Regression calibration for Cox regression under heteroscedastic measurement error - Determining risk factors of cardiovascular diseases from error-prone nutritional replication data

For instance nutritional data are often subject to severe measurement error, and an adequate adjustment of the estimators is indispensable to avoid deceptive conclusions. This paper discusses and extends the method of regression calibration to correct for measurement error in Cox regression. Special attention is paid to the modelling of quadratic predictors, the role of heteroscedastic measurement error, and the efficient use of replicated measurements of the surrogates. The method is used to analyze data from the German part of the MONICA cohort study on cardiovascular diseases. The results corroborate the importance of taking into account measurement error carefully

A nonparametric predictive alternative to the Imprecise Dirichlet Model: the case of a known number of categories

Nonparametric Predictive Inference (NPI) is a general methodology to learn from data in the absence of prior knowledge and without adding unjustified assumptions. This paper develops NPI for multinomial data where the total number of possible categories for the data is known. We present the general upper and lower probabilities and several of their properties. We also comment on differences between this NPI approach and corresponding inferences based on Walley's Imprecise Dirichlet Model

Switching quantum reference frames in the N-body problem and the absence of global relational perspectives

Given the importance of quantum reference systems to both quantum and gravitational physics, it is pertinent to develop a systematic method for switching between the descriptions of physics relative to different choices of quantum reference systems, which is valid in both fields. Here, we continue with such a unifying approach, begun in arxiv:1809.00556, whose key ingredients is a gravity-inspired symmetry principle, which enforces physics to be relational and leads, thanks to gauge related redundancies, to a perspective-neutral structure which contains all frame choices at once and via which frame perspectives can be consistently switched. Formulated in the language of constrained systems, the perspective-neutral structure turns out to be the constraint surface classically and the gauge invariant Hilbert space in the Dirac quantized theory. By contrast, a perspective relative to a specific frame corresponds to a gauge choice and the associated reduced phase and Hilbert space. Quantum reference frame switches thereby amount to a symmetry transformation. In the quantum theory, they require a transformation that takes one from the Dirac to a reduced quantum theory and we show that it amounts to a trivialization of the constraints and a subsequent projection onto the classical gauge fixing conditions. We illustrate this method in the relational $N$-body problem with rotational and translational symmetry. This model is particularly interesting because it features the Gribov problem so that globally valid gauge fixing conditions are impossible which, in turn, implies also that globally valid relational frame perspectives are absent in both the classical and quantum theory. These challenges notwithstanding, we exhibit how one can systematically construct the quantum reference frame transformations for the three-body problem.Comment: 22 pages, plus appendice

Classical and all-floating FETI methods for the simulation of arterial tissues

High-resolution and anatomically realistic computer models of biological soft tissues play a significant role in the understanding of the function of cardiovascular components in health and disease. However, the computational effort to handle fine grids to resolve the geometries as well as sophisticated tissue models is very challenging. One possibility to derive a strongly scalable parallel solution algorithm is to consider finite element tearing and interconnecting (FETI) methods. In this study we propose and investigate the application of FETI methods to simulate the elastic behavior of biological soft tissues. As one particular example we choose the artery which is - as most other biological tissues - characterized by anisotropic and nonlinear material properties. We compare two specific approaches of FETI methods, classical and all-floating, and investigate the numerical behavior of different preconditioning techniques. In comparison to classical FETI, the all-floating approach has not only advantages concerning the implementation but in many cases also concerning the convergence of the global iterative solution method. This behavior is illustrated with numerical examples. We present results of linear elastic simulations to show convergence rates, as expected from the theory, and results from the more sophisticated nonlinear case where we apply a well-known anisotropic model to the realistic geometry of an artery. Although the FETI methods have a great applicability on artery simulations we will also discuss some limitations concerning the dependence on material parameters.Comment: 29 page

Penerapan Model Pembelajaran Langsung Untuk Meningkatkan Hasil Belajar Matematika Siswa Kelas III Sdn Ngagel Rejo Iii/398 Surabaya

Tugas utama seorang guru adalah bertanggung jawab membantu anak didik dalam hal belajar. Dalam proses belajar mengajar, gurulah yang menyampaikan pelajaran, memecahkan masalah-masalah yang terjadi dalam kelas, membuat evaluasi belajar siswa, baik sebelum, sedang maupun sesudah pelajaran berlangsung. Permasalahan yang ingin dikaji dalam penelitian tindakan ini adalah Penelitian ini berdasarkan permasalahan: (1) Bagaimanakah aktivitas guru dalam penerapan model pembelajaran langsung untuk meningkatkan hasil belajar matematika siswa kelas III SDN Ngagel Rejo III/398 Surabaya? (2) Bagaimanakah aktivitas belajar siswa dalam penerapan model pembelajaran langsung untuk meningkatkan hasil belajar matematika siswa kelas III SDN Ngagel Rejo III/398 Surabaya? (3) Bagaimanakah hasil belajar siswa setelah penerapan model pembelajaran langsung untuk meningkatkan hasil belajar matematika siswa kelas III SDN Ngagel Rejo III/398 Surabaya?.Tujuan dari penelitian ini adalah: (1) Mendeskripsikan aktivitas guru dalam penerapan model pembelajaran langsung untuk meningkatkan hasil belajar matematika siswa kelas III SDN Ngagel Rejo III/398 Surabaya. (2)Mendeskripsikan aktivitas belajar siswa dalam penerapan model pembelajaran langsung untuk meningkatkan hasil belajar matematika siswa kelas III SDN Ngagel Rejo III/398 Surabaya. (3) Mendeskripsikan hasil belajar siswa setelah penerapan model pembelajaran langsung untuk meningkatkan hasil belajar matematika siswa kelas III SDN Ngagel Rejo III/398 Surabaya. Dari hasil analisis didapatkan bahwa dengan penerapan model pembelajaran langsung proses pelaksanaan pembelajaran Matematika berjalan aktif dan keaktifan siswa semakin aktif. persentase ketuntasan prestasi belajar siswa mengalami peningkatan dari siklus I sampai siklus II yaitu, siklus I (65,71%), siklus II (94,29%) . Kesimpulan dari penelitian ini adalah penerapan model pembelajaran langsung berdampak positif terhadap keaktifan siswa sehingga berpengaruh terhadap hasil belajar siswa dalam pelajaran Matematika, sehingga model pembelajaran ini bisa digunakan sebagai alternatif untuk meningkatkan hasil belajar siswa dalam proses pembelajaran