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  2. Longest common substring - Wikipedia

    en.wikipedia.org/wiki/Longest_common_substring

    Building the suffix tree takes () time (if the size of the alphabet is constant). If the tree is traversed from the bottom up with a bit vector telling which strings are seen below each node, the k-common substring problem can be solved in Θ ( N K ) {\displaystyle \Theta (NK)} time.

  3. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.

  4. Pearson correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Pearson_correlation...

    The Pandas and Polars Python libraries implement the Pearson correlation coefficient calculation as the default option for the methods pandas.DataFrame.corr and polars.corr, respectively. Wolfram Mathematica via the Correlation function, or (with the P value) with CorrelationTest. The Boost C++ library via the correlation_coefficient function.

  5. Spearman's rank correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Spearman's_rank_correlation...

    Python has many different implementations of the spearman correlation statistic: it can be computed with the spearmanr function of the scipy.stats module, as well as with the DataFrame.corr(method='spearman') method from the pandas library, and the corr(x, y, method='spearman') function from the statistical package pingouin.

  6. Softmax function - Wikipedia

    en.wikipedia.org/wiki/Softmax_function

    A value proportional to the reciprocal of β is sometimes referred to as the temperature: = /, where k is typically 1 or the Boltzmann constant and T is the temperature. A higher temperature results in a more uniform output distribution (i.e. with higher entropy ; it is "more random"), while a lower temperature results in a sharper output ...

  7. Sum of normally distributed random variables - Wikipedia

    en.wikipedia.org/wiki/Sum_of_normally...

    To determine the value (), note that we rotated the plane so that the line x+y = z now runs vertically with x-intercept equal to c. So c is just the distance from the origin to the line x + y = z along the perpendicular bisector, which meets the line at its nearest point to the origin, in this case ( z / 2 , z / 2 ) {\displaystyle (z/2,z/2)\,} .

  8. Dynamic array - Wikipedia

    en.wikipedia.org/wiki/Dynamic_array

    The dynamic array has performance similar to an array, with the addition of new operations to add and remove elements: Getting or setting the value at a particular index (constant time) Iterating over the elements in order (linear time, good cache performance) Inserting or deleting an element in the middle of the array (linear time)

  9. Function of several real variables - Wikipedia

    en.wikipedia.org/wiki/Function_of_several_real...

    The image of a function f(x 1, x 2, …, x n) is the set of all values of f when the n-tuple (x 1, x 2, …, x n) runs in the whole domain of f. For a continuous (see below for a definition) real-valued function which has a connected domain, the image is either an interval or a single value. In the latter case, the function is a constant function.