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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6

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Now showing 1 - 5 of 5
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    PublicationOpen Access
    Nonlinear spectral singularities for confined nonlinearities
    (American Physical Society (APS), 2013) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    We introduce a notion of spectral singularity that applies for a general class of nonlinear Schrodinger operators involving a confined nonlinearity. The presence of the nonlinearity does not break the parity-reflection symmetry of spectral singularities but makes them amplitude dependent. Nonlinear spectral singularities are, therefore, associated with a resonance effect that produces amplified waves with a specific amplitude-wavelength profile. We explore the consequences of this phenomenon for a complex delta-function potential that is subject to a general confined nonlinearity.
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    PublicationOpen Access
    Censoring distances based on labeled cortical distance maps in cortical morphometry
    (Frontiers, 2013) Nishino, Tomoyuki; Alexopolous, Dimitrios; Todd, Richard D.; Botteron, Kelly N.; Miller, Michael I.; Ratnanather, J. Tilak; Department of Mathematics; Ceyhan, Elvan; Undergraduate Student; Faculty Member; Department of Mathematics; College of Sciences
    It has been demonstrated that shape differences in cortical structures may be manifested in neuropsychiatric disorders. Such morphometric differences can be measured by labeled cortical distance mapping (LCDM) which characterizes the morphometry of the laminar cortical mantle of cortical structures. LCDM data consist of signed/labeled distances of gray matter (GM) voxels with respect to GM/white matter (VW) surface. Volumes and other summary measures for each subject and the pooled distances can help determine the morphometric differences between diagnostic groups, however they do not reveal all the morphometric information contained in LCDM distances. To extract more information from LCDM data, censoring of the pooled distances is introduced for each diagnostic group where the range of LCDM distances is partitioned at a fixed increment size; and at each censoring step, the distances not exceeding the censoring distance are kept. Censored LCDM distances inherit the advantages of the pooled distances but also provide information about the location of morphometric differences which cannot be obtained from the pooled distances. However, at each step, the censored distances aggregate, which might confound the results. The influence of data aggregation is investigated with an extensive Monte Carlo simulation analysis and it is demonstrated that this influence is negligible. As an illustrative example, GM of ventral medial prefrontal cortices (VMPFCs) of subjects with major depressive disorder (MDD), subjects at high risk (HR) of MDD, and healthy control (Ctrl) subjects are used. A significant reduction in laminar thickness of the VMPFC in MDD and HR subjects is observed compared to Ctrl subjects. Moreover, the GM LCDM distances (i.e., locations with respect to the GM/WM surface) for which these differences start to occur are determined. The methodology is also applicable to LCDM-based morphometric measures of other cortical structures affected by disease.
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    PublicationOpen Access
    Modeling the interplay between HDV and HBV in chronic HDV/HBV patients
    (Multidisciplinary Digital Publishing Institute (MDPI), 2022) Mhlanga, A.; Zakh, R.; Churkin, A.; Reinharz, V.; Glenn, J.S.; Etzion, O.; Cotler, S.J.; Barash, D.; Dahari H.; Yurtaydın, Süleyman Cihan; Faculty Member; School of Medicine; 189330
    Hepatitis D virus is an infectious subviral agent that can only propagate in people infected with hepatitis B virus. In this study, we modified and further developed a recent model for early hepatitis D virus and hepatitis B virus kinetics to better reproduce hepatitis D virus and hepatitis B virus kinetics measured in infected patients during anti-hepatitis D virus treatment. The analytical solutions were provided to highlight the new features of the modified model. The improved model offered significantly better prospects for modeling hepatitis D virus and hepatitis B virus interactions.
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    PublicationOpen Access
    HMI-PRED 2.0: a biologist-oriented web application for prediction of host-microbe protein-protein interaction by interface mimicry
    (Oxford University Press (OUP), 2022) Lim, H., Tsai, C.J.; Nussinov, R.; Department of Computer Engineering; Department of Chemical and Biological Engineering; Keskin, Özlem; Gürsoy, Attila; Faculty Member; Department of Computer Engineering; Department of Chemical and Biological Engineering; College of Engineering; 26605; 8745
    HMI-PRED 2.0 is a publicly available web service for the prediction of host-microbe protein-protein interaction by interface mimicry that is intended to be used without extensive computational experience. A microbial protein structure is screened against a database covering the entire available structural space of complexes of known human proteins.
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    PublicationOpen Access
    Testing spatial symmetry using contingency tables based on nearest neighbor relations
    (Hindawi, 2014) Department of Mathematics; Ceyhan, Elvan; Undergraduate Student; Faculty Member; Department of Mathematics; College of Sciences
    We consider two types of spatial symmetry, namely, symmetry in the mixed or shared nearest neighbor (NN) structures. We use Pielou’s and Dixon’s symmetry tests which are defined using contingency tables based on the NN relationships between the data points. We generalize these tests to multiple classes and demonstrate that both the asymptotic and exact versions of Pielou’s first type of symmetry test are extremely conservative in rejecting symmetry in the mixed NN structure and hence should be avoided or only the Monte Carlo randomized version should be used. Under RL, we derive the asymptotic distribution for Dixon’s symmetry test and also observe that the usual independence test seems to be appropriate for Pielou’s second type of test. Moreover, we apply variants of Fisher’s exact test on the shared NN contingency table for Pielou’s second test and determine the most appropriate version for our setting. We also consider pairwise and one-versus-rest type tests in post hoc analysis after a significant overall symmetry test. We investigate the asymptotic properties of the tests, prove their consistency under appropriate null hypotheses, and investigate finite sample performance of them by extensive Monte Carlo simulations. The methods are illustrated on a real-life ecological data set.