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You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.
Split PDF files in a number of ways: After every page, even pages or odd pages; After a given set of page numbers; Every n pages; By bookmark level; By size, where the generated files will roughly have the specified size; Rotate PDF files where multiple files can be rotated, either every page or a selected set of pages (i.e. Mb).
PDFtk (short for PDF Toolkit) is a toolkit for manipulating Portable Document Format (PDF) documents. [3] [4] It runs on Linux, Windows and macOS. [5] It comes in three versions: PDFtk Server (open-source command-line tool), PDFtk Free and PDFtk Pro (proprietary paid). [2] It is able to concatenate, shuffle, split and rotate PDF files.
A great many important inequalities in information theory are actually lower bounds for the Kullback–Leibler divergence.Even the Shannon-type inequalities can be considered part of this category, since the interaction information can be expressed as the Kullback–Leibler divergence of the joint distribution with respect to the product of the marginals, and thus these inequalities can be ...
In mathematics and statistics, a quantitative variable may be continuous or discrete if it is typically obtained by measuring or counting, respectively. [1] If it can take on two particular real values such that it can also take on all real values between them (including values that are arbitrarily or infinitesimally close together), the variable is continuous in that interval. [2]
A MEX file is a type of computer file that provides an interface between MATLAB or Octave and functions written in C, C++ or Fortran.It stands for "MATLAB executable". When compiled, MEX files are dynamically loaded and allow external functions to be invoked from within MATLAB or Octave as if they were built-in functions.
The joint entropy of a set of variables is less than or equal to the sum of the individual entropies of the variables in the set. This is an example of subadditivity . This inequality is an equality if and only if X {\displaystyle X} and Y {\displaystyle Y} are statistically independent .
We can rewrite this definition in terms that explicitly highlight the information content of this metric. The set of all partitions of a set form a compact lattice where the partial order induces two operations, the meet and the join , where the maximum ¯ is the partition with only one block, i.e., all elements grouped together, and the minimum is ¯, the partition consisting of all elements ...