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.

Cell image classification using histograms, higher order statistics and adaboost

A cell classification algorithm that uses first, second and third order statistics of pixel intensity distributions over pre-defined regions is implemented and evaluated. A cell image is segmented into 6 regions extending from a boundary layer to an inner circle. First, second and third order statistical features are extracted from histograms of pixel intensities in these regions. Third order statistical features used are one-dimensional bispectral invariants. 108 features were considered as candidates for Adaboost based fusion. The best 10 stage fused classifier was selected for each class and a decision tree constructed for the 6-class problem. The classifier is robust, accurate and fast by design.

Analysis of steel structures for first- and second-order element (displacement and force) solutions

Finite element method (FEM) relies on an approximate function to fit into a governing equation and minimizes the residual error in the integral sense in order to generate solutions for the boundary value problems (nodal solutions). Because of this FEM does not show simultaneous capacities for accurate displacement and force solutions at node and along an element, especially when under the element loads, which is of much ubiquity. If the displacement and force solutions are strictly confined to an element’s or member’s ends (nodal response), the structural safety along an element (member) is inevitably ignored, which can definitely hinder the design of a structure for both serviceability and ultimate limit states. Although the continuous element deflection and force solutions can be transformed into the discrete nodal solutions by mesh refinement of an element (member), this setback can also hinder the effective and efficient structural assessment as well as the whole-domain accuracy for structural safety of a structure. To this end, this paper presents an effective, robust, applicable and innovative approach to generate accurate nodal and element solutions in both fields of displacement and force, in which the salient and unique features embodies its versatility in applications for the structures to account for the accurate linear and second-order elastic displacement and force solutions along an element continuously as well as at its nodes. The significance of this paper is on shifting the nodal responses (robust global system analysis) into both nodal and element responses (sophisticated element formulation).

Non-linear refined finite element elastic analysis of steel frames with generalized transverse member loads

In the finite element modelling of steel frames, external loads usually act along the members rather than at the nodes only. Conventionally, when a member is subjected to these transverse loads, they are converted to nodal forces which act at the ends of the elements into which the member is discretised by either lumping or consistent nodal load approaches. For a contemporary geometrically non-linear analysis in which the axial force in the member is large, accurate solutions are achieved by discretising the member into many elements, which can produce unfavourable consequences on the efficacy of the method for analysing large steel frames. Herein, a numerical technique to include the transverse loading in the non-linear stiffness formulation for a single element is proposed, and which is able to predict the structural responses of steel frames involving the effects of first-order member loads as well as the second-order coupling effect between the transverse load and the axial force in the member. This allows for a minimal discretisation of a frame for second-order analysis. For those conventional analyses which do include transverse member loading, prescribed stiffness matrices must be used for the plethora of specific loading patterns encountered. This paper shows, however, that the principle of superposition can be applied to the equilibrium condition, so that the form of the stiffness matrix remains unchanged with only the magnitude of the loading being needed to be changed in the stiffness formulation. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. The results are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple structural frames.

Higher order universal one-way hash functions from the subset sum assumption

Universal One-Way Hash Functions (UOWHFs) may be used in place of collision-resistant functions in many public-key cryptographic applications. At Asiacrypt 2004, Hong, Preneel and Lee introduced the stronger security notion of higher order UOWHFs to allow construction of long-input UOWHFs using the Merkle-Damgård domain extender. However, they did not provide any provably secure constructions for higher order UOWHFs. We show that the subset sum hash function is a kth order Universal One-Way Hash Function (hashing n bits to m < n bits) under the Subset Sum assumption for k = O(log m). Therefore we strengthen a previous result of Impagliazzo and Naor, who showed that the subset sum hash function is a UOWHF under the Subset Sum assumption. We believe our result is of theoretical interest; as far as we are aware, it is the first example of a natural and computationally efficient UOWHF which is also a provably secure higher order UOWHF under the same well-known cryptographic assumption, whereas this assumption does not seem sufficient to prove its collision-resistance. A consequence of our result is that one can apply the Merkle-Damgård extender to the subset sum compression function with ‘extension factor’ k+1, while losing (at most) about k bits of UOWHF security relative to the UOWHF security of the compression function. The method also leads to a saving of up to m log(k+1) bits in key length relative to the Shoup XOR-Mask domain extender applied to the subset sum compression function.

Enhancement of optical absorption in thin-film solar cells through the excitation of higher-order nanoparticle plasmon modes

Recent research in the rapidly emerging field of plasmonics has shown the potential to significantly enhance light trapping inside thin-film solar cells by using metallic nanoparticles. In this article it is demonstrated the plasmon enhancement of optical absorption in amorphous silicon solar cells by using silver nanoparticles. Based on the analysis of the higher-order surface plasmon modes, it is shown how spectral positions of the surface plasmons affect the plasmonic enhancement of thin-film solar cells. By using the predictive 3D modeling, we investigate the effect of the higher-order modes on that enhancement. Finally, we suggest how to maximize the light trapping and optical absorption in the thin-film cell by optimizing the nanoparticle array parameters, which in turn can be used to fine tune the corresponding surface plasmon modes.

Higher order spectra based support vector machine for arrhythmia classification

Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart by the sympathetic and parasympathetic branches of the autonomic nervous system. HRV analysis is an important tool to observe the heart’s ability to respond to normal regulatory impulses that affect its rhythm. Like many bio-signals, HRV signals are non-linear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of non-linear systems and provides good noise immunity. A computer-based arrhythmia detection system of cardiac states is very useful in diagnostics and disease management. In this work, we studied the identification of the HRV signals using features derived from HOS. These features were fed to the support vector machine (SVM) for classification. Our proposed system can classify the normal and other four classes of arrhythmia with an average accuracy of more than 85%.

A new approach to spatial data interpolation using higher-order statistics

Interpolation techniques for spatial data have been applied frequently in various fields of geosciences. Although most conventional interpolation methods assume that it is sufficient to use first- and second-order statistics to characterize random fields, researchers have now realized that these methods cannot always provide reliable interpolation results, since geological and environmental phenomena tend to be very complex, presenting non-Gaussian distribution and/or non-linear inter-variable relationship. This paper proposes a new approach to the interpolation of spatial data, which can be applied with great flexibility. Suitable cross-variable higher-order spatial statistics are developed to measure the spatial relationship between the random variable at an unsampled location and those in its neighbourhood. Given the computed cross-variable higher-order spatial statistics, the conditional probability density function (CPDF) is approximated via polynomial expansions, which is then utilized to determine the interpolated value at the unsampled location as an expectation. In addition, the uncertainty associated with the interpolation is quantified by constructing prediction intervals of interpolated values. The proposed method is applied to a mineral deposit dataset, and the results demonstrate that it outperforms kriging methods in uncertainty quantification. The introduction of the cross-variable higher-order spatial statistics noticeably improves the quality of the interpolation since it enriches the information that can be extracted from the observed data, and this benefit is substantial when working with data that are sparse or have non-trivial dependence structures.

Compensation for higher order mode coupling between inclined coupling slots and radiating slots in planar slotted waveguide arrays

Summary form only given. Geometric simplicity, efficiency and polarization purity make slot antenna arrays ideal solutions for many radar, communications and navigation applications, especially when high power, light weight and limited scan volume are priorities. Resonant arrays of longitudinal slots have a slot spacing of one-half guide wavelength at the design frequency, so that the slots are located at the standing wave peaks. Planar arrays are implemented using a number of rectangular waveguides (branch line guides), arranged side-by-side, while waveguides main lines located behind and at right angles to the branch lines excite the radiating waveguides via centered-inclined coupling slots. Planar slotted waveguide arrays radiate broadside beams and all radiators are designed to be in phase.

Novel non-linear elastic structural analysis with generalised transverse element loads using a refined finite element

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.