کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8900520 | 1631601 | 2018 | 31 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Neural ideals and stimulus space visualization
ترجمه فارسی عنوان
تجسم فضایی عضلانی و محرک
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
A neural code C is a collection of binary vectors of a given length n that record the co-firing patterns of a set of neurons. Our focus is on neural codes arising from place cells, neurons that respond to geographic stimulus. In this setting, the stimulus space can be visualized as subset of R2 covered by a collection U of convex sets such that the arrangement U forms an Euler diagram for C. There are some methods to determine whether such a convex realization U exists; however, these methods do not describe how to draw a realization. In this work, we look at the problem of algorithmically drawing Euler diagrams for neural codes using two polynomial ideals: the neural ideal, a pseudo-monomial ideal; and the neural toric ideal, a binomial ideal. In particular, we study how these objects are related to the theory of piercings in information visualization, and we show how minimal generating sets of the ideals reveal whether or not a code is 0, 1, or 2-inductively pierced.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Applied Mathematics - Volume 95, April 2018, Pages 65-95
Journal: Advances in Applied Mathematics - Volume 95, April 2018, Pages 65-95
نویسندگان
Elizabeth Gross, Nida Obatake, Nora Youngs,