Genome‐wide detection of CNVs associated with beak deformity in chickens using high‐density 600K SNP arrays

Beak deformity (crossed beaks) is found in several indigenous chicken breeds including Beijing‐You studied here. Birds with deformed beaks have reduced feed intake and poor production performance. Recently, copy number variation (CNV) has been examined in many species and is recognized as a source of genetic variation, especially for disease phenotypes. In this study, to unravel the genetic mechanisms underlying beak deformity, we performed genome‐wide CNV detection using Affymetrix chicken high‐density 600K data on 48 deformed‐beak and 48 normal birds using penncnv . As a result, two and eight CNV regions (CNVRs) covering 0.32 and 2.45 Mb respectively on autosomes were identified in deformed‐beak and normal birds respectively. Further RT‐qPCR studies validated nine of the 10 CNVRs. The ratios of six CNVRs were significantly different between deformed‐beak and normal birds (P < 0.01). Within these six regions, three and 21 known genes were identified in deformed‐beak and normal birds respectively. Bioinformatics analysis showed that these genes were enriched in six GO terms and one KEGG pathway. Five candidate genes in the CNVRs were further validated using RT‐qPCR. The expression of LRIG2 (leucine rich repeats and immunoglobulin like domains 2) was lower in birds with deformed beaks (P < 0.01). Therefore, the LRIG2 gene could be considered a key factor in view of its known functions and its potential roles in beak deformity. Overall, our results will be helpful for future investigations of the genomic structural variations underlying beak deformity in chickens.     

The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting . It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting , in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions.