Optimization of graded multilayer designs for astronomical x-ray telescopes

We developed a systematic method for optimizing the design of depth-graded multilayers for astronomical hard-x-ray and soft-γ-ray telescopes based on the instrument’s bandpass and the field of view. We apply these methods to the design of the conical-approximation Wolter I optics employed by the balloon-borne High Energy Focusing Telescope, using W/Si as the multilayer materials. In addition, we present optimized performance calculations of mirrors, using other material pairs that are capable of extending performance to photon energies above the W K-absorption edge (69.5 keV), including Pt/C, Ni/C, Cu/Si, and Mo/Si

General Statistical Design of an Experimental Problem for Harmonics

Four years ago, the Michelin Tire Corporation proposed a problem on experimental design, to improve the manufacturing process for their tires. The idea is basically to determine the effects of placements for various layers built up in the construction of a tire, to allow the design of a smooth tire with a smooth ride. A highly success solution was developed, and it has been reported that this method introduced savings of over half a million dollars in their test processes. This year, Michelin returned to the workshop with an extension to the original problem, to address specific refinements in the testing method. This report summarizes the work completed in course of the five day workshop. It was clear early in the workshop that this problem could be handled quickly by reviewing the analysis which was done in 2000, and extending those ideas to the new problems at hand. We reviewed the required Fourier techniques to describe the harmonic problem, and statistical techniques to deal with the linear model that described how to accurately measure quantities that come from real experimental measurements. The “prime method” and “good lattice points method” were reviewed and re-analysed so we could understand (and prove) why they work so well. We then looked at extending these methods and successfully found solutions to problem 1) and 2) posed by Michelin. Matlab code was written to test and verify the algorithms developed. We have some ideas on problems 3) and 4), which are also described

Completion and deficiency problems

Given a partial Steiner triple system (STS) of order $n$, what is the order of the smallest complete STS it can be embedded into? The study of this question goes back more than 40 years. In this paper we answer it for relatively sparse STSs, showing that given a partial STS of order $n$ with at most $r \le \varepsilon n^2$ triples, it can always be embedded into a complete STS of order $n+O(\sqrt{r})$, which is asymptotically optimal. We also obtain similar results for completions of Latin squares and other designs. This suggests a new, natural class of questions, called deficiency problems. Given a global spanning property $\mathcal{P}$ and a graph $G$, we define the deficiency of the graph $G$ with respect to the property $\mathcal{P}$ to be the smallest positive integer $t$ such that the join $G\ast K_t$ has property $\mathcal{P}$. To illustrate this concept we consider deficiency versions of some well-studied properties, such as having a $K_k$-decomposition, Hamiltonicity, having a triangle-factor and having a perfect matching in hypergraphs. The main goal of this paper is to propose a systematic study of these problems; thus several future research directions are also given

Paradigms for computational nucleic acid design

The design of DNA and RNA sequences is critical for many endeavors, from DNA nanotechnology, to PCR‐based applications, to DNA hybridization arrays. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Using an extensively studied thermodynamic model, we perform a detailed study of several criteria for designing sequences intended to adopt a target secondary structure. We conclude that superior design methods should explicitly implement both a positive design paradigm (optimize affinity for the target structure) and a negative design paradigm (optimize specificity for the target structure). The commonly used approaches of sequence symmetry minimization and minimum free‐energy satisfaction primarily implement negative design and can be strengthened by introducing a positive design component. Surprisingly, our findings hold for a wide range of secondary structures and are robust to modest perturbation of the thermodynamic parameters used for evaluating sequence quality, suggesting the feasibility and ongoing utility of a unified approach to nucleic acid design as parameter sets are refined further. Finally, we observe that designing for thermodynamic stability does not determine folding kinetics, emphasizing the opportunity for extending design criteria to target kinetic features of the energy landscape

Learning Design and Service Oriented Architectures:a mutual dependency?

This paper looks at how the concept of reusability has gained currency in e-learning. Initial attention was focused on reuse of content, but recently attention has focused on reusable software tools and reusable activity structures. The former has led to the proposal of service-oriented architectures, and the latter has seen the development of the Learning Design specification. The authors suggest that there is a mutual dependency between the success of these two approaches, as complex Learning Designs require the ability to call on a range of tools, while remaining technology neutral. The paper describes a project at the UK Open University, SLeD, which sought to develop a Learning Design player that would utilise the service-oriented approach. This acted both as a means of exploring some of the issues implicit within both approaches and also provided a practical tool. The SLeD system was successfully implemented in a different university, Liverpool Hope, demonstrating some of the principles of re-use