Journal: Frontiers in Neuroinformatics

Article Title: NeuroMeasure: A Software Package for Quantification of Cortical Motor Maps Using Frameless Stereotaxic Transcranial Magnetic Stimulation

doi: 10.3389/fninf.2019.00023

Figure Lengend Snippet: Summary of surface fitting algorithms available in NeuroMeasure.

Article Snippet: Biharmonic (v4) , The same algorithm used in MATLAB's griddata function. See the comprehensive explanation on the Mathworks website griddata documentation: https://www.mathworks.com/help/matlab/ref/griddata.

Techniques:

Journal: PLoS ONE

Article Title: Integral, mean and covariance of the simplex-truncated multivariate normal distribution

doi: 10.1371/journal.pone.0272014

Figure Lengend Snippet: Transformation matrices T v , and constraint vectors c v and d v , that define the truncation c v < T v x < d v for six relevant regions shown in Fig 2 . Dummy inequalities −∞ < x i < ∞ were introduced into the transformation matrices T 1 , T 2 and T 3 to ensure that these matrices have rank equal to their dimension. The order of rows in T 23 , c 23 and d 23 has been switched so that this matrix and these vectors possess the form that would be obtained from a generalised two-step algorithm for ST-MNDs of any dimension described later in the “Materials and methods” section.

Article Snippet: A plausible explanation for this observation is that the two sampling methods remain accurate but the semi-analytical method loses accuracy when n ≥ 4 because, in the presently used implementation of the semi-analytical method, the underlying algorithm that computes integrals of hyperrectangularly-truncated MNDs (“mvncdf” function in MATLAB R2021b) differs between dimensions n < 4 and n ≥ 4 [ ].

Techniques: Transformation Assay

Journal: PLoS ONE

Article Title: Integral, mean and covariance of the simplex-truncated multivariate normal distribution

doi: 10.1371/journal.pone.0272014

Figure Lengend Snippet: Notice that the semi-analytical method (plots in the central column) becomes rather inaccurate, but increasing the accuracy of the integrals of hyperrectangularly-truncated MNDs calculated within this method vastly improves the estimates overall (plots in the right-most column). However, for one of the distributions tested, the covariance matrix was very poorly estimated by the semi-analytical method with increased accuracy (bottom-right plot, results not shown), with the values of some covariance matrix elements predicted to be more than ten orders of magnitude higher than their values predicted by the other methods.

Article Snippet: A plausible explanation for this observation is that the two sampling methods remain accurate but the semi-analytical method loses accuracy when n ≥ 4 because, in the presently used implementation of the semi-analytical method, the underlying algorithm that computes integrals of hyperrectangularly-truncated MNDs (“mvncdf” function in MATLAB R2021b) differs between dimensions n < 4 and n ≥ 4 [ ].

Techniques: