Comparative Analysis of Models of Gene and Neural Networks

Abstract

In the language of mathematics, the method of cognition of the surrounding world in which the description of the object is carried out the name is mathematical modeling. The study of the model is carried out using certain mathematical methods. The systems of the ordinary differential equations modeling artificial neuronal networks and the systems modeling the gene regulatory networks are considered. The one system consists of a sigmoidal function which depends on linear combinations of the arguments minus the linear part. The other system consists of a sigmoidal function which depends on the hyperbolic tangent function. The linear combinations and hyperbolic tangent functions of the arguments are described by one regulatory matrix. For the three-dimensional cases, two types of matrices are considered and the behavior of the solutions of the system is analyzed. The attracting sets are constructed for several cases. Illustrative examples are provided. The list of references consists of 19 items.

Representation of Omitted Variable Bias with the Total Derivative Method

“…Similarly, model misspecifications stemming from a correlation between the error term and the dependent variables could also be explained by the total differential method. Multicollinearity, cross-section dependency, unit root methods including covariate, models including volatility and covariance, and similar issues in econometrics can be examined in more detail by using the total differential method (see Emrimahmutoðlu [3], Hansen [4], Samuilik et al [5], and Manickam et al [6]). Gujarati [8] used this example to illustrate omitted variable bias:…”

A New 3D Chaotic Attractor in Gene Regulatory Network

“…While various sigmoidal functions exist, the one mentioned above is particularly suitable for analysis and visualization [32]. Such systems were considered in [20,[33][34][35].…”

“…Nonlinear ordinary differential equations are the most widespread formalism for modeling genetic regulatory networks [20]. The main contributions of the present study are summarized as follows:…”

Comparative Analysis of Models of Genetic and Neuronal Networks

“…Particular attention is paid to attractors in systems of both types. Previously the comparison was made between three-dimensional systems, modeling GRN and ANN [16]. In this paper we consider first two-dimensional systems of both kinds, and then we construct four-dimensional GRN and ANN systems, comparing their characteristics, such as the ability to have periodic attractors, Lyapunov exponents etc.…”