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Exact(4)
There is a large matrix of pathways and brain areas that work together to influence the pain experience.
Performing the Mahalanobis distance calculation for each pathway produced a distance matrix of pathways by samples.
Once this is completed for all observations it is possible to set up a supervised classification problem where the response vector y denotes the response label of each pathway, and the predictor matrix X is an N × P binary matrix of pathways, where N is the number of pathways and P is the number of edges within the network.
We defined the outlier cutoff as the standard value χ d,.975 2, the square root of the 97.5th percentile of the chi-squared distribution with d degrees of freedom, generating a binary matrix of pathways by samples where 1/0 represents outlier/non-outlier.
Similar(56)
From the scores, a distance matrix of these pathways is built and used to clustering these pathways into pathway groups.
Then a similarity matrix of these pathways was built and used to group the pathways into clusters.
However, in this setting, X is a sparse matrix of binary pathways where we expect and are explicitly looking for dominant pathways.
First, we calculated a matrix of pairwise pathway similarities derived from the hypergeometric distribution as follows.
PARADIGM produces a matrix of integrated pathway activities (IPAs) A where A ij represents the inferred activity of entity i in patient sample j.
The Mahalanobis distance formula is: D M x = χ ‒ μ T S ‒ 1 χ ‒ μ where x is the sample in question, S is the robustly estimated covariance matrix of the pathway subspace, and μ is the robust mean vector.
To inhibit the progressive growth at the invasion zone followed by cartilage and bone degradation without interfering with physiologic matrix remodeling, identification of pathways operative specifically in RASF and not in SF of other origin (e.g. osteoarthritis SF) is essential.
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Justyna Jupowicz-Kozak
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