Nurturing mathematical literacy at lower primary level: impacts on student understanding of formal mathematical concepts

This study investigates to what extent mathematical literacy in lower primary students (aged 6 to 8) in England was developed by a sequence of three lessons. The lessons focused on understanding of two mathematical concepts, tessellation and self-similarity, and their links with lattices and crystals. 117 students completed a pencil-and-paper based open-ended questionnaire six months after the lessons were implemented. The results show that students could articulate the meanings of these concepts. Follow-up interviews with 15 of the students illustrate that visual representations have an important role to play in making students aware of these mathematical concepts, and in developing their capabilities to reason and communicate through use of these concepts

The fabrication of reproducible superconducting scanning tunneling microscope tips

Superconducting scanning tunneling microscope tips have been fabricated with a high degree of reproducibility. The fabrication process relies on sequential deposition of superconducting Pb and a proximity-coupled Ag capping layer onto a Pt/Ir tip. The tips were characterized by tunneling into both normal-metal and superconducting films. The simplicity of the fabrication process, along with the stability and reproducibility of the tips, clear the way for tunneling studies with a well-characterized, scannable superconducting electrode.Comment: 4 pages, 3 figures, REVTeX. Submitted to Rev. Sci. Instru

Massive increase in the stiffness of the human lens nucleus with age: the basis for presbyopia?

Purpose: To determine the stiffness of different regions of human lenses as a function of age, and to correlate the biophysical measurements in the lens center with nuclear water content. Methods: A custom made probe fitted to a dynamic mechanical analyzer was employed to measure stiffness values at 1 mm increments across equatorial sections of individual human lenses. Thermogravimetric analysis was used to determine the percentage water content in the nuclei of human lenses. Results: There was a pronounced increase in lens stiffness over the age range from 14 to 78. In the nucleus, stiffness values varied almost 1,000 fold over this age range, with the largest change observed in lenses between the ages of 20 to 60. Nuclear stiffness values increased on average by a factor of 450. By contrast, in the cortex the average increase in stiffness was approximately 20 fold over this same time period. In lenses younger than age 30, the nucleus was found to be softer than the cortex. This was true for all six lenses examined. In contrast all lenses older than 30 were characterized by having nuclear values higher than those of the cortex. In lenses over the age of 50, the lens nucleus was typically an order of magnitude more rigid than that of the cortex. The crossover age, when the cortical and nuclear stiffness values were similar, was in the 30s. There was no significant change in the water content of the human lens nucleus from age 13 to age 82. Conclusions: There is a marked increase in the stiffness of the human lens with age. This is most pronounced in the nucleus. Since in vivo data indicate that the nucleus must change shape significantly during accommodation, it is highly likely that these measured changes in physical properties will markedly diminish the ability of the lens to accommodate, and thus may be a major contributing factor to presbyopia. Since there was no measurable difference in the water contents of the nuclear regions of the lenses, this marked increase in stiffness is not due to compaction of the lens nucleus

Proteostasis and the Regulation of Intra- and Extracellular Protein Aggregation by ATP-Independent Molecular Chaperones: Lens α-Crystallins and Milk Caseins

Conspectus: Molecular chaperone proteins perform a diversity of roles inside and outside the cell. One of the most important is the stabilization of misfolding proteins to prevent their aggregation, a process that is potentially detrimental to cell viability. Diseases such as Alzheimer\u27s, Parkinson\u27s, and cataract are characterized by the accumulation of protein aggregates. In vivo, many proteins are metastable and therefore under mild destabilizing conditions have an inherent tendency to misfold, aggregate, and hence lose functionality. As a result, protein levels are tightly regulated inside and outside the cell. Protein homeostasis, or proteostasis, describes the network of biological pathways that ensures the proteome remains folded and functional. Proteostasis is a major factor in maintaining cell, tissue, and organismal viability. We have extensively investigated the structure and function of intra- and extracellular molecular chaperones that operate in an ATP-independent manner to stabilize proteins and prevent their misfolding and subsequent aggregation into amorphous particles or highly ordered amyloid fibrils. These types of chaperones are therefore crucial in maintaining proteostasis under normal and stress (e.g., elevated temperature) conditions. Despite their lack of sequence similarity, they exhibit many common features, i.e., extensive structural disorder, dynamism, malleability, heterogeneity, oligomerization, and similar mechanisms of chaperone action. In this Account, we concentrate on the chaperone roles of α-crystallins and caseins, the predominant proteins in the eye lens and milk, respectively. Intracellularly, the principal ATP-independent chaperones are the small heat-shock proteins (sHsps). In vivo, sHsps are the first line of defense in preventing intracellular protein aggregation. The lens proteins αA- and αB-crystallin are sHsps. They play a crucial role in maintaining solubility of the crystallins (including themselves) with age and hence in lens proteostasis and, ultimately, lens transparency. As there is little metabolic activity and no protein turnover in the lens, crystallins are very long lived proteins. Lens proteostasis is therefore very different to that in normal, metabolically active cells. Crystallins undergo extensive post-translational modification (PTM), including deamidation, racemization, phosphorylation, and truncation, which can alter their stability. Despite this, the lens remains transparent for tens of years, implying that lens proteostasis is intimately integrated with crystallin PTMs. Many PTMs do not significantly alter crystallin stability, solubility, and functionality, which thereby facilitates lens transparency. In the long term, however, extensive accumulation of crystallin PTMs leads to large-scale crystallin aggregation, lens opacification, and cataract formation. Extracellularly, various ATP-independent molecular chaperones exist that exhibit sHsp-like structural and functional features. For example, caseins, the major milk proteins, exhibit chaperone ability by inhibiting the amorphous and amyloid fibrillar aggregation of a diversity of destabilized proteins. Caseins maintain proteostasis within milk by preventing deleterious casein amyloid fibril formation via incorporation of thousands of individual caseins into an amorphous structure known as the casein micelle. Hundreds of nanoclusters of calcium phosphate are sequestered within each casein micelle through interactions with short, highly phosphorylated casein sequences. This results in a stable biofluid that contains a high concentration of potentially amyloidogenic caseins and concentrations of calcium and phosphate that can be far in excess of the solubility of calcium phosphate. Casein micelle formation therefore performs vital roles in neonatal nutrition and calcium homeostasis in the mammary gland

Spatiotemporal dynamics in a spatial plankton system

In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a condition for diffusive instability of a locally stable equilibrium. Furthermore, we present a theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that, on increasing the value of the fish predation rates, the sequences spots $\rightarrow$ spot-stripe mixtures$\rightarrow$ stripes$\rightarrow$ hole-stripe mixtures holes$\rightarrow$ wave pattern is observed. Our study shows that the spatially extended model system has not only more complex dynamic patterns in the space, but also has spiral waves.Comment: Published Pape

Observation of quantum depletion in a nonequilibrium exciton-polariton condensate

The property of superfluidity, first discovered in liquid 4He, is closely related to Bose-Einstein condensation (BEC) of interacting bosons. However, even at zero temperature, when one would expect the whole bosonic quantum liquid to become condensed, a fraction of it is excited into higher momentum states via interparticle interactions and quantum fluctuations -- the phenomenon of quantum depletion. Quantum depletion of weakly interacting atomic BECs in thermal equilibrium is well understood theoretically but is difficult to measure. This is even more challenging in driven-dissipative systems such as exciton-polariton condensates(photons coupled to electron-hole pairs in a semiconductor), since their nonequilibrium nature is predicted to suppress quantum depletion. Here, we observe quantum depletion of an optically trapped high-density exciton-polariton condensate by directly detecting the spectral branch of elementary excitations populated by this process. Analysis of the population of this branch in momentum space shows that quantum depletion of an exciton-polariton condensate can closely follow or strongly deviate from the equilibrium Bogoliubov theory, depending on the fraction of matter (exciton) in an exciton-polariton. Our results reveal the effects of exciton-polariton interactions beyond the mean-field description and call for a deeper understanding of the relationship between equilibrium and nonequilibrium BECs.Comment: 18 pages, 5 figures, with supplementary informatio

Hydrodynamic and Aerodynamic Tests of Models of Flying-boat Hulls Designed Flow Aerodynamic Drag - NACA Models 74, 74-A, and 75

The present tests illustrate how the aerodynamic drag of a flying boat hull may be reduced by following closely the form of a low drag aerodynamic body and the manner in which the extent of the aerodynamic refinement is limited by poorer hydrodynamic performance. This limit is not sharply defined but is first evidenced by an abnormal flow of water over certain parts of the form accompanied by a sharp increase in resistance. In the case of models 74-A and 75, the resistance (sticking) occurs only at certain combinations of speed, load, and trim and can be avoided by proper control of the trim at high water speeds. Model 75 has higher water resistance at very high speeds than does model 74-A. With constant speed propellers and high takeoff speeds, it appears that the form of model 75 would give slightly better takeoff performance. Model 74-A, however, has lower aerodynamic drag than does model 75 for the same volume of hull