Mathematical Problems for Complex Networks

Mathematical Problems for Complex Networks

Mathematical Problems for Complex Systems

As most of practical systems have high complexity, complex systems have become a rapidly growing area of mathematics and attracted many researchers. The study of complex systems not only has an important theoretical interest but also is motivated by problems from applied mathematics including physics, chemistry, astronomy, technology, and natural and social sciences. It should be noted that som...

Mathematical problems arising from biochemical reaction networks

Recent developments have suggested the feasibility of mathematical analysis of biochemical reaction networks arising in systems biology and related disciplines, using methods from computational algebra, algebraic geometry and dynamical systems. Because of the nonlinearity of such systems, previous approaches have largely relied on numerical simulation. Mathematical analysis has provided new bio...

A Mathematical Motivation for Complex-Valued Convolutional Networks

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors, followed by (2) taking the absolute value of every entry of the resulting vectors, followed by (3) local averaging. For processing r...

Mathematical models for epidemic spreading on complex networks

We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation, widely exploited for most of the models. Using discrete approach we investigate the epidemic threshold and the quasi-stationary distribution. The main resul...