Considering that the movements of complex system entities take place on continuous, but non-differentiable, curves, concepts, like non-differentiable entropy, informational non-differentiable entropy and informational non-differentiable energy, are introduced. First of all, the dynamics equations of the complex system entities (Schrödinger-type or fractal hydrodynamic-type) are obtained. The la...

Solving equations of the form H(x)=0 is one most faced problem in mathematics and other science fields such as chemistry or physics. This kind cannot be solved without use iterative methods. The Steffensen-type methods, defined using divided differences are derivative free, usually considered to solve these problems when H a non-differentiable operator due its accuracy efficiency. However, gene...

Assuming that the motions of a complex system structural units take place on continuous, but non-differentiable curves of a space-time manifold, the scale relativity model with arbitrary constant fractal dimension (the hydrodynamic and wave function versions) is built. For non-differentiability through stochastic processes of the Markov type, the non-differentiable entropy concept on a space-ti...

We introduce a paradigm for understanding physical scenes without human annotations. At the core of our system is a physical world representation that is first recovered by a perception module and then utilized by physics and graphics engines. During training, the perception module and the generative models learn by visual de-animation — interpreting and reconstructing the visual information st...