We present a single, connected tile which can tile the plane but only nonperiodically. The tile is hexagonal with edge markings, which impose simple rules as to how adjacent tiles are allowed to meet across edges. The first of these rules is a standard matching rule, that certain decorations match across edges. The second condition is a new type of matching rule, which allows tiles to meet only when certain decorations in a particular orientation are given the opposite charge. This forces the tiles to form a hierarchy of triangles, following a central idea of the Socolar–Taylor tilings. However, the new edge-to-edge orientational matching rule forces this structure in a very different way, which allows for a surprisingly simple proof of aperiodicity. We show that the hull of all tilings satisfying our rules is uniquely ergodic and that almost all tilings in the hull belong to a minimal core of tilings generated by substitution. Identifying tilings which are charge-flips of each other, these tilings are shown to have pure point dynamical spectrum and a regular model set structure.

We study irreducible Smale spaces with totally disconnected stable sets and their associated $K$-theoretic invariants. Such Smale spaces arise as Wieler solenoids, and we restrict to those arising from open surjections. The paper follows three converging tracks: one dynamical, one operator algebraic and one $K$-theoretic. Using Wieler’s theorem, we characterize the unstable set of a finite set of periodic points as a locally trivial fibre bundle with discrete fibres over a compact space. This characterization gives us the tools to analyse an explicit groupoid Morita equivalence between the groupoids of Deaconu–Renault and Putnam–Spielberg, extending results of Thomsen. The Deaconu–Renault groupoid and the explicit Morita equivalence lead to a Cuntz–Pimsner model for the stable Ruelle algebra. The $K$-theoretic invariants of Cuntz–Pimsner algebras are then studied using the Cuntz–Pimsner extension, for which we construct an unbounded representative. To elucidate the power of these constructions, we characterize the Kubo–Martin–Schwinger (KMS) weights on the stable Ruelle algebra of a Wieler solenoid. We conclude with several examples of Wieler solenoids, their associated algebras and spectral triples.

Issues of social and economic inequality are increasingly becoming areas of study for archaeologists; however, little work has been done on the uniform application of analytical methods. Here we assess the use of the Gini index for determining wealth inequality in eight Prehispanic central Mexican contexts. We analyze house size at the Late Postclassic sites of Capilco (village), Cuexcomate (town), and Yautepec (city), all in the state of Morelos. Agricultural field sizes for two communities described in a Nahuatl-language census immediately after the Spanish conquest are also analyzed. Our final context is the Xolalpan phase apartment compounds at Teotihuacan. Using these case studies we discuss methodological issues concerning the use of Gini indices to infer social inequality with archaeological data. We find that the Gini index, when applied following the proposed methodological standards, serves as a useful tool for the quantification of inequality across multiple archaeological case studies.

A review of recent literature supports the notion that organisms may achieve nanoscale control over the hierarchical assembly of organic–inorganic materials by compartmentalizing reactions into small volumes containing specifically functionalized macromolecules. Such confinement may introduce a degree of determinism to the stochastic process of nucleation by greatly reducing the number of nucleation events, allowing an organism to control nucleation using “soft” organic substrates. In this way, the polymorph, orientation, shape, and size of a crystalline building block can be selected, and its assembly into a larger structure orchestrated by the organic matrix.

We introduce the notion of orbit equivalence of directed graphs, following Matsumoto’s notion of continuous orbit equivalence for topological Markov shifts. We show that two graphs in which every cycle has an exit are orbit equivalent if and only if there is a diagonal-preserving isomorphism between their $C^{\ast }$-algebras. We show that it is necessary to assume that every cycle has an exit for the forward implication, but that the reverse implication holds for arbitrary graphs. As part of our analysis of arbitrary graphs $E$ we construct a groupoid ${\mathcal{G}}_{(C^{\ast }(E),{\mathcal{D}}(E))}$ from the graph algebra $C^{\ast }(E)$ and its diagonal subalgebra ${\mathcal{D}}(E)$ which generalises Renault’s Weyl groupoid construction applied to $(C^{\ast }(E),{\mathcal{D}}(E))$. We show that ${\mathcal{G}}_{(C^{\ast }(E),{\mathcal{D}}(E))}$ recovers the graph groupoid ${\mathcal{G}}_{E}$ without the assumption that every cycle in $E$ has an exit, which is required to apply Renault’s results to $(C^{\ast }(E),{\mathcal{D}}(E))$. We finish with applications of our results to out-splittings of graphs and to amplified graphs.

We investigate functorial properties of Putnam’s homology theory for Smale spaces. Our analysis shows that the addition of a conjugacy condition is necessary to ensure functoriality. Several examples are discussed that elucidate the need for our additional hypotheses. Our second main result is a natural generalization of Putnam’s Pullback Lemma from shifts of finite type to non-wandering Smale spaces.

We provide a computation of the Čech cohomology of the pinwheel tiling using the Anderson–Putnam complex. A border-forcing version of the pinwheel tiling is produced that allows an explicit construction of the complex for the quotient of the continuous hull by the circle. The cohomology of the continuous hull is given using a spectral sequence argument of Barge, Diamond, Hunton and Sadun.

Metal borides (AlB2, MgB2, Mg0.5Al0.5B2, AlB12, SiB6 and MgAlB14) and boron carbide (B4C) reacted with Al were compared to B, Mg, Al, Mg-Al and Si as potential energetic fuel additives. Stoichiometric physical mixtures of powders corresponding to unreacted boride compounds (Al+2B, Mg+2B, Mg-Al+2B, Al+12B, Si+6B, Mg-Al+14B, and B4C+2Al) were also investigated in comparison to the compounds. Submicron boron was used, which resulted in very fine particle sizes for all materials studied. It was demonstrated that boride compounds were less sensitive to low-temperature oxidation in flowing air than physical mixtures or metallic fuels. Compounds with high mole fractions of boron were generally less sensitive, but their high temperature oxidation behavior showed no improvement over boron. Cylinder expansion testing of MgAlB14 exposed its poor performance in an energetic mixture. However, aluminum and magnesium diborides (AlB2, MgB2 and Mg0.5Al0.5B2) also had relatively low sensitivity and exhibited mechanisms to increase the rate of boron oxidation at high temperatures, showing promise as insensitive high-energy-density fuel additives. Detonation calorimetry of mixtures with AlB2 or Al+2B suggested that the AlB2 mixture released approximately 50% more heat per gram than Al +2B and underwent complete reaction. These results warrant further testing of the diboride compounds in energetic formulations. Due to the high cost of boron and acceptable performance of B4C-Al mixtures, B4C should also be investigated as a lower-cost alternative to boron.

The bacterial toxin colicin E9 is secreted by producing Escherichia coli cells with its 9.5 kDa inhibitor protein Im9 bound tightly to its 14.5 kDa C-terminal DNase domain. Double- and triple-resonance NMR spectra of the isolated DNase domain uniformly labeled with 13C/15N bound to unlabeled Im9 contain more signals than expected for a single DNase conformer, consistent with the bound DNase being present in more than one form. The presence of chemical exchange cross peaks in 750 MHz 15N–1H–15N HSQC–NOESY–HSQC spectra for backbone NH groups of Asp20, Lys21, Trp22, Leu23, Lys69, and Asn70 showed that the bound DNase was in dynamic exchange. The rate of exchange from the major to the minor form was determined to be 1.1 ± 0.2 s−1 at 298 K. Previous NMR studies have shown that the free DNase interchanges between two conformers with a forward rate constant of 1.61 ± 0.11 s−1 at 288 K, and that the bound Im9 is fixed in one conformation. The NMR studies of the bound DNase show that Im9 binds similarly to both conformers of the DNase and that the buried Trp22 is involved in the dynamic process. For the free DNase, all NH groups within a 9 Å radius of any point of the Trp22 ring exhibit heterogeneity suggesting that a rearrangement of the position of this side chain is connected with the conformational interchange. The possible functional significance of this feature of the DNase is discussed.

In addition to archaeologists who make stone tools for experimental purposes, there is a growing number of flintknappers who make lithic artifacts for fun and for profit. The scale of non-academic knapping is little known to archaeologists, and is connected to a flourishing market for antiquities, fakes, replicas, and modern lithic art. Modern stone tools are being produced in vast numbers, and are inevitably muddling the prehistoric record. Modern knappers exploit some material sources heavily, and their debitage creates new sites and contaminates old quarry areas. Modern knapping is, however, a potential source of archaeological insights, and a bridge between the professional community and the interested public. Modern knapping also is creating a “twentieth-century stone age,” and archaeologists working with lithic artifacts need to be aware of the problems and potentials.