Limits...
Asymmetric variate generation via a parameterless dual neural learning algorithm.

Fiori S - Comput Intell Neurosci (2008)

Bottom Line: In a previous work (S.Fiori, 2006), we proposed a random number generator based on a tunable non-linear neural system, whose learning rule is designed on the basis of a cardinal equation from statistics and whose implementation is based on look-up tables (LUTs).The new method proposed here proves easier to implement and relaxes some previous limitations.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Elettronica, Intelligenza Artificiale e Telecomunicazioni (DEIT), Università Politecnica delle Marche Via Brecce Bianche, Ancona I-60131, Italy. fiori@deit.univpm.it

ABSTRACT
In a previous work (S. Fiori, 2006), we proposed a random number generator based on a tunable non-linear neural system, whose learning rule is designed on the basis of a cardinal equation from statistics and whose implementation is based on look-up tables (LUTs). The aim of the present manuscript is to improve the above-mentioned random number generation method by changing the learning principle, while retaining the efficient LUT-based implementation. The new method proposed here proves easier to implement and relaxes some previous limitations.

No MeSH data available.


Related in: MedlinePlus

Neural system, neural dual system, input/output sample spaces andtheir statistical distributions.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC2376097&req=5

fig1: Neural system, neural dual system, input/output sample spaces andtheir statistical distributions.

Mentions: A well-known effect of nonlinear neural systems is towarp the statistical distribution of its input. In particular, we assume thatthe system under consideration has a nonlinear adaptive structure described bythe transference y = f(x), where x ∈ 𝒳 ⊆ ℝdenotes the system input random signal, having probability density function px(x), and y ∈ 𝓎 ⊆ ℝ denotes the outputsignal, having probability density function py(y), as shown in Figure 1. In the hypothesis that the neural systemtransference is strictly monotonic, namely f′ (x) > 0, for all x ∈ 𝒳, the relationship between the input distribution, theoutput distribution, and the system transfer function is known to be [9](1)py(y)=px(x)f′(x) /x=f−1(y), x∈X,where f−1(⋅) denotes theinverse of function f(⋅). Usually, (1) is interpreted as an analysis formula, which allowscomputing the output distribution when the input distribution and the systemtransference function are known. However, the cardinal equation (1) may also be interpreted as a formula that allows fordesigning the nonlinear system when the distribution px(⋅) is known and itis desired that the system responds according to a desired distribution py(⋅). In fact, (1) may be rewritten as the differential equation:(2)f′(x)=px(x)py(f(x)), x∈X.In general, such design operation is rather difficult, because (2) in the unknown f(⋅) involves the solution of a nonlinear differential equation, provided that a consistentboundary condition is specified.


Asymmetric variate generation via a parameterless dual neural learning algorithm.

Fiori S - Comput Intell Neurosci (2008)

Neural system, neural dual system, input/output sample spaces andtheir statistical distributions.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2376097&req=5

fig1: Neural system, neural dual system, input/output sample spaces andtheir statistical distributions.
Mentions: A well-known effect of nonlinear neural systems is towarp the statistical distribution of its input. In particular, we assume thatthe system under consideration has a nonlinear adaptive structure described bythe transference y = f(x), where x ∈ 𝒳 ⊆ ℝdenotes the system input random signal, having probability density function px(x), and y ∈ 𝓎 ⊆ ℝ denotes the outputsignal, having probability density function py(y), as shown in Figure 1. In the hypothesis that the neural systemtransference is strictly monotonic, namely f′ (x) > 0, for all x ∈ 𝒳, the relationship between the input distribution, theoutput distribution, and the system transfer function is known to be [9](1)py(y)=px(x)f′(x) /x=f−1(y), x∈X,where f−1(⋅) denotes theinverse of function f(⋅). Usually, (1) is interpreted as an analysis formula, which allowscomputing the output distribution when the input distribution and the systemtransference function are known. However, the cardinal equation (1) may also be interpreted as a formula that allows fordesigning the nonlinear system when the distribution px(⋅) is known and itis desired that the system responds according to a desired distribution py(⋅). In fact, (1) may be rewritten as the differential equation:(2)f′(x)=px(x)py(f(x)), x∈X.In general, such design operation is rather difficult, because (2) in the unknown f(⋅) involves the solution of a nonlinear differential equation, provided that a consistentboundary condition is specified.

Bottom Line: In a previous work (S.Fiori, 2006), we proposed a random number generator based on a tunable non-linear neural system, whose learning rule is designed on the basis of a cardinal equation from statistics and whose implementation is based on look-up tables (LUTs).The new method proposed here proves easier to implement and relaxes some previous limitations.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Elettronica, Intelligenza Artificiale e Telecomunicazioni (DEIT), Università Politecnica delle Marche Via Brecce Bianche, Ancona I-60131, Italy. fiori@deit.univpm.it

ABSTRACT
In a previous work (S. Fiori, 2006), we proposed a random number generator based on a tunable non-linear neural system, whose learning rule is designed on the basis of a cardinal equation from statistics and whose implementation is based on look-up tables (LUTs). The aim of the present manuscript is to improve the above-mentioned random number generation method by changing the learning principle, while retaining the efficient LUT-based implementation. The new method proposed here proves easier to implement and relaxes some previous limitations.

No MeSH data available.


Related in: MedlinePlus