In going from the state space model i(t)=A.(t)+ Bu(t y(t)= Ca(t)+ Du(t) to the transfer function G(s)=C(sI -A)-B+D need to form the inverse of the matrix(sI- A)-a symbolic inverse- not easy at all For simple cases, we can use the following

This is a bit strange, because previously our figure of merit when comparing one state-space model to another(page 8-8)was whether they reproduced the same same transfer function Now we have two very different models that result in the same transfer function

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1. Model of Communication System Noise Source Sink T Channel T: Transformation Source, sink, and channel are given beforehand Transformation to match the source with the channel

Sliding Filament Model Myosin head Myosin filament Actin binding site Actin filament As the actin filament sin filament. the Rate constants k myosin head can bind to it at the red triangl

3. 1 The AE-NI Model 支出收入模型

Alternative views on gradient sensing Postma and van hastert. 'a diffusion-translocation model for gradient sensing by chemotactic cells Biophys.J.81,1314(2001) Levchenko and Iglesias. Models of eukaryotic gradient sensing: applications to chemotaxis of amoeba and neutrophils

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Assumptions of the classical Linear Model (Clm) e So far, we know that given the Gauss Markov assumptions, OLS IS BLUE e In order to do classical hypothesis testing we need to add another assumption(beyond the Gauss-Markov assumptions) Assume that u is independent of x,x2…,xk and u is normally distributed with zero mean and variance 0: u- Normal(0, 02) Economics 20- Prof anderson

Testing for AR(IS eria Correlation Want to be able to test for whether the errors are serially correlated or not Want to test the null thatp=0 in u,=pu, 1 +et=2.. where u is the model error