In this note we provide alternative proofs for the classical Bode and Poisson type sensitivity integrals and their extensions for both continuous-time and discrete-time systems. Our derivation uses the wellknown properties of Laplace and Z-transformations. This derivation helps establish a connection between Bode and Poisson type sensitivity integrals and Laplace and Z-transforms, hence providing an alternative perspective in interpreting these fundamental integral results.
In leaves of A. thaliana, there exists an intricate network of epidermal surface layer cells responsible for anatomical stability and vigor of flexibility to the entire leaf. Rho GTPases direct this organization of cell polarity, but full understanding of the underlying mechanisms demands further inquiry. We conduct two experiments: (1) a novel procedure is proposed that could be used in other life and plant science studies to quantify microtubule orientation, and (2) shape analysis. We hypothesize ARK2 as a putative interactor in cell polarity maintenance through stabilization of microtubule ordering. We are the first to automate pavement cell phenotype analysis for cell polarity and microtubule orientation. Breakthroughs in the signaling network regulating leaf cell polarity and development will lead science into the frontier of genetically modifying leaves to dramatically increase Earth's plant biomass; impending food shortages in the 21st century will be well served by such research.
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