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Example 1.9: Entropies of the binary symmetric channel (BSC). The BSC is constructed with two inputs (x1 , x2 ) and two outputs (y1 , y2 ), with alphabets over the range A = {0, 1}. The symbol probabilities are P(x1 ) = and P(x2 ) = 1 , and the transition probabilities are P(y1 /x2 ) = P(y2 /x1 ) = p and P(y1 /x1 ) = P(y2 /x2 ) = 1 p (see Figure 1.10). This means that the error probability p is equal for the two possible symbols. The average error probability is equal to P = P(x1 )P(y2 /x1 ) + P(x2 )P(y1 /x2 ) = p + (1 ) p = p The mutual information can be calculated as I (X, Y ) = H (Y ) H (Y / X ) The output Y has two symbols y1 and y2 , such that P(y2 ) = 1 P(y1 ). Since P(y1 ) = P(y1 /x1 )P(x1 ) + P(y1 /x2 )P(x2 ) = (1 p) + p(1 ) = p + p p = + p 2 p the destination or sink entropy is equal to H (Y ) = P(y1 ) log2 = 1 1 + [1 P(y1 )] log2 = P(y1 ) [1 P(y1 )] [P(y1 )] (36)

Find the entropy rate of the edge process {Yi }. 4.27 Entropy rate. Let {Xi } be a stationary {0, 1}-valued stochastic process obeying Xk+1 = Xk Xk 1 Zk+1 , where {Zi } is Bernoulli(p)and denotes mod 2 addition. What is the entropy rate H (X) 4.28 Mixture of processes. Suppose that we observe one of two stochastic processes but don t know which. What is the entropy rate Speci cally, let X11 , X12 , X13 , . . . be a Bernoulli process with parameter p1 , and let X21 , X22 , X23 , . . . be Bernoulli(p2 ). Let = 1 2 with probability with probability

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Using information, motivational enhancement, and skills training to reduce the risk of HIV infection for low-income urban women: A second randomized clinical trial Health Psychology, 19, 3 1 1 Carey, M P, Carey, K B, & Kalichman, S C (1997) Risk for human immunode ciency virus (HIV) infection among adults with a severe mental disorder Clinical Psychology Review, 17, 271 291 Carey, M P, Carey, K B, Maisto, S A, Gleason, J R, Gordon, C M, & Brewer, K K (1999) HIV-risk behavior among outpatients at a state psychiatric hospital: Prevalence and risk modeling Behavior Therapy, 30, 389 406 Carey, M P, Carey, K B, Maisto, S A, Gordon, C M, & Vanable, P A (2001) Prevalence and correlates of sexual activity and HIV-related risk behavior among psychiatric outpatients Journal of Consulting and Clinical Psychology, 69, 846 850.

Carey, M P, Maisto, S A, Kalichman, S C, Forsyth, A D, Wright, E M, & Johnson, B T (1997) Enhancing motivation to reduce the risk of HIV infection for economically disadvantaged urban women Journal of Consulting and Clinical Psychology, 65, 531 541 Carey, M P, Weinhardt, L S, & Carey, K B (1995) Prevalence of infection with HIV among the seriously mentally ill: Review of the research and implications for practice Professional Psychology: Research and Practice, 26, 262 268 Catz, S L, & Kelly, J A (2001) Living with HIV disease In A Baum & J Singer (Eds), Handbook of health psychology (pp 841 850) Hillsdale, NJ: Erlbaum Catz, S L, Kelly, J A, Bogart, L M, Benotsch, E G, & McAuliffe, T L (2000).

Measurements of particulate nitrate have been performed during both ISCAT 1998 and ISCAT 2000, with the second eld campaign yielding concentrations about four times as high (150 ng m 3 ) as the rst one (39 ng m 3 ) [73]. These values suggest a stronger continental in uence in 2000 than in 1998. The origin of aerosol NO cannot be easily identi ed. Possible 3 sources are lightning, NOx inputs from the lower stratosphere and long-range transport of peroxyacetylnitrate (PAN) within the southern hemisphere [73]. At coastal stations nitrogen aerosol in the form of ammonium originates, apart from biogenic oceanic emissions, from the ornithogenic (i.e. guano-enriched) soils as a consequence of the local penguin population [74]. Ornithogenic soils and the bacterial decomposition of uric acid are a source of ammonium, oxalate and potassium and calcium aerosol.

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Patterns, correlates, and barriers to medication adherence among persons prescribed new treatments for HIV disease Health Psychology, 19, 124 133 Celentano, D D, Bond, K C, Lyles, C M, Eiumtrakul, S, Go, V F, Beyrer, C, et al (2000) Preventive intervention to reduce sexually transmitted infections: A eld trial in the Royal Thai Army Archives of Internal Medicine, 160, 535 540 Celentano, D D, Nelson, K E, Lyles, C M, Beyrer, C, Eiumtrakul, S, Go, V F, et al (1998) Decreasing incidence of HIV and sexually transmitted diseases in young Thai men: Evidence for.

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