Packing hyperspheres in high-dimensional Euclidean spaces
نویسندگان
چکیده
منابع مشابه
Packing hyperspheres in high-dimensional Euclidean spaces.
We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions d=4, 5, and 6 to be phi(MRJ) approximately 0.46, 0.31, and 0.20, respectively. To a good approximation, t...
متن کاملSupplementary Material ofDifferentially Private Clustering in High-Dimensional Euclidean Spaces
Non-Private Clustering: There is a wide range of prior work on the problem of center-based clustering in the absence of privacy requirement. It is known that exact optimization of objective function in R is not computationally possible (Dasgupta, 2008) even for the problem of 2-means clustering. To avoid the computational obstacle, several approximation algorithms have been developed, e.g., by ...
متن کاملDifferentially Private Clustering in High-Dimensional Euclidean Spaces
We study the problem of clustering sensitive data while preserving the privacy of individuals represented in the dataset, which has broad applications in practical machine learning and data analysis tasks. Although the problem has been widely studied in the context of lowdimensional, discrete spaces, much remains unknown concerning private clustering in highdimensional Euclidean spaces R. In th...
متن کاملExactly solvable disordered sphere-packing model in arbitrary-dimensional Euclidean spaces.
We introduce a generalization of the well-known random sequential addition (RSA) process for hard spheres in d-dimensional Euclidean space Rd. We show that all of the n-particle correlation functions of this nonequilibrium model, in a certain limit called the "ghost" RSA packing, can be obtained analytically for all allowable densities and in any dimension. This represents the first exactly sol...
متن کاملLines in n-Dimensional Euclidean Spaces
In this paper, we define the line of n-dimensional Euclidean space and we introduce basic properties of affine space on this space. Next, we define the inner product of elements of this space. At the end, we introduce orthogonality of lines of this space. provide the terminology and notation for this paper. (4) (a · b) · x = a · (b · x). (6) a · (x 1 + x 2) = a · x 1 + a · x 2. (7) (a + b) · x ...
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: Physical Review E
سال: 2006
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.74.041127