How Self Organising systems work part2(Intelligent Systems)
1.Neural Stochastic Control (arXiv)
Author : Jingdong Zhang, Qunxi Zhu, Wei Lin
Abstract : Control problems are always challenging since they arise from the real-world systems where stochasticity and randomness are of ubiquitous presence. This naturally and urgently calls for developing efficient neural control policies for stabilizing not only the deterministic equations but the stochastic systems as well. Here, in order to meet this paramount call, we propose two types of controllers, viz., the exponential stabilizer (ES) based on the stochastic Lyapunov theory and the asymptotic stabilizer (AS) based on the stochastic asymptotic stability theory. The ES can render the controlled systems exponentially convergent but it requires a longcomputational time; conversely, the AS makes the training much faster but it can only assure the asymptotic (not the exponential) attractiveness of the control targets. These two stochastic controllers thus are complementary in applications. We also investigate rigorously the linear controller and the proposed neural stochastic controllers in both convergence time and energy cost and numerically compare them in these two indexes. More significantly, we use several representative physical systems to illustrate the usefulness of the proposed controllers in stabilization of dynamical systems.
2.The universality of self-organisation: a path to an atom printer? (arXiv)
Author : Serim Ilday, F. Oemer Ilday
Abstract : More than thirty years ago, Donald Eigler and Erhard Schweizer spelt the letters IBM by positioning 35 individual Xenon atoms at 4 Kelvin temperature using a scanning tunnelling microscope. The arrangement took approximately 22 hours. This was an outstanding demonstration of control over individual atoms. Since then, 3D printers developed into a near-ubiquitous technology. Nevertheless, with typical resolutions in the micrometres, they are far from the atomic scale of control that the IBM demonstration seemed to herald. Even the highest resolution achieved with ultrafast lasers driving two-photon polymerization barely reaches 100 nm, three orders of magnitude distant from the atomic scale. Here, we adopt a long-term view when we ask about the possibility of a 3D atom printer, which can build an arbitrarily shaped object of macroscopic dimensions with control over its atomic structure at room temperature and within a reasonable amount of time. Afterdiscussing the state-of-the-art technology based on direct laser writing, we identify three fundamental challenges to overcome. The first is the fat fingers problem, which refers to laser wavelengths being much larger than the size of the atoms. The second one is complexity explosion; namely, the number of processing steps scales with the inverse cube of the resolution, leading to prohibitively long processing times. The third challenge is the increasing strength of random fluctuations as the size of the smallest volume element to be printed approaches the atomic scale. This requires control over the fluctuations, which we call mischief of fluctuations. Although direct- writing techniques offer sufficient resolution, speed, and excellent flexibility for the mesoscopic scale, each of the three fundamental problems above appears enough to render the atomic scale unreachable. In contrast, the three challenges of direct writing are not fundamental limitations to self-organisation. This chapter proposes a potential path to a 3D atom printer, where laser-driven self-organisation can complement direct-writing techniques by bridging the atomic and mesoscopic scales.
3.Temporal, structural, and functional heterogeneities extend criticality and antifragility in random Boolean networks (arXiv)
Author : Amahury Jafet López-Díaz, Fernanda Sánchez-Puig, Carlos Gershenson
Abstract : Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality— a balance between change and stability, order and chaos — is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks — a general model of discrete dynamical systems — we show that heterogeneity — in time, structure, and function — can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the “optimal” balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic.
