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Extra info for [Article] A note on joint versus gene-specific mixed model analysis of microarray gene expression data

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Proof. 1). Testing the condition ( ∃! j ∈[1, p]) ( n j == n′j + 1) ∧ ( ∀i ≠ j ) ( ni == ni′) is of complexity O(p). Testing the 38 DISTRIBUTION OF COMPUTATIONS WITH CONSTANT PERFORMANCE MODELS condition ( ∃ i ∈[1, p]) ( ni < ni′) is also of complexity O(p). Finally, the total number of iterations of the inner loop of the nest of loops for (i=1; i≤p; i=i+1) for (Δ=ni− ni′ ; Δ≠0; Δ=Δ−1, w=w−1) dk−w=i; cannot exceed the total number of allocations of elements, n. Thus, the overall complexity of the algorithm is upper bounded by n × O(p × log2 p) + n ×O (p) + n × O(p) + p × n × O(1) = O(p × n × log2 p).

18 PROGRAMMING ISSUES After a brief decline in popularity, distributed memory machines containing large numbers of processors have returned to fulfill the promise of delivering high performance to scientific applications. While it would be most convenient for application scientists to simply port their message passing interface (MPI) codes to these machines, perhaps instrument them with a global checkpointing system, and then sit back and enjoy the performance improvements, there are several features of these machines and their typical operating environments that render this impossible: • • • Large Numbers of Processors Mean More Failures.

Thus, the overall complexity of the algorithm is upper bounded by n × O(p × log2 p) + n ×O (p) + n × O(p) + p × n × O(1) = O(p × n × log2 p). 6. The complexity of the Reverse algorithm is a bit worse than the complexity of the DP algorithm. At the same time, as we will see in the next chapter, the Reverse algorithm is better suitable for further extensions to more complicated, nonconstant performance models of heterogeneous processors. Other algorithms of partitioning well-ordered sets, such as the one presented in Barbosa, Tavares, and Padilha (2000), do not guarantee the return of an optimal solution.

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