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Description
Deconvolution of noisy data is an ill-posed problem, and requires some form of regularization to stabilize its solution. Tikhonov regularization is the most common method used, but it depends on the choice of a regularization parameter λ which must generally be estimated using one of several common methods. These methods

Deconvolution of noisy data is an ill-posed problem, and requires some form of regularization to stabilize its solution. Tikhonov regularization is the most common method used, but it depends on the choice of a regularization parameter λ which must generally be estimated using one of several common methods. These methods can be computationally intensive, so I consider their behavior when only a portion of the sampled data is used. I show that the results of these methods converge as the sampling resolution increases, and use this to suggest a method of downsampling to estimate λ. I then present numerical results showing that this method can be feasible, and propose future avenues of inquiry.
ContributorsHansen, Jakob Kristian (Author) / Renaut, Rosemary (Thesis director) / Cochran, Douglas (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
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Description
Christian psychotherapy appears to be useful especially for Christian clients seeking therapy, and is a growing preference among this population. Thus, the need for research on the efficacy and effectiveness of Christian interventions must be recognized. This study reviews 13 effectiveness and 21 efficacy studies of Christian psychotherapeutic interventions in

Christian psychotherapy appears to be useful especially for Christian clients seeking therapy, and is a growing preference among this population. Thus, the need for research on the efficacy and effectiveness of Christian interventions must be recognized. This study reviews 13 effectiveness and 21 efficacy studies of Christian psychotherapeutic interventions in various areas of psychotherapy. The majority of effectiveness and efficacy studies were shown to give positive outcomes for Christian psychotherapy, and overall, Christian psychotherapy is promising as an effective alternative to secular therapy. The need for further research in most areas is discussed.
ContributorsRodriguez, Gina Alexandra (Author) / Valiente, Carlos (Thesis director) / Seeley, Bridget (Committee member) / Skinner, Tad (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / Department of Psychology (Contributor)
Created2014-05
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Description
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and coating materials for engineering or programmable cells for medical uses. Previous research using this

Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and coating materials for engineering or programmable cells for medical uses. Previous research using this model has focused on shape formation and other spatial configuration problems, including line formation, compression, and coating. In this work we study foundational computational tasks that exceed the capabilities of the individual constant memory particles described by the model. These tasks represent new ways to use these self-organizing systems, which, in conjunction with previous shape and configuration work, make the systems useful for a wider variety of tasks. We present an implementation of a counter using a line of particles, which makes it possible for the line of particles to count to and store values much larger than their individual capacities. We then present an algorithm that takes a matrix and a vector as input and then sets up and uses a rectangular block of particles to compute the matrix-vector multiplication. This setup also utilizes the counter implementation to store the resulting vector from the matrix-vector multiplication. Operations such as counting and matrix multiplication can leverage the distributed and dynamic nature of the self-organizing system to be more efficient and adaptable than on traditional linear computing hardware. Such computational tools also give the systems more power to make complex decisions when adapting to new situations or to analyze the data they collect, reducing reliance on a central controller for setup and output processing. Finally, we demonstrate an application of similar types of computations with self-organizing systems to image processing, with an implementation of an image edge detection algorithm.
ContributorsPorter, Alexandra Marie (Author) / Richa, Andrea (Thesis director) / Xue, Guoliang (Committee member) / School of Music (Contributor) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
This research project dug into mathematics in music, exploring the various ways a number series was used in the 20th century to create musical compositions. The Fibonacci Series (FS) is an infinite number series that is created by taking the two previous numbers to create the next, excluding 0 and

This research project dug into mathematics in music, exploring the various ways a number series was used in the 20th century to create musical compositions. The Fibonacci Series (FS) is an infinite number series that is created by taking the two previous numbers to create the next, excluding 0 and 1 at the very start of the series. As the numbers grow larger, the ratios between the numbers of the FS approach the value of another mathematical concept known as the Golden Mean (GM). The GM is so closely related to the series that it is used interchangeably in terms of proportions and overall structure of musical pieces. This is similar to how both the FS and GM are found in aspects of nature, like to all too well-known conch shell spiral.

The FS in music was used in a variety of ways throughout the 20th century, primarily focusing on durations and overall structure in its use. Examples of this are found in Béla Bartók’s Music for Strings, Percussion, and Celeste (1936), Allegro barbaro (1911), Karlheinz Stockhausen’s Klavierstück IX (1955), and Luigi Nono’s il canto sospeso (1955). These works are analyzed in detail within my research, and I found every example to have a natural feel to them even if its use of the FS is carefully planned out by the composer. Bartók’s works are the least precise of my examples but perhaps the most natural ones. This imprecision in composition may be considered a more natural use of the FS in music, since nature is not always perfect either. However, in works such as Stockhausen’s, the structure is meticulously formatted in such that the precision is masked by a cycle as to appear more natural.

The conclusion of my research was a commissioned work for my instrument, the viola. I provided my research to composer Jacob Miller Smith, a DMA Music Composition student at ASU, and together we built the framework for the piece he wrote for me. We utilized the life cycle of the Black-Eyed Susan, a flower that uses the FS in its number of petals. The life cycle of a flower is in seven parts, so the piece was written to have seven separate sections in a palindrome within an overall ABA’ format. To utilize the FS, Smith used Fibonacci number durations for rests between notes, note/gesture groupings, and a mapping of 12358 as the set (01247). I worked with Smith during the process to make sure that the piece was technically suitable for my capabilities and the instrument, and I premiered the work in my defense.

The Fibonacci Series and Golden Mean in music provides a natural feel to the music it is present in, even if it is carefully planned out by the composer. More work is still to be done to develop the FS’s use in music, but the examples presented in this project lay down a framework for it to take a natural place in music composition.
ContributorsFerry, Courtney (Author) / Knowles, Kristina (Thesis director) / Buck, Nancy (Committee member) / School of Music (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-12