status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
A population is defined as [...]
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
A [...] is a quantity computed from or used to describe a sample.
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---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
The [...] is the absolute frequency of each interval divided by the total number of observations.
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
The probability of an event estimated as a relative frequency of occurrence is called an [...]
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---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
General Formula for Labeling Problems
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not read | reprioritisations | ||
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last reprioritisation on | reading queue position [%] | |||
started reading on | finished reading on |
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In the bivariate case the expression for the mutual information is:
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The pseudoinverse is defined and unique for all matrices whose entries are real or complex numbers. It can be computed using the singular value decomposition.
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For , a pseudoinverse of is defined as a matrix satisfying all of the following four criteria:
Moore-Penrose Pseudo-inverse
exists for any matrix , but when the latter has full rank, can be expressed as a simple algebraic formula.
In particular, when has linearly independent columns (and thus matrix is invertible), can be computed as:
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If N-dimensional x is partitioned as follows
and accordingly μ and Σ are partitioned as follows
then the distribution of x_{1} conditional on x_{2} = a is multivariate normal (x_{1} | x_{2} = a) ~ N( μ , Σ ) where
and covariance matrix
This matrix is the Schur complement of Σ_{22} in Σ. This means that to calculate the conditional covariance matrix, one inverts the overall covariance matrix, drops the rows and columns corresponding to the variables being conditioned upon, and then inverts back to get the conditional covariance matrix. Here is the generalized inverse of .
Note that knowing that x_{2} = a alters the variance, though the new variance does not depend on the specific value of a; perhaps more surprisingly, the mean is shifted by ; compare this with the situation of not knowing the value of a, in which case x_{1} would have distribution .
An interesting fact derived in order to prove this result, is that the random vectors and are independent.
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To obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to drop the irrelevant variables (the variables that one wants to marginalize out) from the mean vector and the covariance matrix. The proof for this follows from the definitions of multivariate normal distributions and linear algebra.^{[16]}
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In geometry, an affine transformation, affine map^{[1]} or an affinity (from the Latin, affinis, "connected with") is a function between affine spaces which preserves points, straight lines and planes. Also, sets of parallel lines remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line.
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In linear algebra, eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way.
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If the process depends only on |x − x'|, the Euclidean distance (not the direction) between x and x', then the process is considered isotropic. A process that is concurrently stationary and isotropic is considered to be homogeneous;^{[7]} in practice these properties reflect the differences (or rather the lack of them) in the behaviour of the process given the location of the observer.
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Periodicity refers to inducing periodic patterns within the behaviour of the process. Formally, this is achieved by mapping the input x to a two dimensional vector u(x) = (cos(x), sin(x)).
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In the bivariate case where x is partitioned into X_{1} and X_{2}, the conditional distribution of X_{1} given X_{2} is
where is the correlation coefficient between X_{1} and X_{2}.
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In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers:
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
the [...] is defined as
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
In the bivariate case, the conditional mean of X_{1} given X_{2} is [...]
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
Periodicity maps the input x to a two dimensional vector [...]
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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started reading on | finished reading on |
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not read | reprioritisations | ||
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started reading on | finished reading on |
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---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not read | reprioritisations | ||
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last reprioritisation on | reading queue position [%] | |||
started reading on | finished reading on |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
[...] is the factorization of a matrix into a canonical form
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
eigendecomposition is sometimes also called [...]
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
eigendecomposition factorises a matrix into a [...] form
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
To obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to [...]
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
the distribution of x_{1} conditional on x_{2} = a is multivariate normal (x_{1} | x_{2} = a) ~ N( μ , Σ ) where and covariance matrix
status | not read | reprioritisations | ||
---|---|---|---|---|
last reprioritisation on | reading queue position [%] | |||
started reading on | finished reading on |
the distribution of x_{1} conditional on x_{2} = a is multivariate normal (x_{1} | x_{2} = a) ~ N( μ , Σ ) where μ [...] and covariance matrix Σ [...]
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
The pseudoinverse can be computed using [...].
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not read | reprioritisations | ||
---|---|---|---|---|
last reprioritisation on | reading queue position [%] | |||
started reading on | finished reading on |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
In the bivariate normal case the expression for the mutual information is [...]
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not read | reprioritisations | ||
---|---|---|---|---|
last reprioritisation on | reading queue position [%] | |||
started reading on | finished reading on |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not read | reprioritisations | ||
---|---|---|---|---|
last reprioritisation on | reading queue position [%] | |||
started reading on | finished reading on |
status | not read | reprioritisations | ||
---|---|---|---|---|
last reprioritisation on | reading queue position [%] | |||
started reading on | finished reading on |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not read | reprioritisations | ||
---|---|---|---|---|
last reprioritisation on | reading queue position [%] | |||
started reading on | finished reading on |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|
repetition number in this series | 0 | memorised on | scheduled repetition | ||||
scheduled repetition interval | last repetition or drill |
OOP is about producing well organized code — an important determinant of productivity
status | not read | reprioritisations | ||
---|---|---|---|---|
last reprioritisation on | reading queue position [%] | |||
started reading on | finished reading on |