A general procedure for the derivation of principal domains of higher-order spectra

A general procedure to determine the principal domain (i.e., nonredundant region of computation) of any higher-order spectrum is presented, using the bispectrum as an example. The procedure is then applied to derive the principal domain of the trispectrum of a real-valued, stationary time series. These results are easily extended to compute the principal domains of other higher-order spectra

Position, rotation, and scale invariant recognition of images using higher-order spectra

A new approach to recognition of images using invariant features based on higher-order spectra is presented. Higher-order spectra are translation invariant because translation produces linear phase shifts which cancel. Scale and amplification invariance are satisfied by the phase of the integral of a higher-order spectrum along a radial line in higher-order frequency space because the contour of integration maps onto itself and both the real and imaginary parts are affected equally by the transformation. Rotation invariance is introduced by deriving invariants from the Radon transform of the image and using the cyclic-shift invariance property of the discrete Fourier transform magnitude. Results on synthetic and actual images show isolated, compact clusters in feature space and high classification accuracies

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale and amplification invariant, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

Higher order spectral analysis of Chua's circuit

Higher order spectral analysis is used to investigate nonlinearities in time series of voltages measured from a realization of Chua's circuit. For period-doubled limit cycles, quadratic and cubic nonlinear interactions result in phase coupling and energy exchange between increasing numbers of triads and quartets of Fourier components as the nonlinearity of the system is increased. For circuit parameters that result in a chaotic Rossler-type attractor, bicoherence and tricoherence spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. When the circuit exhibits a double-scroll chaotic attractor the bispectrum is zero, but the tricoherences are high, consistent with the importance of higher-than-second order nonlinear interactions during chaos associated with the double scroll.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.

Higher-Order spectra of nonlinear polynomial models for Chua's circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

On the behaviour of higher-order spectral features for object recognition in the presence of various types of noise

This paper presents results on the robustness of higher-order spectral features to Gaussian, Rayleigh, and uniform distributed noise. Based on cluster plots and accuracy results for various signal to noise conditions, the higher-order spectral features are shown to be better than moment invariant features.

Monocular amblyopia and higher order aberrations

This study compared the corneal and total higher order aberrations between the fellow eyes in monocular amblyopia. Nineteen amblyopic subjects (8 refractive and 11 strabismic) (mean age 30 ± 11 years) were recruited. A range of biometric and optical measurements were collected from the amblyopic and non-amblyopic eye including; axial length, corneal topography and total higher order aberrations. For a sub-group of eleven non-presbyopic subjects (6 refractive and 5 strabismic amblyopes, mean age 29 ± 10 years) total higher order aberrations were also measured during accommodation (2.5 D stimuli). Amblyopic eyes were significantly shorter and more hyperopic compared to non-amblyopic eyes and the interocular difference in axial length correlated with both the magnitude of anisometropia and amblyopia (both p < 0.01). Significant differences in higher order aberrations were observed between fellow eyes, which varied with the type of amblyopia. Refractive amblyopes displayed higher levels of 4th order corneal aberrations C(4, 0)(spherical aberration), C(4, 2)(secondary astigmatism 90°) and C(4, −2)(secondary astigmatism along 45°) in the amblyopic eye compared to the non-amblyopic eye. Strabismic amblyopes exhibited significantly higher levels of C(3, 3)(trefoil) in the amblyopic eye for both corneal and total higher order aberrations. During accommodation, the amblyopic eye displayed a significantly greater lag of accommodation compared to the non-amblyopic eye, while the changes in higher order aberrations were similar in magnitude between fellow eyes. Asymmetric visual experience during development appears to be associated with asymmetries in higher order aberrations, in some cases proportional to the magnitude of anisometropia and dependent upon the amblyogenic factor.

Curriculum design and higher order skills : challenging assumptions

This paper is based on an Australian Learning & Teaching Council (ALTC) funded evaluation in 13 universities across Australia and New Zealand of the use of Engineers Without Borders (EWB) projects in first-year engineering courses. All of the partner institutions have implemented this innovation differently and comparison of these implementations affords us the opportunity to assemble "a body of carefully gathered data that provides evidence of which approaches work for which students in which learning environments". This study used a mixed-methods data collection approach and a realist analysis. Data was collected by program logic analysis with course co-ordinators, observation of classes, focus groups with students, exit survey of students and interviews with staff as well as scrutiny of relevant course and curriculum documents. Course designers and co-ordinators gave us a range of reasons for using the projects, most of which alluded to their presumed capacity to deliver experience in and learning of higher order thinking skills in areas such as sustainability, ethics, teamwork and communication. For some students, however, the nature of the projects decreased their interest in issues such as ethical development, sustainability and how to work in teams. We also found that the projects provoked different responses from students depending on the nature of the courses in which they were embedded (general introduction, design, communication, or problem-solving courses) and their mode of delivery (lecture, workshop or online).

Analysis of higher-order aberrations in a large clinical population

Purpose: To use a large wavefront database of a clinical population to investigate relationships between refractions and higher order aberrations and between aberrations of right and left eyes. Methods: Third and fourth-order aberration coefficients and higher-order root-mean-squared aberrations (HO RMS), scaled to a pupil size of 4.5 mm diameter, were analysed in a population of about 24,000 patients from Carl Zeiss Vision's European wavefront database. Correlations were determined between the aberrations and the variables of refraction, near addition and cylinder. Results: Most aberration coefficients were significantly dependent upon these variables, but the proportions of aberrations that could be explained by these factors were less than 2% except for spherical aberration (12%), horizontal coma (9%) and HO RMS (7%). Near addition was the major contributor for horizontal coma (8.5% out of 9.5%) and spherical equivalent was the major contributor for spherical aberration (7.7% out of 11.6%). Interocular correlations were highly significant for all aberration coefficients, varying between 0.16 and 0.81. Anisometropia was a variable of significance for three aberrations (vertical coma, secondary astigmatism and tetrafoil), but little importance can be placed on this because of the small proportions of aberrations that can be explained by refraction (all less than 1.0 %). Conclusions: Most third- and fourth-order aberration coefficients were significantly dependent upon spherical equivalent, near addition and cylinder, but only horizontal coma (9%) and spherical aberration (12%) showed dependencies of greater than 2%. Interocular correlations were highly significant for all aberration coefficients, but anisometropia had little influence on aberration coefficients.

Higher order thinking in chemistry curriculum and its assessment

Higher-order thinking has featured persistently in the reform agenda for science education. The intended curriculum in various countries sets out aspirational statements for the levels of higher-order thinking to be attained by students. This study reports the extent to which chemistry examinations from four Australian states align and facilitate the intended higher-order thinking skills stipulated in curriculum documents. Through content analysis, the curriculum goals were identified for each state and compared to the nature of question items in the corresponding examinations. Categories of higher-order thinking were adapted from the OECD’s PISA Science test to analyze question items. There was considerable variation in the extent to which the examinations from the states supported the curriculum intent of developing and assessing higher-order thinking. Generally, examinations that used a marks-based system tended to emphasize lower-order thinking, with a greater distribution of marks allocated for lower-order thinking questions. Examinations associated with a criterion-referenced examination tended to award greater credit for higher-order thinking questions. The level of complexity of chemistry was another factor that limited the extent to which examination questions supported higher-order thinking. Implications from these findings are drawn for the authorities responsible for designing curriculum and assessment procedures and for teachers.

Robust image hash functions using higher order spectra

Robust hashing is an emerging field that can be used to hash certain data types in applications unsuitable for traditional cryptographic hashing methods. Traditional hashing functions have been used extensively for data/message integrity, data/message authentication, efficient file identification and password verification. These applications are possible because the hashing process is compressive, allowing for efficient comparisons in the hash domain but non-invertible meaning hashes can be used without revealing the original data. These techniques were developed with deterministic (non-changing) inputs such as files and passwords. For such data types a 1-bit or one character change can be significant, as a result the hashing process is sensitive to any change in the input. Unfortunately, there are certain applications where input data are not perfectly deterministic and minor changes cannot be avoided. Digital images and biometric features are two types of data where such changes exist but do not alter the meaning or appearance of the input. For such data types cryptographic hash functions cannot be usefully applied. In light of this, robust hashing has been developed as an alternative to cryptographic hashing and is designed to be robust to minor changes in the input. Although similar in name, robust hashing is fundamentally different from cryptographic hashing. Current robust hashing techniques are not based on cryptographic methods, but instead on pattern recognition techniques. Modern robust hashing algorithms consist of feature extraction followed by a randomization stage that introduces non-invertibility and compression, followed by quantization and binary encoding to produce a binary hash output. In order to preserve robustness of the extracted features, most randomization methods are linear and this is detrimental to the security aspects required of hash functions. Furthermore, the quantization and encoding stages used to binarize real-valued features requires the learning of appropriate quantization thresholds. How these thresholds are learnt has an important effect on hashing accuracy and the mere presence of such thresholds are a source of information leakage that can reduce hashing security. This dissertation outlines a systematic investigation of the quantization and encoding stages of robust hash functions. While existing literature has focused on the importance of quantization scheme, this research is the first to emphasise the importance of the quantizer training on both hashing accuracy and hashing security. The quantizer training process is presented in a statistical framework which allows a theoretical analysis of the effects of quantizer training on hashing performance. This is experimentally verified using a number of baseline robust image hashing algorithms over a large database of real world images. This dissertation also proposes a new randomization method for robust image hashing based on Higher Order Spectra (HOS) and Radon projections. The method is non-linear and this is an essential requirement for non-invertibility. The method is also designed to produce features more suited for quantization and encoding. The system can operate without the need for quantizer training, is more easily encoded and displays improved hashing performance when compared to existing robust image hashing algorithms. The dissertation also shows how the HOS method can be adapted to work with biometric features obtained from 2D and 3D face images.

Higher-order aberrations and anisometropia

Purpose/aim Myopia incidence is increasing around the world. Myopisation is considered to be caused by a variety of factors. One consideration is whether higher-order aberrations (HOA) influence myopisation. More knowledge of optics in anisometropic eyes might give further insight into the development of refractive error. Materials and methods To analyse the possible influence of HOA on refractive error development, we compared HOA between anisometropes and isometropes. We analysed HOA up to the 4th order for both eyes of 20 anisometropes (mean age: 43 ± 17 years) and 20 isometropes (mean age: 33 ±17 years). HOA were measured with the Shack-Hartman i.Profiler (Carl Zeiss, Germany) and were recalculated for a 4 mm pupil. Mean spherical equivalent (MSE) was based on the subjective refraction. Anisometropia was defined as ≥1D interocular difference in MSE. The mean absolute differences between right and left eyes in spherical equivalent were 0.28 ± 0.21 D in the isometropic group and 2.81 ± 2.04 D in the anisometropic group. Interocular differences in HOA were compared with the interocular difference in MSE using correlations. Results For isometropes oblique trefoil, vertical coma, horizontal coma and spherical aberration showed significant correlations between the two eyes. In anisometropes all analysed higher-order aberrations correlated significantly between the two eyes except oblique secondary astigmatism and secondary astigmatism. When analysing anisometropes and isometropes separately, no significant correlations were found between interocular differences of higher-order aberrations and MSE. For isometropes and anisometropes combined, tetrafoil correlated significantly with MSE in left eyes. Conclusions The present study could not show that interocular differences of higher-order aberrations increase with increasing interocular difference in MSE.

Higher-order non-linear analysis of steel structures. Part I : elastic second-order formulation

This paper presents a higher-order beam-column formulation that can capture the geometrically non-linear behaviour of steel framed structures which contain a multiplicity of slender members. Despite advances in computational frame software, analyses of large frames can still be problematic from a numerical standpoint and so the intent of the paper is to fulfil a need for versatile, reliable and efficient non-linear analysis of general steel framed structures with very many members. Following a comprehensive review of numerical frame analysis techniques, a fourth-order element is derived and implemented in an updated Lagrangian formulation, and it is able to predict flexural buckling, snap-through buckling and large displacement post-buckling behaviour of typical structures whose responses have been reported by independent researchers. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. The higher-order element forms a basis for augmenting the geometrically non-linear approach with material non-linearity through the refined plastic hinge methodology described in the companion paper.

Higher-order non-linear analysis of steel structures. Part II : refined plastic hinge formulation

In the companion paper, a fourth-order element formulation in an updated Lagrangian formulation was presented to handle geometric non-linearities. The formulation of the present paper extends this to include material non-linearity by proposing a refined plastic hinge approach to analyse large steel framed structures with many members, for which contemporary algorithms based on the plastic zone approach can be problematic computationally. This concept is an advancement of conventional plastic hinge approaches, as the refined plastic hinge technique allows for gradual yielding, being recognized as distributed plasticity across the element section, a condition of full plasticity, as well as including strain hardening. It is founded on interaction yield surfaces specified analytically in terms of force resultants, and achieves accurate and rapid convergence for large frames for which geometric and material non-linearity are significant. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. In addition to the numerical efficiency, the present versatile approach is able to capture different kinds of material and geometric non-linearities on general applications of steel structures, and thereby it offers an efficacious and accurate means of assessing non-linear behaviour of the structures for engineering practice.