Norm convergence of nilpotent ergodic averages

We show that multiple polynomial ergodic averages arising from nilpotent groups of measure preserving transformations of a probability space always converge in the L^2 norm.Comment: 17 pages. Added further results and example

The inverse sieve problem in high dimensions

We show that if a big set of integer points in [0,N]^d, d>1, occupies few residue classes mod p for many primes p, then it must essentially lie in the solution set of some polynomial equation of low degree. This answers a question of Helfgott and Venkatesh.Comment: 15 pages. Added more examples in Section 5 and some minor change

Acquisition and analysis of adaptive optics imaging polarimetry data

The process of data taking, reduction and calibration of near-infrared imaging polarimetry data taken with the ESO Adaptive Optics System ADONIS is described. The ADONIS polarimetric facility is provided by a rotating wire grid polarizer. Images were taken at increments of 22.5 degrees of polarizer rotation from 0 to 180 degrees, over-sampling the polarization curve but allowing the effects of photometric variations to be assessed. Several strategies to remove the detector signature are described. The instrumental polarization was determined, by observations of stars of negligible polarization, to be 1.7% at J, H and K bands. The lack of availability of unpolarized standard stars in the IR, in particular which are not too bright as to saturate current IR detectors, is highlighted. The process of making polarization maps is described. Experiments at restoring polarimetry data, in order to reach diffraction limited polarization, are outlined, with particular reference to data on the Homunculus reflection nebula around Eta Carinae.Comment: 20 pages, A&A LaTeX2e, 11 figures. To appear in Astronomy & Astrophysics, Supplement Serie

Quantifying critical thinking: Development and validation of the Physics Lab Inventory of Critical thinking (PLIC)

Introductory physics lab instruction is undergoing a transformation, with increasing emphasis on developing experimentation and critical thinking skills. These changes present a need for standardized assessment instruments to determine the degree to which students develop these skills through instructional labs. In this article, we present the development and validation of the Physics Lab Inventory of Critical thinking (PLIC). We define critical thinking as the ability to use data and evidence to decide what to trust and what to do. The PLIC is a 10-question, closed-response assessment that probes student critical thinking skills in the context of physics experimentation. Using interviews and data from 5584 students at 29 institutions, we demonstrate, through qualitative and quantitative means, the validity and reliability of the instrument at measuring student critical thinking skills. This establishes a valuable new assessment instrument for instructional labs.Comment: 16 pages, 4 figure