1,370 research outputs found

    Another integrable case in the Lorenz model

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    A scaling invariance in the Lorenz model allows one to consider the usually discarded case sigma=0. We integrate it with the third Painlev\'e function.Comment: 3 pages, no figure, to appear in J. Phys.

    k-server via multiscale entropic regularization

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    We present an O((logk)2)O((\log k)^2)-competitive randomized algorithm for the kk-server problem on hierarchically separated trees (HSTs). This is the first o(k)o(k)-competitive randomized algorithm for which the competitive ratio is independent of the size of the underlying HST. Our algorithm is designed in the framework of online mirror descent where the mirror map is a multiscale entropy. When combined with Bartal's static HST embedding reduction, this leads to an O((logk)2logn)O((\log k)^2 \log n)-competitive algorithm on any nn-point metric space. We give a new dynamic HST embedding that yields an O((logk)3logΔ)O((\log k)^3 \log \Delta)-competitive algorithm on any metric space where the ratio of the largest to smallest non-zero distance is at most Δ\Delta

    Uniform Sampling for Matrix Approximation

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    Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time significantly. For theoretical performance guarantees, each row must be sampled with probability proportional to its statistical leverage score. Unfortunately, leverage scores are difficult to compute. A simple alternative is to sample rows uniformly at random. While this often works, uniform sampling will eliminate critical row information for many natural instances. We take a fresh look at uniform sampling by examining what information it does preserve. Specifically, we show that uniform sampling yields a matrix that, in some sense, well approximates a large fraction of the original. While this weak form of approximation is not enough for solving linear regression directly, it is enough to compute a better approximation. This observation leads to simple iterative row sampling algorithms for matrix approximation that run in input-sparsity time and preserve row structure and sparsity at all intermediate steps. In addition to an improved understanding of uniform sampling, our main proof introduces a structural result of independent interest: we show that every matrix can be made to have low coherence by reweighting a small subset of its rows

    Worldwide Distribution of a Common Methylenetetrahydrofolate Reductase Mutation

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    Peran Orangtua Terhadap Persepsi dan Pengetahuan Remaja Putri Tentang Menarche di Desa Kuanheun

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    Latar Belakang. Masa remaja merupakan masa peralihan dari masa kanak-kanak menuju dewasa. Salah satu tanda kematangan fisik dan seksual pada perempuan adalah terjadinya menarche. Peristiwa terpenting yang terjadi pada masa pubertas remaja putri adalah datangnya menstruasi pertama yang dinamakan menarche yang menjadi pertanda biologis dari kematangan seksual. Idealnya seorang remaja putri belajar atau mengetahui tentang  menstruasi dari ibunya. Tidak selamanya ibu dapat memberikan informasi tentang menstruasi karena terhalang tradisi yang menganggap tabu untuk membicarakan tentang menstruasi, sehingga mempengaruhi kualitas kesehatan selama menstruasi pada remaja. Tujuan Penelitian. Mengetahui hubungan antara peran orangtua dengan persepsi remaja putri tentang menarche di desa Kuanheun Kecamatan Kupang Barat Kabupaten Kupang. Metode Penelitian Deskriptif non-eksperimental dengan pendekatan Cross-Sectional, pada 40 remaja di desa Kuanheun, pengumpulan data menggunakan kuisioner. Analisis deskriptif dan uji Chi-Square. Hasil Penelitian: peran orang tua dengan pengetahuan remaja tentang menarche termasuk dalam kategori  baik (68,8%), uji statistik menggunakan uji Chi-Square antara peran orangtua dengan pengetahuan remaja tentang menarche tidak ada pengaruh secara signifikan dengan nilai p=0,416 (p>0,05) dan peran orang tua dengan persepsi remaja tentang menarche termasuk dalam kategori  kurang (87,5%), uji Chi-Square antara peran orangtua dengan persepsi remaja tentang menarche ada pengaruh secara signifikan dengan nilai p=0,046 (p<0,05). Kesimpulan: Peran orang tua dalam mempersiapkan menarche bagi remaja putri di desa Kuanheun termasuk dalam kategori baik, dan peran orang tua mempunyai hubungan yang bermakna dengan persepsi remaja putri tentang menarche
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