We end this paper by computing two special cases of Theorem 7. Note that calculations have been done with the help of standard formulas for fractional derivative operator acting on common functions (see [25, 26]).
Our data uncover the possibility of the existence of a macromolecular complex comprised of several different proteins whose genes are mutated in cystic kidney diseases and warrant future studies on common functions, likely important for preventing renal cystogenesis.
Since protein folds are classified into superfamilies based on common functions and evolutionary relationships, it is likely that the PCAIN-based methodology enables handpicking of an optimal functionally-related template molecule for modeling the structure of the unknown protein, thus contributing significantly towards improving the accuracy of structure prediction.
Voxel-by-voxel exploration over the whole brain based on a cosine similarity measure of common function confirmed the specificity of supramodal zones.
The impact of customized and personalized functional modules on the common function modules should be reduced to the minimum.
The authors focus on the common function improving learning, teaching, and educational administration, and they discuss evaluation and accountability more broadly within a framework of validity and utility.
To shed light on the common function of genes targeted by TR4, gene ontology analysis was performed using ConceptGen (http://conceptgen.ncibi.org/core/conceptGen/index.jsp; [ 25]) to identify the functional categories enriched in the overlapping targets in 4 cell types (p-value < 0.05, modified Fisher's exact test).
Interestingly, a comprehensive analysis on regulatory functions identified "transmembrane transport" as a common function present on all three groups.
Thus, fMRI-based summaries of these regions often focus on potential common functions, such as surprise23 or salience24.
The convergence of parkin, PINK1, and α-synuclein on mitochondrial dynamics uncovers a common function of these PARK genes in the mitochondrial stress response and provides a potential physiological basis for the prevalence of α-synuclein pathology in Parkinson disease.
