### Table 1. A Numerical Example of the Reactionless Spatial 3-DoF Mechanism

"... In PAGE 11: ... Hence, starting from this point mass, all the parameters of the bars of the four-bar mechanisms are chosen or calculated using the reactionless conditions. Finally a numerical example of this reactionless 3-DoF mechanism is given in Table1 (point mass mp = 0.1143 kg).... In PAGE 15: ... For example, if a mobile platform can be replaced by three point masses (mpm = 0.1143 kg) a numerical example of the reactionless 3- DoF leg mechanism can be given in Table1 and a reactionless spatial 6-DoF parallel mechanism can finally be obtained. The verification of the reactionless property of the spatial 6-DoF parallel mechanism is also performed using ADAMS.... In PAGE 15: ... Discussion Note that the aim of this paper is to synthesize reactionless spatial 3-DoF and 6-DoF mechanisms. The parameters of the example reactionless mechanism ( Table1 ) were not deter- mined by optimization due to the complexity of the optimiza- tion for the complete system. As was the case with other dynamically balanced mechanisms, the reactionless 3-DoF mechanism was achieved at the expense of a substantial mass increase and complexity of the mechanism.... ..."

### Table 2. IS0 CAM Observations of CLO SS Pairs Name Obs. Filter X X/6X pixel samp. MxN map rms noise

"... In PAGE 6: ...evels are 2 (n=1,2,3, ...) times the rms noise ((~15~~ or g9.7pm for KPG 347) as given in Table2 . MIDDLE PANEL: A log grayscale image of the 15pm to 9.... ..."

### Table 5. Some 3-DoF Parallel Mechanisms Leg Chains Mechanism

"... In PAGE 10: ... For the mechanism shown in Figure 16, the passive leg is with a (Pa)U chain, which leads to one translational DoF and two rotational DoFs of the mechanism. Table5 lists 11 types of 3-DoF parallel mechanisms. 3.... ..."

### Table 3. C-Space Map-Makers for a Manipulator in a Static Environment Dimen- DoF Allowable Geometry Approximate

"... In PAGE 13: ... C-space mapmakers for a mobile robot in a static environment. Table3 . C-space mapmakers for a manipulator in a static environment.... ..."

### Table 1. The set of transformation models used in retinal image registration [8]. To clarify notation in the equations, p = (x; y)T is an image location in I1, q = (u; v)T is the transformed image location in I2, and p0 is the center of the registration region. In addition to the formulations, the table also shows the degrees of freedom (DoF) in each model and the average alignment error on 1024 1024 images.

2003

"... In PAGE 3: ... 3). The initial region and perhaps subsequent regions con- tain too few constraints to reliably estimate the 12 parameters of a quadratic model ( Table1 ) needed for accurate image-wide alignment [8]. Thus, a lower- order model must be used.... In PAGE 4: ...nd in white. The global, image-wide alignment is quite poor. Panel (b) shows the alignment after three iterations of view generation (region growth and model selection) and estimation. No change has yet been made in the model, but in the next iteration (c) a reduced quadratic transformation is selected ( Table1 ). Panel (d) shows the nal alignment using a quadratic transformation.... In PAGE 4: ... The covariance matrix may be approximated by the inverse Hessian of the ob- jective function used in estimation, evaluated at the estimate. In the description of these steps, t denotes the iteration of the view selection and estimation loop, Rt denotes the transformation region, and Mt denotes the transformation model selected for the current view ( Table1 ). ^ t is the vector of estimated parameters... In PAGE 9: ... Dual-Bootstrap ICP is used for (1), (3) and (4), which corre- spond to Problem 1 from the introduction, while M-ICF is used for (2). In the retinal registration problems, the nal transformation model is a 12-parameter quadratic ( Table1 ), and the experimental results are extensive. For the confocal images, the nal transformation is a ne, and the results are preliminary.... ..."

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### Table 2: Exact modal frequencies of a 64 DoF flnite element model and modal frequencies obtained using single level and multilevel methods for the case p = 8.

"... In PAGE 14: ... Column 7 in Table 1 shows the total time for the multilevel subspace iteration method, while column 8 shows the corresponding time and number of iterations required by the (single- level) flnite element subspace iteration method with 64, 128 and 256 degrees of freedom. Columns 3 to 5 in Table2 show the flrst p = 8 modal frequencies obtained after performing subspace iteration at each level; column 2 in Table 2 shows the exact modal frequency of the 64 DoF model computed using MATLAB and column 6 shows the modal frequencies of the same model computed using subspace iterations. Referring to Table 1, we can conclude that as the number of eigenvalues p increases, the multilevel subspace iteration method provides a more rational strategy for determining the flrst few eigenvectors in the flnite element mesh since the resolution required to resolve a particular eigenmode need not be known a priori.... In PAGE 14: ... Column 7 in Table 1 shows the total time for the multilevel subspace iteration method, while column 8 shows the corresponding time and number of iterations required by the (single- level) flnite element subspace iteration method with 64, 128 and 256 degrees of freedom. Columns 3 to 5 in Table 2 show the flrst p = 8 modal frequencies obtained after performing subspace iteration at each level; column 2 in Table2 shows the exact modal frequency of the 64 DoF model computed using MATLAB and column 6 shows the modal frequencies of the same model computed using subspace iterations. Referring to Table 1, we can conclude that as the number of eigenvalues p increases, the multilevel subspace iteration method provides a more rational strategy for determining the flrst few eigenvectors in the flnite element mesh since the resolution required to resolve a particular eigenmode need not be known a priori.... ..."

### Table 3: Average S-Matrix parameters from the data of the four LEP experiments given in Table 2, without the assumption of lepton universality. The 2/DoF of the average is 55/48.

"... In PAGE 3: ...7 standard deviations, as given in Table 6. From Table3 one concludes that the discrepancy arises from the tau channel only which is measured to 1These two deviations are correlated by 19% which dilutes the signi cance of the discrepancy.... ..."

### Table 8: Value-at-Risk and Expected Shortfall at the 95th Percentile. Normal vs. Student-t copula with DoF=12, 100K-path Monte Carlo simulation.

"... In PAGE 27: ... Let us now assume that each of the 100 reference names has an objective default intensity equal to 50 basis points, the remaining parameters unchanged. Table8 compares the two dependence assumptions in terms of the 95% Value-at-Risk and Expected Shortfall that they produce for a number of loss tranches. Where we de ne the Value-at-Risk, VaR := DL 1( ) and the conditional-VaR, CVaR := 1 1 R 1 DL 1(t)dt, where DL is the discounted loss.... ..."

### Table 1. Parallel Data Redistribution Projects Approach I: Component-based Parallel Data Redistributions Project Brief Overview MxN

### Table 1: The set of transformation models used in retinal image registration. To clarify notation in the equations, p = (x; y)T is an image location in I1 and q = (u; v)T is the transformed image location in I2. X(p) = (1; x; y; x2; xy; y2) is a second-order basis. Finally, p0 is the center of the region of overlap between the images. This is required in the reduced quadratic model, but is used in practice in all models. In addition to the formulations, the table also shows the degrees of freedom (DoF) in each model and the average alignment error on 1024 1024 images.

in The Dual-Bootstrap Iterative Closest Point Algorithm with Application to Retinal Image Registration

2003

"... In PAGE 8: ... The transformation is only required to be accurate in this bootstrap region. Also in each iteration, the best transformation model (in this case, similarity, reduced-quadratic, or quadratic | see Table1 ) is automatically selected and the bootstrap region is grown. Several increments of this process are shown in the panels, and the model selected in each bootstrapping iteration is indicated.... In PAGE 23: ... First, for the set of images from any given eye, we can jointly align all images, including pairs that have little or no overlap, using a joint, multi-image mosaicing algo- rithm [10]. This uses constraints generated from pairwise registration, and produces quadratic transformations (see Table1 ) between all pairs of images, even ones that failed pairwise regis- tration. (Viewing the set of images as nodes in an undirected graph and the successful pairwise registrations as edges in the graph, the only requirement is that the graph be connected.... ..."

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