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<p>Historically, music theorists have claimed that the major triad functions as a strong instantiator of key, and that each of its inversions are harmonically equivalent. To examine these assumptions, subjects were tested with the Method of Paired Comparisons, and asked to judge the similarity of root, first inversion, and second inversion major triads drawn from keys of different degrees of musical relatedness. In Experiment 1, where triads were built on the tonics of two maximally-related keys (A and E major), only professional musicians demonstrated a separation of the triads on the basis of key, indicating that inversions of triads built on the same root-note were perceived as sounding similar to one another. The majority of moderately trained and inexperienced subjects tended to use a pitch-height strategy, in which triads containing upper notes that were close in absolute frequency were judged as sounding similar to one another. In Experiment 2, where triads were also included from a distantly related key (Bb major), the majority of professional musicians continued to group all triads on the basis of key, while some moderately-trained subjects confused the maximally-related keys, but perceived them as distinct from the more distant key. Other moderately-trained and musically-inexperienced subjects used a pitch·height strategy for judging similarity. In Experiments 3 and 4, chords were built on seven different rootnotes moving counterclockwise and clockwise, respectively, from a constant standard chord on the Circle of Fifths. The professional and moderately trained subjects tested did not show an especially strong tendency to judge chord similarity on the basis of musical key in either experiment. Inversion equivalence was demonstrated in each of these four experiments by subjects who judged triads built on the same root-note as sounding similar to one another. In Experiment 5, where seven Shepard chords (chords built to obscure pitch-height and inversion cues) were presented to only moderately-trained subjects, similarity judgements now appeared to be based on key. Conclusions are made regarding musical representation in a form described by the theoretic Circle of Fifths in musically-trained individuals.</p> / Thesis / Doctor of Philosophy (PhD)

TITLE: Experiments in DGS AUTHOR: Michal Sláma DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: doc. RNDr. Antonín Jančařík, Ph. D. ABSTRACT The aim of this diploma thesis is to find out whether the pupils of the second stage of primary school, specifically the pupils of the 6th grade, are able to experiment independently in the environment of dynamic geometry with a suitably prepared material. The theoretical basis of the work includes the study of the valid intended curriculum of geometry at the second stage of primary school, the relationship of so-called inquiry-oriented teaching to the possibility of student experimentation in learning geometry, the study of pedagogical theories in connection with inquiry education and also in relation to mathematisation, which is in the teaching of mathematics and geometry necessarily required. The student experiment is conceived here as an independent didactic method. From the point of view of the feasibility of the experiment and subsequent research, the environment of dynamic geometry was chosen - the GeoGebra system. The theoretical part of the work ends with a description of parameters important for the feasibility of experimentation in the environment of dynamic geometry in the teaching of geometry. The research part deals with the...

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Empirical research is inexact and error-prone leading researchers to agree that replication of experiments is a necessary step to validating empirical results. Unfortunately, replicating experiments requires substantial investments in manpower and time. These resource requirements can be reduced by incorporating component reuse when building tools for empirical experimentation. Bokeo is an initiative within the Sequoia Lab of the BYU Computer Science Department to develop a platform to assist in the empirical study of software engineering. The i3Persistence Framework is a component of Bokeo which enables researchers to easily build and rapidly deploy tools for empirical experiments by providing an easy-to-use database management service. We introduce the i3Persistence Framework of Bokeo to assist in the development of software to replicate experiments and conduct studies on data from open-source repositories.

Merging the senses is key to perception, yet how we achieve this remains unclear. New research finds multimodality even in primary sensory areas, but its role is not understood. We address this question by using in vivo 2-photon calcium imaging in awake mice to test several hypotheses about the possible functions primary somatosensory cortex (S1) may subserve in integrating auditory and tactile sensory input. We first test whether S1 encodes pure auditory stimulus identity by training a linear classifier to decode different sounds from S1 activity. We find that decoder accuracy is slightly-but-significantly above chance, suggesting that S1 weakly encodes sounds. We then ask whether S1 encodes specific audio-tactile feature conjunctions by testing decoder performance for distinct combinations of simultaneously-presented auditory and tactile stimuli. We find that accuracy was within chance levels, indicating that sound-evoked suppression of whisker responses is auditory-stimulus non-specific. Subsequently, we test whether passive experience is sufficient to induce either a) Hebbian-like reactivation of tactile stimulus representations by correlated auditory stimuli or b) enhanced mixed selectivity. We find that passive experience results in neither effect. We also find S1’s auditory and audio-tactile encoding properties to be stable in the face of reinforcement conditioning. As part of a separate project, we also present results that reinforcement conditioning enhances encoding of time and temporal surprise in primary somatosensory cortex.

In this research, Bayesian two-stage D-D optimal designs for mixture experiments with or without process variables under model uncertainty are developed. A Bayesian optimality criterion is used in the first stage to minimize the determinant of the posterior variances of the parameters. The second stage design is then generated according to an optimality procedure that collaborates with the improved model from first stage data. Our results show that the Bayesian two-stage D-D optimal design is more efficient than both the Bayesian one-stage D-optimal design and the non-Bayesian one-stage D-optimal design in most cases. We also use simulations to investigate the ratio between the sample sizes for two stages and to observe least sample size for the first stage. On the other hand, we discuss D-optimal second or higher order designs, and show that Ds-optimal designs are a reasonable alternative to D-optimal designs. / Ph. D.

Reliability experiments provide important information regarding the life of a product, including how various factors may affect product life. Current analyses of reliability data usually assume a completely randomized design. However, reliability experiments frequently contain subsampling which is a restriction on randomization. A typical experiment involves applying treatments to test stands, with several items placed on each test stand. In addition, raw materials used in experiments are often produced in batches. In some cases one batch may not be large enough to provide materials for the entire experiment and more than one batch must be used. These batches lead to a design involving blocks. This dissertation proposes two methods for analyzing reliability experiments with random blocks and subsampling. The first method is a two-stage method which can be implemented in software used by most practitioners, but has some limitations. Therefore, a more rigorous nonlinear mixed model method is proposed. / Ph. D.

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