"... In PAGE 2: ... The length L determines if the scattering center is localized or distributed, while the frequency dependence relates to the curvature of the scattering primitive; one obtains = 1 for flat surface scattering, = 1 2 for singly-curved surfaces, and = 0 for doubly-curved surfaces. Table1 shows how the and L parameters di erentiate between several canonical scattering shapes. The model in (1){(2) is based on GTD and physical optics approximations for scattering behavior and, while parsimonious, is able to describe a large class of scatterers.... ..."

"... In PAGE 29: ... One advantage of the previous formalism is that the generalization of the canonical decom- position to the case of N views is straightforward. Thus the elements of the description are exactly the same as for three views, and can be summarized in the Table4 where it can be veri#0Ced that the total number of parameters is always 11N. Table 4: The geometries of N views: canonical representation... ..."

"... In PAGE 95: ... Robustness The parameter ranges over which the oscillators function are shown in Figure 35. The robustness scores for the four asymmetric half-center oscillators are shown in Table ( Table3 ). There is no consistent e ect of reducing the complexity of the model on the parameter range where the model produces half-center oscillations.... ..."

"... In PAGE 15: ... One maximal conductance was varied at a time, while all others were set to their canonical values. Table2 shows the range of maximal conductance of each current that supports bursting activity for both models. The single neuron model is very sensitive to the variation of gleak and P g , each of which can only be varied in a range of ~1 nS.... In PAGE 17: ... This inhibition stabilizes oscillation within the system to variations in intrinsic membrane properties of the oscillator interneurons. In the model of the heart interneuron half-center oscillator, bursting occurs over a wider range of the maximal conductance of intrinsic membrane currents than in a single cell model ( Table2 ). Bursting of the single-cell model is especially sensitive to leak current parameters and the maximal conductance of IP, while bursting of the half-center oscillator model is much less sensitive (Table 2, compare Fig.... In PAGE 17: ... In the model of the heart interneuron half-center oscillator, bursting occurs over a wider range of the maximal conductance of intrinsic membrane currents than in a single cell model (Table 2). Bursting of the single-cell model is especially sensitive to leak current parameters and the maximal conductance of IP, while bursting of the half-center oscillator model is much less sensitive ( Table2 , compare Fig.... ..."

"... In PAGE 9: ...5 : Functions An XQuery function containing an XQuery expression can be rewritten in an equivalent function containing a canonical expression. In Table13 , a function is defined (local: section) with a parameter in input. This input is defined by the for clause: for $f in doc( catalog.... ..."

"... In PAGE 30: ... The canonical structure is the most used and cited frequently but its usefulness in multivariate context is the least (Rencher, 1998; Johnson and Wichern, 2002). Within Each Data Set (Intra-set Correlation): a) Biological and Landscape Metrics: The correlation of each of the original variables with its canonical variate is given in Table3 a. For the first canonical variate, the direction of contribution was positive for the Hab, Rich and EPT, and was negative for the IBI and AgPT (Table 3a).... In PAGE 30: ... The canonical biota variate (Bio1 and Bio2) explained 41% of the variation in biological variables. b) Chemical and Landscape Metrics: Chem1 and Land1 basically represent the DO, EC and Slope3, respectively ( Table3 b). Chem2 and Land2 were loaded mainly by pH and Pct_for, respectively (Table 3b).... In PAGE 30: ... b) Chemical and Landscape Metrics: Chem1 and Land1 basically represent the DO, EC and Slope3, respectively (Table 3b). Chem2 and Land2 were loaded mainly by pH and Pct_for, respectively ( Table3 b). Chem1 and Land1 denote the common pattern between the two data sets that is contributed by Slope3 and DO.... In PAGE 30: ... The canonical landscape variates (Land1 and Land2) account for 57% of the variation in landscape variables, and the canonical chem variates (Chem1 and Chem2) account for 81% of the variation in water chemistry variables. c) Chemical and Biological Metrics: The direction of correlation was positive for all biological variables with the first canonical biological variate (Bio1, Table3 c). The highest correlation was with EPT (0.... In PAGE 30: ...74) and DO (-0.58), with Chem1 and Chem2, respectively ( Table3 c). The canonical Bio variates (Bio1 and Bio2) account for 49% of the variation in bio variables, and the canonical chem variates (Chem1 and Chem2) account for 71% of the variation in water chemistry variables.... In PAGE 30: ...xcept for EC (-0.74) and DO (-0.58), with Chem1 and Chem2, respectively (Table 3c). The canonical Bio variates (Bio1 and Bio2) account for 49% of the variation in bio variables, and the canonical chem variates (Chem1 and Chem2) account for 71% of the variation in water chemistry variables. One important point to make here is the discrepance in sign for some coefficients in a variate (page 19) and in the correlation ( Table3 ). For example, the coefficient values for the IBI and Rich (page 19, Landscape-Biological) have opposite values than for correlation (Table 3a).... In PAGE 30: ... One important point to make here is the discrepance in sign for some coefficients in a variate (page 19) and in the correlation (Table 3). For example, the coefficient values for the IBI and Rich (page 19, Landscape-Biological) have opposite values than for correlation ( Table3 a). This is normally explained by the collinearity between variables.... In PAGE 31: ...32, and -0.239; Table3 a). As pointed out earlier, Land1 was heavily weighted by Slope3.... In PAGE 31: ... b) Chemical and Landscape Metrics: Chemical parameters responded differently with changes in landscape. The correlation between the original chemical variables with both Land1 and Land2 ( Table3 b) indicated that there is a direct positive response of DO to the changes in Landscape, and it had the opposite response for pH and EC.... In PAGE 31: ...ad the opposite response for pH and EC. The strongest relationship was for DO (0.67). The magnitude of the correlation of DO with the Land1 is basically the response of DO to the topographical feature (Slope3). A high Pct_bar caused higher EC (Land1 and Chem1; Table3 b). All chemical variables were found to correlate positively with the Land2, with the highest value being for the pH.... In PAGE 31: ... The strength of the relationship may reveal the adequacy of the chemical data as a surrogate to biological data, which will be cost effective for future studies. The correlation between the chemical variable with both Bio1 and Bio2 ( Table3 c) indicates that there was a direct positive response of all biological data with Chem1 and Chem2. The strongest relationship was found for the EPT and Rich (0.... In PAGE 31: ...as found for the EPT and Rich (0.535 and 0.366) on Chem1, respectively. Chemical variables EC and DO correlate negatively with Bio1 and Bio2, respectively. The magnitude of the correlation of EC and DO with Bio1 and Bio2 ( Table3 c) basically influences the lower abundance of the EPT and Rich. The canonical Chemistry variates (Chem1 and Chem2) explain 15% variation of the biota.... In PAGE 31: ...g., EPT and Land1; Table3 a) is squared, the results are known as the squared multiple correlation or R2. For example, the square of 0.... In PAGE 31: ... For example, the square of 0.633 (correlation of EPT with Land1; Table3 ) is 0.4002.... ..."

"... In PAGE 5: ... 5.1 Accuracy Improvement Timing results from both QuadStat and CanoStat are shown in Table1 and compared with that from Monte Carlo simulation. The estimation error is also shown in the table from which it is clear that there is a significant accuracy improvement just by switching the delay model from canonical to quadratic.... ..."

"... In PAGE 11: ... Regular exponential families include many famous distribution laws such as Bernoulli (multinomial), Normal (univariate, multivariate and recti ed), Pois- son, Laplacian, negative binomial, Rayleigh, Wishart, Dirichlet, and Gamma distributions. Table2 summarizes the various relevant parts of the canonical decompositions of some of these usual statistical distributions. Observe that the product of any two distributions of the same exponential family is another exponential family distribution that may not have any- more a nice parametric form (except for products of normal distribution pdfs that yield again normal distribution pdfs).... In PAGE 13: ... Before proving the theorem, we note that rF ( ) = Z x f(x) expfh ; f(x)i F ( ) + C(x)gdx : (8) The coordinates of def= rF ( ) = [R x f(x)p(xj )dx] = E (f(x)) are called the expecta- tion parameters. As an example, consider the univariate normal distribution N ( ; ) with su cient statistics [x x2]T (see Table2 ). The expectation parameters are = rF ( ) = [ 2 + 2]T , where = R x x p(xj )dx and 2 + 2 = R x x2p(xj )dx.... ..."