### Table 3b. Solution Statistics for Model 2 (Minimization)

1999

"... In PAGE 4: ...6 Table 2. Problem Statistics Model 1 Model 2 Pt Rows Cols 0/1 Vars Rows Cols 0/1 Vars 1 4398 4568 4568 4398 4568 170 2 4546 4738 4738 4546 4738 192 3 3030 3128 3128 3030 3128 98 4 2774 2921 2921 2774 2921 147 5 5732 5957 5957 5732 5957 225 6 5728 5978 5978 5728 5978 250 7 2538 2658 2658 2538 2658 120 8 3506 3695 3695 3506 3695 189 9 2616 2777 2777 2616 2777 161 10 1680 1758 1758 1680 1758 78 11 5628 5848 5848 5628 5848 220 12 3484 3644 3644 3484 3644 160 13 3700 3833 3833 3700 3833 133 14 4220 4436 4436 4220 4436 216 15 2234 2330 2330 2234 2330 96 16 3823 3949 3949 3823 3949 126 17 4222 4362 4362 4222 4362 140 18 2612 2747 2747 2612 2747 135 19 2400 2484 2484 2400 2484 84 20 2298 2406 2406 2298 2406 108 Table3 a. Solution Statistics for Model 1 (Maximization) Pt Initial First Heuristic Best Best LP Obj.... In PAGE 5: ...) list the elapsed time when the heuristic procedure is first called and the objective value corresponding to the feasible integer solution returned by the heuristic. For Table3 a, the columns Best LP Obj. and Best IP Obj.... In PAGE 5: ... report, respectively, the LP objective bound corresponding to the best node in the remaining branch-and-bound tree and the incumbent objective value corresponding to the best integer feasible solution upon termination of the solution process (10,000 CPU seconds). In Table3 b, the columns Optimal IP Obj., bb nodes, and Elapsed Time report, respectively, the optimal IP objective value, the total number of branch-and-bound tree nodes solved, and the total elapsed time for the solution process.... ..."

### Table 4.3: Asymptotic adder complexities (unit-gate model).

1997

### Table 4.3: Asymptotic adder complexities (unit-gate model).

1997

### Table 4.3: Asymptotic adder complexities (unit-gate model).

1997

### Table 1: A list of evolution terms for parametric models has a corresponding expression on the embedding, a0 , associated with the level-set models.

2002

"... In PAGE 11: ... The corresponding level-set formulation is given by Equation 8. Table1 shows a list of expressions used in the evolution of parameterized surfaces and their equivalents for level-set representations. Also given are the assumptions about the... In PAGE 12: ... Second is the problem of computational complexity and the fact that we have converted a surface problem to a volume problem, increasing the dimensionality of the domain over which the evolution equations must be solved. The level-set terms in Table1 are combined, based on the needs of the application, to cre- ate a partial differential equation on a0a34a33 a29 a11a119a134 a35 . The solutions to these equations are computed using finite differences.... In PAGE 13: ... 6.1 Up-wind Schemes The terms in Table1 fall into two basic categories: the first-order terms (items 1 and 2 in Table 1) and the second-order terms (items 3 through 5). The first-order terms describe a moving wave front with a space-varying velocity (expression 1) or speed (expression 2).... In PAGE 13: ... 6.1 Up-wind Schemes The terms in Table 1 fall into two basic categories: the first-order terms (items 1 and 2 in Table1 ) and the second-order terms (items 3 through 5). The first-order terms describe a moving wave front with a space-varying velocity (expression 1) or speed (expression 2).... In PAGE 25: ...ng cubes [5]. These results are obtained without any user input. Distance transforms on the CSG models are computed near the level surface using an analytical description and extended into the volume using a level-set method [37]. The application in this section shows how level-set models moving according to the first- order term given in expression 2 in Table1 can fit other objects by moving with a speed... In PAGE 27: ...Table1 , a second-order flow that depends on the principal curvatures of the surface itself. 7.... In PAGE 29: ... Thus, a second-order flow can create smooth blends between objects in a way that does not require specific knowledge of the shapes or topologies of the object involved. The application in the next section, 3D scene reconstruction, shows how a combination of first- order and second-order terms from Table1 are combined to create technique that fits models to data while maintaining certain smoothness constraints and thereby offsetting the effects of noise. 7.... In PAGE 31: ...3.1 Objective function for multiple range maps The evolution equation for the estimation of optimal surfaces is shown in [42] to consist of two parts: a138 a29 a138 a134 a25a28a71a56a147 a33 a29a40a35a117a136 a109 a208a207 a33 a24a196a35 a39 (39) This first part, a71a56a147 a33 a29a40a35a117a136 , is the data term, which is a movement with variable speed (as in expression 2 from Table1 ) that is the cumulative effect from all of the individual range... ..."

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### TABLE I OPTIMIZED REGULARIZATION PARAMETERC AND SMOOTHING PARAMETERS FOR THE COMBINED OLIGO KERNEL. ALL RESULTS REFER TO 50 TRIALS WITH DIFFERENT PARTITIONINGS OF THE DATA. C

Cited by 1

### Table 1: Comparison the performances (as measured by Eqn(35)) between the feedforward networks trained with the smoothing regularizer and those trained with standard weight decay for the function estimation. The results shown are the mean and the standard deviation over 10 models with different initial weights.

"... In PAGE 17: ... Figure 1 shows the downsampled training and test errors versus the regularization parameters. The performances in Table1 are the optimal results over all these regularization parameters. This gives the best potential result each network can obtain.... In PAGE 17: ... We believe that such results will more directly reflect, and more precisely compare, the efficacy of different regularizers. Table1 shows that the potential predictive errors with the smoothing regularizer are smaller than those with standard weight decay. Figure 2 gives an example and compares the approximation functions obtained with standard weight decay and our smoothing regularizer to the true function.... ..."

### Table 1: Optimal parameter values for the di erent functional models

"... In PAGE 12: ...ictors. The rst 36 years, from 1950, were considered as a learning subset. The optimal hn; q or ` values minimized the MSE when predicting years from the 32nd to the 36th. These optimal values, displayed in Table1 , were used to tune the predictors in order to forecast the ten last years from the 37th to the 46th. The data were pretty regular, and the smoothing had a minor e ect.... In PAGE 16: ... This is in agreement with Carbon and Delecroix (1993), who showed that a classical kernel predictor generally gives better results than a SARIMA model. Examination of Table1 suggests that functional FAR forecasts outper- form the other methods. The local FAR(1) model forecasts the smoother EN data better than does the smooth FAR(1) model, yet the smooth FAR(1) method forecasts better the noisier SO data.... ..."

### Table 1: Parameters in online smoothing model: This table summarizes the key parameters in the smoothing model.

"... In PAGE 7: ... Intuitively, after any invocation to the smoothing algorithm, the server slides over time units before it invokes the the online smoothing algorithm with a smoothing window starting time units past the beginning of the smoothing window for the first invocation. Table1 summarizes the key parameters, which guide our derivation of the smoothing constraints, as well as our performance evaluation in Section 4. 3.... In PAGE 9: ... Similarly, modest values of w, BC, BS, and P allow online smoothing to achieve most of the performance gains of the optimal offline algorithm. 4 Performance Evaluation The performance evaluation in this section studies the interaction between the parameters in Table1 to help in determining how to provision server, client, and network resources for online smoothing. The study focuses on bandwidth requirements, in terms of the peak rate, coefficient of variation (standard deviation normalized by the mean rate), and the effective bandwidth of the smoothed video stream.... ..."

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