Different actors like teachers, course designers and content providers need to gain more information about the way the resources provided with Moodle are used by the students so they can adjust and adapt their offer better. In this contribution we show that Excel Pivot Tables can be used to conduct a flexible analytical processing of usage data and gain valuable information. An advantage of Exc...

Background: Advocates of medial portal drilling claim that the transtibial technique results in a more vertical positioning of the graft, which could lead to subsequent failure and/or a residual pivot shift on postoperative examination. However, advocates of transtibial drilling state that with appropriate placement and adequate notchplasty, their technique places the graft in a more anatomical...

This paper gives sensitivity analyses by two approaches for L and U in the factor-ization A = LU for general perturbations in A which are suuciently small in norm. By the matrix-vector equation approach, we derive the condition numbers for the L and U factors. By the matrix equation approach we derive corresponding condition estimates. We show how partial pivoting and complete pivoting aaect th...

Limited-memory incomplete Cholesky factorizations can provide robust preconditioners for sparse symmetric positive-definite linear systems. In this paper, the focus is on extending the approach to sparse symmetric indefinite systems in saddle-point form. A limited-memory signed incomplete Cholesky factorization of the form LDL is proposed, where the diagonal matrix D has entries ±1. The main ad...

Unlike the method without pivoting, Gaussian elimination with partial pivoting consecutively applies row permutation to matrix A in order to avoid possible akk diagonal entries of matrix A being equal to zero. Gaussian elimination with partial pivoting solves the matrix equation Ax = b decomposing matrix A into a lower L and upper U triangular matrices such that PA = LU, where P is a row permut...

We consider ranking and clustering problems related to the aggregation of inconsistent information, in particular, rank aggregation, (weighted) feedback arc set in tournaments, consensus and correlation clustering, and hierarchical clustering. Ailon, Charikar, and Newman [4], Ailon and Charikar [3], and Ailon [2] proposed randomized constant factor approximation algorithms for these problems, w...