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.     

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.     

Optimization of Pathogen Capture in Flowing Fluids with Magnetic Nanoparticles

Magnetic nanoparticles have been employed to capture pathogens for many biological applications; however, optimal particle sizes have been determined empirically in specific capturing protocols. Here, a theoretical model that simulates capture of bacteria is described and used to calculate bacterial collision frequencies and magnetophoretic properties for a range of particle sizes. The model predicts that particles with a diameter of 460 nm should produce optimal separation of bacteria in buffer flowing at 1 L h⁻¹. Validating the predictive power of the model, Staphylococcus aureus is separated from buffer and blood flowing through magnetic capture devices using six different sizes of magnetic particles. Experimental magnetic separation in buffer conditions confirms that particles with a diameter closest to the predicted optimal particle size provide the most effective capture. Modeling the capturing process in plasma and blood by introducing empirical constants (c_e), which integrate the interfering effects of biological components on the binding kinetics of magnetic beads to bacteria, smaller beads with 50 nm diameters are predicted that exhibit maximum magnetic separation of bacteria from blood and experimentally validated this trend. The predictive power of the model suggests its utility for the future design of magnetic separation for diagnostic and therapeutic applications.