**5. References**


the construction of Hamiltonian cycles and suboptimal cycles with a length close to that of

Resulting algorithm allows us to construct optimal Hamilton cycles in 3D-tori with number of nodes up to 32768. The usage of this algorithm is actual in modern supercomputers having topology of the 3D-torus for organization of inter-processor communications in

Recurrent neural (Hopfield and Wang) network is a universal technique for solution of optimization problems but it is a local optimization technique, and we need additional modifications (for example, penalty coefficients and splitting) to improve the technique

The proposed algorithm for the construction of Hamiltonian cycles is less universal but more powerful because it implements a global optimization approach and so it is very more

The traditional topology aware mappings ((Parhami, 2002; Yu, Chung & Moreira, 2006; Balaji, Gupta, Vishnu & Beckman, 2011)) are constructed especially for regular graphs (hypercubes and tori) of distributed computer systems. The proposed neural network algorithms are more universal and can be used for mapping program graphs onto graphs of

Balaji, P.; Gupta, R.; Vishnu, A. & Beckman, P. (2011). Mapping Communication Layouts to

Bertsekas, D.P. & Tsitsiklis, J.N. (1989). *Parallel and Distributed Computation: Numerical* 

Chapman, B., Jost, G. & van der Pas, R. (2008). *Using OpenMP : portable shared memory* 

da Silva, I. N.; Amaral, W. C.; Arruda, L. V. & Flauzino, R. A. (2008). Recurrent Neural

Dijkstra, E.W. (1974). Self-stabilizing Systems in Spite of Distributed Control. *Commun.* 

Feng, G. & Douligeris C. (2001). The Convergence and Parameter Relationship for Discrete-

Hopfield, J.J. & Tank, D.W. (1985). Neural Computation of Decisions in Optimization

Hung, D.L. & Wang, J. (2003). Digital hardware realization of a recurrent neural network for solving the assignment problem, *Neurocomputing,* Vol. 51, pp.447-461

*Methods*, Athena scientific, Bellmont, Massachusets: Prentis Hall

*parallel programming* , Cambridge, Massachusetts :The MIT Press

Haykin, S. (1999). *Neural Networks. A Comprehensive Foundation*, Prentice Hall Inc.

Problems, *Biological Cybernetics*, Vol.52, pp.141-152

Network Hardware Characteristics on Massive-Scale Blue Gene Systems, *Comput.* 

Approach for Solving Several Types of Optimization Problems, *Recurrent Neural Networks*, Eds. Xiaolin Hu and P. Balasubramaniam, Croatia: Intech, pp.

Time Continuous-State Hopfield Networks, *Proc. of Intern. Joint Conference on* 

Hamiltonian ones are determined.

scalability.

**5. References** 

229-254

*Neural Networks* 

parallel solution of complicated problems.

scalable than the traditional recurrent neural networks.

*Sci. Res. Dev.*, Vol. 26, pp.247–256

*ACM,* Vol.17, No.11, pp. 643-644

distributed computer systems with defects of edges and nodes.


**11** 

Walid A. Zgallai1,2

*1Wokingham 2Dubai 1U. K. 2U. A. E.* 

**Detection and Classification of Adult and Fetal** 

**Embedded Volterra and Higher-Order Statistics** 

The fetal heart rate (FHR) is a useful tool in the assessment of the condition of the fetal before and during labour. Fetal Electrocardiography (FECG) (Sureau, 1996) uses noninvasive surface electrodes placed on the maternal abdomen is another tool for FHR recording (Sureau, 1996). The fetal signal is weak relative to the maternal signal and to the competing noise. Widrow et al. (Widrow et al., 1975) proposed an adaptive filtering and adaptive noise cancellation method to extract the FECG from the composite maternal ECG signal. Auto-correlation and cross correlation techniques (Van Bemmel, 1968) and spatial filtering techniques (Van Oosterom, 1986, and Bergveld and Meijier 1981) have been proposed. These methods require multiple maternal thoracic ECG signals. Other methods were proposed for the rejection of the disturbing maternal ECG signal (Sureau, 1996). The automated long-term evaluation of FECG is regarded as less robust than CTG. A failure rate of approximately 30% is quoted as an almost unanimous norm (Herbert et al., 1993). The advantage of FECG is that it can be implemented in small and relatively low-cost devices

A proposed technique employing wavelet transform (Khamene and Negahadariapour, 2002) exploits the most distinct features of the signal, leading to more robustness with respect to signal perturbations. The algorithm is validated using high SNR data. Dynamic modelling has been proposed (Schreiber, and D Kaplan, 1996). The data has comparatively high SNR and the fetal heartbeats can be detected by an adaptive matched filter and requires much shorter data samples than the dynamic modelling. The dynamic modelling apparent success at high SNR is offset by the required lengthy data. Due to the beat-to-beat fluctuations of the shape and duration of the ECG waveform, the normal ECG cannot be considered to be deterministic. Determinism is found in adult and fetal ECGs for data lengths of 10,000 samples (Rizk et al., 2002). The independent component analysis (ICA) has been carried out under assumptions (Lathauwer et al., 2000), the validity of each has been challenged (Rizk et

**1. Introduction** 

(Lin et al., 1997).

al., 2001).

**ECG Using Recurrent Neural Networks,** 

Yu, H.; Chung, I.H. & Moreira, J. (2006). Topology Mapping for Blue Gene/L Supercomputer, *Proceedings of the 2006 ACM/IEEE conference on Supercomputing*, ACM Press, New York, NY, USA, pp. 5264
