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Using the same Y outcome vector and applying the same least squares calculation now gives b2 = (1111.11, 11.89, 1104.11) and Y = (11.22, 2.11, 2.78, 2.00) . However, the variance covariance matrix reacts sharply to the movement toward singularity as seen in the standardized correlation matrix: 1196.70 0.48 0.99 0.48 . Cs = 0.48 13.70 0.99 0.48 1193.00 Indeed, if X3 = 2.999, X X is singular (with regard to precision in Gauss and Splus) and we must use the generalized inverse. This produces b3 = GX Y = (1.774866, 5.762093, 1.778596) and Y = XGX Y = (11111.11, 11.89, 11104.11) . The resulting pseudovariance matrix (calculated now from G 2 ) produces larger standard deviations for the rst and third explanatory variables, re ecting greater uncertainty, again displayed as a standardized correlation matrix: 11967.0327987 0.4822391 0.9999999 13.698 0.4818444 . Cs = 0.4822391 0.9999999 0.4818444 11963.3201730 6.8 GENERALIZED CHOLESKY DECOMPOSITION We now describe the classic Cholesky decomposition and recent generalizations designed to handle nonpositive de nite matrices. A matrix C is positive de nite if for any x vector except x = 0, x Cx > 0, or in other words, if C has all positive eigenvalues. Symmetric positive de nite matrices are nonsingular, have only positive numbers on the diagonal, and have positive determinants for all principal leading submatrices. The Cholesky matrix is de ned as V in the decomposition C = V V. We thus construct our pseudovariance matrix as V V, where V = GCHOL(H ), GCHOL( ) is the generalized Cholesky described below, and H is the Moore Penrose generalized inverse of the Hessian.

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DO i=1,M xy=par2(ma(i),xp(i))-par2(pa(i),xp(i)) !mix from !ma & pa par2(keep+ix(i),:)=par2(ma(i),:) ! rst !offspring variable par2(keep+ix(i)+1,:)=par2(pa(i),:) !second !offspring variable par2(keep+ix(i),xp(i))=par2(ma(i),xp(i))-r(i)*xy ! rst offspring variable par2(keep+ix(i)+1,xp(i))=par2(pa(i),xp(i))+r(i)*xy !second offspring variable IF(xp(i)<npar) THEN !Perform crossover when !last variable not selected DO j=1,xp(i) par2(keep+ix(i),j)=par2(keep+ix(i),j) par2(keep+ix(i)+1,j)=par2(keep+ix(i)+1,j) END DO DO j=xp(i)+1,npar par2(keep+ix(i),j)=par2(keep+ix(i)+1,j) par2(keep+ix(i)+1,j)=par2(keep+ix(i),j) END DO END IF END DO par=par2 !_______________________________________________________ ! Mutate the population !Allocate arrays (block 3) ALLOCATE(temp_arr_1(nmut),mrow(nmut),mcol(nmut),ind2 & (nmut),STAT=status) IF(status/=0) THEN WRITE(*,*) Error allocating the arrays of allocation & block 3 of the main program. STOP END IF CALL RANDOM_NUMBER(temp_arr_1) mrow=CEILING(temp_arr_1*(popsize-1))+1 ind2=grade_up(mrow,DIM=1) mrow=mrow(ind2) CALL RANDOM_NUMBER(temp_arr_1) mcol=CEILING(temp_arr_1*npar)

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I am currently working on developing a brand-new product for auto dealers. The business analyst in my organization wrote use cases, but they lacked the ow of the whole system. To get the initial feedback from the dealers about the nal product, we hired a graphic artist to come up with a quick comp for the entire system and provide basic navigation between pages. These comps were developed as simple jpeg images, which were modi ed repeatedly based on the feedback from the dealers. We cannot use these comps in our code, hence they became throwaway prototypes for us. They were ideal for getting the user experience. Then there was another problem in which we needed to export some dealer information to publish on their website, with each website taking data in a different format and using a different protocol for communication (some use form post, some use ftp, some use e-mail, etc.). Since the requirement wasn t clear and was unknown for the future customers, we had to try out a system based on Microsoft s work ow engine, which was just to show that it would be easy to change based on this requirement. Once we understood the technology better and designed the basic structure for this prototype, all the subsequent detailed implementation was based on this initial framework. This is a perfect example of an evolutionary prototype. Atul Menon, Solution Architect

29. Define a language for specifying component configuration directives. These directives supply the component configurator with the information it needs to

The class diagram for the Active Object pattern is shown below:

Intent The Thing-Information pattern eliminates the focus -shifting that occurs during the modeling process by referring to two frequently used foci (thing focus and information focus) in business modeling and how they are related to each other.

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