Several classic tilings, including rhombuses and dominoes, possess height functions which allow us to 1) prove ergodicity and polynomial mixing times for Markov chains based on local moves, 2) use coupling from the past to sample perfectly random tilings, 3) map the statistics of random tilings at large scales to physical models of random surfaces, and and 4) are related to the “arctic circle” ...

During the viral life cycle adenoviruses produce excess capsid proteins. Human adenovirus serotype 3 (Ad3) synthesizes predominantly an excess of free pentons, the complexes of pentameric penton base and trimeric fiber proteins, which are responsible for virus penetration. In infected cells Ad3 pentons spontaneously assemble into dodecahedral virus-like nano-particles containing twelve pentons....

We comment on the recent paper by Balog and Niedermaier [1]. Balog and Niedermaier’s scaling hypothesis for the spectral densities in the O(3) nonlinear σ model [1] does not seem to be supported by the Monte Carlo data. As we showed in a recent paper [2], the numerics indicate that the continuum limit of the lattice O(3) σ model agrees as well with the S-matrix prediction [3] as with the contin...

Three-dimensional plasmonic superlattice microcavities, made from programmable atom equivalents comprising gold nanoparticles functionalized with DNA, are used as a testbed to study directional light emission. DNA-guided nanoparticle colloidal crystallization allows for the formation of micrometer-scale single-crystal body-centered cubic gold nanoparticle superlattices, with dye molecules coupl...

Aristotelian diagrams visualize the logical relations among a finite set of objects. These 1 diagrams originated in philosophy, but recently they have also been used extensively in artificial 2 intelligence, in order to study (connections between) various knowledge representation formalisms. 3 In this paper we develop the idea that Aristotelian diagrams can be fruitfully studied as geometrical ...

The notion of a competition graph was introduced by J. E. Cohen in 1968. The competition graph C(D) of a digraph D is a (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many new isolated vertices is...

The architecture of the human rhinovirus is shown to be based on a crystallographic polyhedron (the ico-dodecahedron) with 60 triangular facets and 32 vertices at points of a body-centered icosahedral lattice. The ico-dodecahedron is only slightly different from the T = 3 icosadeltahedron of Caspar & Klug [Cold Spring Harbor Symp. Quant. Biol. (1962), 27, 1-24]. The capsid of the virion is enca...

The self-assembly of individual nanoparticles into dimers-so-called heterodimers-is relevant for a broad range of applications, in particular in the vibrant field of nanoplasmonics and nanooptics. In this paper we report the synthesis and characterization of material- and shape-selected nanoparticle heterodimers assembled from individual particles via electrostatic interaction. The versatility ...