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ggplot2 is an open-source data visualization package for the statistical programming language R.Created by Hadley Wickham in 2005, ggplot2 is an implementation of Leland Wilkinson's Grammar of Graphics—a general scheme for data visualization which breaks up graphs into semantic components such as scales and layers. ggplot2 can serve as a replacement for the base graphics in R and contains a ...
The IBM GCR code above meets this condition, since the maximal run length of zeros at the beginning of any 5-bit code is one, and likewise the maximal run length at the end of any code is one, making a total run length of two at the junction between adjacent codes. (An example of the maximal run length occurring between codes can be seen in the ...
This is a list of limits for common functions such as elementary functions. In this article, the terms a , b and c are constants with respect to x . Limits for general functions
R is a programming language for statistical computing and data visualization.It has been adopted in the fields of data mining, bioinformatics and data analysis. [9]The core R language is augmented by a large number of extension packages, containing reusable code, documentation, and sample data.
Using these highly efficient codes and with the computing power in today's digital signal processors, it is now possible to reach very close to the Shannon limit. In fact, it was shown that LDPC codes can reach within 0.0045 dB of the Shannon limit (for binary additive white Gaussian noise (AWGN) channels, with very long block lengths). [1]
The maximum possible size of a subset of the symbols that can all be distinguished from each other is the independence number of the graph, the size of its maximum independent set. For instance, ' α ( C 5 ) = 2 {\displaystyle \alpha (C_{5})=2} : the 5-cycle has independent sets of two vertices, but not larger.
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The Reed–Muller RM(r, m) code of order r and length N = 2 m is the code generated by v 0 and the wedge products of up to r of the v i, 1 ≤ i ≤ m (where by convention a wedge product of fewer than one vector is the identity for the operation).