears not to have been noted before.     

Effect of the cultivation mode on red pigments production from Monascus ruber

In submerged cultures performed in chemically defined fermentation medium containing glucose and glutamate, the growth and production of water‐soluble red pigments and citrinin by the filamentous fungus Monascus ruber were studied under various carbon/nitrogen (C/N) ratios. The specific production of the red pigments was optimal at a glucose/glutamate ratio of about 10 and then steadily decreased at higher C/N ratio. In contrast, the production of the mycotoxin increased with increased C/N with an optimum in the range of 30–45. In a fed‐batch mode, it was also found that the production of pigments was not favoured in fed‐batch mode by feeding the medium with glucose while keeping the C/N ratio lower than 10. This low production likely resulted from concurrent high accumulation of L‐malic acid that was reported to inhibit this production. In contrast, this mode of cultivation was rather favourable for the production of the mycotoxin.     

Apparent power-law distributions in animal movements can arise from intraspecific interactions

Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species (Euphydryas editha taylori) was best fit by a bounded PL, evidence of a Lévy flight, while the other (Euphydryas phaeton) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight.