Geometry in the Transition from Primary to Post-Primary

This article is intended as a kind of precursor to the document Geometry for Post-primary School Mathematics, part of the Mathematics Syllabus for Junior Certicate issued by the Irish National Council for Curriculum and Assessment in the context of Project Maths. Our purpose is to place that document in the context of an overview of plane geometry, touching on several important pedagogical and historical aspects, in the hope that this will prove useful for teachers.Comment: 19 page

Monte Carlo Simulation of Deffuant opinion dynamics with quality differences

In this work the consequences of different opinion qualities in the Deffuant model were examined. If these qualities are randomly distributed, no different behavior was observed. In contrast to that, systematically assigned qualities had strong effects to the final opinion distribution. There was a high probability that the strongest opinion was one with a high quality. Furthermore, under the same conditions, this major opinion was much stronger than in the models without systematic differences. Finally, a society with systematic quality differences needed more tolerance to form a complete consensus than one without or with unsystematic ones.Comment: 8 pages including 5 space-consuming figures, fir Int. J. Mod. Phys. C 15/1

Structural Covariance in the Hard Sphere Fluid

We study the joint variability of structural information in a hard sphere fluid biased to avoid crystallisation and form fivefold symmetric geometric motifs. We show that the structural covariance matrix approach, originally proposed for on-lattice liquids [Ronceray and Harrowell, JCP 2016], can be meaningfully employed to understand structural relationships between different motifs and can predict, within the linear-response regime, structural changes related to motifs distinct from that used to bias the system

Upper limits on gravitational-wave signals based on loudest events

Searches for gravitational-wave bursts have often focused on the loudest event(s) in searching for detections and in determining upper limits on astrophysical populations. Typical upper limits have been reported on event rates and event amplitudes which can then be translated into constraints on astrophysical populations. We describe the mathematical construction of such upper limits.Comment: 8 pages, 1 figur

Propagation and organization in lattice random media

We show that a signal can propagate in a particular direction through a model random medium regardless of the precise state of the medium. As a prototype, we consider a point particle moving on a one-dimensional lattice whose sites are occupied by scatterers with the following properties: (i) the state of each site is defined by its spin (up or down); (ii) the particle arriving at a site is scattered forward (backward) if the spin is up (down); (iii) the state of the site is modified by the passage of the particle, i.e. the spin of the site where a scattering has taken place, flips ($\uparrow \Leftrightarrow \downarrow$). We consider one dimensional and triangular lattices, for which we give a microscopic description of the dynamics, prove the propagation of a particle through the scatterers, and compute analytically its statistical properties. In particular we prove that, in one dimension, the average propagation velocity is $= 1/(3-2q)$, with $q$ the probability that a site has a spin $\uparrow$, and, in the triangular lattice, the average propagation velocity is independent of the scatterers distribution: $= 1/8$. In both cases, the origin of the propagation is a blocking mechanism, restricting the motion of the particle in the direction opposite to the ultimate propagation direction, and there is a specific re-organization of the spins after the passage of the particle. A detailed mathematical analysis of this phenomenon is, to the best of our knowledge, presented here for the first time.Comment: 30 pages, 15 separate figures (in PostScript); submitted to J. Stat. Phy

Comparing the yield of Staphylococcus aureus recovery with static versus agitated broth incubation

Given the lack of standardization of methodologies for microbial recovery from built environments, we sought to compare the yield of Staphylococcus aureus with a broth enrichment method when incubated in agitated versus static conditions. Five unique strains of S. aureus at five different concentrations were cultured to compare direct plating, agitated broth enrichment, and static broth enrichment culture methods. All samples were incubated at 35° in ambient air. The lowest concentration recovered across three replicates and five strains did not differ between culture methods (Fisher’s exact test, p=0.50); notably, recovery of S. aureus was equivalent between static and agitated broth incubation. When broth enrichment was used (both static and agitated), the burden of S. aureus growth was higher (by semiquantitative assessment of 4-quadrant streaking) compared to the direct plating culture method. Optimizing strategies for microbial recovery is essential, particularly in areas of lower biomass, given the paucity of research concerning microbial communities of built environments. The results of this study, in conjunction with other experiments investigating microbiomes of built environments, can help inform protocols for standardizing culturing methods within built environments

Heart enhancers with deeply conserved regulatory activity are established early in zebrafish development.

During the phylotypic period, embryos from different genera show similar gene expression patterns, implying common regulatory mechanisms. Here we set out to identify enhancers involved in the initial events of cardiogenesis, which occurs during the phylotypic period. We isolate early cardiac progenitor cells from zebrafish embryos and characterize 3838 open chromatin regions specific to this cell population. Of these regions, 162 overlap with conserved non-coding elements (CNEs) that also map to open chromatin regions in human. Most of the zebrafish conserved open chromatin elements tested drive gene expression in the developing heart. Despite modest sequence identity, human orthologous open chromatin regions recapitulate the spatial temporal expression patterns of the zebrafish sequence, potentially providing a basis for phylotypic gene expression patterns. Genome-wide, we discover 5598 zebrafish-human conserved open chromatin regions, suggesting that a diverse repertoire of ancient enhancers is established prior to organogenesis and the phylotypic period