Tangled Embeddings of One-Dimensional Continua
نویسندگان
چکیده
منابع مشابه
Metric Embeddings--Beyond One-Dimensional Distortion
Metric spaces and their embeddings have recently played a prominent role in the development of new algorithms. So far, most of the emphasis was on embeddings that preserve pairwise distances. A very intriguing concept introduced by Feige [Fei00], allows us to quantify the extent to which higher-dimensional structures are preserved by a given embedding. We investigate this concept for several ba...
متن کاملTransmission properties of one dimensional fractal structures
In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...
متن کاملPower1D: a Python toolbox for numerical power estimates in experiments involving one-dimensional continua
The unit of experimental measurement in a variety of scientific applications is the one-dimensional (1D) continuum: a dependent variable whose value is measured repeatedly, often at regular intervals, in time or space. A variety of software packages exist for computing continuum-level descriptive statistics and also for conducting continuum-level hypothesis testing, but very few offer power com...
متن کاملInfinite Dimensional Word Embeddings
We describe a method for learning word embeddings with stochastic dimensionality. Our Infinite Skip-Gram (iSG) model specifies an energy-based joint distribution over a word vector, a context vector, and their dimensionality, which can be defined over a countably infinite domain by employing the same techniques used to make the Infinite Restricted Boltzmann Machine (Côté & Larochelle, 2015) tra...
متن کاملLow dimensional embeddings of ultrametrics
In this note we show that every n-point ultrametric embeds with constant distortion in l O(logn) p for every ∞ ≥ p ≥ 1. More precisely, we consider a special type of ultrametric with hierarchical structure called a k-hierarchically well-separated tree (k-HST). We show that any k-HST can be embedded with distortion at most 1 + O(1/k) in l O(k2 logn) p . These facts have implications to embedding...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.2307/2037061