Random prism: an alternative to random forests

Ensemble learning techniques generate multiple classifiers, so called base classifiers, whose combined classification results are used in order to increase the overall classification accuracy. In most ensemble classifiers the base classifiers are based on the Top Down Induction of Decision Trees (TDIDT) approach. However, an alternative approach for the induction of rule based classifiers is the Prism family of algorithms. Prism algorithms produce modular classification rules that do not necessarily fit into a decision tree structure. Prism classification rulesets achieve a comparable and sometimes higher classification accuracy compared with decision tree classifiers, if the data is noisy and large. Yet Prism still suffers from overfitting on noisy and large datasets. In practice ensemble techniques tend to reduce the overfitting, however there exists no ensemble learner for modular classification rule inducers such as the Prism family of algorithms. This article describes the first development of an ensemble learner based on the Prism family of algorithms in order to enhance Prism’s classification accuracy by reducing overfitting.

Parallel random prism: a computationally efficient ensemble learner for classification

Generally classifiers tend to overfit if there is noise in the training data or there are missing values. Ensemble learning methods are often used to improve a classifier's classification accuracy. Most ensemble learning approaches aim to improve the classification accuracy of decision trees. However, alternative classifiers to decision trees exist. The recently developed Random Prism ensemble learner for classification aims to improve an alternative classification rule induction approach, the Prism family of algorithms, which addresses some of the limitations of decision trees. However, Random Prism suffers like any ensemble learner from a high computational overhead due to replication of the data and the induction of multiple base classifiers. Hence even modest sized datasets may impose a computational challenge to ensemble learners such as Random Prism. Parallelism is often used to scale up algorithms to deal with large datasets. This paper investigates parallelisation for Random Prism, implements a prototype and evaluates it empirically using a Hadoop computing cluster.

Probability of survival in a random exchange economy with dependent agents

In this paper I analyze the general equilibrium in a random Walrasian economy. Dependence among agents is introduced in the form of dependency neighborhoods. Under the uncertainty, an agent may fail to survive due to a meager endowment in a particular state (direct effect), as well as due to unfavorable equilibrium price system at which the value of the endowment falls short of the minimum needed for survival (indirect terms-of-trade effect). To illustrate the main result I compute the stochastic limit of equilibrium price and probability of survival of an agent in a large Cobb-Douglas economy.

Terminal: a miracle play with popular music from the end of the world

Terminal: A Miracle Play with Popular Music from the End of the World is a film and live performance project exploring the politics of post-apocalyptic fiction. A theatrical staging of a morality play for end times and future folk music, it recasts eschatology, as a foundational myth for a future society. Post-apocalyptic writing and cinema are grounded in an ethos of survivalism. Invoking Rousseau’s state of nature, or time before government, these fictions propose violent scenarios in which nuclear holocaust, environmental catastrophe and other disasters generate an individualistic politics of pure pragmatism, negating the possibility of democratic deliberation. Terminal narrates this familiar scenario, but at the same time questions its validity. The film, shot on black and white VHS at Kurt Schwitters’ Merzbarn in Cumbria, dramatises a series of conversations between future-historical archetypes about the needs and pressures of the situation in which they find themselves at the end of the world. The performers then gather to play worshipful songs about acid rain, radiation sickness and eating the dog, using a mix of conventional, obscure and makeshift instruments In the tradition of books such as Russell Hoban’s Riddley Walker and Arthur M. Miller Jr.’s A Canticle for Liebowitz, Terminal imagines artistic expression and new folk traditions for a world to come after the apocalypse. If, as Slavoj Žižek would have it, it is easier to imagine the end of the world than to think of the end of capitalism, the project juxtaposes these two endpoints to test out how alternative scenarios might emerge from the collaborative practice of making theatre and music against a setting of social collapse.

The MaPS project: mapping teacher conceptions of musical development

The chapter starts from the premise that an historically- and institutionally-formed orientation to music education at primary level in European countries privileges a nineteenth century Western European music aesthetic, with its focus on formal characteristics such as melody and rhythm. While there is a move towards a multi-faceted understanding of musical ability, a discrete intelligence and willingness to accept musical styles or 'open-earedness', there remains a paucity of documented evidence of this in research at primary school level. To date there has been no study undertaken which has the potential to provide policy makers and practitioners with insights into the degree of homogeneity or universality in conceptions of musical ability within this educational sector. Against this background, a study was set up to explore the following research questions: 1. What conceptions of musical ability do primary teachers hold a) of themselves and; b) of their pupils? 2. To what extent are these conceptions informed by Western classical practices? A mixed methods approach was used which included survey questionnaire and semi-structured interview. Questionnaires have been sent to all classroom teachers in a random sample of primary schools in the South East of England. This was followed up with a series of semi-structured interviews with a sub-sample of respondents. The main ideas are concerned with the attitudes, beliefs and working theories held by teachers in contemporary primary school settings. By mapping the extent to which a knowledge base for teaching can be resistant to change in schools, we can problematise primary schools as sites for diversity and migration of cultural ideas. Alongside this, we can use the findings from the study undertaken in an English context as a starting point for further investigation into conceptions of music, musical ability and assessment held by practitioners in a variety of primary school contexts elsewhere in Europe; our emphasis here will be on the development of shared understanding in terms of policies and practices in music education. Within this broader framework, our study can have a significant impact internationally, with potential to inform future policy making, curriculum planning and practice.

Boundaries and Bridges: the influence of James Cooksey Culwick on the development of the teaching and learning of music in nineteenth century Ireland

James Cooksey Culwick (1845-1907) was born in England. Trained as chorister and organist in Lichfield Cathedral, he moved to Ireland at twenty- one and remained until his death in 1907. Although his reputation as scholar, musician and teacher was acknowledged widely during his lifetime - he received an honorary doctorate from University of Dublin (1893) - little is known about the contribution he made to music education. This paper addresses this gap in the literature and argues that it was Culwick's singular achievement to pay attention to music pedagogy at secondary level, by recognizing that music could be seen as a serious career option for girls, and by providing resources for teachers which emphasised the development of an 'art-feeling' in pupils of all abilities. In addition, he considered Irish music as an art which had significance as music first, and Irish music second, and advocated a 'laudable tolerance' for opposing views on matters of cultural identity to Ireland at the end of the nineteenth century.

Music and Metaphor

Peter Kivy’s contour theory provides a promising explanation of the way we describe instrumental music as expressive of emotions. I argue that if, unlike Kivy, we emphasise the metaphorical character of such descriptions, the contour theory, as a strategy for unpacking such metaphors, can be defended convincingly against common objections. This approach is more satisfactory than those of Scruton and Peacocke, who make much of metaphorical experiences, but leave the underlying metaphors unexplained. Moreover, it gives the contour theory a wider scope than Kivy intended, for even very specific narrative descriptions of music in non-musical terms are perfectly legitimate as long as they are presented, and justified, as metaphors, that is, as mere comparisons, rather than as interpretative claims about the music’s actual contents.

Validating the reported random errors of ACE‐FTS measurements

In order to validate the reported precision of space‐based atmospheric composition measurements, validation studies often focus on measurements in the tropical stratosphere, where natural variability is weak. The scatter in tropical measurements can then be used as an upper limit on single‐profile measurement precision. Here we introduce a method of quantifying the scatter of tropical measurements which aims to minimize the effects of short‐term atmospheric variability while maintaining large enough sample sizes that the results can be taken as representative of the full data set. We apply this technique to measurements of O3, HNO3, CO, H2O, NO, NO2, N2O, CH4, CCl2F2, and CCl3F produced by the Atmospheric Chemistry Experiment–Fourier Transform Spectrometer (ACE‐FTS). Tropical scatter in the ACE‐FTS retrievals is found to be consistent with the reported random errors (RREs) for H2O and CO at altitudes above 20 km, validating the RREs for these measurements. Tropical scatter in measurements of NO, NO2, CCl2F2, and CCl3F is roughly consistent with the RREs as long as the effect of outliers in the data set is reduced through the use of robust statistics. The scatter in measurements of O3, HNO3, CH4, and N2O in the stratosphere, while larger than the RREs, is shown to be consistent with the variability simulated in the Canadian Middle Atmosphere Model. This result implies that, for these species, stratospheric measurement scatter is dominated by natural variability, not random error, which provides added confidence in the scientific value of single‐profile measurements.

Random Prism: a noise-tolerant alternative to Random Forests

Ensemble learning can be used to increase the overall classification accuracy of a classifier by generating multiple base classifiers and combining their classification results. A frequently used family of base classifiers for ensemble learning are decision trees. However, alternative approaches can potentially be used, such as the Prism family of algorithms that also induces classification rules. Compared with decision trees, Prism algorithms generate modular classification rules that cannot necessarily be represented in the form of a decision tree. Prism algorithms produce a similar classification accuracy compared with decision trees. However, in some cases, for example, if there is noise in the training and test data, Prism algorithms can outperform decision trees by achieving a higher classification accuracy. However, Prism still tends to overfit on noisy data; hence, ensemble learners have been adopted in this work to reduce the overfitting. This paper describes the development of an ensemble learner using a member of the Prism family as the base classifier to reduce the overfitting of Prism algorithms on noisy datasets. The developed ensemble classifier is compared with a stand-alone Prism classifier in terms of classification accuracy and resistance to noise.

Storytelling in song: television music, narrative and allusion in 'The O.C.'

Television’s long-form storytelling has the potential to allow the rippling of music across episodes and seasons in interesting ways. In the integration of narrative, music and meaning found in The O.C. (Fox, FOX 2003-7), popular song’s allusive and referential qualities are drawn upon to particularly televisual ends. At times embracing its ‘disruptive’ presence, at others suturing popular music into narrative, at times doing both at once. With television studies largely lacking theories of music, this chapter draws on film music theory and close textual analysis to analyse some of the programme's music moments in detail. In particular it considers the series-spanning use of Jeff Buckley’s cover of ‘Hallelujah’ (and its subsequent oppressive presence across multiple televisual texts), the end of episode musical montage and the use of recurring song fragments as theme within single episodes. In doing so it highlights music's role in the fragmentation and flow of the television aesthetic and popular song’s structural presence in television narrative. Illustrating the multiplicity of popular song’s use in television, these moments demonstrate song’s ability to provide narrative commentary, yet also make particular use of what Ian Garwood describes as the ability of ‘a non-diegetic song to exceed the emotional range displayed by diegetic characters’ (2003:115), to ‘speak’ for characters or to their feelings, contributing to both teen TV’s melodramatic affect and narrative expression.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.