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One of the basic laws of physics, the second law of thermodynamics, states that the entropy of an isolated system is nondecreasing. We now explore the relationship between the second law and the entropy function that we de ned earlier in this chapter. In statistical thermodynamics, entropy is often de ned as the log of the number of microstates in the system. This corresponds exactly to our notion of entropy if all the states are equally likely. But why does entropy increase We model the isolated system as a Markov chain with transitions obeying the physical laws governing the system. Implicit in this assumption is the notion of an overall state of the system and the fact that knowing the present state, the future of the system is independent of the past. In such a system we can nd four different interpretations of the second law. It may come as a shock to nd that the entropy does not always increase. However, relative entropy always decreases. 1. Relative entropy D( n || n ) decreases with n. Let n and n be two probability distributions on the state space of a Markov chain at time n, and let n+1 and n+1 be the corresponding distributions at time n + 1. Let the corresponding joint mass functions be denoted by p and q. Thus, p(xn , xn+1 ) = p(xn )r(xn+1 |xn ) and q(xn , xn+1 ) = q(xn )r(xn+1 |xn ), where r( | ) is the probability transition function for the Markov chain. Then by the chain rule for relative entropy, we have two expansions: D(p(xn , xn+1 )||q(xn , xn+1 )) = D(p(xn )||q(xn )) + D(p(xn+1 |xn )||q(xn+1 |xn ))
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If your design calls for control of individual movie clips, the actions in this book are what you need. You can add actions that make it possible for you to modify one or more properties of a movie clip, enable you to clone a movie clip, allow the user to drag a movie clip, and more.
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measure. One s psychological impairment, however, cannot de nitively be determined in the same way that a physical impairment can be detected by diagnostic imaging techniques, so proxy criteria often are used as alternatives. Another option frequently used in studies of response distortion is the analogue study. In this approach, the investigator randomly assigns the sample to one of two conditions: instructions to respond honestly or instructions to distort responses. In a typical analogue study, the experimenter would administer a scale or measure to a sample. Half of the participants would be given instructions to respond as honestly as possible. The other half would be instructed to use a particular response set (e.g., you are attempting to convince the evaluator that you have a severe mental illness). The mean scores of the two groups would be compared to determine whether there were signi cant differences, and the presence of such a difference would be interpreted as evidence of the scale s ability to distinguish honest from nonhonest (malingering) responders. Rogers (1997) also recommended that subjects in analogue research on malingering and deception be debriefed following their participation in an experiment for two reasons: (a) to ensure they understood and complied with the instructions, and (b) to explore at least qualitatively the different strategies that people may use to portray themselves as being more or less troubled than they actually are. What are the problems with analogue research It is perhaps not surprising that any reasonably designed scale for assessment of exaggerated symptoms will show large differences between normal participants asked to respond honestly (who presumably would have few if any symptoms), and honest participants asked to appear pathological (who presumably would seek to report a signi cant number of symptoms). In any applied context, the between-groups distinction is likely to be much more dif cult, particularly because some people who minimize or exaggerate their problems do have actual symptoms or disorders. Someone who uses malingering as a response style may still have a serious mental disorder. Thus, on its face the analogue study in this context would not appear to be a very rigorous test for the validity of a measure. This dilemma is further compounded by two problems one conceptual and the other motivational inherent in the analogue design. The conceptual problem is one that some have previously referred to as the simulation-malingering paradox: That is, the design uses information obtained from individuals who comply with instructions to respond dishonestly to make inferences about people who do not comply with instructions to respond honestly. Arguably, this raises a question about generalizability. Further threatening external validity are the potential differences in motivation and
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FIGURE 3-8: Mini DIN 8 and DB-9 cables in the third-hand tool, stripped and tinned for the circuit
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Proof of Theorem 16.7.1: We will prove the theorem for m = 2. The proof extends in a straightforward fashion to the case m > 2. Denote the stocks by 1 and 2. The key idea is to express the wealth at time n,
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A second category of frequently used medications is antidepressants, including tricyclics (Tofranil) and selective serotonin reuptake inhibitors (Prozac). These medications have proven to be effective in many double-blind studies, though not more so than cognitive behavior therapy or manualized interpersonal psychotherapy, according to NIMH clinical trials. Nevertheless, they have brought about a fundamental change in the practice of outpatient psychiatry, which is much more involved with adjusting drug regimens and less involved with psychotherapy than it used to be (Shorter, 1997). Lithium seems an effective treatment for manic states and also has prophylactic value in managing bipolar disorder. Again, while clinicians have made contributions to this area (Jamison, 1992; Jamison & Akiskal, 1983), its administration was a medical responsibility. The same thing can be said about methylphenidate or Ritalin, the most frequently prescribed drug for children, used in the treatment of attention de cit hyperactivity disorder (ADHD). Clinical psychologists have been involved in evaluating the effects of stimulant drugs (Conners, Sitarenios, Parker, & Epstein, 1998) and in determining whether behavior therapy can be an effective treatment. Barkley (1990) used Ritalin to examine the parent child relations in children with ADHD. The parents of these children tend to be overcontrolling but are less so when their child is on Ritalin, thus indicating they are responsive to their child s level of hyperactivity. However, not all clinical psychologists were content with restricting their role to research with drugs. During the 1980s, a movement began to permit clinical psychologists with proper additional training to prescribe these medications. The government sponsored a demonstration project to show its feasibility, and with that accomplished a few university training programs began to offer courses that would prepare clinical psychologists to assume that role. Although the majority of clinical psychologists showed little interest in gaining prescription privileges (Piotrowski & Lubin, 1989), that interest may be more broadly kindled in the coming generations. An APA division for psychologists who do have an interest in prescribing psychotropic medications has been recently established. In 1995 APA Division 12, the Society of Clinical Psychology, set up a task force to identify empirically supported psychological interventions for various types of psychopathology. Such an identi cation has decided implications for health service insurers, who can use it to determine if practitioners are entitled to be reimbursed for their services. A listing of such treatments tends to endorse behavior therapy approaches more so than psychotherapy, which has led to understandable anguish among psychotherapists, who believe their effects are not fairly evaluated when overt symptoms are the major focus.
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