کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897034 | 1630629 | 2018 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The geometry of nodal sets and outlier detection
ترجمه فارسی عنوان
هندسه مجموعه های گره و تشخیص خروجی
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let (M,g) be a compact manifold and let âÎÏk=λkÏk be the sequence of Laplacian eigenfunctions. We present a curious new phenomenon which, so far, we only managed to understand in a few highly specialized cases: the family of functions fN:MâRâ¥0fN(x)=âkâ¤N1λk|Ïk(x)|âÏkâLâ(M) and their extrema seem strangely suited for the detection of anomalous points on the manifold. It may be heuristically interpreted as the sum over distances to the nearest nodal line and potentially hints at a new phenomenon in spectral geometry. We give rigorous statements on the unit square [0,1]2 (where minima localize in Q2) and on Paley graphs (where fN recovers the geometry of quadratic residues of the underlying finite field Fp). Numerical examples show that the phenomenon seems to arise on fairly generic manifolds.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 185, April 2018, Pages 48-64
Journal: Journal of Number Theory - Volume 185, April 2018, Pages 48-64
نویسندگان
Xiuyuan Cheng, Gal Mishne, Stefan Steinerberger,