Detecting Disease Association With Rare Variants Using Weighted Entropy

BackgroundThe rapid development of sequencing technology and simultaneously the availability of large quantities of sequence data provides an unprecedented opportunity for researchers to conduct studies to detect rare variants associated with the disease. However, none of current existing statistical methods has uniform power in all scenarios because they more or less are affected by nonfunctional variants and variants with opposite effect. The present study focuses on identifying rare variant associated with the disease.Resultswe present a robust approach to identify rare variant using weighted entropy theory.This approach here takes the proportion of the minor allele among all k variants as its probability distribution, which reduces the noise incurred by non-causal variants, and uses a weight to strike a balance between deleterious rare variants and protective rare variants, which makes our method impacted less by variants with opposite effect. Through simulation studies, we investigate the performance of our method for rare variant association analyses as well as for common variant association analyses and compared it with Burden test and the SKAT-O test. Simulation study show that the proposed method is valid and outperform two existing methods. Meanwhile, the proposed method is affected slightly by non-causal variants and opposite effect variants with high and stable power for various paraments set.ConclusionsWe conclude that the proposed method here can be used effectively to detect rare variant associated with the disease.

A Consistent BGK Model with Velocity-Dependent Collision Frequency for Gas Mixtures

We derive a multi-species BGK model with velocity-dependent collision frequency for a non-reactive, multi-component gas mixture. The model is derived by minimizing a weighted entropy under the constraint that the number of particles of each species, total momentum, and total energy are conserved. We prove that this minimization problem admits a unique solution for very general collision frequencies. Moreover, we prove that the model satisfies an H-Theorem and characterize the form of equilibrium.

On Entropy-type Measures and Divergences with Applications in Engineering, Management and Applied Sciences

In this work we review Entropy-type measures and Divergences, discuss their properties and unfold their diverse applicability. In addition, we compare distances between populations and distributions via weighted Entropy-type measures relying mainly on Relative Entropy and Jeffrey’s Distance with weights. Finally, we introduce the Absolute Weighted Relative Entropy and the Absolute Weighted Jeffrey’s Distance. Two applications are presented for illustration, one from Geosciences and one from Financial Mathematics.