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Results: fast_protein_cluster is an optimized and extensible toolkit that supports Root Mean Square Deviation after optimal superposition (RMSD) and Template Modeling score (TM-score) as metrics.
To detect the optimal superposition, we used the MaxSub algorithm54, in the implementation given within the MaxCluster tool (www.sbg.bio.ic.ac.uk/maxcluster/index.html#MaxSub).
Different neuroscientific questions give rise to different requirements for optimal superposition of structure and function.
This is the case when SM X, P UX, P X is the optimal superposition coding in terms of achievable rates.
Asymptotically, we know that when M → ∞, SM X, P UX, P X is the optimal superposition coding scheme because it allows the capacity region for two-user AWGN BC using Gaussian alphabet for each user to be achieved.
One of these is basis pursuit (BP) [32], which is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest ℓ1 norm of coefficients among all such decompositions: min x 1 subject to y - Φ x < ε. (3).
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It is interesting to note, though, that the original TM-align superpositions yeald better SI scores than the optimal superpositions.
The algorithm described above for calculating optimal superpositions with missing data is implemented in the command-line UNIX program THESEUS (Theobald and Wuttke, 2006a, b).
This PubChem3D similarity search is a multistep process designed: to filter out conformer pairs that cannot possibly be neighbors, to generate a near-optimal superposition between conformer pairs, and to perform a final optimization of the superposition to maximize the shape volume overlap between conformer pairs.
In the second step, the MaxPairs algorithm is run to compute the set of (near- optimal superpositionear- optimalhe superpositions that rigorously maximize the namely of pairs of athesuperpositionsfithatderigorously
Theobald, D. L. & Steindel, P. A. Optimal simultaneous superpositioning of multiple structures with missing data.
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