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Determining Properties of Synaptic Structure in a Neural Network through Spike Train Analysis

Description: A "complex" system typically has a relatively large number of dynamically interacting components and tends to exhibit emergent behavior that cannot be explained by analyzing each component separately. A biological neural network is one example of such a system. A multi-agent model of such a network is developed to study the relationships between a network's structure and its spike train output. Using this model, inferences are made about the synaptic structure of networks through cluster analysis of spike train summary statistics A complexity measure for the network structure is also presented which has a one-to-one correspondence with the standard time series complexity measure sample entropy.
Date: May 2007
Creator: Brooks, Evan
Partner: UNT Libraries

Mathematical Modeling of Charged Liquid Droplets: Numerical Simulation and Stability Analysis

Description: The goal of this thesis is to study of the evolution of 3D electrically charged liquid droplets of fluid evolving under the influence of surface tension and electrostatic forces. In the first part of the thesis, an appropriate mathematical model of the problem is introduced and the linear stability analysis is developed by perturbing a sphere with spherical harmonics. In the second part, the numerical solution of the problem is described with the use of the boundary elements method (BEM) on an adaptive mesh of triangular elements. The numerical method is validated by comparison with exact solutions. Finally, various numerical results are presented. These include neck formation in droplets, the evolution of surfaces with holes, singularity formation on droplets with various symmetries and numerical evidence that oblate spheroids are unstable.
Date: May 2006
Creator: Vantzos, Orestis
Partner: UNT Libraries

Analysis Of Sequential Barycenter Random Probability Measures via Discrete Constructions

Description: Hill and Monticino (1998) introduced a constructive method for generating random probability measures with a prescribed mean or distribution on the mean. The method involves sequentially generating an array of barycenters that uniquely defines a probability measure. This work analyzes statistical properties of the measures generated by sequential barycenter array constructions. Specifically, this work addresses how changing the base measures of the construction affects the statististics of measures generated by the SBA construction. A relationship between statistics associated with a finite level version of the SBA construction and the full construction is developed. Monte Carlo statistical experiments are used to simulate the effect changing base measures has on the statistics associated with the finite level construction.
Date: December 2002
Creator: Valdes, LeRoy I.
Partner: UNT Libraries

Gibbs/Equilibrium Measures for Functions of Multidimensional Shifts with Countable Alphabets

Description: Consider a multidimensional shift space with a countably infinite alphabet, which serves in mathematical physics as a classical lattice gas or lattice spin system. A new definition of a Gibbs measure is introduced for suitable real-valued functions of the configuration space, which play the physical role of specific internal energy. The variational principle is proved for a large class of functions, and then a more restrictive modulus of continuity condition is provided that guarantees a function's Gibbs measures to be a nonempty, weakly compact, convex set of measures that coincides with the set of measures obeying a form of the DLR equations (which has been adapted so as to be stated entirely in terms of specific internal energy instead of the Hamiltonians for an interaction potential). The variational equilibrium measures for a such a function are then characterized as the shift invariant Gibbs measures of finite entropy, and a condition is provided to determine if a function's Gibbs measures have infinite entropy or not. Moreover the spatially averaged limiting Gibbs measures, i.e. constructive equilibria, are shown to exist and their weakly closed convex hull is shown to coincide with the set of true variational equilibrium measures. It follows that the "pure thermodynamic phases", which correspond to the extreme points in the convex set of equilibrium measures, must be constructive equilibria. Finally, for an even smoother class of functions a method is presented to construct a compatible interaction potential and it is checked that the two different structures generate the same sets of Gibbs and equilibrium measures, respectively.
Date: May 2011
Creator: Muir, Stephen R.
Partner: UNT Libraries

The Validation of a Short-cycle Formative Assessment Observation Protocol for Science and Mathematics Instruction

Description: Over the years, teachers, administrators, and policy makers have been concerned with optimizing learning for all students. The No Child Left Behind Act put an emphasis on summative assessments, which measure what students have learned. In contrast, formative assessment has been shown in many studies to improve student achievement and motivation because it is applied while students are learning. The purpose of this study was to investigate, for middle and high school mathematics and science instruction, the validity and reliability of a newly developed observation instrument called AssessToday, which is used in a single class period to assess a teacher’s use of short-cycle formative assessment. The content validity of the instrument was supported through an extensive literature review, feedback from experts in the field of formative assessment, and an examination of 98 classroom observations. For assessing reliability of the instrument, inter-rater reliability coefficients were calculated using data collected by trained observers who independently rated teachers during the same class period using three measures: percentage of agreement between raters, Cohen’s kappa, and Fleiss kappa. Cohen’s kappa (N = 36 pairs) ranged from .62 to 1.00 for all observer pairs with an average kappa of .75 for mathematics (n = 16 pairs) and .76 for science (n = 20 pairs). The recommended threshold for kappa is k = .70. An exploratory factor analysis was conducted on the observation data and the determined factors related to the theoretical framework established in the literature. The results affirmed that the instrument is a tool to be utilized in short-cycle formative assessment with middle and high school science and mathematics teachers.
Date: December 2013
Creator: Heitz, Layne
Partner: UNT Libraries

Optimal Strategies for Stopping Near the Top of a Sequence

Description: In Chapter 1 the classical secretary problem is introduced. Chapters 2 and 3 are variations of this problem. Chapter 2, discusses the problem of maximizing the probability of stopping with one of the two highest values in a Bernoulli random walk with arbitrary parameter p and finite time horizon n. The optimal strategy (continue or stop) depends on a sequence of threshold values (critical probabilities) which has an oscillating pattern. Several properties of this sequence have been proved by Dr. Allaart. Further properties have been recently proved. In Chapter 3, a gambler will observe a finite sequence of continuous random variables. After he observes a value he must decide to stop or continue taking observations. He can play two different games A) Win at the maximum or B) Win within a proportion of the maximum. In the first section the sequence to be observed is independent. It is shown that for each n>1, theoptimal win probability in game A is bounded below by (1-1/n)^{n-1}. It is accomplished by reducing the problem to that of choosing the maximum of a special sequence of two-valued random variables and applying the sum-the-odds theorem of Bruss (2000). Secondly, it is assumed the sequence is i.i.d. The best lower bounds are provided for the winning probabilities in game B given any continuous distribution. These bounds are the optimal win probabilities of a game A which was examined by Gilbert and Mosteller (1966).
Date: December 2015
Creator: Islas Anguiano, Jose Angel
Partner: UNT Libraries

Transfer From a UTeach Replication Site to the Classroom: A Study of First and Second Year Instructional Practices

Description: Concerns based adoption model (CBAM) instruments were used to examine instructional practices of six graduates from a highly stylized, inquiry-based secondary math and science preparation program. Teachers were in the first or second years of teaching mathematics in six different secondary settings, ranging from poverty to wealthy schools. CBAM assumptions were tested. The primary assumption about concerns was that new teachers’ highest concerns would be within the self and task dimensions. According to Hall and Hord, it was assumed that the levels of use are typically in the orientation and preparation stages as a new teacher begins to implement an innovation, in the case of this study, inquiry-based instruction. All three instruments of the CBAM model were used for data collection and included: the Survey of Concerns Questionnaire, Innovation Components Configuration Map, and Levels of Use matrix. Teachers were observed, interviewed, and surveyed, three times each, across a five-month period. The findings from this study showed that the teachers had similar concerns and levels of use, which supported the assumptions outlined by the CBAM principles. Across the six teachers, the self and task concerns were high, aligning with the assumptions. However, unrelated and impact dimensions were noted, in opposition to the assumption. Likewise, assumptions of the levels of use were upheld in the orientation and preparation levels of use noted in the observations. Some mechanical levels of use were observed for a few of the teachers, an anomaly to the assumption.
Date: May 2015
Creator: Fields, Melanie
Partner: UNT Libraries

Dimensions in Random Constructions.

Description: We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.
Date: May 2002
Creator: Berlinkov, Artemi
Partner: UNT Libraries

The Development of Algebraic Reasoning in Undergraduate Elementary Preservice Teachers

Description: Although studies of teacher preparation programs have documented positive changes in mathematical knowledge for teaching with preservice teachers in mathematics content courses, this study focused on the impact of a mathematics methods course and follow-up student teaching assignment. The presumption was that preservice teachers would show growth in their mathematical knowledge during methods since the course was structured around active participation in mathematics, research-based pedagogy, and was concurrent with a two-day-per-week field experience in a local elementary school. Survey instruments utilized the computer adaptive test version of the Mathematical Knowledge for Teaching (MKT) measures from the Learning Mathematics for Teaching Project, and the Attitudes and Beliefs (towards mathematics) survey from the Mathematical Education of Elementary Teachers Project. A piecewise growth model analysis was conducted on data collected from 176 participants at 5 time-points (methods, 3 time-points; student teaching, 2 time-points) over a 9 month period. Although the participants' demographics were typical of U.S. undergraduate preservice teachers, findings suggest that initial low-level of mathematical knowledge, and a deep-rooted belief that there is only one way to solve mathematics problems, limited the impact of the methods and student teaching courses. The results from this study indicate that in (a) number sense, there was no significant change during methods (p = .392), but a significant decrease during student teaching (p < .001), and in (b) algebraic thinking, there was a significant decrease during methods (p < .001), but no significant change during student teaching (p = .653). Recommendations include that the minimum teacher preparation program entry requirements for mathematical knowledge be raised and that new teachers participate in continued professional development emphasizing both mathematical content knowledge and reform-based pedagogy to continue to peel away deep-rooted beliefs towards mathematics.
Date: December 2012
Creator: Hayata, Carole Anne
Partner: UNT Libraries