MATH Research Publications

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The collection of peer-reviewed research articles (co)authored by faculty of the Department of Mathematics and Statistics.

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    Estimating several survival functions under uniform stochastic ordering
    (Elsevier B.V., 2024-01) Arnold, Sebastian; El Barmi, Hammou; Mukerjee, Hari; Ziegel, Johanna
    El Barmi and Mukerjee (2016, Journal of Multivariate Analysis 144, 99-109) studied the estimation of survival functions of k samples under uniform stochastic ordering constraints. There were two crucial errors in the consistency proof. Here, we provide alternative estimators and show consistency.
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    Computation of potential flow in multiply connected domains using conformal mapping
    (Kent State University, 2023) DeLillo, Thomas K.; Mears, Justin Laurence; Sahraei, Saman
    This paper describes a method to calculate the potential flow in domains in the complex plane exterior to a finite number of closed curves using conformal mapping. A series method is used to compute the potential flow over multiply connected circle domains. The flow is then mapped from the circle domain to the target physical domain by a method which approximates the Laurent series of the conformal map. The circulations around each boundary can be specified. For flow over multi-element airfoils, the circulations are computed to satisfy the Kutta condition at the trailing edges. The linear systems which are solved on the circle domain for both the potential flow and the conformal maps are of the form identity plus a low-rank matrix, allowing for the efficient use of conjugate-gradient-like methods.
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    Nitrogen-Vacancy Magnetic Relaxometry of Nanoclustered Cytochrome C Proteins
    (American Chemical Society, 2024-01) Lamichhane, Suvechhya; Timalsina, Rupak; Schultz, Cody; Fescenko, Ilja; Ambal, Kapildeb; Liou, Sy-Hwang; Lai, Rebecca Y.; Laraoui, Abdelghani
    Nitrogen-vacancy (NV) magnetometry offers an alternative tool to detect paramagnetic centers in cells with a favorable combination of magnetic sensitivity and spatial resolution. Here, we employ NV magnetic relaxometry to detect cytochrome C (Cyt-C) nanoclusters. Cyt-C is a water-soluble protein that plays a vital role in the electron transport chain of mitochondria. Under ambient conditions, the heme group in Cyt-C remains in the Fe$^{3+}$ state, which is paramagnetic. We vary the concentration of Cyt-C from 6 to 54 μM and observe a reduction of the NV spin-lattice relaxation time (T$_1$) from 1.2 ms to 150 μs, which is attributed to the spin noise originating from the Fe$^{3+}$ spins. NV T$_1$ imaging of Cyt-C drop-casted on a nanostructured diamond chip allows us to detect the relaxation rates from the adsorbed Fe$^{3+}$ within Cyt-C.
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    Discontinuous Galerkin Methods for Network Patterning Phase-Field Models
    (Springer, 2023-12) Yang, Lei; Liu, Yuan; Jiang, Yan; Zhang, Mengping
    In this paper, we propose a class of discontinuous Galerkin methods under the scalar auxiliary variable framework (SAV-DG) to solve a biological patterning model in the form of parabolic-elliptic partial differential equation system. In particular, mixed-type discontinuous Galerkin approximations are used for the spatial discretization, aiming to achieve a balance between the high resolution and computational cost. Second and third order backward differentiation formulas are considered under SAV framework for discrete energy stability. Numerical experiments are provided to show the effectiveness of the fully discrete schemes and the governing factors of patterning formation.
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    A uniqueness theorem for inverse problems in quasilinear anisotropic media II
    (American Institute of Mathematical Sciences, 2024-02) Kholil, Md Ibrahim; Sun, Ziqi
    We study the question of whether one can uniquely determine scalar quasilinear conductivity in an anisotropic medium by making voltage and current measurements at the boundary. We prove a global uniqueness in the C$^{2,α}$ category, by showing that the C$^{2,α}$ quasilinear conductivity in an anisotropic medium can be uniquely determined by the voltage and current measurements at the boundary, i.e., by the Dirichlet to Neumann map, assuming that an anisotropic linear conductivity can be identified by its Dirichlet to Neumann map up to a diffeomorphism that fixes the boundary.
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