Consensus under Misaligned Orientations

This paper presents a consensus algorithm under misaligned orientations, which is defined as (i) misalignment to global coordinate frame of local coordinate frames, (ii) biases in control direction or sensing direction, or (iii) misaligned virtual global coordinate frames. After providing a mathematical formulation, we provide some sufficient conditions for consensus or for divergence. Besides the stability analysis, we also conduct some analysis for convergence characteristics in terms of locations of eigenvalues. Through a number of numerical simulations, we would attempt to understand the behaviors of misaligned consensus dynamics.Comment: 23 pages, 9 figure

Gene Ontology classification into molecular function of all genes significantly (p<0.05) differentially expressed in response to 1 mM and 100 pM melatonin.

<p>Genes were classified into at least one category using AmiGO GO slimmer. The proportion of genes that fall into each category were calculated by dividing the number of genes assigned to a category by the total number of genes that could be classified for each treatment.</p><p>*Indicates Molecular function is unknown.</p

Schematic overview of genes exhibiting a change of 2-fold or more in response to melatonin associated with stress response and signaling.

<p>Fold change in transcript levels is represented by the color scale with darkest blue indicating genes with the greatest increase in transcript levels (4-fold or greater) and darkest red indicating genes with the greatest decrease in transcript levels (at least 4-fold). Each gene involved in stress responses is represented once.</p

Total number of clean and mapped reads and bases for each sample following mRNA-seq.

<p>Sequences were mapped to the Arabidopsis TAIR10 genome using TopHat.</p

Effect of melatonin on paraquat-induced oxidative stress.

<p>Arabidopsis leaves were detached and floated in solution containing 0, 10(top row) or presence (bottom row) of 1 mM melatonin. After 48 hours, leaves exposed to paraquat in the absence of melatonin were photobleached while leaves incubated with melatonin during exposure to paraquat remained green.</p

qRT-PCR analysis confirming overall results of RNA-seq experiments.

<p>The fold changes in transcript levels identified in RNA-seq experiments for 15 selected genes are graphed in A (up-regulated) and C (down-regulated). qRT-PCR was performed using the same samples for RNA-seq experiments with primers for the selected genes showing up-regulated (B) or down-regulated (D) by 1 mM melatonin. All q-RT-PCR were repeated four times. * p<0.05, ** p<0.01, ***p<0.001.</p

Scatter plots show genomic scale reproducibility.

<p>The scatter plots comparing the clean reads of two biological duplicates from control (A), 100 pM melatonin (B) and 1 mM melatonin (C) treatments. Genes are represented by dots. For each gene, the RNA expression level in one rep is given on the x axis and the same gene in the other rep is given on the y axis.</p

Redox-related genes and peroxidases affected by 1 mM melatonin.

<p>Redox-related genes and peroxidases affected by 1 mM melatonin.</p

Cell wall related genes with at least a 2 fold change in expression levels in response to 1 mM Melatonin.

<p>Cell wall related genes with at least a 2 fold change in expression levels in response to 1 mM Melatonin.</p

Receptors, kinases, and genes involved in calcium signaling whose expression levels were affected by 1 mM melatonin by at least 2 fold.

<p>Receptors, kinases, and genes involved in calcium signaling whose expression levels were affected by 1 mM melatonin by at least 2 fold.</p