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Table 3 illustrates the advantages of using this reformulation. Note that the instance DLSI pr is solved by linear programming (without branching) even though NI gt; 1. Also note that one result of the increased size of the reformulations is that the linear programs take longer to solve. However, this is more than compensated for by the improvement in the bounds.
"... In PAGE 27: ... Table3 : DLSI instances before and after reformulation 5.3 DLSBI and related models Here we used the reformulation (3){(6), (64){(69).... ..."
Table 3: The coe cients of a bi-orthogonal linear-phase two-band PR lter bank. Note that the low-pass lter is symmetric whereas the high-pass lter is anti-symmetric.
"... In PAGE 12: ... Also note that the the complementary lter is sensitive to the value of = 1 and deviation from ?90:5 can result in a lter which may not have the desired high-pass characteristic. Another example is given in Figure 4, where the possible complementary lters of a linear-phase lter H(z), tabulated in Table3 , are shown. Again k is set to 3 which translates into an end-to-end delay of 7.... ..."
TABLE I TABLE 1. STATISTICAL SIGNIFICANCE OF LINEAR COEFFICIENTS FOR SEVERAL PREDICTORS. TRAVEL TIMES BETWEEN 7:30AM (VARIABLE T0730) AND 7:55 (VARIABLE T0755) ARE USED TO PREDICT THE TRAVEL TIME AT 8:00AM IN A LINEAR MODEL. ESTIMATES FOR THE LINEAR COEFFICIENTS OF THE REGRESSION MODEL ARE SHOWN IN COLUMN LIN. COEFF. COLUMN t-VALUE IS THE t-STATISTIC FOR THE COMPUTED STANDARD ERROR OF THE LINEAR COEFFICIENT, AND Pr( gt; jtj) IS THE PROBABILITY THAT SUCH A LARGE VALUE OF t WOULD BE OBSERVED PURELY BY CHANCE WHEN THE REGRESSION COEFFICIENT IS IN FACT ZERO. ONLY THE MOST RECENT TRAVEL TIME (T0755) HAS MAJOR STATISTICAL SIGNIFICANCE AS A LINEAR PREDICTOR; THE CONSTANT TERM (INTERCEPT) IS ALSO SIGNIFICANT AT THE 2:23% CONFIDENCE LEVEL, WHICH SIMPLY MEANS THAT TRAVEL TIME BETWEEN 7:55AM AND 8:00AM IS INCREASING.
2005
TABLE I TABLE 1. STATISTICAL SIGNIFICANCE OF LINEAR COEFFICIENTS FOR SEVERAL PREDICTORS. TRAVEL TIMES BETWEEN 7:30AM (VARIABLE T0730) AND 7:55 (VARIABLE T0755) ARE USED TO PREDICT THE TRAVEL TIME AT 8:00AM IN A LINEAR MODEL. ESTIMATES FOR THE LINEAR COEFFICIENTS OF THE REGRESSION MODEL ARE SHOWN IN COLUMN LIN. COEFF. COLUMN t-VALUE IS THE t-STATISTIC FOR THE COMPUTED STANDARD ERROR OF THE LINEAR COEFFICIENT, AND Pr( gt; jtj) IS THE PROBABILITY THAT SUCH A LARGE VALUE OF t WOULD BE OBSERVED PURELY BY CHANCE WHEN THE REGRESSION COEFFICIENT IS IN FACT ZERO. ONLY THE MOST RECENT TRAVEL TIME (T0755) HAS MAJOR STATISTICAL SIGNIFICANCE AS A LINEAR PREDICTOR; THE CONSTANT TERM (INTERCEPT) IS ALSO SIGNIFICANT AT THE 2:23% CONFIDENCE LEVEL, WHICH SIMPLY MEANS THAT TRAVEL TIME BETWEEN 7:55AM AND 8:00AM IS INCREASING.
2005
Table IV : The recognition results obtained from the sets SA and SB. We are currently studying the use of this channel in speech recognition. Note that with such a model, the entire question of quot;time warping quot; would be subsumed in appropriately modelling the distribution G. Also, we have only dealt with the concepts of syntactic PR in which the patterns are represented quot;linearly quot; as strings. The problem of developing optimal classifiers for PR systems using two-dimensional structures such as trees and webs still remains open. We currently have some initial results for the case of ordered tree representations.
Table 10. Regression coe cients (logit units) of a two-dimensional linear logit analysis of the selections probabilities; 0=intercept, 1=slope of the disease, 2 = slope of the symptom Experiment or experimental condition a Coe cients 1 2 3 4Dx9 4Pr9 5
1997
"... In PAGE 32: ... As the estimates for the interaction coe cients were much smaller than those for the main e ects, we report only results without interaction terms. Table10 shows the point estimates of the regression coe cients for logits. The logits were re-transformed to proba- bilities.... In PAGE 32: ... Figure 6 shows the predictions of the selection probabilities resulting from the regression models for experiments 1, 2, 3, 4Dx9, 4Pr9, and 5. The regression coe cients in Table10 and the associated predictions in Figure 6 are very similar for the six experiments. Moreover, the regression coe cients for the disease and the symptom are very similar.... ..."
Cited by 1
Table 1. Runtimes for some Matrix Robustness instances. Dimension is after elimination of all-zero rows, Dimension/EC (equivalence classes) after additionally subsuming pairwise dependent vectors. The result is the number of rows that have to be deleted to get the matrix to drop in rank. For the runtimes, simple means plain algorithm without speed-up techniques, EC means exploiting equivalence classes, and UB means exploiting upper bounds determined by previous MIPs in a pass. Finally, LP is the runtime for the linear programming based approach and PR the runtime for the pseudorank heuristic. Dimension Result Runtime in seconds
"... In PAGE 10: ... The pseudorank based algorithm achieves an optimal result for all instances, while the LP method gives rather bad results for some instances. Note that the column Result in Table1 shows that for our current real-world instances the solution sizes are rather small and probably com- plete enumeration of row subsets in order of increasing size would work as well. However, larger solution sizes are conceivable, and therefore we study randomly generated instances with larger solution sizes in what follows.... ..."
Table 1. Runtimes for some Matrix Robustness instances. Dimension is after elimination of all-zero rows, Dimension/EC (equivalence classes) after additionally subsuming pairwise dependent vectors. The result is the number of rows that have to be deleted to get the matrix to drop in rank. For the runtimes, simple means plain algorithm without speed-up techniques, EC means exploiting equivalence classes, and UB means exploiting upper bounds determined by previous MIPs in a pass. Finally, LP is the runtime for the linear programming based approach and PR the runtime for the pseudorank heuristic. Dimension Result Runtime in seconds
"... In PAGE 10: ... The pseudorank based algorithm achieves an optimal result for all instances, while the LP method gives rather bad results for some instances. Note that the column Result in Table1 shows that for our current real-world instances the solution sizes are rather small and probably com- plete enumeration of row subsets in order of increasing size would work as well. However, larger solution sizes are conceivable, and therefore we study randomly generated instances with larger solution sizes in what follows.... ..."
Table 2: An example task list for a participant. Condition (the order in which participants experienced the different algorithms) changed for each participant.
2001
"... In PAGE 5: ... All participants completed the tasks in the same order, but for each task, the order in which participants experienced the three algorithms was counterbalanced. Thus, as shown in Table2 , for the first task, a participant may have done task 1 using the Linear algorithm, then the PR-Lin algorithm, and then the Adapt algorithm. However, other participants may have done the first task using the Adapt algorithm first, then the Linear algorithm, and then the PR-Lin algorithm.... ..."
Cited by 9
Table 2.3 summarizes the complexity of different word-level decision diagrams to represent the integer functions and operations such as X, X + Y , X #03 Y , X 2 and 2X . Note that *BMDs and K*BMDs have more compact representations than others.
1998
Cited by 6
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