The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Dengue fever and el nino-southern oscillation in Queensland, Australia : a time series predictive model

Background It remains unclear over whether it is possible to develop an epidemic forecasting model for transmission of dengue fever in Queensland, Australia. Objectives To examine the potential impact of El Niño/Southern Oscillation on the transmission of dengue fever in Queensland, Australia and explore the possibility of developing a forecast model of dengue fever. Methods Data on the Southern Oscillation Index (SOI), an indicator of El Niño/Southern Oscillation activity, were obtained from the Australian Bureau of Meteorology. Numbers of dengue fever cases notified and the numbers of postcode areas with dengue fever cases between January 1993 and December 2005 were obtained from the Queensland Health and relevant population data were obtained from the Australia Bureau of Statistics. A multivariate Seasonal Auto-regressive Integrated Moving Average model was developed and validated by dividing the data file into two datasets: the data from January 1993 to December 2003 were used to construct a model and those from January 2004 to December 2005 were used to validate it. Results A decrease in the average SOI (ie, warmer conditions) during the preceding 3–12 months was significantly associated with an increase in the monthly numbers of postcode areas with dengue fever cases (β=−0.038; p = 0.019). Predicted values from the Seasonal Auto-regressive Integrated Moving Average model were consistent with the observed values in the validation dataset (root-mean-square percentage error: 1.93%). Conclusions Climate variability is directly and/or indirectly associated with dengue transmission and the development of an SOI-based epidemic forecasting system is possible for dengue fever in Queensland, Australia.

Combination of Kalman filter and least error square techniques in power system

An algorithm based on the concept of combining Kalman filter and Least Error Square (LES) techniques is proposed in this paper. The algorithm is intended to estimate signal attributes like amplitude, frequency and phase angle in the online mode. This technique can be used in protection relays, digital AVRs, DGs, DSTATCOMs, FACTS and other power electronics applications. The Kalman filter is modified to operate on a fictitious input signal and provides precise estimation results insensitive to noise and other disturbances. At the same time, the LES system has been arranged to operate in critical transient cases to compensate the delay and inaccuracy identified because of the response of the standard Kalman filter. Practical considerations such as the effect of noise, higher order harmonics, and computational issues of the algorithm are considered and tested in the paper. Several computer simulations and a laboratory test are presented to highlight the usefulness of the proposed method. Simulation results show that the proposed technique can simultaneously estimate the signal attributes, even if it is highly distorted due to the presence of non-linear loads and noise.

Automated error correction of business process models

As order dependencies between process tasks can get complex, it is easy to make mistakes in process model design, especially behavioral ones such as deadlocks. Notions such as soundness formalize behavioral errors and tools exist that can identify such errors. However these tools do not provide assistance with the correction of the process models. Error correction can be very challenging as the intentions of the process modeler are not known and there may be many ways in which an error can be corrected. We present a novel technique for automatic error correction in process models based on simulated annealing. Via this technique a number of process model alternatives are identified that resolve one or more errors in the original model. The technique is implemented and validated on a sample of industrial process models. The tests show that at least one sound solution can be found for each input model and that the response times are short.

Queer/error : gay media systems and processes of abjection

Gay community media functions as a system with three nodes, in which the flows of information and capital theoretically benefit all parties: the gay community gains a sense of cohesion and citizenship through media; the gay media outlets profit from advertisers’ capital; and advertisers recoup their investments in lucrative ‘pink dollar’ revenue. But if a necessary corollary of all communication systems is error or noise, where—and what—are the errors in this system? In this paper we argue that the ‘error’ in the gay media system is Queerness, and that the gay media system ejects (in a process of Kristevan abjection) these Queer identities in order to function successfully. We examine the ways in which Queer identities are excluded from representation in such media through a discourse and content analysis of The Sydney Star Observer (Australia’s largest gay and lesbian paper). First, we analyse the way Queer bodies are excluded from the discourses that construct and reinforce both the ideal gay male body and the notions of homosexual essence required for that body to be meaningful. We then argue that abject Queerness returns in the SSO’s discourses of public health through the conspicuous absence of the AIDS-inflicted body (which we read as the epitome of the abject Queer), since this absence paradoxically conjures up a trace of that which the system tries to expel. We conclude by arguing that because the ‘Queer error’ is integral to the SSO, gay community media should practise a politics of Queer inclusion rather than exclusion.

A dynamic approach to forecast rental growth

Numerous econometric models have been proposed for forecasting property market performance, but limited success has been achieved in finding a reliable and consistent model to predict property market movements over a five to ten year timeframe. This research focuses on office rental growth forecasts and overviews many of the office rent models that have evolved over the past 20 years. A model by DiPasquale and Wheaton is selected for testing in the Brisbane, Australia office market. The adaptation of this study did not provide explanatory variables that could assist in developing a reliable, predictive model of office rental growth. In light of this result, the paper suggests a system dynamics framework that includes an econometric model based on historical data as well as user input guidance for the primary variables. The rent forecast outputs would be assessed having regard to market expectations and probability profiling undertaken for use in simulation exercises. The paper concludes with ideas for ongoing research.

Design of a preliminary error impact analysis model for spatial safety assessment of earthmoving operations

Regardless of technology benefits, safety planners still face difficulties explaining errors related to the use of different technologies and evaluating how the errors impact the performance of safety decision making. This paper presents a preliminary error impact analysis testbed to model object identification and tracking errors caused by image-based devices and algorithms and to analyze the impact of the errors for spatial safety assessment of earthmoving and surface mining activities. More specifically, this research designed a testbed to model workspaces for earthmoving operations, to simulate safety-related violations, and to apply different object identification and tracking errors on the data collected and processed for spatial safety assessment. Three different cases were analyzed based on actual earthmoving operations conducted at a limestone quarry. Using the testbed, the impacts of the errors were investigated for the safety planning purpose.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical VC dimension, empirical VC entropy, and margin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.

Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.