When linear and weak discrepancy are equal

When linear and weak discrepancy are equal

The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable, then |hL(x)− hL(y)| ≤ k. Whereas the weak discrepancy is the least k such that there is a weak extension W of P such that if x and y are incomparable, then |hW (x)− hW (y)| ≤ k. This paper resolves a question of Tanenbaum, Trenk, and Fishburn on characterizing w...

When some are more equal than others.

Linear And Hereditary Discrepancy

Let A be a m n{matrix. Linear and hereditary discrepancy are deened as lindisc(A) := maxfminfkA(p ")k 1 j " 2 ff1; 1g n g jp 2 1; 1] n g herdisc(A) := maxfminfk(a ij) i2m];j2J "k 1 j " 2 ff1; 1g n g jJ n]g: We're investigating connections between the two concepts. Best results known are lindisc(A) 2(1 2 2 n) herdisc(A) for any matrix A and an example of an A satisfying lindisc(A) = 2(1 1 n+1) h...

Linear Discrepancy and Bandwidth

The linear discrepancy of a partially ordered set P = (X;), denoted by ld(P), is the least integer k for which there exists an injection f : X ! Z satisfying (i) if x y, then f (x) < f (y); and (ii) if x and y are incomparable, then jf(x)?f(y)j k. There is an apparent connection between ld(P) and the bandwidth of the incomparability graph of P. We prove that, in fact, these two quantities are a...

All linear methods are equal } and extendible to ( some ) nonlinearities

Several linear methods of residual generation for fault detection and diagnosis are reviewed. The parity relation approach is introduced in some detail, for both additive and parametric faults. The Chow–Willsky scheme, various diagnostic observers and principal component analysis are compared to the additive version. The ‘local approach’ and the least-squares estimation of parameter changes are...