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Department: search.filters.department.Department of MathematicsSubject: search.filters.subject.Computational biology

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    Analysis of cortical morphometric variability using labeled cortical distance maps
    (Int Press Boston, Inc, 2017) Nishino, T.; Botteron, K. N.; Miller, M. I.; Ratnanather, J. T.; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Morphometric (i.e., shape and size) differences in the anatomy of cortical structures are associated with neuro-developmental and neuropsychiatric disorders. Such differences can be quantized and detected by a powerful tool called Labeled Cortical Distance Map (LCDM). The LCDM method provides distances of labeled gray matter (GM) voxels from the GM/white matter (WM) surface for specific cortical structures (or tissues). Here we describe a method to analyze morphometric variability in the particular tissue using LCDM distances. To extract more of the information provided by LCDM distances, we perform pooling and censoring of LCDM distances. In particular, we employ Brown-Forsythe (BF) test of homogeneity of variance (HOV) on the LCDM distances. HOV analysis of pooled distances provides an overall analysis of morphometric variability of the LCDMs due to the disease in question, while the HOV analysis of censored distances suggests the location(s) of significant variation in these differences (i.e., at which distance from the GM/WM surface the morphometric variability starts to be significant). We also check for the influence of assumption violations on the HOV analysis of LCDM distances. In particular, we demonstrate that BF HOV test is robust to assumption violations such as the non-normality and within sample dependence of the residuals from the median for pooled and censored distances and are robust to data aggregation which occurs in analysis of censored distances. We recommend HOV analysis as a complementary tool to the analysis of distribution/location differences. We also apply the methodology on simulated normal and exponential data sets and assess the performance of the methods when more of the underlying assumptions are satisfied. We illustrate the methodology on a real data example, namely, LCDM distances of GM voxels in ventral medial prefrontal cortices (VMPFCs) to see the effects of depression or being of high risk to depression on the morphometry of VMPFCs. The methodology used here is also valid for morphometric analysis of other cortical structures.
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    Modeling reflex asymmetries with implicit delay differential equations
    (Elsevier, 1998) Mallet-Paret, J; Department of Mathematics; Atay, Fatihcan; Faculty Member; Department of Mathematics; College of Sciences; 253074
    Neuromuscular reflexes with time-delayed negative feedback, such as the pupil light reflex, have different rates depending on the direction of movement. This asymmetry is modeled by an implicit first-order delay differential equation in which the value of the rate constant depends on the direction of movement. Stability analyses are presented for the cases when the rate is: (1) an increasing and (2) a decreasing function of the direction of movement. It is shown that the stability of equilibria in these dynamical systems depends on whether the rate constant is a decreasing or increasing function. In particular, when the asymmetry has the shape of an increasing step function, it is possible to have stability which is independent of the value of the time delay or the steepness (i.e., gain) of the negative feedback. (C) 1998 Society for Mathematical Biology.
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    Segregation indices for disease clustering
    (Wiley-Blackwell, 2014) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Spatial clustering has important implications in various fields. In particular, disease clustering is of major public concern in epidemiology. In this article, we propose the use of two distance-based segregation indices to test the significance of disease clustering among subjects whose locations are from a homogeneous or an inhomogeneous population. We derive the asymptotic distributions of the segregation indices and compare them with other distance-based disease clustering tests in terms of empirical size and power by extensive Monte Carlo simulations. The null pattern we consider is the random labeling (RL) of cases and controls to the given locations. Along this line, we investigate the sensitivity of the size of these tests to the underlying background pattern (e.g., clustered or homogenous) on which the RL is applied, the level of clustering and number of clusters, or to differences in relative abundances of the classes. We demonstrate that differences in relative abundances have the highest influence on the empirical sizes of the tests. We also propose various non-RL patterns as alternatives to the RL pattern and assess the empirical power performances of the tests under these alternatives. We observe that the empirical size of one of the indices is more robust to the differences in relative abundances, and this index performs comparable with the best performers in literature in terms of power. We illustrate the methods on two real-life examples from epidemiology. Copyright (c) 2013 John Wiley & Sons, Ltd.