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knowledge management, or legal reasoning. Although the legal domain remains very sensitive to the features of particular statutes and regulations, some of the Legal-Core Ontologies (LCO) are intended to share a common kernel of legal notions. LCO remain in the domain of a general knowledge shared by legal theorists, national, or international jurists and comparative lawyers.

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To understand how we can reduce the redundant data update overhead, we rst need to study the computation of the redundant blocks using the RSE code. Let B be the total number of xed-size media data blocks in the system and denote the jth block of a media object by v j . For simplicity we consider only one media object in the rest of the section. The results can be readily extended to multiple media objects.

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Let (N h) and h be the number of data nodes and redundant nodes in the system respectively. Assuming the number of redundant nodes in the system is xed, then we can apply the (N , h)-RSE code to compute the h redundant data blocks in each group of (N h) data blocks using di,0 f 1,1 f 1,2 f 1,3 . . . f 1,N h f 2,1 f 2,2 f 2,3 . . . f 2,N h di,1 F D= . . . . . . . . . . . . . . . f h,1 f h,2 f h,3 . . . f h,N h di,N h 1 1 1 1 ... 1 di,0 1 2 3 ... N h di,1 = . (15.2) . . . . . . . . . . . . . . 1 2h 1 3h 1 ci,0 ci,1 = . =C . . ci,h 1 . . . (N h)h 1 di,N h 1

However, our data indicate that there is a kind of speci c legal knowledge, which belongs properly to the legal and judicial culture, and that is not being captured by the current LCO.

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ME: [silence] HARVEY: [silence] GEORGE: This year we ll walk away from 60 million dollars in possible management fees that we could just pay out to ourselves in this office Instead of putting that sixty million dollars in our own pockets, we ll reinvest it, we ll put it to work That sixty million by the end of next year might be worth eighty million And guess what We get a cut of the profits So if we do well, we get paid well Do you see how charging a management fee like 2 percent would reward us even if we were not performing well ME: [silence] HARVEY: George, I think he s still thinking about the sixty million dollars GEORGE: Ha! I don t blame him My wife thinks about it all the time But, think, Harry Think about it for a moment.

where the F, D, and C are the Vandermonde matrix [4], the media data vector, and the redundant data vector respectively; and di, j , ci,k represent data block j ( j = 0, 1, . . . , N h 1) and redundant block k (k = 0, 1, . . . , h 1) of parity group i. Elements in F are constants computed from f i, j = j i 1 . Note that the matrix multiplication in equation (15.2) is computed over Galois Fields of 2w where N < 2w . For example, by setting w = 16, then the code can support up to 65,535 nodes. Reconsider the generation of a redundant data block before and after addition of one data node in Figure 15.11 and Figure 15.12 respectively. We can observe that in many cases, the reorganized parity group still comprises some data blocks from the original parity group before reorganization. For example, in expanding a system from N nodes to N + 1 nodes, the rst parity group will be reorganized from the composition of {v0 , v1 , . . . , v N h 1 } to {v0 , v1 , . . . , v N h 1 , v N h }, which differs by only one data block v N h . This means that the resultant matrix computations in equation (15.2) will differ by only one variable in the data vector. This raises the question of whether we can reuse the original redundant data in computing the new redundant data, discussed next. Consider the original con guration in Figure 15.11. The rst two redundant data in redundant node r1 , denoted by c0,1 and c1,1 , are computed from

c0,1 =