In the field of biological regulation, models extracted from experimental works are usually complex networks comprising intertwined feedback circuits. R. Thomas and coworkers introduced a qualitative description of such regulatory networks, then they used the concept of circuit-characteristic states to identify all steady states and functional circuits. These characteristic states play an essen...

In this paper, we propose a new modular approach called neuroglial consisting of two neural networks slow and fast which emulates a biological reality recently discovered. The implementation is based on complex multi-time scale systems; validation is performed on the model of the asynchronous machine. We applied the geometric approach based on the Gerschgorin circles for the decoupling of fast ...

Singular Value Decomposition (SVD) is a technique based on linear projection theory, which has been frequently used for data analysis. It constitutes an optimal (in the sense of least squares) decomposition of a matrix in the most relevant directions of the data variance. Usually, this information is used to reduce the dimensionality of the data set in a few principal projection directions, thi...

It is well known that the initialization of weights in deep neural networks can have a dramatic impact on learning speed. For example, ensuring the mean squared singular value of a network’s input-output Jacobian isO(1) is essential for avoiding the exponential vanishing or explosion of gradients. The stronger condition that all singular values of the Jacobian concentrate near 1 is a property k...

Any line is associated with a two-parameter group of polar complexes relative to a given first-order line complex that are called tangential complexes when the line belongs to the complex. The congruence that is determined by the tangential complex of a complex line is of a special kind, in that both of its directrices coincide in a single line that is the complex line itself. It is of a specia...

We are concerned with polynomial ordinary differential systems that arise from modelling chemical reaction networks. For such systems, which may be of high dimension and depend on many parameters, it is frequently interest to obtain a reduction in certain parameter ranges. Singular perturbation theory, as initiated by Tikhonov Fenichel, provides path toward reductions. In the present paper we d...

In this paper, the solution of a moving Volterra-type screw dislocation in an orthotropic layer, bonded between two piezoelectric layers is obtained using complex Fourier transform. The dislocation solution is then employed as strain nuclei to derive singular integral equations for a medium weakened by multiple moving cracks. These equations, which are classified as, Cauchy singular equations, ...

Secret key extraction is a crucial issue in physical layer security and a less complex and, at the same time, a more robust scheme for the next generation of 5G and beyond. Unlike previous works on this topic, in which Orthogonal Frequency Division Multiplexing (OFDM) sub-channels were considered to be independent, the effect of correlation between sub-channels on the secret key rate is address...

This paper investigates finite-time synchronization of the singular hybrid coupled networks. The singular systems studied in this paper are assumed to be regular and impulse-free. Some sufficient conditions are derived to ensure finite-time synchronization of the singular hybrid coupled networks under a state feedback controller by using finite-time stability theory. A numerical example is fina...