Parametric Jensen-Shannon Statistical Complexity and Its Applications on Full-Scale Compartment Fire Data

Symmetrization in the Calculation Pipeline of Gauss Function-Based Modeling of Hydrophobicity in Protein Structures

In this paper, we show, discuss, and compare the effects of symmetrization in two calculation subroutines of the Fuzzy Oil Drop model, a coarse-grained model of density of hydrophobicity in proteins. In the FOD model, an input structure is enclosed in an axis-aligned ellipsoid called a drop. Two profiles of hydrophobicity are then calculated for its residues: theoretical (based on the 3D Gauss function) and observed (based on pairwise hydrophobic interactions). Condition of the hydrophobic core is revealed by comparing those profiles through relative entropy, while analysis of their local differences allows, in particular, determination of the starting location for the search for protein–protein and protein–ligand interaction areas. Here, we improve the baseline workflow of the FOD model by introducing symmetry to the hydrophobicity profile comparison and ellipsoid bounding procedures. In the first modification (FOD–JS), Kullback–Leibler divergence is enhanced with its Jensen–Shannon variant. In the second modification (FOD-PCA), the molecule is optimally aligned with the axes of the coordinate system via principal component analysis, and the size of its drop is determined by the standard deviation of all its effective atoms, making it less susceptible to structural outliers. Tests on several molecules with various shapes and functions confirm that the proposed modifications improve the accuracy, robustness, speed, and usability of Gauss function-based modeling of the density of hydrophobicity in protein structures.

Refined Young Inequality and Its Application to Divergences

We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also studied some properties on the difference between the weighted arithmetic mean and the weighted geometric mean. Applying the newly obtained inequalities, we show some results on the Tsallis divergence, the Rényi divergence, the Jeffreys–Tsallis divergence and the Jensen–Shannon–Tsallis divergence.