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  • Undergraduate Poster Abstracts
  • Applied Mathematics

    Room Chesapeake 7

    ap059 ANALYZING FMRI BRAIN SCANS OF SUBJECTS PREDISPOSED TO HUNTINGTON'S DISEASE USING PERSISTENT HOMOLOGY

    • Leyda Almodovar Velazquez ;
    • Isabel Darcy ;

    n/a

    ANALYZING FMRI BRAIN SCANS OF SUBJECTS PREDISPOSED TO HUNTINGTON'S DISEASE USING PERSISTENT HOMOLOGY

    Leyda Almodovar Velazquez, Isabel Darcy.

    The University of Iowa, Iowa City, IA.

    Huntington's disease (HD) is an inherited brain disease that results in the progressive degeneration of nerve cells in the brain. HD has a broad impact on the person's motor, cognitive, and psychiatric faculties, with symptoms appearing around the ages of 30 to 50. While there exist medications to alleviate some of the symptoms associated with the disease, there is no cure or preventive treatment available. The goal of this investigation is to study the brain network structures of healthy subjects and subjects predisposed to HD in order to identify different brain behavior among the subjects. Functional magnetic resonance imaging (fMRI) is a non-invasive neuroimaging procedure for measuring brain activity. This technique has been used for assessing the effects of degenerative disease on brain function. Data was collected from fMRI experiments with 96 subjects between the ages of 6 and 18, some of them predisposed to HD. Cutting edge tools from topological data analysis, an area where topology, statistics, and computational geometry intersect, were applied to the data. Specifically, persistent homology software, e.g., Perseus, was used to group and visualize the data at different resolutions by varying parameters such as the threshold and clustering coefficient. Our experiments did not capture a significant difference between the brains of healthy subjects and the brains of subjects predisposed to HD. Further experimentation is required in order to validate our results.

    ap060 DATA VALIDATED MODEL OF ANDROGEN SUPPRESSION FOR PROSTATE CANCER AND ITS INSIGHTS

    • Javier Baez Jr. ;
    • Yang Kuang ;

    n/a

    DATA VALIDATED MODEL OF ANDROGEN SUPPRESSION FOR PROSTATE CANCER AND ITS INSIGHTS

    Javier Baez Jr., Yang Kuang.

    Arizona State University, Tempe, AZ.

    Mathematical models are essential in our efforts to forecast and quantify the treatment effectiveness of prostate cancer patients undergoing intermittent androgen deprivation (IAD). We developed a simple mathematical model to study IAD and used clinical data to validate our model using measurements of patients’ androgen levels and prostate specific antigen (PSA). Our model is the first to fit both measured PSA and androgen levels accurately. We also present mathematical analysis of our model that is biologically meaningful and raise more biological questions.

    ap061 SCALING LAWS OF DEFORMATION AND TRANSFORMATION OF FRACTAL MEDIA

    • Mario Zepeda Aguilar ;
    • Lev Steinberg ;

    n/a

    SCALING LAWS OF DEFORMATION AND TRANSFORMATION OF FRACTAL MEDIA

    Mario Zepeda Aguilar, Lev Steinberg.

    University of Puerto Rico, Mayaguez Campus, Mayaguez, PR.

    We will present an extension of continuum mechanics to the fractal media at mesoscopic scale. The mechanics at this scale consider the material bodies as a fractal media and study the material deformation and transformation as well. We assume that the mesoscopic deformation does not affect material structure however the transformation of the fractal media does involve the change of mesoscopic properties. These changes include the variation of characteristics of fractal dimension of internal material structure. We also assume that the forces responsible for these transformations are, by definition, the configuration stress and couple stress. For the material deformation, we will present the integral forms of equations for the conservation of fractional mass, linear, and angular momentum in terms of stress and couple stress of deformed fractal bodies. The constitutive formulas for the deformation can be written by analogy with the Cosserat continuum. The conservation laws for the transformation of fractal bodies will also be discussed. We will show that constitutive formulas for the transformation should include fractional derivatives techniques.

    ap062 MODELING SIZE DISTRIBUTION OF TRANSPOSABLE ELEMENTS WITH FRAGMENTATION EQUATIONS

    • Mario Banuelos ;
    • Suzanne Sindi ;

    n/a

    MODELING SIZE DISTRIBUTION OF TRANSPOSABLE ELEMENTS WITH FRAGMENTATION EQUATIONS

    Mario Banuelos, Suzanne Sindi.

    University of California, Merced, Merced, CA.

    Transposable elements (TEs), segments of DNA capable of self-replication, are abundant in a significant portion of both eukaryotes and prokaryotes. Over generations, their location and distribution in the host genome changes through transposition and deletion events. When replicating, TEs sometimes create mutations in existing genes. Since TE replication is faster than spontaneous deletions, these elements typically persist in the host genome even if these sequences are no longer able to replicate. Although recent studies find TEs may serve a regulatory function for the host, both empirical and theoretical studies suggest that they often have deleterious effects, such as hemophilia or a predisposition to cancer in humans. We studied the replication of transposable elements by modeling the density of full-length sequences as well as partial length sequences resulting from mutations of the host genome. Our deterministic model takes into account both insertions and deletions in the genome. We analyzed the zeroth and first moment of the size-distribution and demonstrate we can describe the full system using only these first 2 moments. We derived solutions to both the discrete and continuous fragmentation equations. Finally, we compared our analytical results with empirical distributions of TEs from sequenced genomes to infer parameters of the TE replication dynamics as well as estimate the time of the earliest TE insertion events. We hypothesize that this information will lead to a greater understanding of the proliferation of TEs in various genomes and will help in the reconstruction of the phylogeny of organisms.