Query Complexity of Derivative-Free Optimization

This paper provides lower bounds on the convergence rate of Derivative Free Optimization (DFO) with noisy function evaluations, exposing a fundamental and unavoidable gap between the performance of algorithms with access to gradients and those with access to only function evaluations. However, there are situations in which DFO is unavoidable, and for such situations we propose a new DFO algorithm that is proved to be near optimal for the class of strongly convex objective functions. A distinctive feature of the algorithm is that it uses only Boolean-valued function comparisons, rather than function evaluations. This makes the algorithm useful in an even wider range of applications, such as optimization based on paired comparisons from human subjects, for example. We also show that regardless of whether DFO is based on noisy function evaluations or Boolean-valued function comparisons, the convergence rate is the same

Active Ranking using Pairwise Comparisons

This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise comparisons. We are interested in natural situations in which relationships among the objects may allow for ranking using far fewer pairwise comparisons. Specifically, we assume that the objects can be embedded into a $d$-dimensional Euclidean space and that the rankings reflect their relative distances from a common reference point in $R^d$. We show that under this assumption the number of possible rankings grows like $n^{2d}$ and demonstrate an algorithm that can identify a randomly selected ranking using just slightly more than $d log n$ adaptively selected pairwise comparisons, on average. If instead the comparisons are chosen at random, then almost all pairwise comparisons must be made in order to identify any ranking. In addition, we propose a robust, error-tolerant algorithm that only requires that the pairwise comparisons are probably correct. Experimental studies with synthetic and real datasets support the conclusions of our theoretical analysis.Comment: 17 pages, an extended version of our NIPS 2011 paper. The new version revises the argument of the robust section and slightly modifies the result there to give it more impac

Teaching Teachers for the Future (TTF) Project: Development of the TTF TPACK survey instrument

This paper presents a summary of the key findings of the TTF TPACK Survey developed and administered for the Teaching the Teachers for the Future (TTF) Project implemented in 2011. The TTF Project, funded by an Australian Government ICT Innovation Fund grant, involved all 39 Australian Higher Education Institutions which provide initial teacher education. TTF data collections were undertaken at the end of Semester 1 (T1) and at the end of Semester 2 (T2) in 2011. A total of 12881 participants completed the first survey (T1) and 5809 participants completed the second survey (T2). Groups of like-named items from the T1 survey were subject to a battery of complementary data analysis techniques. The psychometric properties of the four scales: Confidence - teacher items; Usefulness - teacher items; Confidence - student items; Usefulness- student items, were confirmed both at T1 and T2. Among the key findings summarised, at the national level, the scale: Confidence to use ICT as a teacher showed measurable growth across the whole scale from T1 to T2, and the scale: Confidence to facilitate student use of ICT also showed measurable growth across the whole scale from T1 to T2. Additional key TTF TPACK Survey findings are summarised

A note on the calculation of the effective range

The closed form of the first order non-linear differential equation that is satisfied by the effective range within the variable phase formulation of scattering theory is discussed. It is shown that the conventional method of determining the effective range, by fitting a numerical solution of the Schr\"odinger equation to known asymptotic boundary conditions, can be modified to include the first order contribution of a long range interaction.Comment: 4 page

Self-aligned fabrication process for silicon quantum computer devices

We describe a fabrication process for devices with few quantum bits (qubits), which are suitable for proof-of-principle demonstrations of silicon-based quantum computation. The devices follow the Kane proposal to use the nuclear spins of 31P donors in 28Si as qubits, controlled by metal surface gates and measured using single electron transistors (SETs). The accurate registration of 31P donors to control gates and read-out SETs is achieved through the use of a self-aligned process which incorporates electron beam patterning, ion implantation and triple-angle shadow-mask metal evaporation

Defects Annealing of Si^+ Implanted GaAs at RT and 100°C

Annealing behavior of point defects near room temperature is studied by measuring the strain relaxation of Si+ implanted GaAs. Polished semi-insulating GaAs wafers were implanted with 300keV Si^+ at liquid nitrogen (LN_2) and room temperature (RT). The strain profile was obtained by the X-ray Double Crystal Diffraction (DCD) technique and kinematical fitting. The maximum strain of the samples stored at RT and elevated temperature 100°C in air, decreases with time, which indicates the reduction of point defects. Relaxation is exponential in time. At least two time constants of 0.24hrs and 24hrs are needed to fit the data, suggesting that two different processes are responsible for annealing defects. Time constants are obtained for different doses at RT and LN_2 implantation temperature, and found to be insensitive to both these quantities. The activation energy for defect migration is estimated using simple diffusion model