Periodic dynamics of coupled cell networks I: rigid patterns of synchrony and phase relations

It has recently been proved by Golubitsky and coworkers that in any network of coupled dynamical systems, the possible 'rigid' patterns of synchrony of hyperbolic equilibria are determined by purely combinatorial properties of the network, known as 'balanced equivalence relations'. A pattern is 'rigid' if it persists under small 'admissible' perturbations of the differential equation — ones that respect the network structure. We discuss a natural generalisation of these ideas to time-periodic states, and motivate two basic conjectures, the Rigid Synchrony Conjecture and the Rigid Phase Conjecture. These conjectures state that for rigid hyperbolic time-periodic patterns, cells with synchronous dynamics must have synchronous input cells, and cells with phase-related dynamics must have input cells that have the same phase relations. We provide evidence supporting the two conjectures, by proving them for a special class of periodic orbits, which we call 'tame', under strong assumptions on the network architecture and the symmetries of the periodic state. The discussion takes place in the formal setting of coupled cell networks. We prove that rigid patterns of synchrony are balanced, together with the analogous result for rigid patterns of phase relations. The assumption on the network architecture simplifies the geometry of admissible vector fields, while tameness rules out patterns with non-trivial local or multilocal symmetry. The main idea is to perturb an admissible vector field in a way that retains sufficient control over the associated perturbed periodic orbit. We present two techniques for constructing these perturbations, both using a general theorem on groupoid-symmetrisation of vector fields, which has independent interest. In particular we introduce a method of 'patching' that makes local changes to an admissible vector field. Having established these results for all-to-all coupled networks and tame periodic orbits we prove more general versions that require these assumptions only on a suitable quotient network. These conditions are weaker and encompass a larger class of networks and periodic orbits. We give an example to show that rigidity cannot be relaxed to hyperbolicity. We also prove, without any technical assumptions, that rigidly synchronous or phase-related cells must be input-isomorphic, a necessary precondition for the two conjectures to hold.     

Nanoweb Formation: 2D Self‐Assembly of Semiconductor Gallium Oxide Nanowires/Nanotubes

This paper reports a method to produce networks of crystalline gallium oxide comprised of one‐dimensional (1D) nanostructures. Because of the unique arrangement of wires, these crystalline networks are termed as ‘nanowebs’. Nanowebs are of great technological interest since they contain wire densities of the order of 10⁹ cm^–2. A possible mechanism for the fast self‐assembly of crystalline metal oxide nanowires involves multiple nucleation and coalescence via oxidation–reduction reactions at the molecular level. The preferential growth of nanowires parallel to the substrate enabled them to coalesce into regular polygonal networks. The individual segments of the polygonal network consist of both nanowires and nanotubules of β‐gallium oxide. Individual wire properties contribute to a nanoweb’s overall capacity and the implications for devices based on nanowebs are expected to be enormous.     

Silica removal from Mokai, New Zealand, geothermal brine by treatment with lime and a cationic precipitant

Preliminary experiments using two chemicals (CaO, a quicklime, and a cationic nitrogen-bearing precipitant, EC-004) to remove silica from geothermal brine were undertaken at the Mokai geothermal plant, New Zealand. The brine was mixed with the reagent (CaO or EC-004). The reaction was studied from the start of the experiment (NRT, 0 min, no retaining time) and after 15 min (15RT) at 90 °C. The concentration of silica in the brine was initially 954 mg/l, and decreased linearly with increasing reagent concentration. When CaO is added, the silica concentration at 15RT was 200 mg/l lower than at NRT and became almost zero on addition of 1.5 g/l. In contrast, when EC-004 is added, the total silica concentration nearly reaches the solubility of amorphous silica at 90 °C. In order to prevent silica scaling in Mokai brines cooled to 90 °C, the CaO and EC-004 added should be individually adjusted to 0.5 g/l and 80 mg/l, respectively.     

Indexing transitional knowledge.

Various indexes have been proposed to mark when a child is on the verge of acquiring new knowledge. This article described a new method for indexing this point of transition, which is based on the specificity of children's verbal explanations. The degree to which children were specific in their verbal explanations was related to whether they benefited from instruction. In particular, children who were vague in their explanations (i.e., less specific) benefited from instruction more than children who were explicit in their explanations (i.e., more specific). This index provides insights into the child's mental state prior to acquiring new knowledge. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Location of Aluminum in Substituted Calcium Silicate Hydrate (C-S-H) Gels as Determined by 29Si and 27Al NMR and EELS

Solid-state ²⁷Al and ²⁹Si magic angle spinning NMR spectroscopy has been combined with electron energy loss spectroscopy carried out in the transmission electron microscope to determine the location of Al substituting in a semicrystalline C-S-H gel present in a hydrated synthetic slag glass. The gel is found to contain mainly pentameric silicate chains in which the central silicon is substituted by aluminum.     

Are IQ scores valid for children who are poor readers?

Remedial services for children with reading problems are often allocated according to discrepancies between reading and IQ scores. Results of some recent research suggest, however, that IQ scores of poor readers do not covary with their levels of functioning in other cognitive domains. This study evaluated whether the external validity of IQ scores (from the Wechsler Intelligence Scale for Children—Revised [WAIS—R]) was moderated by reading levels within 2 separate samples of a total of 382 referred children (aged 7–16 yrs). It was found that IQ scores had expected correlations with external measures of verbal, visual-spatial, short-term memory, and arithmetic ability, and that these relations were invariant across levels of reading skill. (PsycINFO Database Record (c) 2010 APA, all rights reserved)