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Regarding the second model: the multiplicity of equally valid mapping positions for sequences repeated in a genome obfuscates their correct assignment to a genomic region, making reads from such regions less "mappable," both intrinsically and due to the processes by which software searches for significant alignments.
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Our proposed assembler IDBA-Tran calculates the probability that a k-mer or short simple path (contigs) contains error using not only the multiplicity of the k-mer or contig (or their neighboring k-mers or contigs) but also uses a multi-normal distribution to model the multiplicities of all k-mers in the whole connected component.
The p p based ANN model calculates the multiplicity distribution of charged particles and the inelastic cross section of the p p collision at high energies.
The results, therefore, suggest that employing the constrained-equilibrium assumption may significantly reduce the modeling task of heavy hydrocarbon fuels, where the intrinsic dimensionality of the model, multiplicity of pathways and the required rates render the modeling task intractable.
This is a somewhat more advanced model and demonstrates the multiplicity of size of porosity that may exist within a porous carbon from micro to macroporosity.
Lastly, we were not able to introduce diagnosis into the model, because of the multiplicity of categories.
Quake works by modeling the weighted multiplicity histogram of k-mers as a combination of two separate distributions (one from erroneous reads, one from accurate reads), and using that model to determine the best cutoff threshold.
Single-label classification and regression cannot model this multiplicity.
However, in modeling this system, the multiplicity and bi-threshold behavior are not theoretically possible according to the designed interactions.
On a cluster-by-cluster basis, we developed conceptual Boolean models for illustrating the multiplicity of the roles of bZIP1 in the control of gene expression by L and/or N, based on the ANOVA output generated for each cluster (see Figure 3, 4 and Additional file 4, for details see Methods).
By generating our datasets through an evolution strategy not wedded to any specific model, we achieved datasets that represent the multiplicity of models possible under the desired attribute construction of high-order interaction without low-order interaction.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com