text:
Lanczos algorithm

The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the $$m$$ "most useful" (tending towards extreme highest/lowest) eigenvalues and eigenvectors of an $$n \times n$$ Hermitian matrix, where $$ m $$ is often but not necessarily much smaller than $$ n $$. Although computationally efficient in principle, the method as initially formulated was not useful, due to its numerical instability.

In 1970, Ojalvo and Newman showed how to make the method numerically stable and applied it to the solution of very large engineering structures subjected to dynamic loading. This was achieved using a method for purifying the Lanczos vectors (i.e. by repeatedly reorthogonalizing each newly generated vector with all previously generated ones) to any degree of accuracy, which when not performed, produced a series of vectors that were highly contaminated by those associated with the lowest natural frequencies.

In their original work, these authors also suggested how to select a starting vector (i.e. use a random-number generator to select each element of the starting vector) and suggested an empirically determined method for determining $$ m $$, the reduced number of vectors (i.e. it should be selected to be approximately 1.5 times the number of accurate eigenvalues desired). Soon thereafter their work was followed by Paige, who also provided an error analysis. In 1988, Ojalvo produced a more detailed history of this algorithm and an efficient eigenvalue error test.

The algorithm

 * Input a Hermitian matrix $$A$$ of size $$n \times n$$, and optionally a number of iterations $$m$$ (as default, let $$m=n$$).
 * Strictly speaking, the algorithm does not need access to the explicit matrix, but only a function $$v \mapsto A v$$ that computes the product of the matrix by an arbitrary vector. This function is called at most $$m$$ times.
 * Output an $$n \times m$$ matrix $$V$$ with orthonormal columns and a tridiagonal real symmetric matrix $$T = V^* A V$$ of size $$m \times m$$. If $$m=n$$, then $$V$$ is unitary, and $$ A = V T V^* $$.
 * Warning The Lanczos iteration is prone to numerical instability. When executed in non-exact arithmetic, additional measures (as outlined in later sections) should be taken to ensure validity of the results.
 * Let $$v_1 \in \mathbb{C}^n$$ be an arbitrary vector with Euclidean norm $$1$$.
 * Abbreviated initial iteration step:
 * Let $$ w_1' = A v_1 $$.
 * Let $$ \alpha_1 = w_1'^* v_1 $$.
 * Let $$ w_1 = w_1' - \alpha_1 v_1 $$.
 * For $$ j=2,\dots,m $$ do:
 * Let $$ \beta_j = \| w_{j-1} \| $$ (also Euclidean norm).
 * If $$ \beta_j \neq 0 $$, then let $$ v_j = w_{j-1} / \beta_j $$,
 * else pick as $$v_j$$ an arbitrary vector with Euclidean norm $$1$$ that is orthogonal to all of $$ v_1,\dots,v_{j-1} $$.
 * Let $$ w_j' = A v_j $$.
 * Let $$ \alpha_j = w_j'^* v_j $$.
 * Let $$ w_j = w_j' - \alpha_j v_j  - \beta_j v_{j-1} $$.
 * Let $$V$$ be the matrix with columns $$ v_1,\dots,v_m $$. Let $$T = \begin{pmatrix}

\alpha_1 & \beta_2 &          &             &              & 0 \\ \beta_2 & \alpha_2 & \beta_3  &             &              & \\ & \beta_3 & \alpha_3 & \ddots      &              & \\ &         & \ddots   & \ddots      & \beta_{m-1}  & \\ &         &          & \beta_{m-1} & \alpha_{m-1} & \beta_m \\ 0       &          &          &             & \beta_m      & \alpha_m \\ \end{pmatrix}$$.
 * Note $$ A v_j = w_j' = \beta_{j+1} v_{j+1} + \alpha_j v_j + \beta_j v_{j-1} $$ for $$ 2 < j < m $$.

There are in principle four ways to write the iteration procedure. Paige and other works show that the above order of operations is the most numerically stable. In practice the initial vector $$v_1$$ may be taken as another argument of the procedure, with $$\beta_j=0$$ and indicators of numerical imprecision being included as additional loop termination conditions.

Not counting the matrix–vector multiplication, each iteration does $$O(n)$$ arithmetical operations. The matrix–vector multiplication can be done in $$O(dn)$$ arithmetical operations where $$d$$ is the average number of nonzero elements in a row. The total complexity is thus $$O(dmn)$$, or $$O(dn^2)$$ if $$m=n$$; the Lanczos algorithm can be very fast for sparse matrices. Schemes for improving numerical stability are typically judged against this high performance.

The vectors $$v_j$$ are called Lanczos vectors. The vector $$ w_j' $$ is not used after $$ w_j $$ is computed, and the vector $$ w_j $$ is not used after $$ v_{j+1} $$ is computed. Hence one may use the same storage for all three. Likewise, if only the tridiagonal matrix $$T$$ is sought, then the raw iteration does not need $$ v_{j-1} $$ after having computed $$ w_j $$, although some schemes for improving the numerical stability would need it later on. Sometimes the subsequent Lanczos vectors are recomputed from $$v_1$$ when needed.

Application to the eigenproblem
The Lanczos algorithm is most often brought up in the context of finding the eigenvalues and eigenvectors of a matrix, but whereas an ordinary diagonalization of a matrix would make eigenvectors and eigenvalues apparent from inspection, the same is not true for the tridiagonalization performed by the Lanczos algorithm; nontrivial additional steps are needed to compute even a single eigenvalue or eigenvector. Nonetheless, applying the Lanczos algorithm is often a significant step forward in computing the eigendecomposition.

If $$\lambda$$ is an eigenvalue of $$T$$, and $$x$$ its eigenvector ($$Tx=\lambda x$$), then $$ y = V x $$ is a corresponding eigenvector of $$A$$ with the same eigenvalue:

$$\begin{align} A y &= A V x \\ &= V T V^* V x \\ &= V T I x \\ &= V T x \\ &= V (\lambda x) \\ &= \lambda V x \\& = \lambda y.\end{align}$$

Thus the Lanczos algorithm transforms the eigendecomposition problem for $$A$$ into the eigendecomposition problem for $$T$$. The combination of good performance for sparse matrices and the ability to compute several (without computing all) eigenvalues are the main reasons for choosing to use the Lanczos algorithm.
 * 1) For tridiagonal matrices, there exist a number of specialised algorithms, often with better computational complexity than general-purpose algorithms. For example, if $$T$$ is an $$m \times m$$ tridiagonal symmetric matrix then:
 * 2) * The continuant recursion allows computing the characteristic polynomial in $$O(m^2)$$ operations, and evaluating it at a point in $$O(m)$$ operations.
 * 3) * The divide-and-conquer eigenvalue algorithm can be used to compute the entire eigendecomposition of $$T$$ in $$O(m^2)$$ operations.
 * 4) * The Fast Multipole Method can compute all eigenvalues in just $$O(m \log m)$$ operations.
 * 5) Some general eigendecomposition algorithms, notably the QR algorithm, are known to converge faster for tridiagonal matrices than for general matrices. Asymptotic complexity of tridiagonal QR is $$O(m^2)$$ just as for the divide-and-conquer algorithm (though the constant factor may be different); since the eigenvectors together have $$m^2$$ elements, this is asymptotically optimal.
 * 6) Even algorithms whose convergence rates are unaffected by unitary transformations, such as the power method and inverse iteration, may enjoy low-level performance benefits from being applied to the tridiagonal matrix $$T$$ rather than the original matrix $$A$$. Since $$T$$ is very sparse with all nonzero elements in highly predictable positions, it permits compact storage with excellent performance vis-à-vis caching. Likewise, $$T$$ is a real matrix with all eigenvectors and eigenvalues real, whereas $$A$$ in general may have complex elements and eigenvectors, so real arithmetic is sufficient for finding the eigenvectors and eigenvalues of $$T$$.
 * 7) If $$n$$ is very large, then reducing $$m$$ so that $$T$$ is of a manageable size will still allow finding the more extreme eigenvalues and eigenvectors of $$A$$; in the $$m \ll n$$ region, the Lanczos algorithm can be viewed as a lossy compression scheme for Hermitian matrices, that emphasises preserving the extreme eigenvalues.

Application to tridiagonalization
Though the eigenproblem is often the motivation for applying the Lanczos algorithm, the operation the algorithm primarily performs is tridiagonalization of a matrix, for which numerically stable Householder transformations have been favoured since the 1950s. During the 1960s the Lanczos algorithm was disregarded. Interest in it was rejuvenated by the Kaniel–Paige convergence theory and the development of methods to prevent numerical instability, but the Lanczos algorithm remains the alternative algorithm that one tries only if Householder is not satisfactory.

Aspects in which the two algorithms differ include:
 * Lanczos takes advantage of $$A$$ being a sparse matrix, whereas Householder does not, and will generate fill-in.
 * Lanczos works throughout with the original matrix $$A$$ (and has no problem with it being known only implicitly), whereas raw Householder wants to modify the matrix during the computation (although that can be avoided).
 * Each iteration of the Lanczos algorithm produces another column of the final transformation matrix $$V$$, whereas an iteration of Householder produces another factor in a unitary factorisation $$ Q_1 Q_2 \dots Q_n$$ of $$V$$. Each factor is however determined by a single vector, so the storage requirements are the same for both algorithms, and $$V = Q_1 Q_2 \dots Q_n$$ can be computed in $$O(n^3)$$ time.
 * Householder is numerically stable, whereas raw Lanczos is not.
 * Lanczos is highly parallel, with only $$O(n)$$ points of synchronisation (the computations of $$\alpha_j$$ and $$\beta_j$$). Householder is less parallel, having a sequence of $$O(n^2)$$ scalar quantities computed that each depend on the previous quantity in the sequence.

Derivation of the algorithm
There are several lines of reasoning which lead to the Lanczos algorithm.

A more provident power method
The power method for finding the eigenvalue of largest magnitude and a corresponding eigenvector of a matrix $$A$$ is roughly
 * Pick a random vector $$u_1 \neq 0$$.
 * For $$ j \geqslant 1 $$ (until the direction of $$u_j$$ has converged) do:
 * Let $$ u_{j+1}' = A u_j.$$
 * Let $$ u_{j+1} = u_{j+1}' / \| u_{j+1}' \|.$$
 * In the large $$j$$ limit, $$u_j$$ approaches the normed eigenvector corresponding to the largest magnitude eigenvalue.

A critique that can be raised against this method is that it is wasteful: it spends a lot of work (the matrix–vector products in step 2.1) extracting information from the matrix $$A$$, but pays attention only to the very last result; implementations typically use the same variable for all the vectors $$u_j$$, having each new iteration overwrite the results from the previous one. It may be desirable to instead keep all the intermediate results and organise the data.

One piece of information that trivially is available from the vectors $$u_j$$ is a chain of Krylov subspaces. One way of stating that without introducing sets into the algorithm is to claim that it computes

 * a subset $$\{v_j\}_{j=1}^m$$ of a basis of $$\Complex^n$$ such that $$Ax \in \operatorname{span}(v_1,\dotsc,v_{j+1}) $$ for every $$x \in \operatorname{span}(v_1,\dotsc,v_j)$$ and all $$1 \leqslant j < m;$$

this is trivially satisfied by $$v_j = u_j$$ as long as $$u_j$$ is linearly independent of $$u_1,\dotsc,u_{j-1}$$ (and in the case that there is such a dependence then one may continue the sequence by picking as $$v_j$$ an arbitrary vector linearly independent of $$u_1,\dotsc,u_{j-1}$$). A basis containing the $$u_j$$ vectors is however likely to be numerically ill-conditioned, since this sequence of vectors is by design meant to converge to an eigenvector of $$A$$. To avoid that, one can combine the power iteration with a Gram–Schmidt process, to instead produce an orthonormal basis of these Krylov subspaces. The relation between the power iteration vectors $$u_j$$ and the orthogonal vectors $$v_j$$ is that
 * 1) Pick a random vector $$u_1$$ of Euclidean norm $$1$$. Let $$v_1 = u_1$$.
 * 2) For $$j = 1,\dotsc,m-1$$ do:
 * 3) Let $$ u_{j+1}' = A u_j $$.
 * 4) For all $$ k = 1, \dotsc, j $$ let $$g_{k,j} = v_k^* u_{j+1}'$$. (These are the coordinates of $$ A u_j = u_{j+1}' $$ with respect to the basis vectors $$v_1,\dotsc,v_j$$.)
 * 5) Let $$ w_{j+1} = u_{j+1}' - \sum_{k=1}^j g_{k,j} v_k$$. (Cancel the component of $$u_{j+1}'$$ that is in $$\operatorname{span}(v_1,\dotsc,v_j)$$.)
 * 6) If $$w_{j+1} \neq 0$$ then let $$ u_{j+1} = u_{j+1}' / \| u_{j+1}' \| $$ and $$ v_{j+1} = w_{j+1} / \| w_{j+1} \| $$,
 * otherwise pick as $$ u_{j+1} = v_{j+1} $$ an arbitrary vector of Euclidean norm $$1$$ that is orthogonal to all of $$v_1,\dotsc,v_j$$.
 * $$ A u_j = \| u_{j+1}'\| u_{j+1} = u_{j+1}' = w_{j+1} + \sum_{k=1}^j g_{k,j} v_k = \| w_{j+1}\| v_{j+1} + \sum_{k=1}^j g_{k,j} v_k $$.

Here it may be observed that we do not actually need the $$u_j$$ vectors to compute these $$v_j$$, because $$u_j - v_j \in \operatorname{span}(v_1,\dotsc,v_{j-1})$$ and therefore the difference between $$ u_{j+1}' = A u_j $$ and $$ w_{j+1}' = A v_j $$ is in $$\operatorname{span}(v_1,\dotsc,v_j)$$, which is cancelled out by the orthogonalisation process. Thus the same basis for the chain of Krylov subspaces is computed by A priori the coefficients $$h_{k,j}$$ satisfy
 * 1) Pick a random vector $$v_1$$ of Euclidean norm $$1$$.
 * 2) For $$j = 1,\dotsc,m-1$$ do:
 * 3) Let $$ w_{j+1}' = A v_j $$.
 * 4) For all $$ k = 1, \dotsc, j $$ let $$h_{k,j} = v_k^* w_{j+1}'$$.
 * 5) Let $$ w_{j+1} = w_{j+1}' - \sum_{k=1}^j h_{k,j} v_k $$.
 * 6) Let $$ h_{j+1,j} = \| w_{j+1} \| $$.
 * 7) If $$h_{j+1,j} \neq 0$$ then let $$ v_{j+1} = w_{j+1} / h_{j+1,j} $$,
 * otherwise pick as $$ v_{j+1} $$ an arbitrary vector of Euclidean norm $$1$$ that is orthogonal to all of $$v_1,\dotsc,v_j$$.
 * $$ A v_j = \sum_{k=1}^{j+1} h_{k,j} v_k $$ for all $$ j < m $$;

the definition $$ h_{j+1,j} = \| w_{j+1} \| $$ may seem a bit odd, but fits the general pattern $$ h_{k,j} = v_k^* w_{j+1}' $$ since

 * $$ v_{j+1}^* w_{j+1}' = v_{j+1}^* w_{j+1} = \| w_{j+1} \| v_{j+1}^* v_{j+1} = \| w_{j+1} \|.$$

Because the power iteration vectors $$u_j$$ that were eliminated from this recursion satisfy $$u_j \in \operatorname{span}(v_1,\ldots,v_j),$$ the vectors $$\{v_j\}_{j=1}^m$$ and coefficients $$h_{k,j}$$ contain enough information from $$A$$ that all of $$u_1,\ldots,u_m$$ can be computed, so nothing was lost by switching vectors. (Indeed, it turns out that the data collected here give significantly better approximations of the largest eigenvalue than one gets from an equal number of iterations in the power method, although that is not necessarily obvious at this point.)

This last procedure is the Arnoldi iteration. The Lanczos algorithm then arises as the simplification one gets from eliminating calculation steps that turn out to be trivial when $$A$$ is Hermitian—in particular most of the $$h_{k,j}$$ coefficients turn out to be zero.

Elementarily, if $$A$$ is Hermitian then

 * $$ h_{k,j} = v_k^* w_{j+1}' = v_k^* A v_j = v_k^* A^* v_j = (A v_k)^* v_j.$$

For $$ k < j-1 $$ we know that $$ A v_k \in \operatorname{span}(v_1,\ldots,v_{j-1}) $$, and since $$ v_j $$ by construction is orthogonal to this subspace, this inner product must be zero. (This is essentially also the reason why sequences of orthogonal polynomials can always be given a three-term recurrence relation.) For $$ k = j-1 $$ one gets

 * $$ h_{j-1,j} = (A v_{j-1})^* v_j = \overline{v_j^* A v_{j-1} } = \overline{ h_{j,j-1} } = h_{j,j-1} $$

since the latter is real on account of being the norm of a vector. For $$ k = j $$ one gets

 * $$ h_{j,j} = (A v_j)^* v_j = \overline{v_j^* A v_j } = \overline{h_{j,j}},$$

meaning this is real too.

More abstractly, if $$V$$ is the matrix with columns $$v_1,\ldots,v_m$$ then the numbers $$h_{k,j}$$ can be identified as elements of the matrix $$H = V^*AV$$, and $$h_{k,j} = 0$$ for $$k > j+1;$$ the matrix $$H$$ is upper Hessenberg. Since

 * $$ H^* = \left (V^* A V \right )^* = V^* A^* V = V^* A V = H $$

the matrix $$H$$ is Hermitian. This implies that $$H$$ is also lower Hessenberg, so it must in fact be tridiagional. Being Hermitian, its main diagonal is real, and since its first subdiagonal is real by construction, the same is true for its first superdiagonal. Therefore, $$H$$ is a real, symmetric matrix—the matrix $$T$$ of the Lanczos algorithm specification.

Simultaneous approximation of extreme eigenvalues
One way of characterising the eigenvectors of a Hermitian matrix $$A$$ is as stationary points of the Rayleigh quotient

 * $$r(x) = \frac{x^* A x} {x^* x}, \qquad x \in\Complex^n.$$

In particular, the largest eigenvalue $$\lambda_\max$$ is the global maximum of $$r$$ and the smallest eigenvalue $$\lambda_\min$$ is the global minimum of $$r$$.

Within a low-dimensional subspace $$\mathcal{L}$$ of $$\Complex^n$$ it can be feasible to locate the maximum $$x$$ and minimum $$y$$ of $$r$$. Repeating that for an increasing chain $$\mathcal{L}_1 \subset \mathcal{L}_2 \subset \cdots$$ produces two sequences of vectors: $$x_1, x_2, \ldots$$ and $$y_1, y_2, \dotsc $$ such that $$x_j, y_j \in \mathcal{L}_j $$ and

 * $$\begin{align}

r(x_1) &\leqslant r(x_2) \leqslant \cdots \leqslant \lambda_\max \\ r(y_1) &\geqslant r(y_2) \geqslant \cdots \geqslant \lambda_\min \end{align}$$

The question then arises how to choose the subspaces so that these sequences converge at optimal rate.

From $$x_j$$, the optimal direction in which to seek larger values of $$r$$ is that of the gradient $$\nabla r(x_j)$$, and likewise from $$y_j$$ the optimal direction in which to seek smaller values of $$r$$ is that of the negative gradient $$-\nabla r(y_j)$$. In general

 * $$\nabla r(x) = \frac{2}{x^* x} ( A x - r(x) x ), $$

so the directions of interest are easy enough to compute in matrix arithmetic, but if one wishes to improve on both $$x_j$$ and $$y_j$$ then there are two new directions to take into account: $$Ax_j$$ and $$Ay_j;$$ since $$x_j$$ and $$y_j$$ can be linearly independent vectors (indeed, are close to orthogonal), one cannot in general expect $$Ax_j$$ and $$Ay_j$$ to be parallel. It is not necessary to increase the dimension of $$\mathcal{L}_j$$ by $$2$$ on every step if $$\{\mathcal{L}_j\}_{j=1}^m$$ are taken to be Krylov subspaces, because then $$Az \in \mathcal{L}_{j+1}$$ for all $$z \in \mathcal{L}_j,$$ thus in particular for both $$z = x_j$$ and $$z = y_j$$.

In other words, we can start with some arbitrary initial vector $$x_1 = y_1,$$ construct the vector spaces

 * $$ \mathcal{L}_j = \operatorname{span}( x_1, A x_1, \ldots, A^{j-1} x_1 ) $$

and then seek $$ x_j, y_j \in \mathcal{L}_j $$ such that

 * $$ r(x_j) = \max_{z \in \mathcal{L}_j} r(z) \qquad \text{and} \qquad r(y_j) = \min_{z \in \mathcal{L}_j} r(z).$$

Since the $$j$$th power method iterate $$u_j$$ belongs to $$\mathcal{L}_j,$$ it follows that an iteration to produce the $$x_j$$ and $$y_j$$ cannot converge slower than that of the power method, and will achieve more by approximating both eigenvalue extremes. For the subproblem of optimising $$r$$ on some $$\mathcal{L}_j $$, it is convenient to have an orthonormal basis $$\{ v_1, \ldots, v_j \}$$ for this vector space. Thus we are again led to the problem of iteratively computing such a basis for the sequence of Krylov subspaces.

Convergence and other dynamics
When analysing the dynamics of the algorithm, it is convenient to take the eigenvalues and eigenvectors of $$A$$ as given, even though they are not explicitly known to the user. To fix notation, let $$\lambda_1 \geqslant \lambda_2 \geqslant \dotsb \geqslant \lambda_n$$ be the eigenvalues (these are known to all be real, and thus possible to order) and let $$z_1,\dotsc,z_n$$ be an orthonormal set of eigenvectors such that $$A z_k = \lambda_k z_k$$ for all $$k=1,\dotsc,n$$.

It is also convenient to fix a notation for the coefficients of the initial Lanczos vector $$v_1$$ with respect to this eigenbasis; let $$d_k = z_k^* v_1$$ for all $$k=1,\dotsc,n$$, so that $$ \textstyle v_1 = \sum_{k=1}^n d_k z_k$$. A starting vector $$v_1$$ depleted of some eigencomponent will delay convergence to the corresponding eigenvalue, and even though this just comes out as a constant factor in the error bounds, depletion remains undesirable. One common technique for avoiding being consistently hit by it is to pick $$v_1$$ by first drawing the elements randomly according to the same normal distribution with mean $$0$$ and then rescale the vector to norm $$1$$. Prior to the rescaling, this causes the coefficients $$d_k$$ to also be independent normally distributed stochastic variables from the same normal distribution (since the change of coordinates is unitary), and after rescaling the vector $$(d_1,\dotsc,d_n)$$ will have a uniform distribution on the unit sphere in $$\mathbb{C}^n$$. This makes it possible to bound the probability that for example $$|d_1| < \varepsilon$$.

The fact that the Lanczos algorithm is coordinate-agnostic – operations only look at inner products of vectors, never at individual elements of vectors – makes it easy to construct examples with known eigenstructure to run the algorithm on: make $$A$$ a diagonal matrix with the desired eigenvalues on the diagonal; as long as the starting vector $$v_1$$ has enough nonzero elements, the algorithm will output a general tridiagonal symmetric matrix as $$T$$.

Kaniel–Paige convergence theory
After $$m$$ iteration steps of the Lanczos algorithm, $$T$$ is an $$m \times m$$ real symmetric matrix, that similarly to the above has $$m$$ eigenvalues $$\theta_1 \geqslant \theta_2 \geqslant \dots \geqslant \theta_m.$$ By convergence is primarily understood the convergence of $$\theta_1$$ to $$\lambda_1$$ (and the symmetrical convergence of $$\theta_m$$ to $$\lambda_n$$) as $$m$$ grows, and secondarily the convergence of some range $$\theta_1, \ldots, \theta_k$$ of eigenvalues of $$T$$ to their counterparts $$\lambda_1, \ldots, \lambda_k$$ of $$A$$. The convergence for the Lanczos algorithm is often orders of magnitude faster than that for the power iteration algorithm.

The bounds for $$\theta_1$$ come from the above interpretation of eigenvalues as extreme values of the Rayleigh quotient $$r(x)$$. Since $$\lambda_1$$ is a priori the maximum of $$r$$ on the whole of $$\Complex^n,$$ whereas $$\theta_1$$ is merely the maximum on an $$m$$-dimensional Krylov subspace, we trivially get $$ \lambda_1 \geqslant \theta_1$$. Conversely, any point $$x$$ in that Krylov subspace provides a lower bound $$r(x)$$ for $$\theta_1$$, so if a point can be exhibited for which $$\lambda_1 - r(x)$$ is small then this provides a tight bound on $$\theta_1$$.

The dimension $$m$$ Krylov subspace is

 * $$\operatorname{span} \left \{v_1, A v_1, A^2 v_1, \ldots, A^{m-1} v_1 \right \},$$

so any element of it can be expressed as $$p(A) v_1$$ for some polynomial $$p$$ of degree at most $$m-1$$; the coefficients of that polynomial are simply the coefficients in the linear combination of the vectors $$v_1, A v_1, A^2 v_1, \ldots, A^{m-1} v_1 $$. The polynomial we want will turn out to have real coefficients, but for the moment we should allow also for complex coefficients, and we will write $$p^*$$ for the polynomial obtained by complex conjugating all coefficients of $$p$$. In this parametrisation of the Krylov subspace, we have

 * $$r(p(A)v_1) = \frac{(p(A) v_1)^* A p(A) v_1}{(p(A) v_1)^* p(A) v_1} = \frac{v_1^* p(A)^* A p(A) v_1}{v_1^* p(A)^* p(A) v_1} = \frac{v_1^* p^*(A^*) A p(A) v_1 }{v_1^* p^*(A^*) p(A) v_1} = \frac{ v_1^* p^*(A) A p(A) v_1 }{v_1^* p^*(A) p(A) v_1}$$

Using now the expression for $$v_1$$ as a linear combination of eigenvectors, we get

 * $$ A v_1 = A \sum_{k=1}^n d_k z_k = \sum_{k=1}^n d_k \lambda_k z_k$$

and more generally

 * $$q(A) v_1 = \sum_{k=1}^n d_k q(\lambda_k) z_k $$

for any polynomial $$q$$.

Thus

 * $$\lambda_1 - r(p(A)v_1) = \lambda_1 - \frac{v_1^* \sum_{k=1}^n d_k p^*(\lambda_k) \lambda_k p(\lambda_k) z_k}{v_1^* \sum_{k=1}^n d_k p^*(\lambda_k) p(\lambda_k) z_k} = \lambda_1 - \frac{\sum_{k=1}^n |d_k|^2 \lambda_k p(\lambda_k)^* p(\lambda_k)}{\sum_{k=1}^n |d_k|^2 p(\lambda_k)^* p(\lambda_k)} = \frac{\sum_{k=1}^n |d_k|^2 (\lambda_1-\lambda_k) \left| p(\lambda_k) \right|^2 }{\sum_{k=1}^n |d_k|^2 \left| p(\lambda_k) \right|^2 }.$$

A key difference between numerator and denominator here is that the $$k=1$$ term vanishes in the numerator, but not in the denominator. Thus if one can pick $$p$$ to be large at $$\lambda_1$$ but small at all other eigenvalues, one will get a tight bound on the error $$\lambda_1-\theta_1$$.

Since $$A$$ has many more eigenvalues than $$p$$ has coefficients, this may seem a tall order, but one way to meet it is to use Chebyshev polynomials. Writing $$c_k$$ for the degree $$k$$ Chebyshev polynomial of the first kind (that which satisfies $$c_k(\cos x) = \cos(kx)$$ for all $$x$$), we have a polynomial which stays in the range $$[-1,1]$$ on the known interval $$[-1,1]$$ but grows rapidly outside it. With some scaling of the argument, we can have it map all eigenvalues except $$\lambda_1$$ into $$[-1,1]$$. Let

 * $$ p(x) = c_{m-1}\left( \frac{2x - \lambda_2 - \lambda_n}{\lambda_2 - \lambda_n} \right)$$

(in case $$\lambda_2=\lambda_1$$, use instead the largest eigenvalue strictly less than $$\lambda_1$$), then the maximal value of $$| p(\lambda_k)|^2$$ for $$k \geqslant 2$$ is $$1$$ and the minimal value is $$0$$, so

 * $$\lambda_1 - \theta_1 \leqslant \lambda_1 - r(p(A) v_1) = \frac{\sum_{k=2}^n |d_k|^2 (\lambda_1-\lambda_k) |p(\lambda_k)|^2 }{ \sum_{k=1}^n |d_k|^2 |p(\lambda_k)|^2} \leqslant \frac{\sum_{k=2}^n |d_k|^2 (\lambda_1-\lambda_k)}{|d_1|^2 |p(\lambda_1)|^2 } \leqslant \frac{(\lambda_1-\lambda_n) \sum_{k=2}^n |d_k|^2 }{|p(\lambda_1)|^2 |d_1|^2 }.$$

Furthermore

 * $$ p(\lambda_1) = c_{m-1}\left( \frac{2\lambda_1 - \lambda_2 - \lambda_n}{\lambda_2 - \lambda_n} \right) = c_{m-1}\left( 2\frac{\lambda_1 - \lambda_2}{\lambda_2 - \lambda_n} + 1 \right);$$

the quantity

 * $$ \rho = \frac{\lambda_1 - \lambda_2}{\lambda_2 - \lambda_n}$$

(i.e., the ratio of the first eigengap to the diameter of the rest of the spectrum) is thus of key importance for the convergence rate here. Also writing

 * $$ R = e^{\operatorname{arcosh}(1+2\rho)} = 1 + 2\rho + 2\sqrt{\rho^2+\rho},$$

we may conclude that

 * $$\begin{align}

\lambda_1 - \theta_1 &\leqslant \frac{(\lambda_1-\lambda_n) \left(1 - |d_1|^2 \right )}{c_{m-1}(2\rho+1)^2 |d_1|^2} \\[6pt] &= \frac{1 - |d_1|^2}{|d_1|^2} (\lambda_1-\lambda_n) \frac{1}{\cosh^2 ((m-1) \operatorname{arcosh}(1+2\rho))} \\[6pt] &= \frac{1 - |d_1|^2}{|d_1|^2} (\lambda_1-\lambda_n) \frac{4}{\left (R^{m-1} + R^{-(m-1)} \right )^2} \\[6pt] &\leqslant 4 \frac{1 - |d_1|^2}{|d_1|^2} (\lambda_1-\lambda_n) R^{-2(m-1)} \end{align}$$

The convergence rate is thus controlled chiefly by $$R$$, since this bound shrinks by a factor $$R^{-2}$$ for each extra iteration.

For comparison, one may consider how the convergence rate of the power method depends on $$\rho$$, but since the power method primarily is sensitive to the quotient between absolute values of the eigenvalues, we need $$|\lambda_n| \leqslant |\lambda_2|$$ for the eigengap between $$\lambda_1$$ and $$\lambda_2$$ to be the dominant one. Under that constraint, the case that most favours the power method is that $$\lambda_n = -\lambda_2$$, so consider that. Late in the power method, the iteration vector:

 * $$ u = (1-t^2)^{1/2} z_1 + t z_2 \approx z_1 + t z_2,$$

where each new iteration effectively multiplies the $$z_2$$-amplitude $$t$$ by

 * $$\frac{\lambda_2}{\lambda_1} = \frac{\lambda_2}{\lambda_2 + (\lambda_1-\lambda_2)} = \frac{1}{1 + \frac{\lambda_1-\lambda_2}{\lambda_2}} = \frac{1}{1 + 2\rho}.$$

The estimate of the largest eigenvalue is then

 * $$ u^*Au = (1-t^2)\lambda_1 + t^2\lambda_2,$$

so the above bound for the Lanczos algorithm convergence rate should be compared to

 * $$\lambda_1 - u^*Au = (\lambda_1-\lambda_2) t^2,$$

which shrinks by a factor of $$(1+2\rho)^{-2}$$ for each iteration. The difference thus boils down to that between $$ 1+2\rho $$ and $$R = 1 + 2\rho + 2\sqrt{\rho^2+\rho}$$. In the $$\rho \gg 1$$ region, the latter is more like $$ 1+4\rho $$, and performs like the power method would with an eigengap twice as large; a notable improvement. The more challenging case is however that of $$ \rho \ll 1,$$ in which $$R \approx 1 + 2\sqrt{\rho} $$ is an even larger improvement on the eigengap; the $$ \rho \gg 1 $$ region is where the Lanczos algorithm convergence-wise makes the smallest improvement on the power method.

Numerical stability
Stability means how much the algorithm will be affected (i.e. will it produce the approximate result close to the original one) if there are small numerical errors introduced and accumulated. Numerical stability is the central criterion for judging the usefulness of implementing an algorithm on a computer with roundoff.

For the Lanczos algorithm, it can be proved that with exact arithmetic, the set of vectors $$v_1, v_2, \cdots, v_{m+1}$$ constructs an orthonormal basis, and the eigenvalues/vectors solved are good approximations to those of the original matrix. However, in practice (as the calculations are performed in floating point arithmetic where inaccuracy is inevitable), the orthogonality is quickly lost and in some cases the new vector could even be linearly dependent on the set that is already constructed. As a result, some of the eigenvalues of the resultant tridiagonal matrix may not be approximations to the original matrix. Therefore, the Lanczos algorithm is not very stable.

Users of this algorithm must be able to find and remove those "spurious" eigenvalues. Practical implementations of the Lanczos algorithm go in three directions to fight this stability issue:

 * 1) Prevent the loss of orthogonality,
 * 2) Recover the orthogonality after the basis is generated.
 * 3) After the good and "spurious" eigenvalues are all identified, remove the spurious ones.

Variations
Variations on the Lanczos algorithm exist where the vectors involved are tall, narrow matrices instead of vectors and the normalizing constants are small square matrices. These are called "block" Lanczos algorithms and can be much faster on computers with large numbers of registers and long memory-fetch times.

Many implementations of the Lanczos algorithm restart after a certain number of iterations. One of the most influential restarted variations is the implicitly restarted Lanczos method, which is implemented in ARPACK. This has led into a number of other restarted variations such as restarted Lanczos bidiagonalization. Another successful restarted variation is the Thick-Restart Lanczos method, which has been implemented in a software package called TRLan.

Nullspace over a finite field
In 1995, Peter Montgomery published an algorithm, based on the Lanczos algorithm, for finding elements of the nullspace of a large sparse matrix over GF(2); since the set of people interested in large sparse matrices over finite fields and the set of people interested in large eigenvalue problems scarcely overlap, this is often also called the block Lanczos algorithm without causing unreasonable confusion.

Applications
Lanczos algorithms are very attractive because the multiplication by $$A\,$$ is the only large-scale linear operation. Since weighted-term text retrieval engines implement just this operation, the Lanczos algorithm can be applied efficiently to text documents (see latent semantic indexing). Eigenvectors are also important for large-scale ranking methods such as the HITS algorithm developed by Jon Kleinberg, or the PageRank algorithm used by Google.

Lanczos algorithms are also used in condensed matter physics as a method for solving Hamiltonians of strongly correlated electron systems, as well as in shell model codes in nuclear physics.

Implementations
The NAG Library contains several routines for the solution of large scale linear systems and eigenproblems which use the Lanczos algorithm.

MATLAB and GNU Octave come with ARPACK built-in. Both stored and implicit matrices can be analyzed through the eigs function (Matlab/Octave).

Similarly, in Python, the SciPy package has scipy.sparse.linalg.eigsh which is also a wrapper for the SSEUPD and DSEUPD functions functions from ARPACK which use the Implicitly Restarted Lanczos Method.

A Matlab implementation of the Lanczos algorithm (note precision issues) is available as a part of the Gaussian Belief Propagation Matlab Package. The GraphLab collaborative filtering library incorporates a large scale parallel implementation of the Lanczos algorithm (in C++) for multicore.

The PRIMME library also implements a Lanczos-like algorithm.

title: Lanczos algorithm


text:
Max Pechstein

Hermann Max Pechstein (31 December 1881 – 29 June 1955) was a German expressionist painter and printmaker and a member of the Die Brücke group. He fought on the Western Front during World War I and his art was classified as Degenerate Art by the Nazis. More than 300 paintings were removed from German Museums during the Nazi era.

Life and career
Pechstein was born in Zwickau, the son of a craftsman who worked in a textile mill. The family of eight lived on the father's salary. An early contact with the art of Vincent van Gogh stimulated Pechstein's development toward expressionism. He first worked as a decorator in his home town before enrolling at the School of Applied Arts and then at the Royal Art Academy in Dresden, where he met the painter Otto Gussman and the architect Wilhelm Kreis. It was here, starting in 1902, that he became a pupil of Gussmann; a relationship that lasted until 1906 when Pechstein met Erich Heckel and was invited to join the art group Die Brücke. He was the only member to have received formal art training. He was an active member of the Brücke until 1910 and often worked alongside Brücke painters creating a homogeneous style of this period. In 1905 he was in Dresden where the museum of ethnology showed wood carvings from the South Seas. As a result he developed his first woodcut.

In 1907 Pechstein traveled to Italy to receive an award, and upon his return in 1908 spent time in Paris where he met the Fauvist painter Kees van Dongen whom he persuaded to join Die Brücke. Later that year Pechstein moved to Berlin (a move that fellow painters were to make in the following three years). After being categorically rejected from exhibiting in the Berlin Secession in 1910, he helped to found and became chairman of the New Secession and gained recognition for his decorative and colorful prints that were inspired by the art of Van Gogh, Matisse, and the Fauves.

In 1912, after years of rising tensions, Pechstein was expelled from the Brücke after exhibiting some of his work in the aforementioned Berlin Secession all by himself and without paintings of other members of the Brücke. This expulsion was a relatively happy one as Pechstein had been receiving rewards and recognition far beyond his peers owing to his conservative style that appealed to a wider audience. This recognition only distanced him from the group and bred animosity among the members. His paintings eventually became more primitivist, incorporating thick black lines and angular figures. Looking for inspiration, he traveled to Palau in the Pacific Ocean. Upon the outbreak of World War I, Pechstein was interned in Japan and returned to Germany via Shanghai, Manila, and New York. He was sent to fight on the Western Front (World War I) in 1916. Despite his notably conservative stance and style, after the German Revolution of 1918–19, Pechstein joined two radical socialist groups: the Arbeitsrat für Kunst and the November Group (German). Beginning in 1922, Pechstein became a professor at the Berlin Academy.

Beginning in 1933, Pechstein was vilified by the Nazis because of his art. He was banned from painting or exhibiting his art and later that year was fired from his teaching position. A total of 326 of his paintings were removed from German museums. Sixteen of his works were displayed in the Entartete Kunst (Degenerate Art) exhibition of 1937. During this time, Pechstein went into seclusion in rural Pomerania. He was reinstated in 1945, and subsequently won numerous titles and awards for his work.

Many of Pechstein's collectors were Jews whose collections were seized by the Nazis or lost owing to Nazi persecution. In May 2013 the Bavarian State Paintings Collections agreed to restitute Pechstein's White House, (1910) and his Meadow Valley (1911) to the heirs of Curt Glaser. In July 2021, France decided to restitute to the heirs of Hugo Simon the Pechstein entitled Nus dans un paysage. In 2023, Christie's brokered a settlement with the heirs of Robert Graetz, a Jewish textile industrialist and art collector who was deported and murdered by the Nazis, concerning Still Life With a Cup, which Graetz's daughter sold as a refugee in South Africa.

He was a prolific printmaker, producing 421 lithographs, 315 woodcuts and linocuts, and 165 intaglio prints, mostly etchings.

Personal life
He was married to Charlotte Karpolat from 1911 until 1923 and later was married to Marta Möller. He died in West Berlin and is buried in the Evangelischer Friedhof Alt-Schmargendorf in Berlin.

Art market
At a 1999 Sotheby's auction, The Yellow Mask I (1910), the portrait of a woman wearing a yellow mask, was sold for $1.37 million. In 2008, Zirkus mit Dromedaren (c. 1920) was auctioned for £1.9 million in London.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Max Pechstein


text:
Basilar skull fracture

A basilar skull fracture is a break of a bone in the base of the skull. Symptoms may include bruising behind the ears, bruising around the eyes, or blood behind the ear drum. A cerebrospinal fluid (CSF) leak occurs in about 20% of cases and may result in fluid leaking from the nose or ear. Meningitis occurs in about 14% of cases. Other complications include injuries to the cranial nerves or blood vessels.

A basilar skull fracture typically requires a significant degree of trauma to occur. It is defined as a fracture of one or more of the temporal, occipital, sphenoid, frontal or ethmoid bone. Basilar skull fractures are divided into anterior fossa, middle fossa and posterior fossa fractures. Facial fractures often also occur. Diagnosis is typically by CT scan.

Treatment is generally based on the extent and location of the injury to structures inside the head. Surgery may be performed to seal a CSF leak that does not stop, to relieve pressure on a cranial nerve or repair injury to a blood vessel. Prophylactic antibiotics do not provide a clinical benefit in preventing meningitis. A basilar skull fracture occurs in about 12% of people with a severe head injury.

Signs and symptoms

 * Battle's sign – bruising of the mastoid process of the temporal bone.
 * Raccoon eyes – bruising around the eyes, i.e. "black eyes"
 * Cerebrospinal fluid rhinorrhea
 * Cranial nerve palsy
 * Bleeding (sometimes profuse) from the nose and ears
 * Hemotympanum
 * Conductive or perceptive deafness, nystagmus, vomiting
 * In 1–10% of patients, optic nerve entrapment occurs. The optic nerve is compressed by the broken skull bones, causing irregularities in vision.
 * Serious cases usually result in death

Pathophysiology
Basilar skull fractures include breaks in the posterior skull base or anterior skull base. The former involve the occipital bone, temporal bone, and portions of the sphenoid bone; the latter, superior portions of the sphenoid and ethmoid bones. The temporal bone fracture is encountered in 75% of all basilar skull fractures and may be longitudinal, transverse or mixed, depending on the course of the fracture line in relation to the longitudinal axis of the pyramid.

Bones may be broken around the foramen magnum, the hole in the base of the skull through which the brain stem exits and becomes the spinal cord. This may result in injury to the blood vessels and nerves exiting the foramen magnum.

Due to the proximity of the cranial nerves, injury to those nerves may occur. This can cause loss of function of the facial nerve or oculomotor nerve, or hearing loss due to damage of cranial nerve VIII.

Management
Evidence does not support the use of preventive antibiotics, regardless of the presence of a cerebrospinal fluid leak.

Prognosis
Non-displaced fractures usually heal without intervention. Patients with basilar skull fractures are especially likely to get meningitis. The efficacy of prophylactic antibiotics in these cases is uncertain.

Temporal bone fractures
Acute injury to the internal carotid artery (carotid dissection, occlusion, pseudoaneurysm formation) may be asymptomatic or result in life-threatening bleeding. They are almost exclusively observed when the carotid canal is fractured, although only a minority of carotid canal fractures result in vascular injury. Involvement of the petrous segment of the carotid canal is associated with a relatively high incidence of carotid injury.

Motor racing accidents
Basilar skull fractures are a common cause of death in many motor racing accidents. Drivers who have died as a result of basilar skull fractures include Formula One driver Roland Ratzenberger; IndyCar drivers Bill Vukovich Sr., Tony Bettenhausen Sr., Floyd Roberts, and Scott Brayton; NASCAR drivers Dale Earnhardt Sr., Adam Petty, Tony Roper, Kenny Irwin Jr., Neil Bonnett, John Nemechek, J. D. McDuffie, and Richie Evans; CART drivers Jovy Marcelo, Greg Moore, and Gonzalo Rodriguez; and ARCA drivers Blaise Alexander and Slick Johnson. Ernie Irvan is a survivor of a basilar skull fracture sustained at an accident during practice at the Michigan International Speedway in 1994. Race car drivers Stanley Smith and Rick Carelli also survived a basilar skull fracture.

To prevent basilar skull fractures, many motorsports sanctioning bodies mandate the use of head and neck restraints, such as the HANS device. The HANS device has demonstrated its life-saving abilities multiple times, including Jeff Gordon at the 2006 Pocono 500, Michael McDowell at the Texas Motor Speedway in 2008, Robert Kubica at the 2007 Canadian Grand Prix, and Elliott Sadler at the 2003 EA Sports 500/2010 Sunoco Red Cross Pennsylvania 500.

title: Basilar skull fracture


text:
Template talk:Other uses of

Formatting
Per WP:DAB guidelines, article titles should not be placed in italics in top links. Please keep this template in-line with existing guidelines and otheruses templates, or explain why we should switch to a new style of formatting. --Muchness 07:22, 16 March 2006 (UTC)

 * The word "italic" or "italics" appears nowhere on that page. In fact, the examples there are italicised. Other templates of this kind are fairly inconsistent. -- Netoholic @ 07:32, 16 March 2006 (UTC)

 * In the top link examples given on WP:DAB, the header sentences are italicized, but the article titles are not individually formatted. It was the article title formatting that I had issue with, since there's no precedent for this style of formatting in other widely used dab templates or in WP formatting guidelines. --Muchness 07:48, 16 March 2006 (UTC)

irresponsible
It seems really irresponsible to me to use this template and others like it. I just edited a page atop which a notice said

 * "For other uses of colour separation, see ..."

What it actually meant, as far as I could tell, was "For other uses of the TERM "colour separation", see...".

How about "For other uses of slave labor, see ..."?

Michael Hardy 01:12, 20 March 2006 (UTC)

 * Seems to have been fixed now with the addition of double quotation marks. Hairy Dude 03:05, 4 January 2007 (UTC)

Someone should add the s
''[[User:Kitia|Kitia]] 01:45, 30 December 2006 (UTC)

Capitalisation
For example on Pugs, yields:

However, titles of articles in hatnotes should have an initial capital, since that's the normalised form of article names (e.g. from PAGENAME). So this template should capitalise its second argument when it reuses it and adds " (disambiguation)" as the link. Unfortunately, since StringFunctions isn't installed on WP, this doesn't seem to be possible. Hairy Dude 02:33, 15 January 2007 (UTC)

Aha, looks like there is something that does that actually. Wibble yields "Wibble". Possibly this is undesirable given the existence of articles like eBay, but such cases are the exception. Hairy Dude 02:57, 15 January 2007 (UTC)

TfD notice
I've nominated the Otheruses templates for discussion on Templates for deletion. --JB Adder | Talk 14:02, 8 July 2007 (UTC)

Is this template needed?
Sure, it's got over 2,000 transclusions, but looking at some of its uses, I'm beginning to think that in almost every case, replacing it with another template will be a clear improvement. Common uses are: What do people think? If there are no objections, I might go on to ask for a bot to deal with #1 above: replacing with  when X is the same as the article's title or empty. – Uanfala (talk) 12:53, 11 April 2020 (UTC)
 * 1) When the term disambiguated is the same as the article's title. For example, the article Anomie has the hatnote: Here the template can be replaced with the simple Other uses making the hatnote shorter without any loss of function:
 * 2) When the term disambiguated is different from the article title; there are two cases:
 * 3) *The term is a redirect to the article; for example Cat's Cradle has a hatnote to Ice-nine (disambiguation) (that's because Ice-nine redirects to Cat's Cradle). The use of this template here is somewhat confusing, because it's unclear to readers why the hatnote is there. It should be explicit that this is because of the incoming redirect, so the template should be replaced with the standard Redirect.
 * 4) *The term is not a redirect to the article; for example Cash register has a hatnote for Till (disambiguation), but Till doesn't redirect to Cash register so the hatnote should simply be removed per WP:NAMB. In some cases, the hatnote may still be useful – for instance if the two terms are likely to be confused, but in this case it will be better to use Distinguish instead.
 * This template is insane. Its purpose is to display a message that begins "For other uses of X" when, at that point, the reader has no idea other than what. Basically, reading an article's title and then the hatnote, "This is an article about Pizza. For other uses of "rhinoceros", see Rhinoceros (disambiguation)."
 * OK, look at Cash register, with the hatnote "For other uses of "till", see Till (disambiguation)". After the hatnote, it's revealed, "A cash register, sometimes called a till' ...". Fine, "till" is another term for it. But the user got there looking for information on cash registers; if they were looking specifically for the word "till", they would have wound up at Till or Till (disambiguation). How likely is it that somebody researching cash registers would happen to, therefore, be interested in other topics completely unrelated to cash registers just because they're a disambiguation for the word "till"?
 * Finally, besides being mystifying and confusing at the point where the user is reading it and then unhelpful after that, this template is a violation of WP:NOTAMB. Largoplazo (talk) 21:33, 2 February 2022 (UTC)

Suppression of Category:Hatnote templates using unusual parameters on template's page
I've wrapped code of Other uses of/sandbox in to suppress its categorization in Category:Hatnote templates using unusual parameters. Should the categorization be also suppressed on the live template Other uses of? —andrybak (talk) 13:58, 4 July 2020 (UTC)

Template-protected edit request on 31 October 2020
Please apply Special:Diff/953627233/986361870 to suppress categorization of talk pages and user pages into Category:Hatnote templates using unusual parameters. This is similar to what Module:Hatnote does since Special:Diff/967664662. —andrybak (talk) 11:07, 31 October 2020 (UTC)

 * It's early in the morning, so maybe I'm just talking rubbish, but doesn't that code actually exclude all pages that aren't user pages? ProcrastinatingReader (talk) 11:17, 31 October 2020 (UTC)
 * , indeed. Thanks for catching this. Fixed: Special:Diff/953627233/986365782. —andrybak (talk) 11:43, 31 October 2020 (UTC)
 * ✅. And you may want to request template-editor privileges at some point, as you seem to do a lot of template work :) ProcrastinatingReader (talk) 13:28, 31 October 2020 (UTC)
 * I've found a bug in my previous diff. I didn't realize that the variable  was used for the string field , rather than the title object itself. Fix is ready in the sandbox: Special:Diff/986376893/986687262. I've tested this change in preview mode on a user page from  Category:Hatnote templates using unusual parameters. —andrybak (talk) 11:37, 2 November 2020 (UTC)
 * ✅: Special:Diff/986768317. —andrybak (talk) 22:10, 2 November 2020 (UTC)

Template-protected edit request on 2 November 2020
While we're here, I would also suggest to wrap the invocation of the module in , as described in the section above, so that the template page is excluded from the tracking category. —andrybak (talk) 11:40, 2 November 2020 (UTC)
 * ✅: Special:Diff/986783682. —andrybak (talk) 00:15, 3 November 2020 (UTC)

Extra set of quotation marks with multiple uses
Currently, when there are two or more uses, the template produces an extra set of quotation marks around them: ""USE1" or "USE2"". It should just look like "USE1" or "USE2". Same thing with three uses. Could someone please implement a fix to this? Rowing007 (talk) 20:51, 20 April 2023 (UTC)

 * Possibly a result of edits on Module:Other uses of by last year. Could you please give some examples? — Martin (MSGJ · talk) 10:42, 21 April 2023 (UTC)

 * this is noticed on the /doc page at Template:Other uses of/doc. The examples for more than one use do show the unwanted quotation marks.  P.I. Ellsworth  , ed.  put'er there 10:53, 21 April 2023 (UTC)
 * I've reverted Nihiltres most recent change which seems to have fixed the issue — Martin (MSGJ · talk) 11:04, 21 April 2023 (UTC)
 * Yes, excellent! Does appear to have done it. A little concerned about editor, who hasn't edited since before Christmas! Editor , if you still see something squirrelly, please respond here or reopen this request by changing the Edit template-protected template from yes to no.  P.I. Ellsworth  , ed.  put'er there 11:53, 21 April 2023 (UTC)

title: Template talk:Other uses of


text:
User talk:Aku~enwiki

Welcome
Hey there, . Welcome to Wikipedia. Thank you for your contributions. I hope you enjoy being a Wikipedian and decide to stay! Here are a few good links for newcomers (or "oldcomers" for reference):

By the way, you should sign and date your comments on talk and vote pages using four tildes, like this: ~~~~. Three tildes (~~~) produces just your name. If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page. Again, welcome!

Great, just what we need around this place... more three-lettered people. :) Cheers. --Lord Voldemort (Dark Mark) 21:16, 1 September 2005 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Aku. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Aku~enwiki that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name. If you think you might own all of the accounts with this name and this message is in error, please visit Special:MergeAccount to check and attach all of your accounts to prevent them from being renamed.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 21:45, 19 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 10:17, 22 April 2015 (UTC)

title: User talk:Aku~enwiki


text: User talk:65.182.95.67

title: User talk:65.182.95.67


text:
Wikipedia talk:Articles for deletion/Cam Wilson

Copied discussion from Cam Wilson AfD

 * Speedy delete as recreation of previously deleted content. Proto t c 10:03, 1 September 2005 (UTC)
 * only applies if the deleted page was deleted as a result of a VfD, not SD. Unfortunately. Tonywalton | Talk
 * So you're saying that if an article is deleted under A7, and it's recreated, it can't be speedy deleted without coming to AfD? Zoe 19:41, September 1, 2005 (UTC)
 * Basically, yes. Encephalon provided a useful conversation about this on his talk page below. Hope that clears things up; I found it helpful, anyway. --Blackcap | talk 19:57, September 1, 2005 (UTC)

 * WP:CSD G4 ("A substantially identical copy, by any title, of a page that was deleted according to the deletion policy.") says:  This does not apply to content in userspace, content that was speedily deleted, or to content undeleted according to undeletion policy. If the previous deletion was a speedy (under any criterion, not just A7), it gets at least one more shot. Or even more - it could be speedied over and over again. However if it's reposted after a VfD voted "delete", then it merits a db-repost tag under CSD G4 and a deletedcontent tag on the deleted page to stop it being recreated.. What happens if, as seems likely with this article, it gets speedied due to an overwhelming consensus to speedy prior to the VfD period being up is worrying; does that count as a speedy (so db-repost doesn't apply) or a VfD delete (so db-repost does apply)? Tonywalton | Talk 20:02, 1 September 2005 (UTC)

 * From WP:CSD:
 * ''There are a few, limited cases where admins can delete Wikipedia pages "on sight" and without consensus at Wikipedia:Articles for Deletion or Wikipedia:Non-main namespace pages for deletion. Non-admins can ask for an admin to delete such a page, either by listing it on speedy deletions, or by adding a or a  ) header. The parameter Reason should indicate clearly why the page is a candidate for speedy deletion...
 * G4. A substantially identical copy, by any title, of a page that was deleted according to the deletion policy. This does not apply to content in userspace, content that was speedily deleted, or to content undeleted according to undeletion policy. Of course, other criteria than this one may still apply to such pages.

 * CSD are criteria allowing the deletion of articles by one single person (any admin or higher) without the participation of the wider community. If I understand it correctly, the G4 criterion specifies that some pages that have been deleted before may be deleted again on sight, by admins. If a page was previously voted off on AfD, and received the sanction of the community to be deleted, any attempt to recreate it (substantially similarly etc) can be seen as a refusal to abide by the decision of the community; G4 empowers admins to strike those attempts down.
 * Hence, any page that "was deleted according to the deletion policy" (ie. WP:DEL, ie. AfD) may be speedily deleted via G4 if someone attempts to recreate it again.
 * However, a page that was previously speedied was deleted solely through the judgement of one person — the deleting admin. It sounds to me like the second clause in sentence 2 of G4 is an attempt to ensure that no abuse of power takes place (indefinite speedies, as you put it). The page if recreated needs to be seen and judged by the community. Hence, "content that was speedily deleted" cannot again be speedily deleted via G4, even if it was "substantially identical" etc to the page an admin saw when it was first SD'd. That, in any case, is how I understand it. However, it does not take a legal expert to see that quite a few WP guidelines are very vaguely (sometimes even haphazardly) written, and continual improvement in this area will be welcome.— Encephalon  |  ζ   21:17:01, 2005-09-01 (UTC)

Sorry, but "The page if recreated needs to be seen and judged by the community" is completely wrong. If an article is speedied validly (under A7, for example) and is recreated, it can happily be speedied again under A7. The existing criteria still apply, and these are what should be noted as the reason for deletion. - brenneman (t) (c)  23:26, 1 September 2005 (UTC)

 * Aaron, I have a lot of respect for your work on WP and your opinions on policy that I've read elsewhere, but in this particular instance I disagree with you. The CSD rule under which a recreated article can be deleted is G4. That rule specifically disallows speedily deleting an article that was previously only speedily deleted. The clause does not say:
 * "[G4] does not apply to...content that was speedily deleted under all CSD except A7..."
 * It says:
 * "[G4] does not apply to content that was speedily deleted..." Period.
 * If we admit your interpretation, what precisely does this clause mean? I may be reading something wrong, Aaron, if so please point it out; but from where I'm standing I can't see that your interpretation works.
 * In any case, the current Cam Wilson article does not meet A7, as I noted here. It asserts notability. Best— Encephalon |  ζ   05:13:57, 2005-09-02 (UTC)

 * Thank you. I've re-read my commentary on the front page and there is an assertion I should have made more clear: I personally would not have put a speedy tag on this article, I would have sent it to VfD.  I try to be cautious with speedies.  On another note, this is the most agreeable dissent I've ever experienced over deletion!  Everyone should have a biscuit! (I know I haven't your question above, but I will soon.)  brenneman (t) (c)  05:45, 2 September 2005 (UTC)

 * Replied at Wikipedia_talk:Criteria_for_speedy_deletion to centralise discussion. Please reply there regarding general G4 application. -  brenneman (t) (c)  13:58, 4 September 2005 (UTC)


text: User talk:70.50.208.18

title: User talk:70.50.208.18


text: User talk:69.193.140.8

title: User talk:69.193.140.8


text:
User:Drawde83/myLinks

Quick access

 * Google
 * Gmail
 * Slashdot News for nerds, Stuff that matters.
 * Wired
 * Aardvark
 * NZCities
 * Google News
 * My TradeMe
 * Uni Timetable
 * ASB Bank

Quick Searches

 * feautres typo search

Stuff to read
Optical illusion

Wikipedia

 * Wikipedia - User:Drawde83
 * Wikipedia Random
 * GDesklet

Prototype Articles

 * elemenop article should go in here Category:New Zealand musical groups

E-mail

 * hotmail
 * Yahoo! mail
 * CS mail
 * Waikato mail

Entertainment

 * Dilbert
 * Rinkworks
 * Stick Cricket (flash req)
 * Weebl & Bob (flash req)
 * Alcohol and Ammo (flash req)
 * Ouch! Disablity Blog
 * Moniques Diary
 * Ruth's Diary
 * All Movies

University

 * Student Portal
 * Comp Sci papers
 * Comp Sci Dept
 * Waikato Uni Google search

Computers

 * TradeMe - Computers
 * PriceSpy
 * Dick Smith Electronics
 * nz.comp

Linux

 * linux.org
 * wlug
 * Linux questions
 * Google - linux
 * Unofficial Ubuntu 5.04 Starter Guide

Programming

 * Perl monks
 * Java tutorial
 * PHP.net

Misc

 * Cooking with Google
 * Taonga1 Trademe

title: User:Drawde83/myLinks


text:
Bernard Tucker Medal

The Bernard Tucker Medal is awarded by the British Trust for Ornithology for services to ornithology. It is named in memory of Bernard Tucker, their first Secretary. It has been awarded since 1954, usually annually although there are some years when no medals were awarded.

Bernard Tucker Medallists
Source: British Trust for Ornithology

20th Century
•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

21st Century
•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

title: Bernard Tucker Medal


text:
User talk:Luminous~enwiki

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Luminous. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Luminous~enwiki that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name. If you think you might own all of the accounts with this name and this message is in error, please visit Special:MergeAccount to check and attach all of your accounts to prevent them from being renamed.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 01:27, 20 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 15:40, 22 April 2015 (UTC)

title: User talk:Luminous~enwiki


text:
William Rhett

Colonel William Rhett (4 September 1666 – 12 January 1723) was an English-born planter, politician and military officer who immigrated to the Carolinas, where he spent the majority of his life. Born in London, Rhett emigrated to North America in 1694, accompanied by his wife Sarah. He gradually acquired ownership over several slave plantations which specialized in producing rice. Rhett also sat in the South Carolina General Assembly and served in the colonial militia; in 1718, he commanded two chartered sloops and defeated the Barbadian pirate Stede Bonnet in the Battle of Cape Fear River.

Career

Rhett was a colonel in the colonial militia, receiver-general of the Lords Proprietors of Carolina, surveyor, and comptroller of customs for Carolina and the Bahama Islands. He was also an active merchant captain, sailing the vessel Providence between the Carolinas and the Bahamas. In April 1699 the Providence was attacked by Dutch pirate Hendrick van Hoven (alias Captain Hyne or Hind):

"about the latter end of April last, one Capt. Hind, a notorious pirate and sea-rover, having lately got into a brigantine with a mixt company of Dutch, French and other people, came up with an English-built ship mounted with two and twenty guns called the Providence galley, under the command of Capt. William Rhett of Carolina, who made a very generous defence, but was outdone and taken by the said Pirate."

In 1706, Rhett commanded an improvised naval flotilla which fought off a Franco-Spanish attack on Charles Town. In 1718 he provided two sloops to be fitted out as pirate hunters - Henry and Sea Nymph, each with eight guns and a crew of between 60 and 70 men. Rhett assumed the position of captain of this small flotilla and led it to victory in the 1718 Battle of Cape Fear River, capturing Stede Bonnet, the so-called "gentleman pirate." Bonnet escaped from jail with the help of local merchant and fellow pirate Richard Tookerman; he made it as far as Sullivan's Island before Rhett again captured him.

Rhett's house in Charleston, completed in 1716, still stands in its original location at 54 Hasell St., Charleston, South Carolina. It has been restored and is now privately owned. A Confederate politician born Robert Barnwell Smith changed his name to Robert Rhett, an ancestor.

Popular culture

 * William Rhett is a minor character in Tim Powers' novel On Stranger Tides.
 * Lars Arentz-Hansen plays William Rhett in the Starz TV series Black Sails.

title: William Rhett


text:
Moses Mosop

Moses Cheruiyot Mosop (born 7 July 1985) is a Kenyan middle and long distance athlete. He competed for Kenya at the 2004 Olympic Games and went on to take 10,000 metres bronze at the 2005 World Championships in Athletics. He has also been successful in cross country running, having won the silver at the 2007 IAAF World Cross Country Championships as well as team gold with Kenya in 2007 and 2009.

Until 2014-09-30, Mosop was managed by Jos Hermens and coached by Renato Canova. At the 2011-04-18 Boston Marathon, Mosop and countryman Geoffrey Mutai ran what at the time were the fastest times ever recorded for a marathon – 2:03:06 and 2:03:02, respectively – shattering the Boston course record by nearly three minutes.

Early running
Born in Kamasia, Marakwet District, Mosop started running while at primary school and later went to Marakwet High School. He qualified for the 2002 IAAF World Cross Country Championships held in Belfast, where he finished tenth in the junior race. It was in this occasion that he joined the management of the Italian Gianni Demadonna, and started to be coached by Renato Canova, that developed his talent from the youth category up to the current international level.

At the 2002 IAAF World Cross Country Championships in Lausanne he fared slightly better, finishing 7th in the junior race. At the 2003 All-Africa Games, he was fifth in men's 10,000 metres. He made his Olympic debut at the 2004 Athens Olympics and was seventh overall in the 10,000 metres final. Mosop also won the Giro Podistico di Pettinengo 9.6 km race in 2004.

He was the winner of the Almond Blossom Cross Country in March 2005 and placed 18th at the 2005 IAAF World Cross Country Championships soon after. Competing in the 10,000 metres in the 2005 World Championships, he won the bronze medal, setting a personal best of 27:08.96 minutes. He occasionally runs the 3000 and 5000 metres and holds personal bests of 7:36 min and 12:54 min in those events.

He headed further up the podium at the 2007 IAAF World Cross Country Championships. He finished second in the senior race and took the team gold with Kenya. He took back-to-back wins at the Giro al Sas 10K race in 2007 and 2008. In March 2009 he won the Cross di Alà dei Sardi in Sardinia. He returned to world competition two years later, but he could not repeat his medal form at the 2009 World Cross Country Championships (finishing in eleventh place), although he still won team gold with Kenya.

Mosop won the men's race at the 2010 Stramilano Half Marathon, clocking 59:20 for the win over Silas Kipruto. His coach stated that Mosop was progressing as a road runner and might make a move to the marathon distance. Attempting to defend his title at the Giro Media Blenio 10K (which he won in 2009), he finished second in a sprint finish just behind Imane Merga. He was chosen for the Kenyan team at the 2010 IAAF World Half Marathon Championships and he finished in tenth place. At the Zevenheuvelenloop 15K race, he was off the pace and finished sixth – almost two minutes behind Leonard Patrick Komon who set a world record.

2011: Marathon debut and world records
His first race of 2011 was the Paris Half Marathon, where he finished second behind Stephen Kibet. On 2011-04-18, he ran his marathon debut at the Boston Marathon, coming second in a time of 2:03:06. He and fellow countryman Geoffrey Mutai ran what at the time were the fastest times ever recorded for a marathon, shattering the time of the then existing world record (2:03:59 by Haile Gebrselassie) by nearly one minute, and the Boston course record by nearly three minutes. Helped by ideal cool temperatures and a strong tailwind on the point-to-point course, the lead pack reached the halfway mark on record pace of 1:01:54. The two Kenyans broke away from the pack at 30 kilometres and ran stride-for-stride over the last 12 kilometres until a sprint in the final straight-away by Mutai gave him the victory by four seconds, 2:03:02 to 2:03:06.

Because Boston is a point-to-point course, with an overall downhill slope, the times were not officially recognised. The IAAF rules essentially require marathon records to be established on a loop course (thereby neutralising the impact of wind and course elevation changes). The previous record at Boston was 2:05:52, set in 2010 by Robert Kiprono Cheruiyot who was the first to break 2:06 at Boston, while the current world record (yet to be ratified) is 2:02:57, run by Dennis Kimetto at Berlin in 2014.

As part of the 2011 Prefontaine Classic, Mosop was selected in an attempt to break the world record for the infrequently contested 30,000 m on the track. He shattered Toshihiko Seko's thirty-year-old world record by over two and a half minutes, running a time of 1:26:47.4 hours. He also smashed Seko's 25,000 m record by a minute and a half, passing the 25K intermediate mark at 1:12:25.4 hours. He stepped down in distance to run at the B.A.A. 10K in June and took third place on the podium.

2011-10-09, Mosop won the Chicago Marathon with a time of 2:05:37, beating Sammy Wanjiru's course record by four seconds. At the start of 2012, he was sixth at the Paris Half Marathon in preparation for the Rotterdam Marathon the following month. He was the pre-race favourite and attempted to break the marathon world record, but fell behind Yemane Tsegay and Getu Feleke, eventually finishing with a time of 2:05:03 hours. Nevertheless, he was selected for the Kenyan Olympic marathon team, but a tendon injury forced him to withdraw and he was replaced by Emmanuel Mutai.

Personal life
In 2005 Mosop was reported to be married with Rose Cheruiyot (not the runner of the same name) with one daughter. As of 2010, he is married to the runner Florence Kiplagat, with whom he has also a daughter, named Aisha. His brothers Elias Mosop and Philemon Mosop are also runners.

Personal bests
(*) Downhill and point-to-point course
 * All information taken from IAAF profile.

title: Moses Mosop


text:
User talk:Lumif9

Proposed deletion of Luna Amară

The article Luna Amară has been proposed for deletion. The proposed-deletion notice added to the article should explain why.

While all contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the  notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the article to address the issues raised. Removing  will stop the proposed deletion process, but other deletion processes exist. The speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. UnitedStatesian (talk) 17:01, 12 March 2010 (UTC)

title: User talk:Lumif9


text: Template:Other uses of

title: Template:Other uses of


text:
User talk:Brian McNeil

Condolences

 * I was connected with Brian on social media and knew him as a decent man. We shared an appreciation of a certain style of humour, and a certain impatience with politicians. Farewell, Brian, you left the world brighter and better informed than you found it. Guy (help!) 21:49, 27 July 2020 (UTC)
 * Very sorry to hear this. I only met him a few times, in Edinburgh and a memorable conference in Amsterdam, and it was always a delight. Johnbod (talk) 14:57, 29 July 2020 (UTC)
 * Hi Brian. I was sorry to read the news. I hope you rest in peace and thank you for all your contributions to the wikinews community. You made a difference. Farewell. Anthere (talk)
 * I heard about this on social media, which was where I'd encountered Brian McNeil. I know him from his direct manner of speaking and that those who knew him highly valued his opinion as a result of that. He will be missed. Acalamari 11:50, 31 July 2020 (UTC)
 * Just heard from The Signpost. Sad news indeed. Mostly knew him from Wikinews. Did not live to see his beloved Scotland achieve independence. Rest in peace Brian.  Hawkeye7   (discuss)  01:45, 3 August 2020 (UTC)

title: User talk:Brian McNeil


text:
Wikipedia:Articles for deletion/Pull a jim

 This page is an archive of the proposed deletion of the article below. Further comments should be made on the appropriate discussion page (such as the article's talk page or on a Votes for Undeletion nomination). No further edits should be made to this page.

The result of the debate was SPEEDY DELETED by Dmcdevit. -Splash 22:18, 10 September 2005 (UTC)

Pull a jim
Nonsense and vanity. (Speedy?) KeithD (talk) 21:19, 1 September 2005 (UTC)
 * Delete as per Votes for deletion/Pull a jim. Speedy or otherwise. Alf 21:43, 1 September 2005 (UTC)
 * Delete. Silliness (nn, or). -- BD2412 talk 22:07, 1 September 2005 (UTC)
 * Delete Nonsense DV8 2XL 22:18, 1 September 2005 (UTC)
 * Speedy - take your pick - patent nonsense or re-creation or probable attack page? --Doc (?) 22:49, 1 September 2005 (UTC)

Speedied. Re-creation. Zoe 05:27, September 2, 2005 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in an undeletion request). No further edits should be made to this page.


text:
Protective security unit

A protective security unit typically provides policing, security, intelligence and bodyguard services for sovereigns and politicians.

The Republic of Ireland's national police and security service is the Garda Síochána.

The Singapore Police Force's Police Security Command is responsible for protecting Cabinet ministers and dignitaries from foreign nations.

title: Protective security unit


text:
User talk:Mark Taylor

Hello, ! I'm ulayiti, and I'd like to welcome you to Wikipedia! Thanks for your contributions, and I hope you'll like the place enough to stay. Here are a few good links for newcomers:
 * The Five Pillars of Wikipedia
 * How to edit a page
 * Editing tutorial
 * How to write a great article
 * Manual of Style
 * How to avoid common mistakes

When commenting on talk pages or voting, you should always sign your name by typing in four tildes (~~~~). This way people will know who made the comment and can respond to you. If you have any questions at all, feel free to ask me on my talk page. You can also have a look at the help pages or put up a question at the village pump. Welcome to Wikipedia, and happy editing! - ulayiti (talk)  21:19, 1 September 2005 (UTC)

USA Daily COVID-19 Cases
Regarding https://en.wikipedia.org/wiki/Template:2019%E2%80%9320_coronavirus_pandemic_data/United_States_medical_cases, where do you get the recent GA figures? Their website per the notated reference has a case total of 620, yet you indicated total of 753. Can you please notate the source of the data in the references section for the day? Thanks. dudzcom (talk) 04:35, 23 March 2020 (UTC)

May 10 Indiana Case Update
Thanks for cleaning up the May 10 case number for Indiana a little bit ago. I don't know if you saw my question about that number on the Talk page for the template, but I wasn't sure how to resolve the mismatched numbers from the Indiana website. Hopefully you have some insight into why the numbers didn't match. Bz8x8c (talk) 19:18, 11 May 2020 (UTC)

File permission problem with File:Blaine E. Brownell.jpg
Thanks for uploading File:Blaine E. Brownell.jpg, which you've attributed to Sean Airhart. I noticed that while you provided a valid copyright licensing tag, there is no proof that the creator of the file has agreed to release it under the given license.

If you are the copyright holder for this media entirely yourself but have previously published it elsewhere (especially online), please either
 * make a note permitting reuse under the CC-BY-SA or another acceptable free license (see this list) at the site of the original publication; or
 * Send an email from an address associated with the original publication to permissions-en@wikimedia.org, stating your ownership of the material and your intention to publish it under a free license. You can find a sample permission letter here. If you take this step, add OTRS pending to the file description page to prevent premature deletion.

If you did not create it entirely yourself, please ask the person who created the file to take one of the two steps listed above, or if the owner of the file has already given their permission to you via email, please forward that email to permissions-en@wikimedia.org.

If you believe the media meets the criteria at Non-free content, use a tag such as non-free fair use or one of the other tags listed at File copyright tags, and add a rationale justifying the file's use on the article or articles where it is included. See File copyright tags for the full list of copyright tags that you can use.

If you have uploaded other files, consider checking that you have provided evidence that their copyright owners have agreed to license their works under the tags you supplied, too. You can find a list of files you have created in [ your upload log]. Files lacking evidence of permission may be deleted one week after they have been tagged, as described in section F11 of the criteria for speedy deletion. You may wish to read Wikipedia's image use policy. If you have any questions please ask them at the Media copyright questions page. Thank you. — Diannaa (talk) 21:53, 3 July 2021 (UTC)

ArbCom 2022 Elections voter message
 Hello! Voting in the 2022 Arbitration Committee elections is now open until 23:59 (UTC) on. All eligible users are allowed to vote. Users with alternate accounts may only vote once.

The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail.

If you wish to participate in the 2022 election, please review the candidates and submit your choices on the voting page. If you no longer wish to receive these messages, you may add to your user talk page. MediaWiki message delivery (talk) 00:21, 29 November 2022 (UTC)

Disambiguation link notification for December 31
An automated process has detected that when you recently edited American Heritage Museum, you added a link pointing to the disambiguation page Mortar.

(Opt-out instructions.) --DPL bot (talk) 06:06, 31 December 2022 (UTC)

ArbCom 2023 Elections voter message
 Hello! Voting in the 2023 Arbitration Committee elections is now open until 23:59 (UTC) on. All eligible users are allowed to vote. Users with alternate accounts may only vote once.

The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail.

If you wish to participate in the 2023 election, please review the candidates and submit your choices on the voting page. If you no longer wish to receive these messages, you may add to your user talk page. MediaWiki message delivery (talk) 00:23, 28 November 2023 (UTC)

title: User talk:Mark Taylor


text:
Talk:Phase shifting

Please site source for crediting Francis Grasso with phase shifting. All the research I have done does not show this. Mr. Grasso was the first DJ to take 2 copies of the same record and extend the song past its normal 2 & 1/2 minute length, but that's all.

 * I've rephrased the passage referred to by anon above, as the technique is generic, and has been used experimentally by DJs for decades.

 * My biggest concern about this article is that it appears to be describing two entirely different things - "repeating phrases of the same tempo, but different metrical lengths" is not really related to the audio effect, which depends on two identical sounds playing at subtlely different speeds. TheMadBaron 07:23, 30 October 2005 (UTC)

 * I've deleted what I consider to be irrelevant sections. The audio effect is covered in Phasing. TheMadBaron 07:31, 30 October 2005 (UTC)

The first paragraph seems like an acurate (but brief) description of phase shift as I understand it (I'm an Electrical Engineer). The rest of this article is about a musical technique that I never heard of before. Perhaps there should be two seperate pages, one for phase shift, the musical technique, and another for phase shift the physics/mathmatics concept. Although Wave_interference seems to cover the physics/mathmatics concept fairly well. —The preceding unsigned comment was added by Msebast (talk • contribs).

Grasso

 * Francis Grasso is credited with originating phasing as a DJ technique, playing two copies of the same record from the same point at the same time so as to create a phase effect.

I'll leave this out for now since I don't know if it is phasing or phase shifting. Hyacinth 11:12, 27 November 2005 (UTC)

 * According to http://suenomartino.net/btg.htm it was phase shifting, giving a flanging effect. Hyacinth 11:14, 27 November 2005 (UTC)

title: Talk:Phase shifting


text:
User talk:Felix Frederick Bruyns

To Whom It May Concern
The treatment that I have received on this website has been unconscionable and appalling. I have been libeled, made an arbitrary target for personal attack by a sysop and sent an unsolicited and completely unprovoked obscene message  by a man who actually has the nerve to tell me off for complaining about it. I have quite reached the conclusion that this is a website of cruel, hypocritical, dishonest elitists who deliberately  victimize any new user who doesn't stay silent about their relentless abuse. This site is abominably run and is filled with wanton libel and obscenity. On careful consideration, I have decided that Wikipedia is simply not worth my time and that you do not deserve to have a user with integrity on your site. As for the unjust "block", it is of no consequence since I will not do my self the dishonor of associating with you at any point in the future. You lost a knowledgeable contributor through your abuse of me and the loss is yours, not mine. To be honest, I feel ashamed for having my name in any way associated with such a wretched excuse for an encyclopedia that would not exist on a properly regulated  Internet. As for Zoe, Dmcdevit, Knowledge Seeker, DESpiegel and all other users who have abused me, all I can say is that I consider the sources of the abuse and would personally condemn the above  and several others for conduct which, of course, they know they could never engage in if they were in the real, rather than the virtual world. So since right ultimately makes might, I leave this so-called reference tool to destroy itself. It is a blight on the Internet, especially since it claims to be a legitimate encyclopedia, and I will not further dignify its existence with my presence. Felix Frederick Bruyns 18:41, 6 September 2005 (UTC)

 * Thanks for your farewell note on my user-page. But your careless click-and-enter technique has split an earlier comment by someone else; see  Best wishes - Robin Patterson 20:12:21, 2005-09-06 (UTC)

 * Thank you for the email, I appreciate (and did not expect) it. I want to add that the technical issues can be resolved easily, I'm sure, and for now, you just need to look over your edits after submitting them, and fix these when needed (easy enough). Goodluck to you. El_C 22:21, 6 September 2005 (UTC)

 * I'm sorry you had a rough start here, Mr. Bruyns. Wikipedia is a complex place, and sometimes it takes people a bit longer to fit in. I hope you will reconsider your decision to leave. As Wikipedia's popularity continues to climb, perhaps it will be more difficult to stay away. You will always be welcome to come back, but please remember that you must conduct yourself with civility and courtesy—these are more important than how much a contributor knows. I'd be happy to work with you to help you tone down some of your outbursts, as I mentioned to you before. Finally, I assume you included my name above out of frustration, since I can't seem to find the abusive statements I made. If you have a chance, I'd appreciate you pointing them out so I can be sure not to treat future users inappropriately. Thanks, and good luck. — Knowledge Seeker দ 00:26, September 8, 2005 (UTC)

Proposed deletion of Continental conservatism

The article Continental conservatism has been proposed for deletion  because of the following concern:
 * No sources since 2009

While all contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the article to address the issues raised. Removing will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Viriditas (talk) 22:50, 4 August 2012 (UTC)

title: User talk:Felix Frederick Bruyns


text:
Category:Ayyavazhi philosophical concepts

This category gives the articles of philosophical concepts in Ayyavazhi religion.


text:
Wikipedia:WikiProject Missing encyclopedic articles/Hot/A

 * 1) ABC Graphics Suite Abc graphics suite - double check
 * 2) Abdallah of Mourgoula - some French language hits; seems to be a West African leader during the French colonial period
 * 3) Access router - double check?
 * 4) ActiveWorks Activeworks - double check?
 * 5) ActiveX Server Component Activex server component
 * 6) Acoustic signal processing
 * 7) A2WML A2wml - Air2Web markup language
 * 8) Abel Bible Abel bible
 * 9) Abend-AID Abend-aid - double check?
 * 10) Abstbessingen Faience Abstbessingen faience
 * 11) Abukuma-Sammyaku Abukuma-sammyaku - Highland region in Japan, ja:阿武隈高地
 * 12) Academic Art and Architecture Academic art and architecture
 * 13) Acceleration analysis
 * 14) Acceleration measurement
 * 15) Acceleration Operator Acceleration operator
 * 16) Acceleration stress
 * 17) Accessory Mineral Accessory mineral  - check redirect?
 * 18) Acquired character
 * 19) Actinomyxida
 * 20) Actinomyxidian
 * 21) Actinopodea
 * 22) Actionable intelligence
 * 23) Activation analysis - Redirect an AKA? ,
 * 24) Active archiving - double check?
 * 25) Active area
 * 26) Active content
 * 27) Active operating system fingerprinting
 * 28) Active testing
 * 29) Actor-manager system
 * 30) Ad view
 * 31) AD/Cycle Ad/cycle
 * 32) Adadah - minor bible ref?
 * 33) Adalia (Bible) Adalia (bible)  - minor bible ref?
 * 34) Adapter bindings
 * 35) Adaptive signal processing
 * 36) Adaptive sound control
 * 37) Addis Adi Addis adi
 * 38) Address cleansing
 * 39) Address lookup utilities
 * 40) Adds, moves and changes
 * 41) Adeno-SV40 hybrid virus Adeno-sv40 hybrid virus
 * 42) Adithaim - bible ref?
 * 43) Admatha - bible ref
 * 44) Administrative area map level
 * 45) Administrivia
 * 46) Admiral carpet
 * 47) Adobe Document Server Adobe document server
 * 48) Adobe Extreme Adobe extreme
 * 49) Adobe Type Align Adobe type align
 * 50) Adsorption operations
 * 51) Advanced Pick Advanced pick
 * 52) Advanced Time Advanced time
 * 53) AdvanceNet Advancenet
 * 54) Advocate of Moral Reform Advocate of moral reform
 * 55) Aelurus (deity)  - Not mentioned in redirect page
 * 56) Aernout Drost Aernout drost, Dutch author, nl:Aarnout Drost
 * 57) Aeronautical meteorology
 * 58) Affenkapelle Ware Affenkapelle ware
 * 59) African Greek Orthodox Church African greek orthodox church  - someone double check redirect?
 * 60) Ag catalog
 * 61) Aggregation of Christian believers church Aggregation of christian believers church
 * 62) AGHz Aghz
 * 63) AgileAlliance Agilealliance
 * 64) AGPset Agpset
 * 65) Agricultural soil and crop practices
 * 66) Ahamad Nissim Susa Ahamad nissim susa
 * 67) Aharah - redirects to minor bible character
 * 68) Aharhel - redirects to minor bible character
 * 69) Aharon Avni Aharon avni  - painter 1906-1951
 * 70) Ahhiya - double check redirect?
 * 71) Ahilud - redirects to minor bible character
 * 72) Ahmad Bakr Ahmad bakr
 * 73) Ahmad Ibn Abi Ar-Rijal Ahmad ibn abi ar-rijal
 * 74) Ahmadu Ahmadu Garba and Ahmadu Jarr?
 * 75) Ahmet Pasa Bursali Ahmet pasa bursali - 15th century Turkish poet. Turkish wikipedia has an article. https://tr.wikipedia.org/wiki/Ahmed_Pa%C5%9Fa_(%C5%9Fair)
 * 76) Aichbuhl
 * 77) AICPA ITMS Aicpa itms
 * 78) Air armament
 * 79) Air register
 * 80) Airborne radar - double check redirect
 * 81) Aircraft compass system
 * 82) Air-sea interface
 * 83) Airy Compensation Airy compensation
 * 84) Akhillefs Paraskhos Akhillefs paraskhos
 * 85) Akkub  - minor biblical character
 * 86) Akund Floss Akund floss
 * 87) Al Frueh Al frueh
 * 88) Alan Crown Alan crown  - historian of Australian Jewry and scholar of Dead Sea Scrolls
 * 89) Alapa - type of Indian music. - Same as Alap?
 * 90) Ala'ud'din  = Sultan Alauddin Riayat Shah (or Alauddin Riayat), the founder of the Sultanate of Johor
 * 91) Albert-Charles Simonin Albert-charles simonin  - French fr:Albert Simonin
 * 92) Albertina Graphics Collection Albertina graphics collection
 * 93) Al-Birah Al-birah  - town in the West Bank adjacent to Ramallah
 * 94) ALC Loop Alc loop
 * 95) Alcaraz Carpet Alcaraz carpet
 * 96) Alexander (Bible) Alexander (bible)
 * 97) Alexander Frederick Alexander frederick
 * 98) Alexandria Municipal Museum Alexandria municipal museum
 * 99) Alfa éIbrahim Alfa éibrahim
 * 100) Alfalfa Weevil Alfalfa weevil
 * 101) Alfred Brandt Alfred brandt
 * 102) Al-Hammadah al-Hamra' Al-hammadah al-hamra'
 * 103) Al-Haruj al-Aswad Al-haruj al-aswad
 * 104) Ali Zayni al-Abidin Ali zayni al-abidin
 * 105) Aliah - bible - can it be own article?
 * 106) Alice Throckmorton McLean Alice throckmorton mclean  - U.S. social activist
 * 107) Alick Henrici Alick henrici
 * 108) Alicyclic hydrocarbon - double check?
 * 109) Alikreukel
 * 110) Alisal - Other subjects notable?
 * 111) Al-Jifarah Al-jifarah
 * 112) Alkali emissions
 * 113) Al-Kharijah Al-kharijah
 * 114) All rights
 * 115) Al-Lahun Al-lahun
 * 116) Allaire Spectra Allaire spectra
 * 117) AllClear Allclear
 * 118) Allied Coordination Committee Allied coordination committee
 * 119) Alloeocoela
 * 120) All-optical network
 * 121) Alloy structures
 * 122) All-Union Council of Evangelical Christians and Baptists All-union council of evangelical christians and baptists
 * 123) Al-Ma'adi Al-ma'adi  - Egyptian archeological site, south of Cairo - double check?
 * 124) Almansa Dam Almansa dam
 * 125) Almendro
 * 126) Almonry School Almonry school
 * 127) Al-Muayyad Al-muayyad  - bio here
 * 128) Al-Muhallabi Al-muhallabi  - either this poet or this general. - redirects to family
 * 129) Al-Muqattam Al-muqattam  - a place in Egypt (a mountain?)
 * 130) Alonza Lorenzo Alonza lorenzo can be own article?
 * 131) Alpha Four Alpha four
 * 132) Alphageometric
 * 133) Alphanumeric sort
 * 134) Alpujarra Rug Alpujarra rug
 * 135) Altare Glass Altare glass
 * 136) Alternate routing
 * 137) Altitudinal vegetation zones
 * 138) Alundum - double check?
 * 139) Alwand - all covered?
 * 140) Always on - double check?
 * 141) Alwin Gallery Alwin Gallery (London) Alwin gallery
 * 142) Alwin Sculpture Gallery Alwin Sculpture Gallery (Tunbridge Wells) Alwin sculpture gallery
 * 143) Am586  - double check?
 * 144) Amakihi - double check?
 * 145) Amalgamation process
 * 146) Amanominakanushi-no-kami
 * 147) Amaravati Sculpture Amaravati sculpture
 * 148) Amasa Delano Amasa delano
 * 149) Ambiguous user


text:
Wil Nieves

Wilbert "Wil" Nieves (born September 25, 1977) is a Puerto Rican former professional baseball catcher and current minor league coach. He played in Major League Baseball (MLB) for the San Diego Padres, New York Yankees, Washington Nationals, Milwaukee Brewers, Colorado Rockies, Arizona Diamondbacks, and Philadelphia Phillies.

San Diego Padres
Nieves was selected by the Padres in the 47th round of the 1995 MLB draft. He made his major league debut on July 21, 2002, for the San Diego Padres, and played 28 games with them during their 2002 season.

Anaheim/Los Angeles Angels
Nieves was selected off waivers by the Anaheim Angels on December 20, 2002.

New York Yankees
He was traded to the New York Yankees for pitcher Bret Prinz. Nieves won a spot on the Yankees 2007 roster by beating out Todd Pratt and Raul Chavez during spring training. He served as the back-up catcher to Jorge Posada, but was primarily considered Mike Mussina's "personal catcher." Joe Torre experimented with using Nieves to help bolster Mussina out of a rough stretch with good results.

Nieves made his first career non-catching appearance in the ninth inning of a game on July 8, 2007, against the Angels; he played first base when the Yankees ran low on position players.

Following an impressive 2-for-3 performance against the Tampa Bay Devil Rays on July 21, 2007, Nieves was designated for assignment by the Yankees following news that they had acquired José Molina from the Los Angeles Angels of Anaheim. Though respected as a good defensive catcher, Nieves hit just .164 for the Yankees.

"It's just business and I really want this team to go all the way to the playoffs and, hopefully, win the World Series," Nieves said. "They're a bunch of great guys. I love them, Torre and all those guys. They can improve the backup catcher and they're bringing in Molina. He's a great catcher, too."

Nieves cleared waivers, and reported to the Yankees' Triple-A Scranton/Wilkes-Barre Yankees on July 27, 2007. Nieves was the starting catcher for Scranton. He declared free agency in October 2007. He played for Licey in the Dominican Winter League during the off-season.

Washington Nationals
He started the 2008 season in the Washington Nationals organization with the Triple-A Columbus Clippers of the International League. On April 25, 2008, Nieves hit his first major-league home run, a walk-off home run to right field, to give the Nationals a 5–3 win over the Chicago Cubs. Nieves was the backup catcher to starter Jesus Flores in the 2009 season. Nieves was the backup catcher for Iván Rodríguez in 2010.

Milwaukee Brewers
On December 10, 2010, Nieves signed a one-year deal with the Milwaukee Brewers.

Atlanta Braves
He was traded to the Atlanta Braves on July 27, 2011, for $1. He was demoted to Triple-A Gwinnett shortly after, and J. C. Boscan was recalled to be the backup catcher.

Colorado Rockies
On December 18, 2011, Nieves signed a minor league deal with the Colorado Rockies worth $414,000. After hitting .409 with 1 HR in 18 games in spring training, he was reassigned before the season started. On May 25, 2012, Nieves was called up to replace Ramón Hernández, who was placed on the 15-day disabled list. Nieves was hitting .299 with 3 HR and 14 RBI in 28 games with Triple-A Colorado Springs. During his time up there, he acted as a mentor to Wilin Rosario and was used to try to solve Jeremy Guthrie's problems. On July 13, Nieves was placed on the 15-day disabled list with a turf toe in his right foot. However, on August 1, he was designated for assignment to clear roster space. Nieves was hitting .298 with 1 HR and 5 RBI in 16 games. He elected free agency on August 6.

Arizona Diamondbacks
Nieves signed with the Arizona Diamondbacks on August 6, 2012. Nieves scored a two-run homer on his debut August 9, 2012 at the Pittsburgh Pirates in a 6 to 3 win.

Philadelphia Phillies

On December 4, 2013, Nieves signed with the Philadelphia Phillies. Nieves made the Phillies Opening Day roster in 2014 as the backup catcher to Carlos Ruiz. On June 18, he injured his leg while running the bases during a start against Atlanta. He exited the game, and the Phillies recalled catcher Cameron Rupp to serve as Ruiz's backup while Nieves healed. Nieves had only played in 14 games to that date, all starts to give Ruiz some rest.

Return to San Diego Padres
Nieves signed a minor league contract with the San Diego Padres on February 4, 2015. He made the Padres' opening day roster as back-up to catcher Derek Norris after Tim Federowicz suffered a season-ending knee injury during spring training. Nieves appeared in six games for the Padres in 2015 and collected one hit in thirteen at-bats, an April 12 grand slam against the San Francisco Giants. Nieves was designated for assignment on May 4, 2015, and chose to become a free agent.

Braves organization
The Braves signed Nieves to a minor league contract, and he batted .238 for AAA Gwinnett, but the Braves released him on June 22, 2015.

Post-playing career
In 2019, Nieves joined the Boston Red Sox' minor league system as a coach with the Class A-Advanced Salem Red Sox.

title: Wil Nieves