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.

Zernike radial slope polynomials for wavefront reconstruction and refraction

Ophthalmic wavefront sensors typically measure wavefront slope, from which wavefront phase is reconstructed. We show that ophthalmic prescriptions (in power-vector format) can be obtained directly from slope measurements without wavefront reconstruction. This is achieved by fitting the measurement data with a new set of orthonormal basis functions called Zernike radial slope polynomials. Coefficients of this expansion can be used to specify the ophthalmic power vector using explicit formulas derived by a variety of methods. Zernike coefficients for wavefront error can be recovered from the coefficients of radial slope polynomials, thereby offering an alternative way to perform wavefront reconstruction.

Effect of soil parameter uncertainty on seismic response of buried segmented pipeline

Pipelines are important lifeline facilities spread over a large area and they generally encounter a range of seismic hazards and different soil conditions. The seismic response of a buried segmented pipe depends on various parameters such as the type of buried pipe material and joints, end restraint conditions, soil characteristics, burial depths, and earthquake ground motion, etc. This study highlights the effect of the variation of geotechnical properties of the surrounding soil on seismic response of a buried pipeline. The variations of the properties of the surrounding soil along the pipe are described by sampling them from predefined probability distribution. The soil-pipe interaction model is developed in OpenSEES. Nonlinear earthquake time-history analysis is performed to study the effect of soil parameters variability on the response of pipeline. Based on the results, it is found that uncertainty in soil parameters may result in significant response variability of the pipeline.

Permutation polynomials of the form (xp −x +δ)s +L(x)

Recently, several classes of permutation polynomials of the form (x2 + x + δ)s + x over F2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp − x + δ)s + L(x) over Fpm is investigated, where L(x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on F2m are derived. Three classes of permutation polynomials over F3m are also presented.

Revisiting Polya's summation techniques using a spreadsheet : from addition tables to Bernoulli polynomials

Recurrence relations in mathematics form a very powerful and compact way of looking at a wide range of relationships. Traditionally, the concept of recurrence has often been a difficult one for the secondary teacher to convey to students. Closely related to the powerful proof technique of mathematical induction, recurrences are able to capture many relationships in formulas much simpler than so-called direct or closed formulas. In computer science, recursive coding often has a similar compactness property, and, perhaps not surprisingly, suffers from similar problems in the classroom as recurrences: the students often find both the basic concepts and practicalities elusive. Using models designed to illuminate the relevant principles for the students, we offer a range of examples which use the modern spreadsheet environment to powerfully illustrate the great expressive and computational power of recurrences.

Response of segmented bored transit tunnels to surface blast

Increasing threat of terrorism highlights the importance of enhancing the resilience of underground tunnels to all hazards. This paper develops, applies and compares the Arbitrary Lagrangian Eulerian (ALE) and Smooth Particle Hydrodynamics (SPH) techniques to treat the response of buried tunnels to surface explosions. The results and outcomes of the two techniques were compared, along with results from existing test data. The comparison shows that the ALE technique is a better method for describing the tunnel response for above ground explosion with regards to modeling accuracy and computational efficiency. The ALE technique was then applied to treat the blast response of different types of segmented bored tunnels buried in dry sand. Results indicate that the most used modern ring type segmented tunnels were more flexible for in-plane response, however, they suffered permanent drifts between the rings. Hexagonal segmented tunnels responded with negligible drifts in the longitudinal direction, but the magnitudes of in-plane drifts were large and hence hazardous for the tunnel. Interlocking segmented tunnels suffered from permanent drifts in both the longitudinal and transverse directions. Multi-surface radial joints in both the hexagonal and interlocking segments affected the flexibility of the tunnel in the transverse direction. The findings offer significant new information in the behavior of segmented bored tunnels to guide their future implementation in civil engineering applications.

Blast response of segmented bored tunnel using coupled SPH–FE method

Underground transport tunnels are vulnerable to blast events. This paper develops and applies a fully coupled technique involving the Smooth Particle Hydrodynamics and Finite Element techniques to investigate the blast response of segmented bored tunnels. Findings indicate that several bolts failed in the longitudinal direction due to redistribution of blast loading to adjacent tunnel rings. The tunnel segments respond as arch mechanisms in the transverse direction and suffered damage mainly due to high bending stresses. The novel information from the present study will enable safer designs of buried tunnels and provide a benchmark reference for future developments in this area.

Blast response and failure analysis of a segmented buried tunnel

Underground tunnels are vulnerable to terrorist attacks which can cause collapse of the tunnel structures or at least extensive damage, requiring lengthy repairs. This paper treats the blast impact on a reinforced concrete segmental tunnel buried in soil under a number of parametric conditions; soil properties, soil cover, distance of explosive from the tunnel centreline and explosive weight and analyses the possible failure patterns. A fully coupled Fluid Structure Interaction (FSI) technique incorporating the Arbitrary Lagrangian-Eulerian (ALE) method is used in this study. Results indicate that the tunnel in saturated soil is more vulnerable to severe damage than that buried in either partially saturated soil or dry soil. The tunnel is also more vulnerable to surface explosions which occur directly above the centre of the tunnel than those that occur at any equivalent distances in the ground away from the tunnel centre. The research findings provide useful information on modeling, analysis, overall tunnel response and failure patterns of segmented tunnels subjected to blast loads. This information will guide future development and application of research in this field.

Infra-red pupil detection for use in a face recognition system

This paper presents a new method of eye localisation and face segmentation for use in a face recognition system. By using two near infrared light sources, we have shown that the face can be coarsely segmented, and the eyes can be accurately located, increasing the accuracy of the face localisation and improving the overall speed of the system. The system is able to locate both eyes within 25% of the eye-to-eye distance in over 96% of test cases.

They also serve who only stand and wait

Purpose Waiting for service by customers is an important problem for many financial service marketers. Two new approaches are proposed. First, customer evaluation of the service is increased with an ambient scent. Second a cognitive variable is identified which different iates customers by the way they value time so that they can be segmented. Methodology Pretests included focus groups which highlighted financial services and a pilot test were foll owed by a main sample of 607 subjects. Structural equation modelling and multivariate analysis of covariance were used for analysis. Findings A cognitive variable, the need for time management can be used, together with demographic and customer net worth data, to segment a customer base. Two environmental interventions, music and scent, can increase customer satisfaction among customers kept waiting in a line. Research implications Two original approaches to a rapidly growing service marketing problem are identified. Practical implications Service contact points can reduce incidence of "queue rage" and enhance customer satisfaction by either or both of two simple modifications to the service environment or a preventive strategy of offering targeted customers an alternative. Originality A new method of segmentation and a new environmental intervention are proposed .

Fusion of in-vehicle sensor data to develop Intelligent Driver Training System (IDTS)

The over represented number of novice drivers involved in crashes is alarming. Driver training is one of the interventions aimed at mitigating the number of crashes that involve young drivers. To our knowledge, Advanced Driver Assistance Systems (ADAS) have never been comprehensively used in designing an intelligent driver training system. Currently, there is a need to develop and evaluate ADAS that could assess driving competencies. The aim is to develop an unsupervised system called Intelligent Driver Training System (IDTS) that analyzes crash risks in a given driving situation. In order to design a comprehensive IDTS, data is collected from the Driver, Vehicle and Environment (DVE), synchronized and analyzed. The first implementation phase of this intelligent driver training system deals with synchronizing multiple variables acquired from DVE. RTMaps is used to collect and synchronize data like GPS, vehicle dynamics and driver head movement. After the data synchronization, maneuvers are segmented out as right turn, left turn and overtake. Each maneuver is composed of several individual tasks that are necessary to be performed in a sequential manner. This paper focuses on turn maneuvers. Some of the tasks required in the analysis of ‘turn’ maneuver are: detect the start and end of the turn, detect the indicator status change, check if the indicator was turned on within a safe distance and check the lane keeping during the turn maneuver. This paper proposes a fusion and analysis of heterogeneous data, mainly involved in driving, to determine the risk factor of particular maneuvers within the drive. It also explains the segmentation and risk analysis of the turn maneuver in a drive.

Word Segmentation for Chinese Wikipedia Using N-Gram Mutual Information

In this paper, we propose an unsupervised segmentation approach, named "n-gram mutual information", or NGMI, which is used to segment Chinese documents into n-character words or phrases, using language statistics drawn from the Chinese Wikipedia corpus. The approach alleviates the tremendous effort that is required in preparing and maintaining the manually segmented Chinese text for training purposes, and manually maintaining ever expanding lexicons. Previously, mutual information was used to achieve automated segmentation into 2-character words. The NGMI approach extends the approach to handle longer n-character words. Experiments with heterogeneous documents from the Chinese Wikipedia collection show good results.

Thai word segmentation with hidden Markov Model and decision tree

The Thai written language is one of the languages that does not have word boundaries. In order to discover the meaning of the document, all texts must be separated into syllables, words, sentences, and paragraphs. This paper develops a novel method to segment the Thai text by combining a non-dictionary based technique with a dictionary-based technique. This method first applies the Thai language grammar rules to the text for identifying syllables. The hidden Markov model is then used for merging possible syllables into words. The identified words are verified with a lexical dictionary and a decision tree is employed to discover the words unidentified by the lexical dictionary. Documents used in the litigation process of Thai court proceedings have been used in experiments. The results which are segmented words, obtained by the proposed method outperform the results obtained by other existing methods.