The contributions to this quantity overview the mathematical description of advanced phenomena from either a deterministic and stochastic perspective. The interface among theoretical types and the certainty of complexity in engineering, physics and chemistry is explored. The reader will locate details on neural networks, chemical dissipation, fractal diffusion, difficulties in accelerator and fusion physics, trend formation and self-organisation, keep an eye on difficulties in areas of insta- bility, and mathematical modeling in biology.
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