Everything you wanted to know about Data Analysis and Fitting but were afraid to ask

These notes discuss, in a style intended for physicists, how to average data and fit it to some functional form. I try to make clear what is being calculated, what assumptions are being made, and to give a derivation of results rather than just quote them. The aim is put a lot useful pedagogical material together in a convenient place. This manuscript is a substantial enlargement of lecture notes I prepared for the Bad Honnef School on "Efficient Algorithms in Computational Physics", September 10-14, 2012.Comment: 78 pages, 15 figures. Now includes a discussion of overfitting, including both Maximum Likelihood and Bayesian approache

The Rank One Mixed μ Problem and 'Kharitonov-Type' Analysis

The general mixed μ problem has been shown to be NP hard, so that the exact solution of the general problem is computationally intractable, except for small problems. In this paper we consider not the general problem, but a particular special case of this problem, the rank one mixed μ problem. We show that for this case the mixed μ problem is equivalent to its upper bound (which is convex), and it can in fact be computed easily (and exactly). This special case is shown to be equivalent to the so called "affine parameter variation" problem (for a polynomial with perturbed coefficients) which has been examined in detail in the literature, and for which several celebrated "Kharitonov-type" results have been proven

Solar Dynamics Observatory and Hinode observations of a blowout jet in a coronal hole

A blowout jet occurred within the south coronal hole on 9 February 2011 at 09:00 UT and was observed by the Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory, and the EUV Imaging Spectrometer (EIS) and X-Ray Telescope (XRT) onboard the Hinode spacecraft during coronal hole monitoring performed as part of Hinode Operations Program No. 177. Images from AIA show expanding hot and cold loops from a small bright point with plasma ejected in a curtain up to 30 Mm wide. The initial intensity front of the jet had a projected velocity of 200 km/s and line-of-sight (LOS) velocities measured by EIS are between 100 and 250 km/s. The LOS velocities increased along the jet, implying an acceleration mechanism operating within the body of the jet. The jet plasma had a density of 2.7 x 10^8 cm^-3, and a temperature of 1.4 MK. During the event a number of bright kernels were seen at the base of the bright point. The kernels have sizes of about 1000 km, are variable in brightness, and have lifetimes of 1-15 minutes. An XRT filter ratio yields temperatures of 1.5-3.0 MK for the kernels. The bright point existed for at least ten hours, but disappeared within two hours after the jet, which lasted for 30 minutes. HMI data reveal converging photospheric flows at the location of the bright point, and the mixed polarity magnetic flux canceled over a period of four hours on either side of the jet.Comment: 20 pages, 8 figures, accepted by Solar Physic

Data-based mechanistic modelling, forecasting, and control.

This article briefly reviews the main aspects of the generic data based mechanistic (DBM) approach to modeling stochastic dynamic systems and shown how it is being applied to the analysis, forecasting, and control of environmental and agricultural systems. The advantages of this inductive approach to modeling lie in its wide range of applicability. It can be used to model linear, nonstationary, and nonlinear stochastic systems, and its exploitation of recursive estimation means that the modeling results are useful for both online and offline applications. To demonstrate the practical utility of the various methodological tools that underpin the DBM approach, the article also outlines several typical, practical examples in the area of environmental and agricultural systems analysis, where DBM models have formed the basis for simulation model reduction, control system design, and forecastin

Learning flexibility: the environment and a case study

This paper outlines the flexible student learning environment in the Faculty of Engineering and Surveying, before concentrating on evaluating one online learning option. This Faculty provides a variety of high quality on-campus, distance education and on-line academic programmes and various learning strategies for the heterogeneous student cohort (national and international). By accessing appropriate flexible learning and different learning experiences, students are empowered to determine learning opportunities and methodologies to suit their personal needs. The off-campus mode study may disadvantage students since they don’t have the benefit of face-to-face instructions or to participate in formative assessments delivered informally in lectures. This may lead to feelings of remoteness and isolation leading to poorer learning, lower results in assessments, and may also contribute to drop-out rates, particularly in first year courses. To overcome this inequity, the usual training materials presented for a first year course in 2005 were supplemented with PowerPoint lectures, enhanced with synchronous audio, and a series of quizzes to be used as formative assessments. The lectures and quizzes were presented online via a course web site and were designed to become an integral part of the learning experience. An evaluation of the effectiveness of these strategy demonstrated improved students' learning, a positive contribution to the learning experience, increased enjoyment of the course, and a strong learning motivator. Students reported feeling less disenfranchised with the university and having a greater affinity with the lecturer

Properties of the mixed μ problem and its bounds

Upper and lower bounds for the mixed μ problem have recently been developed, and here we examine the relationship of these bounds to each other and to μ. A number of interesting properties are developed and the implications of these properties for the robustness analysis of linear systems and the development of practical computation schemes are discussed. In particular we find that current techniques can only guarantee easy computation for large problems when μ equals its upper bound, and computational complexity results prohibit this possibility for general problems. In this context we present some special cases where computation is easy and make some direct comparisons between mixed μ and “Kharitonov-type” analysis methods