Network logic analysis

Glass L. and Kauffman S. A. (1973). The logical analysis of continuous, nonlinear biochemical control networks. Journal of Theoretical Biology. 39, pp 103-129. 

Thomas R. and Kaufman M. (2001b). Multistationaiity, the basis of cell differentiation and memory, logical analysis of regulatory networks in terms of feedback circuits. Chaos. 11, pp 180-195. 

Glass, L. S.A. Kauffman. 1973. The logical analysis of continuous non-linear biochemical control networks. J. Theor. Biol. 39 103-29. 

Theodoridis, Sergio, and Konstantinos Koutroumbas. Pattern Recognition. 4th ed. Boston Academic Press, 2009. A complex introduction to the field, with information about pattern recognition algorithms, neural networks, logical systems, and statistical analysis. 

Sadiq, R., Kleinei Y. Rajani, B., 2007. Water quality failures in distribution networks— risk analysis using fuzzy logic and evidential reasoning. Risk Analysis, 27(5) 1381 1394. 

A technique widely used by the industry is Critical Path Analysis (CPA or Network Analysis ) which is a method for systematically analysing the schedule of large projects, so that activities within a project can be phased logically, and dependencies identified. All activities are given a duration and the longest route through the network is known as the critical path. 

LOGICAL DESCRIPTION, ANALYSIS, AND SYNTHESIS OF BIOLOGICAL AND OTHER NETWORKS COMPRISING FEEDBACK LOOPS... 

Methods for analysing the response of complex multicomponent-multifunctional systems will be needed. Global responses may be submitted to deconvolution procedures and multicomponent analysis [8.298], making use for instance of pattern recognition [8.238, 8.299], neural network [8.238, 8.300] and fuzzy logic [8.301] approaches. 

Thus, multilinear models were introduced, and then a wide series of tools, such as nonlinear models, including artificial neural networks, fuzzy logic, Bayesian models, and expert systems. A number of reviews deal with the different techniques [4-6]. Mathematical techniques have also been used to keep into account the high number (up to several thousands) of chemical descriptors and fragments that can be used for modeling purposes, with the problem of increase in noise and lack of statistical robustness. Also in this case, linear and nonlinear methods have been used, such as principal component analysis (PCA) and genetic algorithms (GA) [6]. 

Control based on neural network. Similar to fuzzy logic modeling, neural network analysis uses a series of previous data to execute simulations of the process, with a high degree of success, without however using formal mathematical models (Chen and Rollins, 2000). To this goal, it is necessary to define inputs, outputs, and how many layers of neurons will be used, which depends on the number of variables and the available data. 

Fredericks et al. (1985) describe materials characterization by factor analysis of IR spectra . Wold et al. (1987) the principal component analysis , and Haaland and Thomas (1988) materials characterization using factor analyses of FT-IR spectra . Of special importance are the procedures using fuzzy logic and neural networks (Harrington, 1991 Zupan and Gasteiger, 1993). 

Nevertheless, where this procedure is applicable it can lead to elegant solutions to difficult synthetic problems. An example of the power of the method is found in Corey s "network analysis" of longi-foline.9 More recently,10 a synthesis of porantherine grew out of the logic-centered analysis summarized below ... 

In the remainder of this review we focus on the mathematical analysis of the piecewise linear equations largely based on earlier studies [34-48]. In Section IV we show that the logical structure can be mapped onto a hypercube in N dimensions, where each vertex of the hypercube represents the state of each of the N variables, and the dynamics and logical structure in the network are represented as directed edges on the hypercube. 

An underlying motivation for our mathematical analysis is to answer the following questions Once the logical structure in Eq. (3) of a network is set, then what are the possible dynamics in the associated differential equation, Eq. (5), for any choice of parameters What are the dynamics for each particular set cf parameters We are only able to answer this question in some limited cases. 

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