We study model embeddability, which is a variation of the famous embedding problem in probability theory, when apart from the requirement that the Markov matrix is the matrix exponential of a rate matrix, we additionally ask that the rate matrix follows the model structure. We provide a characterisation of model embeddable Markov matrices corresponding to symmetric group-based phylogenetic models. In particular, we provide necessary and sufficient conditions in terms of the eigenvalues of symmetric group-based matrices. To showcase our main result on model embeddability, we provide an application to hachimoji models, which are eight-state models for synthetic DNA. Moreover, our main result on model embeddability enables us to compute the volume of the set of model embeddable Markov matrices relative to the volume of other relevant sets of Markov matrices within the model.
We study model embeddability, which is a variation of the famous embedding problem in probability theory, when apart from the requirement that the Markov matrix is the matrix exponential of a rate matrix, we additionally ask that the rate matrix follows the model structure. We provide a characterisation of model embeddable Markov matrices corresponding to symmetric group-based phylogenetic models. In particular, we provide necessary and sufficient conditions in terms of the eigenvalues of symmetric group-based matrices. To showcase our main result on model embeddability, we provide an application to hachimoji models, which are eight-state models for synthetic DNA. Moreover, our main result on model embeddability, enables us to compute the volume of the set of model embeddable Markov matrices relative to the volume of other relevant sets of Markov matrices within the model.
In phylogenetics, it is important for the phylogenetic network model parameters to be identifiable so that the evolutionary histories of a group of species can be consistently inferred. However, as the complexity of the phylogenetic network models grows, the identifiability of network models becomes increasingly difficult to analyze. As an attempt to analyze the identifiability of network models, we check whether two networks are distinguishable. In this paper, we specifically study the distinguishability of phylogenetic network models associated with level-2 networks. Using an algebraic approach, namely using discrete Fourier transformation, we present some results on the distinguishability of some level-2 networks, which generalize earlier work on the distinguishability of level-1 networks. In particular, we study simple and semisimple level-2 networks. Simple and semisimple level-2 networks can be thought as generalizations of level-1 sunlet and cycle networks, respectively. Moreover, we also compare the varieties associated with semisimple level-2 and cycle networks.
Penelitian ini bertujuan untuk mengetahui pengembangan sikap kooperatif anak melalui kombinasi model DREAM dengan media kartu bergambar pada kelompok B TK Negeri Pembina Kelumpang Hilir Kotabaru. Penelitian ini menggunakan jenis penelitian tindakan kelas yang terdiri dari empat tahapan, yaitu: perencanaan, pelaksanaan, pengamatan, dan refleksi. Subjek penelitian ini adalah anak kelompok B TK Negeri Pembina Kelumpang Hilir Kotabaru berjumlah 6 orang anak. Teknik pengumpulan data menggunakan observasi, wawancara, dan dokumentasi. Hasil penelitian ini menunjukkan adanya perkembangan sikap kooperatif anak dalam proses pembelajaran menggunakan kombinasi model DREAM dengan media kartu bergambar. Hal ini dapat dilihat dari adanya peningkatan presentase sikap kooperatif anak, pada pertemuan 1 sebesar 33%, pertemuan kedua sebesar 67%, pertemuan ketiga sebesar 83%, dan pertemuan keempat sebesar 100%. Berdasarkan hasil penelitian disimpulkan bahwa kombinasi model DREAM dengan media kartu bergambar dapat meningkatkan aktivitas dan hasil capaian perkembangan anak. Disarankan penggunaan model tersebut sebagai salah satu alternatif dalam meningkatkan aktivitas belajar yang berdampak pada peningkatan hasil capaian perkembangan anak dalam bersikap kooperatif dengan teman.
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