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[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 one-sided shift S acting on is a proper isometry with range equal to all vectors which vanish in the first coordinate. The operator S is a compression of T −1 , in the sense that T − 1 y = S x for each x ∈ ℓ 2 ( N ) , {\displaystyle T^{-1}y=Sx{\text{ for each }}x\in \ell ^{2}(\mathbb {N} ),} where y is the vector in ℓ ...
Comma-separated values (CSV) is a text file format that uses commas to separate values, and newlines to separate records. A CSV file stores tabular data (numbers and text) in plain text, where each line of the file typically represents one data record.
An upper shift matrix shifts the components of a column vector one position up, with a zero appearing in the last position. [1] Premultiplying a matrix A by a lower shift matrix results in the elements of A being shifted downward by one position, with zeroes appearing in the top row. Postmultiplication by a lower shift matrix results in a shift ...
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.
The exponential shift theorem can be used to speed the calculation of higher derivatives of functions that is given by the product of an exponential and another function. For instance, if f ( x ) = sin ( x ) e x {\displaystyle f(x)=\sin(x)e^{x}} , one has that
Data augmentation is a statistical technique which allows maximum likelihood estimation from incomplete data. [1] [2] Data augmentation has important applications in Bayesian analysis, [3] and the technique is widely used in machine learning to reduce overfitting when training machine learning models, [4] achieved by training models on several slightly-modified copies of existing data.
The standard definition of a left shift is an absolute band form count greater than 7700/microL. [3] There are competing explanations for the origin of the phrase "left shift," including the left-most button arrangement of early cell sorting machines [4] [5] and a 1920s publication by Josef Arneth, containing a graph in which immature neutrophils, with fewer segments, shifted the median left. [6]