REALIZATION OF BOOLEAN FUNCTIONS VIA CNN WITH VON NEUMANN NEIGHBORHOODS

2006 ◽  
Vol 16 (05) ◽  
pp. 1389-1403 ◽  
Author(s):  
FANGYUE CHEN ◽  
GUOLONG HE ◽  
GUANRONG CHEN
Keyword(s):  
Neural Networks ◽  
Boolean Functions ◽  
Cellular Neural Networks ◽  
Gene Bank ◽  
Truth Table ◽  
Bifurcation Method ◽  
Von Neumann ◽  
The Family ◽  
Binary Input ◽  
Input Variables

Recently, an effective method for realizing linearly separable Boolean functions via Cellular Neural Networks (CNN), called the threshold bifurcation method, was introduced, with a CNN gene bank of four variables established [Chen & Chen, 2005]. Based on this success, the present paper is to further explore the realization of all linearly separable Boolean functions of five variables via CNN with von Neumann neighborhoods. This paper provides: (i) important and essential relations among the genes (or templates) and the offsets of an uncoupled CNN as well as the basis of the binary input vectors set, (ii) a neat truth table of uncoupled CNN with five input variables, (iii) 94572 linearly separable Boolean functions (LSBF) in the family of 225 = 4.294967296 × 109 Boolean functions of five variables, realizable by a single CNN, and (iv) all 94572 CNN linearly separable Boolean genes (LSBG), which can be determined to form the CNN gene bank of five variables.

scholarly journals REALIZATION AND BIFURCATION OF BOOLEAN FUNCTIONS VIA CELLULAR NEURAL NETWORKS

2005 ◽  
Vol 15 (07) ◽  
pp. 2109-2129 ◽  
Author(s):  
FANGYUE CHEN ◽  
GUANRONG CHEN
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Boolean Function ◽  
Boolean Functions ◽  
Cellular Neural Network ◽  
Cellular Neural Networks ◽  
Gene Bank ◽  
Engineering Applications ◽  
Binary Input

In this work, we study the realization and bifurcation of Boolean functions of four variables via a Cellular Neural Network (CNN). We characterize the basic relations between the genes and the offsets of an uncoupled CNN as well as the basis of the binary input vectors set. Based on the analysis, we have rigorously proved that there are exactly 1882 linearly separable Boolean functions of four variables, and found an effective method for realizing all linearly separable Boolean functions via an uncoupled CNN. Consequently, any kind of linearly separable Boolean function can be implemented by an uncoupled CNN, and all CNN genes that are associated with these Boolean functions, called the CNN gene bank of four variables, can be easily determined. Through this work, we will show that the standard CNN invented by Chua and Yang in 1988 indeed is very essential not only in terms of engineering applications but also in the sense of fundamental mathematics.

IDENTIFICATION AND REALIZATION OF LINEARLY SEPARABLE BOOLEAN FUNCTIONS VIA CELLULAR NEURAL NETWORKS

2008 ◽  
Vol 18 (11) ◽  
pp. 3299-3308 ◽  
Author(s):  
BO MI ◽  
XIAOFENG LIAO ◽  
CHUANDONG LI
Keyword(s):  
Neural Networks ◽  
Directed Graph ◽  
Boolean Functions ◽  
Cellular Neural Networks ◽  
Truth Table

In this paper, an effective method for identifying and realizing linearly separable Boolean functions (LSBF) of six variables via Cellular Neural Networks (CNN) is presented. We characterized the basic relations between CNN genes and the truth table of Boolean functions. In order to implement LSBF independently, a directed graph is employed to sort the offset levels according to the truth table. Because any linearly separable Boolean gene (LSBG) can be derived separately, our method will be more practical than former schemes [Chen & Chen, 2005a, 2005b; Chen & He, 2006].

ON THE MARGIN OF COMPLETE STABILITY FOR A CLASS OF CELLULAR NEURAL NETWORKS

2008 ◽  
Vol 18 (05) ◽  
pp. 1343-1361 ◽  
Author(s):  
MAURO DI MARCO ◽  
MAURO FORTI ◽  
ALBERTO TESI
Keyword(s):  
Neural Networks ◽  
Dynamical Behavior ◽  
Stability Margin ◽  
Cellular Neural Networks ◽  
Third Order ◽  
Dimensional Parameter ◽  
The Family ◽  
A New Technique ◽  
Two Parameters

In this paper, the dynamical behavior of a class of third-order competitive cellular neural networks (CNNs) depending on two parameters, is studied. The class contains a one-parameter family of symmetric CNNs, which are known to be completely stable. The main result is that it is a generic property within the family of symmetric CNNs that complete stability is robust with respect to (small) nonsymmetric perturbations of the neuron interconnections. The paper also gives an exact evaluation of the complete stability margin of each symmetric CNN via the characterization of the whole region in the two-dimensional parameter space where the CNNs turn out to be completely stable. The results are established by means of a new technique to investigate trajectory convergence of the considered class of CNNs in the nonsymmetric case.

FINGERPRINT FEATURE EXTRACTION VIA CNN WITH VON NEUMANN NEIGHBORHOOD

2007 ◽  
Vol 17 (11) ◽  
pp. 4145-4151 ◽  
Author(s):  
YIJUN LOU ◽  
FANGYUE CHEN ◽  
JUNBIAO GUAN
Keyword(s):  
Feature Extraction ◽  
Gene Bank ◽  
Von Neumann ◽  
Input Variables ◽  
Fingerprint Feature Extraction ◽  
Fingerprint Feature

In this paper, we study fingerprint feature extraction via CNN with Von Neumann neighborhood. The extraction was implemented by using CNN with nine input variables, and we find that the process could also be implemented with only five variables, and an easier algorithm without compromising the effectiveness. According to the CNN model with five input variables and the corresponding CNN gene bank done by Chen et al. [2006, Http1], we can determine the CNN gene easily. Simultaneously, we also find some results in one of the references are incorrect.

ИСПОЛЬЗОВАНИЕ НЕЙРОСЕТЕВЫХ АЛГОРИТМОВ В ЗАДАЧАХ ВЫЧИСЛИТЕЛЬНОЙ ЛИТОГРАФИИ

2020 ◽  
Vol 96 (3s) ◽  
pp. 543-548
Author(s):  
Н.Н. Балан ◽  
А.А. Березин ◽  
Е.С. Горнев ◽  
В.В. Иванов ◽  
Е.В. Ипатова ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
The Family ◽  
Pros And Cons

Работа посвящена вопросам применения нейросетевых алгоритмов в литографических расчетах. Дан обзор основного круга задач вычислительной литографии, допускающих целесообразность применения нейросетей для их решения. Описаны преимущества и недостатки нейросетевых решений, рекомендуемых для использования в рассматриваемых задачах. This paper is dedicated to the task of applying neural network-based algorithms to lithographic calculations. It reviews the family of problems in computational lithography to which neural networks are applicable. Pros and cons of such solutions have been discussed.

Prediction Modeling of PM-10 in Chiangmai City Moat by Using Artificial Neural Networks

2015 ◽  
Vol 781 ◽  
pp. 628-631 ◽  
Author(s):  
Rati Wongsathan ◽  
Issaravuth Seedadan ◽  
Metawat Kavilkrue
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Prediction Model ◽  
Chiang Mai ◽  
Adverse Health Effects ◽  
High Pollution ◽  
Artificial Neural ◽  
Input Variables ◽  
Pm 10 ◽  
Respiratory Conditions

A mathematical prediction model has been developed in order to detect particles with a diameter of 10 micrometers or less (PM-10) that are responsible for adverse health effects because of their ability to cause serious respiratory conditions in areas of high pollution such as Chiang Mai City moat area. The prediction model is based on 3 types of Artificial Neural Networks (ANNs), including Multi-layer perceptron (MLP-NN), Radial basis function (RBF-NN), and hybrid of RBF and Genetic algorithm (RBF-NN-GA). The model uses 8 input variables to predict PM-10, consisting of 4 air pollution substances ( CO, O3, NO2 and SO2) and 4 meteorological variables related PM-10 (wind speed, temperature, atmospheric pressure and relative humidity). These 3 types of ANN have proved efficient instrument in predicting the PM-10. However, the performance of RBF-NN was superior in comparison with MLP-NN and RBF-NN-GA respectively.

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