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, cytokines) or cell-associated signals (ie, insoluble extracellular matrix or membrane-bound molecules), in the coculture effect have not yet been clearly de ned An understanding of the mechanisms mediating the stabilization of hepatocytes in coculture would have broad implications in liver cell biology and, speci cally, would aid in the development of functional hepatic tissue constructs In addition to static culture systems, several bioreactor designs have also been developed as in vitro hepatocyte culture models Perfusion systems would facilitate enhanced nutrient delivery to hepatocytes, which are highly metabolic, and additionally, in contrast to a batch process, would enable the continuous processing of blood or serum, potentially useful for extracorporeal devices Overall, the bioreactor systems developed to date fall into the following categories: at plate, hollow ber, perfusion scaffolds, and packed beds, each with accompanying advantages and disadvantages [Allen et al, 2001] (Fig 152).

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In particular, the combination of a at plate reactor system with sandwich culture or coculture has been illustrated to improve hepatocyte stability for long-term analysis [Bader et al, 1995; Tilles et al, 2001] Additionally, a recent three-dimensional perfusion bioreactor system has been developed based on the morphogenesis of hepatocytes into three-dimensional structures in an array of channels [Powers et al, 2002a,b] Similar to static culture.

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This equation asserts that there is a linear relationship between y on the one hand and some function of x on the other. Now, 1 is a model parameter, so that it is a constant whose value is unknown. Is there some value that 1 could take such that if 1 took that value, there would no longer exist a linear relationship between xand y Consider what would happen if 1 were zero. Then the regression equation would be y = 0 + (0)x + In other words, when 1 = 0, the regression equation becomes y = 0 + That is, a linear relationship between x and y no longer exists. On the other hand, if 1 takes on any conceivable value other than zero, a linear relationship of some kind exists between the response and the predictor. Much of our regression inference in this chapter is based on this key idea: that the linear relationship between x and y depends on the value of 1 .

+ c vec(A)vec(A)']Dm)-1

where (a) follows from the de nition of entropy rate of a stationary process, (b) follows from Fano s inequality, (c) follows from the data processing inequality (since V n X n Y n V n forms a Markov chain) and (d) follows from the memorylessness of the channel. Now letting n , we have Pr(V n = V n ) 0 and hence H (V) C. (7.150)

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Fig. 2.5 Rainfall becoming recharge: sketch graphs illustrating the nature of the time-lags and attenuation ( smearing ) of the rainfall signal which occurs as recharge moves through the unsaturated zone to reach the water table. The shading patterns used in the top portion of the plot (identifying individual rain storms) is maintained in the lower portion, to show when the water introduced by each storm actually arrives at the water table. Note that although rainfall is discontinuous, time-lag and attenuation result in a continuous (if variable) input of recharge from late September onwards. (The time-scales shown here assume a relatively thin unsaturated zone in permeable strata; time-lags are likely to be much greater in other circumstances.)

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Therefore, the minimum distance of a linear block code Cb (n, k) is the minimum value of the weight of the non-zero codewords of that code. As an example, the linear block code analysed in previous examples has minimum distance dmin = 3, because this is the minimum value of the weight evaluated over all the non-zero codewords of this code (see Table 2.1).