Negative Feedback Loops. Suppose some quantities -*1 (0 , x2(t), ...,*(/) can be modeled by differential equations of the formdx i * = -* 1' 1bxndx2 ~dtdxn dt= X\ - k2X2xn 1 ~ ' knXnwhere b is positive and the kt are positive. (The matrix of this system has negative numbers on the diagonal, 1 s directly below the diagonal, and a negative number in the top right comer.) We say that the quantities x\.......xn describe a (linear) negative feedback loop. a. Describe the significance of the entries in this system, in practical terms. b. Is a negative feedback loop with two components (n = 2) necessarily stable? c. Is a negative feedback loop with three components necessarily stable?

Chapter 7 The basics of sampling The important terminology: o Population: entire set of people you are interested in. o Sample: the subset of people you actually study. o Census: a study that involves the entire population. IMPORTANT QUESTION: Do your findings generalize from your sample to your population Representative Sample Representative sample: all members of the population have an equal chance of being included in the sample. o Good external validity, generalizability. o Difficult to accomplish. Bias (unrepresentative) sample: some people in the population have a much better chance being included in the sample than others. Biased Sample 2 types of biased samples: o Convenience sample: sampling f