### Table 3: A Non-Linear Cycle Test

2005

"... In PAGE 13: ... However, we would like to demonstrate that the method apos;s accuracy is not limited to linear fast/continuous reactions. Here, we use a apos;Non-linear Cycle Test apos;, containing three fast/contin- uous and two slow reactions (described in Table3 ) and perform a series of accuracy measurements to determine how the error in the probability distribution, mean, and variance of the solution changes with the system size. The system size is a parameter in the reaction network that Here, we take the system size to be the number of initial reactant and product molecules in the fast/continuous reactions.... ..."

### Table 3. Further non-linearities with arbitrary parameters

"... In PAGE 12: ...J. Wiltshire Table3 (continued). Further non-linearities with arbitrary parameters No Nonlinear terms Matrix Class (4.... ..."

### Table 3. Comparison of models for the non-linear function approximation.

2003

"... In PAGE 7: ...and validation data set, respectively. Table3 contains comparison results of di erent models for the static function approximation and provides, in addition, re- sults achieved with the neural tree model developed in this paper. It is obvious that the proposed neural tree model worked well for generating an approxi- mating model of the static non-linear system.... ..."

### Table 3 Typing rules for affine linear and non-linear Homer

2007

"... In PAGE 9: ...We define the typing of processes, abstractions, and concretions using the rules in Table3 . The type system conservatively generalises the prior type (effect) system for Homer [13], which we can obtain by removing the (embed) rule and taking S to be a singleton set, making it possible to delete all references to sorts from abstraction and concretion types, and completely remove side-conditions and environments.... ..."

### Table 1: Matlab results of using a linear interpolation com- pared to a non-linear interpolation.

2003

"... In PAGE 2: ....3. System Performance The performance of systems of 2n current cells was investi- gated as thermometerdecoding will be chosen as the switch- ing scheme in the final circuit. Table1 presents the perfor- mance of Matlab emulations of both nonlinear and linear... ..."

Cited by 3

### Table 1. Matlab results of using a linear interpolation compared to a non-linear interpolation.

"... In PAGE 4: ...The performance of systems of 2n current cells was investigated as thermometer decoding will be chosen as the switching scheme in the final circuit. Table1 presents the performance of Matlab emulations of both nonlinear and linear interpolation systems for increasing n. The performance is surprisingly good for a small number of current sources.... ..."

### Table 1: Matlab results of using a linear interpolation com- pared to a non-linear interpolation.

"... In PAGE 2: ....3. System Performance The performance of systems of a33 a42 current cells was investi- gated as thermometer decoding will be chosen as the switch- ing scheme in the final circuit. Table1 presents the perfor- mance of Matlab emulations of both nonlinear and linear... ..."

### Table 1. Matlab results of using a linear interpolation compared to a non-linear interpolation.

"... In PAGE 4: ...The performance of systems of a39 a48 current cells was investigated as thermometer decoding will be chosen as the switching scheme in the final circuit. Table1 presents the performance of Matlab emulations of both nonlinear and linear interpolation systems for increasing a102 . The performance is surprisingly good for a small number of current sources.... ..."

### Table 1 shows that non-linear MLPs provide better performances than linear equivalent systems. There- fore, non-linearity introduced by the sigmoid function improves the network performance. The sigmoid func- tion can be considered having three regions: linear (approximately to y=x/2) , non-linear and saturation, Figure 2. The linear region is approximately in the range of -0.5 to 0.5 output value.

"... In PAGE 2: ...6 11.4 Table1 : Performance of linear and nonlinear predic- tors. Results show that non-linear MLPs provide better per- formance than linear equivalent systems (Table 1).... In PAGE 2: ... Results show that non-linear MLPs provide better per- formance than linear equivalent systems (Table 1). Table1 also shows that MLPs with multi-output struc- ture (model 2) give improved performances over MLPs with a single output (model 1). This is quite di er- ent in other applications such as speech and speaker recognition, in which model 1 structure is preferred.... ..."

### Table 5 Results for progressive collapse example # Sigm. Min. rms Iters. Total CPU time (100 runs) No. of non-linear parameters

"... In PAGE 12: ... 298 We have used program NSG and different number of nodes with sigmoid activation functions, in a sigle hidden 299 layer fully connected perceptron, with three input and one output node. In Table5 and Fig. 5 we summarize the results 300 on a 800 MHz Celeron PC, running under the Solaris x86 operating system.... ..."