### Table 5: Solving the small, random problems. Exact objective values and the objective error from the parallel algorithm are shown. Also shown are cpu times (seconds) for GAMS/OSL apos;s primal simplex on an HP 9000/730 workstation. iterations. Both runs spend a long time slowly adjusting the penalty parameter downwards, without making much progress towards primal feasibility. We conclude that establishing a good, initial penalty parameter, and/or allowing it to change dynamically under algorithmic control are crucial for good performance.

1996

"... In PAGE 29: ...3 Discussion of Results The massively parallel algorithm was implemented on the Connection Machine CM{2 in C/Paris, and the stochastic programs were solved at the North-East Parallel Architectures Center (NPAC) at Syracuse University, and at AHPCRC at the University of Minnesota, using SUN 4 front-ends. Results of solving the rst two sets of test problems are reported in Table 3 and Table5 . We report the initial and nal penalty parameter values, the number of major iterations (each consisting of 25 minor iterations, followed by a non-anticipativity projection and proximal point update), the number of seconds for solution on a 16K CM{2 (excluding input/output), the objective value returned, and the error in this value from the exact, optimal values, which were obtained using GAMS/OSL.... In PAGE 32: ... We conclude that establishing a good, initial penalty parameter, and/or allowing it to change dynamically under algorithmic control are crucial for good performance. Random Problems Results for the medium-size, random problems are given in Table5 . These problems, with from 2 up to 9 stages and about 256 scenarios, were solved in about 6-8 minutes using 16K processors.... ..."

Cited by 11

### Table 1. With all this in mind, we state our procedure as follows. Assume we know the dynamics f and the gradients with respect to state and control variables. For each particular case (each pair x(S); x(T)) run the program successively according to the following algorithm:

"... In PAGE 21: ...Table1 (and looking at the Figures 1{6), we see that, for a xed N, the distance between x(N) and x(T) always decreases as (the upper bound on control) increases. Also, with a pre-set quot;, the number of iterations needed to reach the quot;-neighbourhood of x(T) decreases as increases.... In PAGE 21: ... Ergodicity ensures that a small neighbourhood of any state near or on the attractor is reachable from any other state near or on the attractor. Another conclusion to be drawn from Table1 is that, except for small values of N, the distance from x(N) to x(T) decreases as N increases, as expected. There appears to be some anomaly for small values of N (cf.... In PAGE 21: ... There appears to be some anomaly for small values of N (cf. Table1 , N = 5 and N = 6), but this is to be expected, as the reachable set in a small number of iterations from a given x(S) does not cover the attractor very well. An illustration of a set reachable in 4 iterations is given in Figure 8.... ..."

### Table 2. Simulation parameters for IEEE

2003

"... In PAGE 7: ... Simulation parameters for the control algorithm The configuration of the access point and mobile stations is mostly based on the default parameter values proposed for the Direct Sequence Spread Spectrum (DSSS) system in IEEE 802.11b standard, like the length of RTS, CTS, ACK, MAC header, the slot time, the SIFS, the DIFS, the PLCP preamble, etc, as given in Table2 . Some other parameters, which are related to applications or defined for the dynamic control algorithm, are summarized in Table 3.... ..."

Cited by 1

### lable. Kinematically controllable dynamic systems

### Table 2: Operation count for NE dynamics variables.

1998

"... In PAGE 9: ... The number of multiplications and additions necessary for calculation of the NE dynamics terms (from Table 1) is used to estimate the relative execution times for the conventional serial NE dynamics algorithm, the Binder/Herzog parallel algorithm, and versions of the new parallel algorithm introduced here. The values shown in Table2 are for the general case. Terms that appear in the equations of multiple variables are assumed to be calculated once... In PAGE 11: ... link are executed on one processor (processor 1 performs the forward portion for link 1 and the backward portion for link 3, processor 4 performs the backward portions for links 2 and 3). Therefore, the cycle times corresponding to Table2 , where redundant computations are counted only once, were used. For this example, the minimum cycle time for the control loop is 857 cycles, which is an improvementover the Binder/Herzog method (see Table 4).... ..."

Cited by 1

### Table 2: Operation count for NE dynamics variables.

1998

"... In PAGE 9: ... The number of multiplications and additions necessary for calculation of the NE dynamics terms (from Table 1) is used to estimate the relative execution times for the conventional serial NE dynamics algorithm, the Binder/Herzog parallel algorithm, and versions of the new parallel algorithm introduced here. The values shown in Table2 are for the general case. Terms that appear in the equations of multiple variables are assumed to be calculated once... In PAGE 11: ... link are executed on one processor (processor 1 performs the forward portion for link 1 and the backward portion for link 3, processor 4 performs the backward portions for links 2 and 3). Therefore, the cycle times corresponding to Table2 , where redundant computations are counted only once, were used. For this example, the minimum cycle time for the control loop is 857 cycles, which is an improvementover the Binder/Herzog method (see Table 4).... ..."

Cited by 1

### Table 3: Dynamical Automaton 2: transitions.

"... In PAGE 25: ... Actual dynamical implementation of the correction mechanism is a focus of current research. The Input Map for the Dynamical Automaton we used to model transitive sentences with relative clause modi ers is shown in Table3 . The automaton uses 9 partition states and moves around on a 3-dimensional fractal.... In PAGE 30: ...De nition Start (1/2, 1/2, 1/2) Comp1 (0, 0, 0) + opencube Comp2 (0, 1/2, 0) + opencube V1 (1/2, 0, 0) + opencube V2 (1/2, 1/2, 0) + opencube NObj1 (0, 0, 1/2) + opencube NObj2 (0, 1/2, 1/2) + opencube NSubj1 (1/2, 0, 1/2) + opencube NSubj2 (1/2, 1/2, 1/2) + opencube Note: opencube is the set f(x; y; z) : 0 lt; x lt; 1=2; 0 lt; y lt; 1=2; 0 lt; z lt; 1=2g. Note: Compartment A as labelled in Table3 is the union of the compartments A1 and A2 shown above for A 2 fComp; V; NObj; NSubjg. Table 4: Dynamical Automaton 2: compartment de nitions.... ..."

### Table 2: Simulation results of SDP control policy (

2004

"... In PAGE 5: ... This simulation set-up allows us to study the performance of control algorithms under standard testing conditions. Through the continuous-time simulation, the performance of the control policy from SDP is compared with our prior work over different driving cycles as given in Table2 . The Rule-Based (DDP) refers to a rule-based control strategy trained based on the results of deterministic dynamic programming results [4].... ..."

Cited by 3

### Table 1: Event speci cations and simulated reliabilities and costs for the translating algorithms.

"... In PAGE 14: ... The reliability of the only algorithm used, a PI controller with no explicit compensation of dynamics, is necessarily smaller than that of any of the active compliance algorithms translating e2, since no force control exists. Table1 shows the reliabilities and costs assigned to the simulation models of each primitive algorithm (except R(e4) = 1 and C(e4) = 0). The values were assigned based on the physical considerations above.... ..."

### Table 3. Descritpion of the arm dynamics and controller parameters

"... In PAGE 45: ... Computational costs of the error function gradient. Table3 . Meaning of the dynamics parameters Table 4.... ..."