"... In PAGE 2: ...f numerical software, e.g. the LAPACK++ package [5]. 2 Overview of LIBLAC 2.1 Vector and Matrix Types LIBLAC supports the standard scalar types listed in Table1 . In the following, we will use the generic pre x X (and occasionally also Y) to denote the element type of Table 1: Scalar types supported by LIBLAC.... ..."

"... In PAGE 9: ... This delay leads to select the proper resulting type from the set. Table1 shows a classification of functions into 7 groups. In the first group, the functions are defined for scalar types, the number of in and out arguments is fixed, and the out- come value is also a scalar type.... In PAGE 10: ... We have extended the classifi- cation taking these aspects into account. Table1 contains information on shapes. Shape can be inferred statically for functions in group I and II.... ..."

"... In PAGE 9: ... This delay leads to select the proper resulting type from the set. Table1 shows a classification of functions into 7 groups. In the first group, the functions are defined for scalar types, the number of in and out arguments is fixed, and the out- come value is also a scalar type.... In PAGE 10: ... We have extended the classifi- cation taking these aspects into account. Table1 contains information on shapes. Shape can be inferred statically for functions in group I and II.... ..."

"... In PAGE 10: ... Note that because of the ow equivalence pointed out in section 3 our estimates for the probability of permanence also apply to Lotka-Volterra (LV) equations with one dimension less and rk = akn; bij = aij ? anj (16) However, the probability distributions are not the same for the elements of A in the replicator equation and for the o -diagonal elements of B in the Lotka-Volterra model. Table1 lists the density functions used in this contribution. The probability for the quadratic form xAx and detA to have a certain sign is clearly 1=2.... In PAGE 26: ... Table1 : Probability Densitity functions used in this paper. All calculations have been performed for the replicator model (SR) (column A).... ..."

"... In PAGE 8: ... Table1 : Probability Densitity functions used in this paper. All calculations have been performed for the replicator model (SR) (column A).... In PAGE 10: ... Note that because of the ow equivalence pointed out in section 3 our estimates for the probability of permanence also apply to Lotka-Volterra (LV) equations with one dimension less and rk = akn; bij = aij ? anj (16) However, the probability distributions are not the same for the elements of A in the replicator equation and for the o -diagonal elements of B in the Lotka-Volterra model. Table1 lists the density functions used in this contribution. The probability for the quadratic form xAx and detA to have a certain sign is clearly 1=2.... ..."

"... In PAGE 3: ... This suggested that it is possible to design a wavelet fil- ter such that the energy of the coefficients is packed within a spe- cific region of the truncated Volterra kernels, resulting in a better predistortion. Finally, Table3 shows the tremendous reduction of computational complexity of the truncated 5th-order Volterra in- verses, compared to the original one with memory span C3 BPBEBH (last row). predistorter Pinv(5,1) Pinv(5,3) Pinv(5,5) AC BF Daubechies 14 0.... ..."

"... In PAGE 13: ...y the four models is shown in Fig. 2. This expected behaviour is explained in terms of the eigenvalue spread of the functional covariance matrix of the Fourier and Volterra models. Table1 shows this eigenvalue spread for two model orders N={6, 16}, and for several input distributions (particularly, two uniformly distributed PDFs with ranges [- 1,1] and [-2,2], and three zero-mean Gaussian distributions with standard deviations sX={1/3, 1, 2}). Six models are tested: Volterra (Volt), Odd Volterra (O-Volt), Even Volterra (E-Volt); Fourier (Four), Odd Fourier (O-Four) and Even Fourier (E-Four).... In PAGE 13: ...sX,3sX] for Gaussian distributions, providing an overflow probability of 2.7e-3. The covariance matrices are computed from 5000 data samples and the eigenvalue spread is estimated averaging 10 independent realisations. Thus, Table1 evidences the overall extraordinary advantage of the constant power functionals of the Fourier model with respect to the polynomial functionals of the Volterra model, even in case of dealing with a non-uniformly distributed signal. 5.... In PAGE 13: ...2. Identification of NLSs with memory Table 2 shows the eigenvalue spread of the functional covariance matrix of several Volterra and Fourier models with Q=2, for orders N={5, 10} and for the same input distributions of Table1 . As in the previous subsection, the superiority of the Fourier model is evident.... ..."

"... In PAGE 3: ...) where gi gdsi and qj correspond to tramconductance, output conductance and mixing products connected with output umductance phenomena. Typical values are given in Table1 . Hence it can be seen that large signal output conductance is more than a nonlinear resistance across the drain source port.... In PAGE 4: ... For yhfo.045 and gl given in Table1 , R~m2kR, which is supported by Fig 7, but the gain continues to rise linearly. Even if vgs is the input signal, linearity will not occur for realistic values of RL.... In PAGE 4: ...3) and the Volterra coefficients derived from pulse measurements. The Volterra coefficients are given in Table1 . In Fig 7 we can see that the Parker Skellern approximation does tend towards linearity for high RL as predicted in Section 4.... ..."