### Table 2: Di erent Petsc KSP Objects Results complex computation problems has been done with non periodic boundary condition with introduc- ing a decomposition of the operator into a set of homogeneous problems with Dirichlet boundary conditions, solve once for all, and a time dependant inhomogeneous problem with periodic boundary conditions. We attempt to use the PETSc 2.0 library in order to implicit further our scheme. The implementation of the method with this library provides goods accuracy agreement, but not yet good parallelism e ciency.

"... In PAGE 4: ... Once the numerical algorithm will be choosen, we will further enhance the performances of the implementation. Table2 described the results reached with various KSP objects of the Petsc library on the test case matrix. We xed the (r)elative, (a)bsolute, and (d)ivergence tolerances for the convergence.... ..."

### Table 2. An inhomogeneous sample

"... In PAGE 5: ...2 Inhomogeneous Sample: Maximal Indicative Subsets In the inhomogeneous case, a sample does not have a greatest common denominator of abiotic conditions. An example sample (from the Pommeren site) is shown in Table2 , together with the possible values for the three abiotic factors for each plant species. Focusing on the acidity of a terrain shows that Angelica sylvestris and Carex acutiformis, for example, only grow under basic or neutral conditions, whereas, for example, Carex nigra and Carex panicea, found in the same sample, only grow on a slightly or fairly acid site.... ..."

### Table 2. An inhomogeneous sample

"... In PAGE 5: ...2 Inhomogeneous Sample: Maximal Indicative Subsets In the inhomogeneous case, a sample does not have a greatest common denominator of abiotic conditions. An example sample (from the Pommeren site) is shown in Table2 , together with the possible values for the three abiotic factors for each plant species. Focusing on the acidity of a terrain shows that Angelica sylvestris and Carex acutiformis, for example, only grow under basic or neutral conditions, whereas, for example, Carex nigra and Carex panicea, found in the same sample, only grow on a slightly or fairly acid site.... ..."

### Table 2 Computation results of the inhomogeneity indicator.

"... In PAGE 6: ...umination. The pressed cork texture was taken from Ref. 19, and a Gaussian inhomogeneity i~x! was superposed to it according to g~x!5g~x,y!5F2 x ~N21!DxG@t~x!1i~x!# 1const t~x!i~x! x ~N21!Dx . ~26! The computation results of the inhomogeneity indicator are shown in Table2 . Because of the lower harmonic dis- tortion, the computation of H2$%was performed in the frequency domain.... ..."

### Table 1: Inhomogeneous FBDS pool Time

2007

"... In PAGE 15: ...144459 Table 2: Part of risk-neutral cumulative default probabilities instruments in the pool is 15%. The pool structure of the inhomogeneous FBDS is defined in Table1 ; the homogeneous pool has the same structure except that the notional values are 100 for all names. Part of the risk-neutral cumulative default probabilities for different credit ratings are listed in Table 2.... ..."

### Table 2: Estimation of an inhomogeneous variation of the Potts model.

in Estimation of Markov Random Field prior parameters using Markov chain Monte Carlo Maximum Likelihood

"... In PAGE 13: .... Descombes, R. Morris, J. Zerubia, M. Berthod Parameters = 0:53 (N0 = 48070) = 0:5493 (N0 = 35699) Estimates ^ = 0:529 (hN0i = 48072) ^ = 0:5488 (hN0i = 35699) Sample Table 1: Estimation of the Potts model parameter To estimate we have to estimate a, b and c. The associated distribution is written: Pa;b;c(X) = 1 Z(a; b; c) exp 2 4? X c=fs;s0g2C a i + p 2 + b j + q 2 + c xs6 =xs0 3 5 : (26) This model can be written in the form of equation (1): Pa;b;c(X) = 1 Z(a; b; c) exp [?cN0(X) ? bN1(X) ? aN2(X)] ; (27) where: N0(X) = #X; the number of inhomogeneous cliques N1(X) = X inhomogeneous cliques j + q 2 = N0(X) j + q 2 inh:cl: N2(X) = X inhomogeneous cliques i + p 2 = N0(X) i + p 2 inh:cl: Table2 shows samples from this model and the parameters estimated from these samples.... ..."

### Table 2. Estimation of an inhomogeneous variation of the Potts model.

### Table 4: sub-tasks of the inhomogeneous application

### Table 1. Expected and Calculated Properties of the Two Regions in the Inhomogeneous Phantom

2003

"... In PAGE 4: ... 4H20850. In addition, informa- tion about the location of the regions can be used to calculate the absolute properties of the two regions H20849 Table1 H20850 that, when used as the initial values for the reconstruction, allows the perturbation to be recon- structed on top of the background properties of the two regions H20849Fig. 5H20850.... ..."

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### Table 3: Methods for segmentation. I: Inhomogeneity correction, A: Atlas prior.

2001

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