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As described above (See Section 3), several techniques are available for inducing differentiation of ES cells in the absence of self-renewing agents, and the resulting mixture of cells can be enriched for a speci c combination of surface receptor expression by one of the above isolation techniques. The cells derived by these means must be characterized to validate gene expression, phenotype, and in vivo functionality. Recently, we established the successful isolation of endothelial cells from human ES cells [Levenberg et al., 2002]. The isolation procedure was as follows. The hES cells were grown on gelatin-coated dishes over mitomycin-treated MEF. The growth medium consisted of 80% KO DMEM and 20% KO serum-free formulation, with glutamine, and supplements of -mercaptoethanol, bFGF, LIF, and nonessential amino acids [Schuldiner et al., 2000]. To form EB aggregates, the cells were dissociated with 1 mg/ml collagenase type IV and grown in Petri dishes. EBs at 13 15 days were dissociated with trypsin and incubated with uorescently labeled CD31 antibody for 30 min before cell sorting with a FACStar ow sorter. The CD31+ cells were replated and grown in vitro in endothelial cell growth medium.

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latent transition models In order to assess the statistical power of any test involving the G2, the distribution of the G2 under the alternative hypothesis, called the noncentral distribution, is needed As the central distribution of G2 is unknown when the contingency table is sparse, it follows that the noncentral distribution is unknown as well Of course, the usual factors that affect statistical power operate in this context namely, sample size, choice of alpha, and effect size which in model selection is the overall difference between the true model and the model under consideration It is possible that the Bayesian posterior predictive check distribution approach to hypothesis testing discussed above will provide an avenue for assessing statistical power for latent class models Sample Size and Related Considerations In addition to statistical power considerations, other sample size considerations come up in LCA and LTA.

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Sparseness can take a toll on parameter estimation Several simulation studies (Collins et al, 1993; Collins & Tracy, 1997; Collins & Wugalter, 1992) have demonstrated that parameter estimation in LTA remains unbiased even in very sparse data tables However, the standard errors of certain parameters can become unacceptably large This is particularly true for the parameters, as these transition probabilities are conditioned on the latent class membership and latent status membership at Time 1, and thus often based on considerably smaller Ns than the other parameters In addition, identi cation problems become more frequent as sparseness increases This means that researchers who are faced with small samples currently are unlikely to be able to make use of LCA and LTA in their current forms The problems with small samples are due to a lack of information Naturally, small samples contain less information than do large samples.

More work needs to be done in the area of latent class and latent transition models applied to small samples A Two-Sequence Latent Class Model Previously in this chapter we discussed models using discrete or continuous exogenous variables to predict latent class membership Flaherty and Collins (1999) have developed LTA models in which one stage sequence (eg, substance use) can be used to predict another (eg, depression) This twosequence model can address a number of interesting research questions Suppose we wish to examine initial level and changes in depression (eg, as modeled in our example discussed previously) conditional on initial level and changes in substance use behavior Some questions may pertain to a single time of measurement For example, how are people in.

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All operations performed in the calculation of this generator polynomial are done in GF(28 ). This is the generator polynomial of RS codes CRS (255, 251), CRS (28, 24) and CRS (32, 28). As explained above, systematic encoding of a given message polynomial m(X ) consists in taking the remainder polynomial of the division of X 4 m(X ) by g(X ). This remainder polynomial is of degree 2t 1 or less, and represents the 4 bytes added by this encoding. As a result of both shortened RS codes having the same generator polynomial, in this concatenated scheme, the code vector generated by the outer code, the shortened RS code CRS (28, 24), has to be altered, in order to conveniently enable operation of the second encoder. This is so because, as said above, the generator polynomial for both shortened RS codes in this concatenation is the same. Indeed, after the encoding of a vector of 24 bytes into a code vector of 28 bytes, the resulting code vector belongs to the code, and so it is a multiple of g(X ). Even after shifting by 4 bytes the positions of this code polynomial before the second encoding, it is very likely that the shifted code vector of the inner code is still a code vector of the shortened

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