Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length

By exploiting the unique properties of periodic stratified media we demonstrate simultaneously phase matching and enhancement of the optical field under second order nonlinear interaction. This leads to a second harmonic efficiency growth faster than the fifth power of the structure length, far better than the usual quadratic behavior associated with second order nonlinear effects.     

Greater than 20%-efficient frequency doubling of 1532-nm nanosecond pulses in quasi-phase-matched germanosilicate optical fibers

We fabricated second-order nonlinear gratings in D-shaped germanosilicate fibers, using thermal poling and periodic electrodes defined by standard photolithography. These gratings, which are up to 75 mm long, were used for efficient quasi-phase-matched frequency doubling of 1.532-mum nanosecond pulses from a high-power erbium-doped fiber amplifier. Average second-harmonic powers as high as 6.8 mW and peak powers greater than 1.2 kW at 766 nm were generated, with average and peak conversion efficiencies as high as 21% and 30%, respectively.     

Calculus students’ understanding of the vertex of the quadratic function in relation to the concept of derivative

The purpose of this study was to gain insight into 30, first year calculus students’ understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up group interviews. Students’ personal meanings of the vertex, including misconceptions, were explored, along with students’ understanding to solve problems pertaining to the derivative of a quadratic function. Results give evidence of students’ weak schema of the vertex, lack of connection between different problem types and the importance of linguistics in relation to levels of APOS theory. A preliminary genetic decomposition was developed based on the results. Future research is suggested as a continuation to improve student understanding of the relationship between the vertex of quadratic functions and the derivative.     

MaxSynBio: Avenues Towards Creating Cells from the Bottom Up

A large German research consortium mainly within the Max Planck Society (“MaxSynBio”) was formed to investigate living systems from a fundamental perspective. The research program of MaxSynBio relies solely on the bottom‐up approach to synthetic biology. MaxSynBio focuses on the detailed analysis and understanding of essential processes of life through modular reconstitution in minimal synthetic systems. The ultimate goal is to construct a basic living unit entirely from non‐living components. The fundamental insights gained from the activities in MaxSynBio could eventually be utilized for establishing a new generation of biotechnological processes, which would be based on synthetic cell constructs that replace the natural cells currently used in conventional biotechnology.     

Determination of the pion charge form factor at Q2=1.60 and 2.45 (GeV/c)2

The 1H(e,e'pi+)n cross section was measured at four-momentum transfers of Q2=1.60 and 2.45 GeV2 at an invariant mass of the photon nucleon system of W=2.22 GeV. The charged pion form factor (F(pi)) was extracted from the data by comparing the separated longitudinal pion electroproduction cross section to a Regge model prediction in which F(pi) is a free parameter. The results indicate that the pion form factor deviates from the charge-radius constrained monopole form at these values of Q2 by one sigma, but is still far from its perturbative quantum chromodynamics prediction.     

Small-group searches for mathematical proofs and individual reconstructions of mathematical concepts

This is a study of mathematics students working in small groups. Our research methodology allows us to examine how individual ideas develop in a social context. The research perspective used in this study is based on a co-constructive view of learning. Groups of three or four undergraduate mathematics majors, with prior experience writing mathematical proofs together, were asked to prove three statements. Computer software, such as Geometers Sketchpad, was available. Group work sessions were videotaped. Later, individuals viewed segments of the group video and were asked to reflect on group activities. Students in some groups did not share a common conception of proof, which seemed to hamper their collaboration. We observed interactions that fit with the co-constructive theory, with bidirectional interactions that shaped both group and individual conceptions of the tasks. These changes in understanding may result from parallel and successive internalization and externalization of ideas by individuals in a social context.     

On Non-Equally Spaced Wavelet Regression

Wavelet-based regression analysis is widely used mostly for equally-spaced designs. For such designs wavelets are superior to other traditional orthonormal bases because of their versatility and ability to parsimoniously describe irregular functions. If the regression design is random, an automatic solution is not available. For such non equispaced designs we propose an estimator that is a projection onto a multiresolution subspace in an associated multiresolution analysis. For defining scaling empirical coefficients in the proposed wavelet series estimator our method utilizes a probabilistic model on the design of independent variables. The paper deals with theoretical aspects of the estimator, in particular MSE convergence rates.     

Bayesian Inference with Wavelets: Density Estimation

Abstract

We propose a prior probability model in the wavelet coefficient space. The proposed model implements wavelet coefficient thresholding by full posterior inference in a coherent probability model. We introduce a prior probability model with mixture priors for the wavelet coefficients. The prior includes a positive prior probability mass at zero which leads to a posteriori thresholding and generally to a posteriori shrinkage on the coefficients. We discuss an efficient posterior simulation scheme to implement inference in the proposed model. The discussion is focused on the density estimation problem. However, the introduced prior probability model on the wavelet coefficient space and the Markov chain Monte Carlo scheme are general.