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        Bone microarchitecture and bone mineral density in Graves’ disease

        Hiya Boro,Rakhi Malhotra,Suraj Kubihal,Saurav Khatiwada,Vinay Dogra,Velmurugan Mannar,Ashok Kumar Ahirwar,Vandana Rastogi 대한골다공증학회 2023 Osteoporosis and Sarcopenia Vol.9 No.2

        Objectives: Graves' disease (GD) is the most common cause of thyrotoxicosis. There are many studies that have evaluated bone mineral density (BMD) in Graves’ disease. However, the strength of a bone also depends on its microarchitecture which can be assessed by various techniques. Trabecular bone score (TBS) is a new method for assessing bone microarchitecture that is non-invasive and easily performed. Methods: The present study was a cross-sectional study that involved 50 patients with active GD and 50 healthy controls. Both groups were subjected to an assessment of biochemical parameters followed by measurement of BMD and TBS on the same dual energy X-ray absorptiometry (DXA) machine. Results: The mean age of patients with active GD (N ¼ 50) was 31.9 ± 10.9 years while that of controls was 31.2 ± 4.9 years (P ¼ 0.640). The female: male ratio was the same for both groups (F ¼ 31, M ¼ 19). The mean lumbar spine BMD, femoral neck BMD, total hip BMD, and distal radius BMD were significantly reduced in GD when compared to that in controls. The mean absolute lumbar spine TBS in GD was 1.263 ± 0.101 while that in controls was 1.368 ± 0.073 (P < 0.001). On multivariate regression analysis, the factors that predicted TBS were serum thyroxine (T4) and L1-L4 BMD. Conclusions: Patients with Graves’ disease had reduced bone density at all sites and degraded microarchitecture. Long-term studies are required to understand the pattern of recovery of bone microarchitecture after the restoration of euthyroidism.

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        Methods of finding the initial values of parameters in the maximum likelihood estimating equations for a logistic regression model and comparison of their final solutions using different criterion functions

        Subir Ghosh,Hiya Banerjee 한국통계학회 2010 Journal of the Korean Statistical Society Vol.39 No.4

        We present two methods of finding the initial values of parameters of the maximum likelihood estimating equations (MLEE) for a logistic regression model using two criterion functions.Wethen use the initial values and the corresponding criterion functions to obtain the final solutions of MLEE. Most experiments include more than two doses for determining a lethal dose like ED50. With more than two doses, we do not have an exact analytical expression for the solution of estimating equations. However, for two doses, we do have an exact analytic expression for the solution of estimating equations. The iterative methods make use of the initial values of the parameters. We have used the search algorithm for performing the optimization to find the final solutions of MLEE. The proposed approach starts with all possible pairs of doses from the doses considered in the experiment. It then chooses the pair giving the optimum value of a criterion function and the corresponding exact solutions for the parameters based on two observations in the pair as the initial values of parameters for solving MLEE for all observations. The proposed methods are transparent in the selection of the initial values of parameters. The proposed methods are computer intensive like bootstrap and jackknife methods popular among statisticians. We illustrate our two methods of finding the initial values with an observed beetle mortality data. We then apply them to obtain the final solutions using two criterion functions. We observe that the numerical values of ED50 for the initial values of the parameters obtained by our approach are almost the same as the numerical values of ED50 for the final solutions. This closeness of the estimated ED50 values from our initial parameter values to the estimated ED50 values from the final solutions is a strong feature of our proposed methods. Moreover,the proposed methods compare favorably with SAS and R in terms of CPU time values.

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        Hysteresis and synchronization in an inhomogeneous system

        Das Alaka,Biswas Sujay,Mondal Hiya 한국물리학회 2023 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.83 No.12

        The phenomena of dynamic hysteresis and synchronization of oscillators are explored in an inhomogeneously coupled logistic map lattice. Here inhomogeneity means two different values of the map constant at the even site and the odd site. The value of the map constant corresponding to all even sites is equal. The same applies to all odd sites. We observe two coexisting attractors for the same values of coupling constant (ε) and the inhomogeneity parameter (γ) indicating the presence of hysteresis in the system. The existence of two attractors lies in the selection of initial values of the modes with different strategies. One attractor consists of fully synchronous or partially synchronous oscillators, while the other contains spatially asynchronous oscillators in the region of the hysteresis loop. The complete synchronization of modes happens in the first attractor only for ε = 0.5, when all the modes take up the same value. For partial synchronization, all the odd modes are clustered into a group, while all the even modes are also clustered into another group. The region of the hysteresis loop changes with the value of inhomogeneity constant γ. The spatial behavior of the attractors is analyzed using Kuramoto’s order parameter R. The total hysteresis loop area between two attractors in the ε - R plane decreases with an increase in inhomogeneity constant γ within the interval 0.2 < γ < 3.8. Hysteresis is further investigated using the plot of the phase synchronization ratio. We find a region in the γ - ε plane where the phases of the modes are asynchronous for a strategy but coherent for another strategy of choosing the initial condition.

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