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In information theory, polar codes are a linear block error-correcting codes. The code construction is based on a multiple recursive concatenation of a short kernel code which transforms the physical channel into virtual outer channels.
[4]: 114 A DataFrame is a 2-dimensional data structure of rows and columns, similar to a spreadsheet, and analogous to a Python dictionary mapping column names (keys) to Series (values), with each Series sharing an index. [4]: 115 DataFrames can be concatenated together or "merged" on columns or indices in a manner similar to joins in SQL.
The value for must be solved for in this manner because for all values of , is only defined for < < +, and is periodic (with period ). This means that the inverse function will only give values in the domain of the function, but restricted to a single period.
In this polar decomposition, the unit circle has been replaced by the line x = 1, the polar angle by the slope y/x, and the radius x is negative in the left half-plane. If x 2 ≠ y 2 , then the unit hyperbola x 2 − y 2 = 1 and its conjugate x 2 − y 2 = −1 can be used to form a polar decomposition based on the branch of the unit hyperbola ...
For example, a table of 128 rows with a Boolean column requires 128 bytes a row-oriented format (one byte per Boolean) but 128 bits (16 bytes) in a column-oriented format (via a bitmap). Another example is the use of run-length encoding to encode a column.
Note that winsorizing is not equivalent to simply excluding data, which is a simpler procedure, called trimming or truncation, but is a method of censoring data.. In a trimmed estimator, the extreme values are discarded; in a winsorized estimator, the extreme values are instead replaced by certain percentiles (the trimmed minimum and maximum).
List of topologies – List of concrete topologies and topological spaces; Locally convex topological vector space – A vector space with a topology defined by convex open sets; Polar set – Subset of all points that is bounded by some given point of a dual (in a dual pairing) Topologies on spaces of linear maps; Topology consistent with the ...
The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. [1]