Time to focus again on matrix metalloproteinases? Results of complex network analysis involving the pathophysiology of HER2-positive breast cancer.

Breast cancer is the most common cancer in women worldwide, with significant advances in understanding its multifactorial nature in recent years. The complex structure of molecular and cellular interactions in cancer pathophysiology presents challenges for developing effective treatments. One theoretical model used to study these interactions is the Graph model or Complex Networks, which uses mathematical methods to create graphical figures by connecting vertices (factors) through edges (interactions).

Stickiness and recurrence plots: An entropy-based approach.

The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RPs), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting regular and chaotic regions. We show that the recurrence time entropy (RTE) is positively correlated to the largest Lyapunov exponent, with a high correlation coefficient.

Dynamics, multistability, and crisis analysis of a sine-circle nontwist map.

We propose a one-dimensional dynamical system, the sine-circle nontwist map, that can be considered a local approximation of the standard nontwist map and an extension of the paradigmatic sine-circle map. The map depends on three parameters, exhibiting a simple mathematical form but with a rich dynamical behavior. We identify periodic, quasiperiodic, and chaotic solutions for different parameter sets with the Lyapunov exponent and Slater's theorem.