By numerically applying the recursive Darboux transformation technique, we study high-order rational solutions of the nonlinear Schrödinger equation that appear spatiotemporally as triangular arrays of Peregrine solitons. These can be considered as rogue wave cascades and complement previously discovered circular cluster forms. In this analysis, we reveal a general parametric restriction for th...

Multiplicative processes and multifractals proved useful in various applications ranging from hydrodynamic turbulence to computer network traffic. Placing multifractal analysis in the more general framework of infinitely divisible laws, we design processes which possess at the same time stationary increments as well as multifractal and more general infinitely divisible scaling over a continuous...

Cascades of period-doubling bifurcations have attracted much interest from researchers of dynamical systems in the past two decades as it is one of the routes to onset of chaos. In this paper we consider routes to onset of chaos involving homoclinic-doubling bifurcations. ∗Partially supported by Grant-in-Aid for Scientific Research (No. 08740139), Ministry of Education, Science and Culture, Japan.

Cascades of information-sharing are a primary mechanism by which content reaches its audience on social media, and an active line of research has studied how such cascades, which form as content is reshared from person to person, develop and subside. In this paper, we perform a large-scale analysis of cascades on Facebook over significantly longer time scales, and find that a more complex pictu...

Two well characterized signal transduction cascades regulating fungal development and virulence are the MAP kinase and cAMP signaling cascades. Here we review the current state of knowledge on cAMP signaling cascades in fungi. While the processes regulated by cAMP signaling in fungi are as diverse as the fungi themselves, the components involved in signal transduction are remarkably conserved. ...

The rise of social networks has greatly contributed to creating information cascades. Overtime, new nodes are added the cascade network, which means network is dynamically variable. At same time, there often only a few in before join. Therefore, it becomes key task predict diffusion after dynamic based on small number observed previous period. However, existing methods limited for short cascade...

Linear-systems theory can be used to characterize the performance of many imaging systems in terms of signal-transfer and noise-transfer relationships. Using this approach, complex systems are described as serial cascades of simple processes. In a series of articles by Shaw, Rabbani, Van Metter, Barrett, Wagner and others, key processes have been identified and relationships developed which des...