Diversity of accuracy profiles for absolute pitch recognition

Most advanced musicians are able to identify and label a heard pitch if given an opportunity to compare it to a known reference note. This is called ‘relative pitch’ (RP). A much rarer skill is the ability to identify and label a heard pitch without the need for a reference. This is colloquially referred to as ‘perfect pitch’, but appears in the academic literature as ‘absolute pitch’ (AP). AP is considered by many as a remarkable skill. As people do not seem able to develop it intentionally, it is generally regarded as innate. It is often seen as a unitary skill and that a set of identifiable criteria can distinguish those who possess the skill from those who do not. However, few studies have interrogated these notions. The present study developed and applied an interactive computer program to map pitch-labelling responses to various tonal stimuli without a known reference tone available to participants. This approach enabled the identification of the elements of sound that impacted on AP. Pitch-labelling responses of 14 participants with AP were recorded for their accuracy. Each participant’s response to the stimuli was unique. Their accuracy of labelling varied across dimensions such as timbre, range and tonality. The diversity of performance between individuals appeared to reflect their personal musical experience histories.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

Neurocognitive profiles of people with comorbid depression and alcohol use : implications for psychological interventions

Depression and alcohol use disorders frequently co-occur and are highly prevalent. Both conditions are known to impair cognitive functioning, yet research into the role of these impairments in response to Cognitive Behaviour Therapy (CBT) is limited. The purpose of the present study was to examine the relationship between baseline neuropsychological performance, severity of depressive symptoms and alcohol use disorders. Participants with current depression and hazardous alcohol use were functioning in the average range on all neuropsychological measures prior to treatment entry. Baseline measures of drinking severity and a range of cognitive functions were inversely correlated. After controlling for other baseline variables, superior baseline cognitive functioning predicted greater reductions in depression severity after 17 weeks. These predictive effects occurred across both brief and extended interventions. Findings suggest that improvement in depression following psychological treatment is enhanced by greater fluid reasoning ability and is predicted by executive functioning, regardless of the treatment length or problem focus.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Different cognitive profiles for single compared with recurrent fallers without Dementia

Relationships between self-reported retrospective falls and cognitive measures (executive function, reaction time, processing speed, working memory, visual attention) were examined in a population based sample of older adults (n = 658). Two of the choice reaction time tests involved inhibiting responses to either targets of a specific color or location with hand and foot responses. Potentially confounding demographic variables, medical conditions and postural sway were controlled for in logistic regression models, excluding participants with possible cognitive impairment. A factor analysis of cognitive measures extracted factors measuring reaction time, accuracy and inhibition, and visual search. Single fallers did not differ from non-fallers in terms of health, sway or cognitive function, except that they performed worse on accuracy and inhibition. In contrast, recurrent fallers performed worse than non-fallers on all measures. Results suggest that occasional falls in late life may be associated with subtle age-related changes in the pre-frontal cortex leading to failures of executive control, whereas recurrent falling may result from more advanced brain ageing that is associated with generalized cognitive decline.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

The relationship between communication and team performance : testing moderators and identifying communication profiles in established work teams

Communication is one team process factor that has received considerable research attention in the team literature. This literature provides equivocal evidence regarding the role of communication in team performance and yet, does not provide any evidence for when communication becomes important for team performance. This research program sought to address this evidence gap by a) testing task complexity and team member diversity (race diversity, gender diversity and work value diversity) as moderators of the team communication — performance relationship; and b) testing a team communication — performance model using established teams across two different task types. The functional perspective was used as the theoretical framework for operationalizing team communication activity. The research program utilised a quasi-experimental research design with participants from a large multi-national information technology company whose Head Office was based in Sydney, Australia. Participants voluntarily completed two team building exercises (a decision making and production task), and completed two online questionnaires. In total, data were collected from 1039 individuals who constituted 203 work teams. Analysis of the data revealed a small number of significant moderation effects, not all in the expected direction. However, an interesting and unexpected finding also emerged from Study One. Large and significant correlations between communication activity ratings were found across tasks, but not within tasks. This finding suggested that teams were displaying very similar profiles of communication on each task, despite the tasks having different communication requirements. Given this finding, Study Two sought to a) determine the relative importance of task versus team effects in explaining variance in team communication measures for established teams; b) determine if established teams had reliable and discernable team communication profiles and if so, c) investigate whether team communication profiles related to task performance. Multi-level modeling and repeated measures analysis of variance (ANOVA) revealed that task type did not have an effect on team communication ratings. However, teams accounted for 24% of the total variance in communication measures. Through cluster analysis, five reliable and distinct team communication profiles were identified. Consistent with the findings of the multi-level analysis and repeated measures ANOVA, teams’ profiles were virtually identical across the decision making and production tasks. A relationship between communication profile and performance was identified for the production task, although not for the decision making task. This research responds to calls in the literature for a better understanding of when communication becomes important for team performance. The moderators tested in this research were not found to have a substantive or reliable effect on the relationship between communication and performance. However, the consistency in team communication activity suggests that established teams can be characterized by their communication profiles and further, that these communication profiles may have implications for team performance. The findings of this research provide theoretical support for the functional perspective in terms of the communication – performance relationship and further support the team development literature as an explanation for the stability in team communication profiles. This research can also assist organizations to better understand the specific types of communication activity and profiles of communication that could offer teams a performance advantage.