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The removal of carefully-selected examples from training data has recently emerged as an effective way of improving the robustness of machine learning models. However, the best way to select these examples remains an open question. In this paper, we consider the problem from the perspective of unsupervised domain adaptation (UDA). We propose AdaPrune, a method for UDA whereby training examples are removed to attempt to align the training distribution to that of the target data. By adopting the maximum mean discrepancy (MMD) as the criterion for alignment, the problem can be neatly formulated and solved as an integer quadratic program. We evaluate our approach on a real-world domain shift task of bioacoustic event detection. As a method for UDA, we show that AdaPrune outperforms related techniques, and is complementary to other UDA algorithms such as CORAL. Our analysis of the relationship between the MMD and model accuracy, along with t-SNE plots, validate the proposed method as a principled and well-founded way of performing data pruning.

Additive manufacturing (AM; 3D printing) in aluminium using laser powder bed fusion provides a new design space for lightweight mirror production. Printing layer-by-layer enables the use of intricate lattices for mass reduction, as well as organic shapes generated by topology optimisation, resulting in mirrors optimised for function as opposed to subtractive machining. However, porosity, a common AM defect, is present in printed aluminium and it is a result of the printing environment being either too hot or too cold, or gas entrapped bubbles within the aluminium powder. When present in an AM mirror substrates, porosity manifests as pits on the reflective surface, which increases micro-roughness and therefore scattered light. There are different strategies to reduce the impact of porosity: elimination during printing, coating the aluminium print in nickel phosphorous, or to apply a heat and pressure treatment to close the pores, commonly known as a hot isostatic press (HIP). This paper explores the application of HIP on printed aluminium substrates intended for mirror production using single point diamond turning (SPDT). The objective of the HIP is to reduce porosity whilst targeting a small grain growth within the aluminium, which is important in allowing the SPDT to generate surfaces with low micro-roughness. For this study, three disks, 50 mm diameter by 5 mm, were printed in AlSi10Mg at 0 deg, 45 deg, and 90 deg with respect to the build plate. X-ray computed tomography (XCT) was conducted before and after the HIP cycle to confirm the effectiveness of HIP to close porosity. The disks were SPDT and the micro-roughness evaluated. Mechanical testing and electron backscatter diffraction (EBSD) was used to quantify the mechanical strength and the grain size after HIP., Comment: 14 pages, 8 figures, submitted to SPIE Astronomical Telescopes & Instrumentation, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation VI (Conference 13100, Paper 141)

This paper considers the problem of model selection under domain shift. Motivated by principles from distributionally robust optimisation (DRO) and domain adaptation theory, it is proposed that the training-validation split should maximise the distribution mismatch between the two sets. By adopting the maximum mean discrepancy (MMD) as the measure of mismatch, it is shown that the partitioning problem reduces to kernel k-means clustering. A constrained clustering algorithm, which leverages linear programming to control the size, label, and (optionally) group distributions of the splits, is presented. The algorithm does not require additional metadata, and comes with convergence guarantees. In experiments, the technique consistently outperforms alternative splitting strategies across a range of datasets and training algorithms, for both domain generalisation (DG) and unsupervised domain adaptation (UDA) tasks. Analysis also shows the MMD between the training and validation sets to be strongly rank-correlated ($\rho=0.63$) with test domain accuracy, further substantiating the validity of this approach.

This note includes an assessment of the partially overlapping samples t-tests in scenarios where elements of the test are at their extremes, including where only one sample contains independent observations

Inverse normal transformations applied to the partially overlapping samples t-tests by Derrick et.al. (2017) are considered for their Type I error robustness and power. The inverse normal transformation solutions proposed in this paper are shown to maintain Type I error robustness. For increasing degrees of skewness they also offer improved power relative to the parametric partially overlapping samples t-tests. The power when using inverse normal transformation solutions are comparable to rank based non-parametric solutions., Comment: Inverse Normal Transformations Partially overlapping samples

We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumption that the same is known for quasi-split unitary groups. The classification of automorphic representations is given in terms of automorphic representations of general linear groups. The classification of irreducible admissible representations is given in terms of Langlands parameters., Comment: 220 pages; v3 added acknowledgement of financial support, corrected more typos

Working collaboratively with the researchers, a small team of teachers developed and taught a lesson based on the Teaching for Abstraction model (White & Mitchelmore, 2010). This paper reports how one teacher learned about the model and implemented it in her lesson. It was found that she had assimilated several key features of the model, such as starting with several embodiments of the target concept and guiding students to look for similarities between them. However, she had some difficulty focusing students' attention clearly on the underlying mathematical similarity. It was concluded that teachers need to experience more examples of Teaching for Abstraction before they can to reify and apply the model faithfully. [The study reported in this paper was supported by a grant from the National Centre of Science, Information and Communication Technology, and Mathematics Education for Rural and Regional Australia (SiMERR).]

Software design is crucial to successful software development, yet is a demanding multi-objective problem for software engineers. In an attempt to assist the software designer, interactive (i.e. human in-the-loop) meta-heuristic search techniques such as evolutionary computing have been applied and show promising results. Recent investigations have also shown that Ant Colony Optimization (ACO) can outperform evolutionary computing as a potential search engine for interactive software design. With a limited computational budget, ACO produces superior candidate design solutions in a smaller number of iterations. Building on these findings, we propose a novel interactive ACO (iACO) approach to assist the designer in early lifecycle software design, in which the search is steered jointly by subjective designer evaluation as well as machine fitness functions relating the structural integrity and surrogate elegance of software designs. Results show that iACO is speedy, responsive and highly effective in enabling interactive, dynamic multi-objective search in early lifecycle software design. Study participants rate the iACO search experience as compelling. Results of machine learning of fitness measure weightings indicate that software design elegance does indeed play a significant role in designer evaluation of candidate software design. We conclude that the evenness of the number of attributes and methods among classes (NAC) is a significant surrogate elegance measure, which in turn suggests that this evenness of distribution, when combined with structural integrity, is an implicit but crucial component of effective early lifecycle software design., Comment: 31 pages including appendices

We formalise a notion of $p$-adic Langlands functoriality for the definite unitary group. This extends the classical notion of Langlands functoriality to the setting of eigenvarieties. We apply some results of Chenevier to obtain some cases of $p$-adic Langlands functoriality by interpolating known cases of classical Langlands functoriality.

Following Arthur's study of the representations of the orthogonal and symplectic groups, we prove many cases of both the local and global Arthur conjectures for tempered representations of the unitary group. This completes the proof of Arthur's description of the discrete series representations of the quasi-split $p$-adic unitary group, and Arthur's description of the tempered discrete automorphic representations of the unitary group, satisfying certain technical conditions., Comment: This article has been withdrawn by the author due to an error in the proof of the main result. The error will be corrected in a future article

It is claimed that, since mathematics is essentially a self-contained system, mathematical objects may best be described as "abstract-apart." On the other hand, fundamental mathematical ideas are closely related to the real world and their learning involves empirical concepts. These concepts may be called "abstract-general" because they embody general properties of the real world. A discussion of the relationship between abstract-apart objects and abstract-general concepts leads to the conclusion that a key component in learning about fundamental mathematical objects is the "formalisation" of empirical concepts. A model of the relationship between mathematics and mathematics learning is presented which also includes more advanced mathematical objects. [For complete proceedings, see ED489538.]

This paper is concerned with the strategies being adopted for vocational education and training (VET) in Australia and the lessons that could be learned for them from policies in other countries. Six issues are considered in the paper, each relates to or more of the objectives and particular strategies in the Australia's National Strategy for Vocational Education and Training 2004-2010: (1) Workforce/adult training and retraining in the light of ageing and shifting occupational structures; (2) Equity issues for indigenous and other groups; (3) Managing demand and funding so that priorities are met; (4) Developments in qualification structures and quality assurance; (5) Enhancing provider capacity to ensure quality and responsiveness; and (6) Regional and community capacity building. The approach taken was to analyse national strategies, policies, objectives and priorities of government agencies to provide a point of comparison with Australia's National Strategy for VET. Analysis was most focused on the United Kingdom and New Zealand, and limited for Canada, due to the decentralised nature of that system. Implications for Australia are set out by strategy. (Contains 6 footnotes and 2 boxes.)

Taylor-Wiles type lifting theorems allow one to deduce that for $\rho$ a "sufficiently nice" $l$-adic representation of the absolute Galois group of a number field whose semi-simplified reduction modulo $l$, denoted $\overline{\rho}$, comes from an automorphic representation then so does $\rho$. The recent lifting theorems of Barnet-Lamb-Gee-Geraghty-Taylor impose a technical condition, called \emph{$m$-big}, upon the residual representation $\overline{\rho}$. Snowden-Wiles proved that for a sufficiently irreducible compatible system of Galois representations, the residual images are \emph{big} at a set of places of Dirichlet density $1$. We demonstrate the analogous result in the \emph{$m$-big} setting using a mild generalization of their argument.

We study some tempered endoscopic cases of Langlands functoriality on the $n$-variable unitary groups via the simple stable trace formula. This extends previous work of Rogawski and Clozel-Harris-Labesse. Ramakrishnan and Kim-Shahidi have proved the existence of the automorphic tensor product for $GL_2 \times GL_2$ and $GL_2 \times GL_3$. We apply our endoscopic results to, in a sense, "lift" these theorems and deduce the existence of the automorphic tensor product for the quasi-split unitary groups $U^*_2 \times U^*_2$ and $U^*_2 \times U^*_3$. We then formulate the notion of overconvergent Langlands functoriality on the definite unitary group. We apply some results of Chenevier to obtain morphisms of eigenvarieties that extend classical endoscopic Langlands functoriality. This enables us to obtain, in the \emph{small slope} setting, some classical cases of non-tempered endoscopic Langlands functoriality. To conclude, we apply the recent potential automorphy results of Barnet-Lamb-Gee-Geraghty-Taylor to obtain some cases of the potential automorphic tensor product for higher rank unitary groups., Comment: This paper has been withdrawn as its content has been replaced/improved by the Authors articles "Tempered automorphic representations of the unitary group" and "p-adic Langlands Functoriality for the definite unitary group"

The purpose of this project was to review the use of price measures in education and training and to consider the types of measures that could be applied. There are several contexts in which price measures are needed and the context will affect the type of measure of price change that is needed. Section 1 of the report discusses budget estimates and planning accountability for efficient and equitable use of funds; and research involving consideration of resources. Section 2 is an overview of the major forms of price indexes. Section 3 reports on the current use made by national authorities of measures of price changes in relation to education expenditure. Section 4 reviews the current use of price deflators with a view to the most appropriate index for the particular purpose. Section 5 considers price measures for the wage and non-wage components of vocational education training (VET) expenses and their limitations for the purposes specified. Summary and concluding comments are presented in Section 6. Two appendices are included: (1) Review of Selected Price Measures and their Limitations; and (2) Selected CPI Groups, Sub-Groups and Expenditure Classes. (Contains 7 footnotes, 5 boxes and 9 tables.)

An angles teaching sequence was designed, in which students were guided to abstract a general concept from physical activities with concrete materials. The three design principles used were familiarity, similarity recognition, and reification. The resulting teaching sequence was tested in a field study involving 25 teachers of Grades 3-4. The data collected demonstrate the significance of the three design principles, and the results from pre- and post-assessment interviews provide evidence for the overall effectiveness of the lesson sequence. Also earlier findings that angle is a multifaceted concept which is difficult to learn are supported. (Contains 3 figures.) [For complete proceedings, see ED500860.]

The GK-12 program of the National Science Foundation is an innovative program for enriching the value of graduate and advanced undergraduate students' education while simultaneously enriching science and mathematics teaching at the K-12 level. GK-12 is a fellowship program that offers graduate students and advanced undergraduates the opportunity to serve as resources for K-12 teachers of science and mathematics. An evaluation was conducted to provide information about GK-12. One component of the evaluation was the qualitative analysis of case studies from 12 purposively selected sites, and the other was a quantitative analysis of survey data from all project sites. Findings show that the areas most often cited as strongest program areas were: (1) content knowledge gains for teachers; (2) positive role models for students; (3) improved school-university relationship; and (4) improved communication and instructional skills of Fellows. The two areas most often cited as "less strong" were: (1) clarification of the Fellows' and teachers' roles; and (2) summer training. The most often cited implication for the GK-12 Program as a whole was sustainability. Overall, the program appears to be meeting its goals. To provide better information, surveys are being conducted of all Fellows, about 1,000 cooperating teachers, about 1,000 graduate students not receiving GK-12 support, and school district staff in participating school districts. (SLD)

The aim of this research is twofold: Firstly, to model and solve a complex nurse scheduling problem with an integer programming formulation and evolutionary algorithms. Secondly, to detail a novel statistical method of comparing and hence building better scheduling algorithms by identifying successful algorithm modifications. The comparison method captures the results of algorithms in a single figure that can then be compared using traditional statistical techniques. Thus, the proposed method of comparing algorithms is an objective procedure designed to assist in the process of improving an algorithm. This is achieved even when some results are non-numeric or missing due to infeasibility. The final algorithm outperforms all previous evolutionary algorithms, which relied on human expertise for modification.

The method of Teaching for Abstraction was applied in grades 2 and 4 to individual teaching interviews focusing on the angle concept. Responses of three students who successfully matched different physical angle situations are compared to responses of three that did not. The teaching method was generally supported, but it appears that more emphasis needs to be given to the examination of within-situation and within-context similarities before matching across contexts, and hence abstraction of the angle concept, can proceed. (Contains 10 references and 1 figure.) (Author)

This paper explores a framework for research on the development of the angle concept based on theories of abstraction. The framework suggests that children initially acquire a body of disconnected angle knowledge situated in everyday experiences, group the situations to form angle contexts, and then form an abstract angle concept. The framework is explored using grade 4 students (N=36). The students appear to form distinct concepts of slopes, turns, hinges, bends, rebounds, and corners, but are often unaware of the common angle features of these contexts. The findings are discussed using a comparison with a previous study of grade 2 students and suggest that students' responses often show failure to use standard terminology rather than a lack of knowledge of the underlying physical relations. Contains 22 references. (DDR)

Describes three transitional mathematics courses designed to upgrade high school math courses and lure more low-achieving students into college-preparatory math courses: California's Math A Program; Rochester, New York's Stretch Regents Program; and Buffalo, New York's University of Chicago School Math Project. Transcript data from 4,800 students showed that students took more challenging, useful math; learned more; and improved self-esteem. (MLH)

Responses to rate-of-change problems were collected during and after 24 hours of conceptual calculus instruction given to first-year university students. Analysis revealed three categories of error in which variables were treated as symbols to be manipulated rather than quantities to be related. Contains test questions. (Author/MKR)

A simplified method has been developed for determining bond durability under exposure to water or high humidity conditions. It uses a small number of test specimens with relatively short times of water exposure at elevated temperature. The method is also gravimetric; the only equipment being required is an oven, specimen jars, and a conventional laboratory balance.