Biological System Modeling based on Fourier Series

2012 ◽  
Author(s):  
R. Guzman-Cabrera ◽  
J. R. Guzman-Sepulveda ◽  
M. Torres-Cisneros ◽  
O. G. Ibarra Manzano
Keyword(s):  
Fourier Series ◽  
Biological System ◽  
System Modeling ◽  
Biological System Modeling

NEURAL SYSTEM MODELING AND SIMULATION USING HYBRID FUNCTIONAL PETRI NET

2012 ◽  
Vol 10 (01) ◽  
pp. 1240006 ◽  
Author(s):  
YIN TANG ◽  
FEI WANG
Keyword(s):  
Petri Net ◽  
System Modeling ◽  
Neural System ◽  
Biological Data ◽  
Adrenergic System ◽  
Hybrid Functional ◽  
Classical Systems ◽  
Supplementary Material ◽  
Biological System Modeling ◽  
Electrical Chemistry

The Petri net formalism has been proved to be powerful in biological modeling. It not only boasts of a most intuitive graphical presentation but also combines the methods of classical systems biology with the discrete modeling technique. Hybrid Functional Petri Net (HFPN) was proposed specially for biological system modeling. An array of well-constructed biological models using HFPN yielded very interesting results. In this paper, we propose a method to represent neural system behavior, where biochemistry and electrical chemistry are both included using the Petri net formalism. We built a model for the adrenergic system using HFPN and employed quantitative analysis. Our simulation results match the biological data well, showing that the model is very effective. Predictions made on our model further manifest the modeling power of HFPN and improve the understanding of the adrenergic system. The file of our model and more results with their analysis are available in our supplementary material.

Fourier Series Neural Network Analysis of a Steer-by-Wire System

2002 ◽  
Author(s):  
Val D. Mills ◽  
John R. Wagner ◽  
Imtiaz Haque
Keyword(s):  
Neural Network ◽  
Fourier Series ◽  
System Modeling ◽  
Nonlinear Behavior ◽  
Behavioral Model ◽  
Activation Function ◽  
Steering System ◽  
Attractive Alternative ◽  
Steer By Wire ◽  
Wire System

Automotive steering system research has traditionally focused on improving vehicle handling and safety, as well as investigating lateral dynamic issues. The emergence of hybrid vehicles provides a motivation for steer-by-wire technology in terms of power source availability and improved performance. From a design perspective, steering systems are difficult to accurately model due to the inherent nonlinearities present in the steering assembly, chassis, wheels, and tire/road interface. One modeling strategy that merits further attention is the Fourier Series Neural Network (FSNN) which has been proven effective for the characterization of dynamic systems. A neural network can approximate nonlinear functions to a high degree of accuracy, given an adequate network structure and sufficient training. In this paper, a Fourier Series activation function neural network will be studied to identify a steer-by-wire system. A behavioral model has been developed for the driver interface and directional control assembly of the rack and pinion steer-by-wire system. Representative numerical results are presented to demonstrate the FSNN’s ability to predict the system’s overall transfer function. This engineering tool may provide an attractive alternative to rigorous system modeling, and inherently captures the response characteristics due to the nonlinear behavior.

Topology Optimization of IPM Motors using Fourier Series

2017 ◽  
Vol 137 (3) ◽  
pp. 245-253
Author(s):  
Hidenori Sasaki ◽  
Hajime Igarashi
Keyword(s):  
Fourier Series ◽  
Topology Optimization

The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series

2008 ◽  
Vol 45 (3) ◽  
pp. 321-331
Author(s):  
István Blahota ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Maximal Operator ◽  
Fejér Means

In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H2/3 ( G2 ) to the space L2/3 ( G2 ).

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