Problems
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response, but the response can act back on itself. Feedback may be instantaneous or
delayed. When action strength is physically limited, positive feedback systems will
saturate. Feedback systems can have quasi-stable states (configurations which are
centered around steady conditions). For example, there may be two different quasistable conditions (‘bistable’), which is the basis for digital computer memory units
(‘flip-flop’ devices) for temporarily storing a single bit of information.
A number of questions arise in the study of regulatory systems:
1. What are the probabilities for each possible quasi-stable state?
2. What is the response or delay time for various loops in the regulation, compared
to associated activity times?
3. Do oscillations between quasi-stable states occur for the expected range of
parameters being controlled by the system? If not, is the system close to such
oscillations?
4. Will sporadic solutions 14 occur in the expected range of the parameters being
controlled?
5. If the system is perturbed, what is the lifetime of the perturbation before quasistability is restored, and how does this lifetime compare with associated activity
times?
6. To what degree might the system be disturbed before regulation fails?
7. How robust is the regulation? If parts of the network are blocked or mutated,
will the system still be capable of regulation? Are there alternate pathways in
the scheme?
8. Are there repair and/or recovery mechanisms?
9. Is the regulatory system transformable under changes in the environment? If so,
how rapid is this response compared to times typical to environmental changes?
10. Are there any other nearby or distantly related optimal schemes for the same
regulation?
Mathematical models of regulatory systems permitting at least numerical and
approximate solutions have been successful in discovering subtle properties. Sometimes, even very simple models carry much of the system’s behavior. Mathematical
models based on the dynamical behavior of emergent agents in the physical system
may be difficult to solve, but are worthy of exploration, helping us use the model for
predictions and for alternate designs.
Problems
12.1 If your brain during heavy thinking releases 90 W of heat into air at temperature 22 ◦ C, while during little thinking it releases 70 W, estimate the maximum order
(measured by drop in entropy) your brain could have produced each second?
14 Chaos may develop in non-linear systems. See Chap. 15.
555
response, but the response can act back on itself. Feedback may be instantaneous or
delayed. When action strength is physically limited, positive feedback systems will
saturate. Feedback systems can have quasi-stable states (configurations which are
centered around steady conditions). For example, there may be two different quasistable conditions (‘bistable’), which is the basis for digital computer memory units
(‘flip-flop’ devices) for temporarily storing a single bit of information.
A number of questions arise in the study of regulatory systems:
1. What are the probabilities for each possible quasi-stable state?
2. What is the response or delay time for various loops in the regulation, compared
to associated activity times?
3. Do oscillations between quasi-stable states occur for the expected range of
parameters being controlled by the system? If not, is the system close to such
oscillations?
4. Will sporadic solutions 14 occur in the expected range of the parameters being
controlled?
5. If the system is perturbed, what is the lifetime of the perturbation before quasistability is restored, and how does this lifetime compare with associated activity
times?
6. To what degree might the system be disturbed before regulation fails?
7. How robust is the regulation? If parts of the network are blocked or mutated,
will the system still be capable of regulation? Are there alternate pathways in
the scheme?
8. Are there repair and/or recovery mechanisms?
9. Is the regulatory system transformable under changes in the environment? If so,
how rapid is this response compared to times typical to environmental changes?
10. Are there any other nearby or distantly related optimal schemes for the same
regulation?
Mathematical models of regulatory systems permitting at least numerical and
approximate solutions have been successful in discovering subtle properties. Sometimes, even very simple models carry much of the system’s behavior. Mathematical
models based on the dynamical behavior of emergent agents in the physical system
may be difficult to solve, but are worthy of exploration, helping us use the model for
predictions and for alternate designs.
Problems
12.1 If your brain during heavy thinking releases 90 W of heat into air at temperature 22 ◦ C, while during little thinking it releases 70 W, estimate the maximum order
(measured by drop in entropy) your brain could have produced each second?
14 Chaos may develop in non-linear systems. See Chap. 15.