Preservice teachers’ pictorial strategies for a multistep multiplicative fraction problem

Previous research has documented that preservice teachers (PSTs) struggle with under- standing fraction concepts and operations, and misconceptions often stem from their understanding of the referent whole. This study expands research on PSTs’ understanding of wholes by investigating pictorial strategies that 85 PSTs constructed for a multistep fraction task in a multiplicative context. The results show that many PSTs were able to construct valid pictorial strategies, and the strategies were widely diverse with respect to how they made sense of an unknown referent whole of a fraction in multiple steps, how they represented the wholes in their drawings, in which order they did multiple steps, and which type of model they used (area or set). Based on their wide range of pictorial strategies, we discuss potential benefits of PSTs’ construction of their own representations for a word problem in developing problem solving skills

Carbon nanotube: a low-loss spin-current waveguide

We demonstrate with a quantum-mechanical approach that carbon nanotubes are excellent spin-current waveguides and are able to carry information stored in a precessing magnetic moment for long distances with very little dispersion and with tunable degrees of attenuation. Pulsed magnetic excitations are predicted to travel with the nanotube Fermi velocity and are able to induce similar excitations in remote locations. Such an efficient way of transporting magnetic information suggests that nanotubes are promising candidates for memory devices with fast magnetization switchings

Stratifying quotient stacks and moduli stacks

Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X/H], where X is a projective scheme and H is a linear algebraic group with internally graded unipotent radical acting linearly on X, in such a way that each stratum [S/H] has a geometric quotient S/H. This leads to stratifications of moduli stacks (for example, sheaves over a projective scheme) such that each stratum has a coarse moduli space.Comment: 25 pages, submitted to the Proceedings of the Abel Symposium 201

Forgetful maps between Deligne-Mostow ball quotients

We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P^1, and classify the forgetful maps that extend to a map of orbifolds between the stable completions. The cases where this happens include the Livn\'e fibrations and the Mostow/Toledo maps between complex hyperbolic surfaces. They also include a retraction of a 3-dimensional ball quotient onto one of its 1-dimensional totally geodesic complex submanifolds

Metallochaperones Are Needed for Mycobacterium tuberculosis and Escherichia coli Nicotinamidase-Pyrazinamidase Activity.

Mycobacterium tuberculosis nicotinamidase-pyrazinamidase (PZAse) is a metalloenzyme that catalyzes conversion of nicotinamide-pyrazinamide to nicotinic acid-pyrazinoic acid. This study investigated whether a metallochaperone is required for optimal PZAse activity. M. tuberculosis and Escherichia coli PZAses (PZAse-MT and PZAse-EC, respectively) were inactivated by metal depletion (giving PZAse-MT-Apo and PZAse-EC-Apo). Reactivation with the E. coli metallochaperone ZnuA or Rv2059 (the M. tuberculosis analog) was measured. This was repeated following proteolytic and thermal treatment of ZnuA and Rv2059. The CDC1551 M. tuberculosis reference strain had the Rv2059 coding gene knocked out, and PZA susceptibility and the pyrazinoic acid (POA) efflux rate were measured. ZnuA (200 μM) achieved 65% PZAse-EC-Apo reactivation. Rv2059 (1 μM) and ZnuA (1 μM) achieved 69% and 34.3% PZAse-MT-Apo reactivation, respectively. Proteolytic treatment of ZnuA and Rv2059 and application of three (but not one) thermal shocks to ZnuA significantly reduced the capacity to reactivate PZAse-MT-Apo. An M. tuberculosis Rv2059 knockout strain was Wayne positive and susceptible to PZA and did not have a significantly different POA efflux rate than the reference strain, although a trend toward a lower efflux rate was observed after knockout. The metallochaperone Rv2059 restored the activity of metal-depleted PZAse in vitro Although Rv2059 is important in vitro, it seems to have a smaller effect on PZA susceptibility in vivo. It may be important to mechanisms of action and resistance to pyrazinamide in M. tuberculosis Further studies are needed for confirmation.IMPORTANCE Tuberculosis is an infectious disease caused by the bacterium Mycobacterium tuberculosis and remains one of the major causes of disease and death worldwide. Pyrazinamide is a key drug used in the treatment of tuberculosis, yet its mechanism of action is not fully understood, and testing strains of M. tuberculosis for pyrazinamide resistance is not easy with the tools that are presently available. The significance of the present research is that a metallochaperone-like protein may be crucial to pyrazinamide's mechanisms of action and of resistance. This may support the development of improved tools to detect pyrazinamide resistance, which would have significant implications for the clinical management of patients with tuberculosis: drug regimens that are appropriately tailored to the resistance profile of a patient's individual strain lead to better clinical outcomes, reduced onward transmission of infection, and reduction of the development of resistant strains that are more challenging and expensive to treat