Please answer anything you can!!
248 Dynamic Systems Biology Modeling and Simulation IMPULSE INPUT 2 4 EXPONENTIAL INPUT 8 Fig. 5.23 E5.3 For the following two multicompartment models (Fig. 5.23), initial conditions (ICs) are zero everywhere and all k arrows (edges) shown are nonzero a) Determine how many distinct, nonconstant modes can be measured at each of the outputs y2. ?3sy5 and y6, given the inputs at the input arrows shown, impulse on State any assumptions needed about the eigenvalues of the solutions, and possibly b) Repeat part (a), but with two nonzero ICs, namely: yi0)-1 and yd0)-1. The the left and a single-exponential input on the right. also the single-exponential input. rest are zero c) Repeat part (a) again, with all ICs-0, but step inputs in both places. d) In Part (a), suppose the exponential input has an exponent identical to one of the poles of the transfer function of the compartment model structure. How does this change the answers to (a)? Use transfer function analysis to answer this. e) Are there any cycles in these models? Where? simultaneous impulse inputs into compartments 1 and 9? probe any node (compartment) in the network model schematized in Fig. 5.25 answer to the following questions. Some questions have more than one in all 8 nodes (compartments) E5.4 In Fig. 5.24, how many modes can be measured at each of the named outputs, given E5.5 You are given lab instrumentation for generating any input function with which to You also can measure the dynamic response from any node. Answer and explain your possible answer, or maybe none at all. Unless otherwise specified, all initial conditions are zero a) You measure a single exponential mode from the output port of node 3. What is the only possible input function that could generate this output from 3, and where must it be applied (to what node)? 248 Dynamic Systems Biology Modeling and Simulation IMPULSE INPUT 2 4 EXPONENTIAL INPUT 8 Fig. 5.23 E5.3 For the following two multicompartment models (Fig. 5.23), initial conditions (ICs) are zero everywhere and all k arrows (edges) shown are nonzero a) Determine how many distinct, nonconstant modes can be measured at each of the outputs y2. ?3sy5 and y6, given the inputs at the input arrows shown, impulse on State any assumptions needed about the eigenvalues of the solutions, and possibly b) Repeat part (a), but with two nonzero ICs, namely: yi0)-1 and yd0)-1. The the left and a single-exponential input on the right. also the single-exponential input. rest are zero c) Repeat part (a) again, with all ICs-0, but step inputs in both places. d) In Part (a), suppose the exponential input has an exponent identical to one of the poles of the transfer function of the compartment model structure. How does this change the answers to (a)? Use transfer function analysis to answer this. e) Are there any cycles in these models? Where? simultaneous impulse inputs into compartments 1 and 9? probe any node (compartment) in the network model schematized in Fig. 5.25 answer to the following questions. Some questions have more than one in all 8 nodes (compartments) E5.4 In Fig. 5.24, how many modes can be measured at each of the named outputs, given E5.5 You are given lab instrumentation for generating any input function with which to You also can measure the dynamic response from any node. Answer and explain your possible answer, or maybe none at all. Unless otherwise specified, all initial conditions are zero a) You measure a single exponential mode from the output port of node 3. What is the only possible input function that could generate this output from 3, and where must it be applied (to what node)
