Policy, design and management: the in-vivo laboratory for the science of complex socio-technical systems

Complex systems scientists cannot by themselves perform experiments on complex socio-technical systems. The best they can do is to perform experiments alongside policy makers who are constantly engaged in experiments as the design and manage the systems the systems for which they are responsible. In this context the nature of prediction in the implementation of real systems is much more complicated than it is in traditional science. The goals identified by policymakers change through time, and this is usually managed through the design and management processes. The combination of policy and design is the opportunity – the only opportunity – for complex systems scientists to engage and to be allowed to be involved in in-vivo experiments in large socio-technical systems. In turn this opens up new methodological approaches and questions for the science of complex systems

Quantal-Classical Duality and the Semiclassical Trace Formula

We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum of actions of periodic orbits in the classical description. This duality is investigated in the present paper. The duality holds for chaotic as well as for integrable systems. For billiards the quantal spectrum (eigenvalues of the Helmholtz equation) and the classical spectrum (lengths of periodic orbits) are two manifestations of the billiard's boundary. The trace formula expresses this link as a Fourier transform relation between the corresponding spectral densities. It follows that the two-point statistics are also simply related. The universal correlations of the quantal spectrum are well known, consequently one can deduce the classical universal correlations. An explicit expression for the scale of the classical correlations is derived and interpreted. This allows a further extension of the formalism to the case of complex billiard systems, and in particular to the most interesting case of diffusive system. The concept of classical correlations allows a better understanding of the so-called diagonal approximation and its breakdown. It also paves the way towards a semiclassical theory that is capable of global description of spectral statistics beyond the breaktime. An illustrative application is the derivation of the disorder-limited breaktime in case of a disordered chain, thus obtaining a semiclassical theory for localization. A numerical study of classical correlations in the case of the 3D Sinai billiard is presented. We gain a direct understanding of specific statistical properties of the classical spectrum, as well as their semiclassical manifestation in the quantal spectrum.Comment: 42 pages, 17 figure

Complex quotients by nonclosed groups and their stratifications

We define the notion of complex stratification by quasifolds and show that such spaces occur as complex quotients by certain nonclosed subgroups of tori associated to convex polytopes. The spaces thus obtained provide a natural generalization to the nonrational case of the notion of toric variety associated with a rational convex polytope.Comment: Research announcement. Updated version, shortened, exposition improved, 8 p

Representation of complex probabilities and complex Gibbs sampling

Complex weights appear in Physics which are beyond a straightforward importance sampling treatment, as required in Monte Carlo calculations. This is the well-known sign problem. The complex Langevin approach amounts to effectively construct a posi\-tive distribution on the complexified manifold reproducing the expectation values of the observables through their analytical extension. Here we discuss the direct construction of such positive distributions paying attention to their localization on the complexified manifold. Explicit localized repre\-sentations are obtained for complex probabilities defined on Abelian and non Abelian groups. The viability and performance of a complex version of the heat bath method, based on such representations, is analyzed.Comment: Proceedings of Lattice 2017 (The 35th International Symposium on Lattice field Theory). 8 pages, 4 figure

Complex Beauty

Complex systems and their underlying convoluted networks are ubiquitous, all we need is an eye for them. They pose problems of organized complexity which cannot be approached with a reductionist method. Complexity science and its emergent sister network science both come to grips with the inherent complexity of complex systems with an holistic strategy. The relevance of complexity, however, transcends the sciences. Complex systems and networks are the focal point of a philosophical, cultural and artistic turn of our tightly interrelated and interdependent postmodern society. Here I take a different, aesthetic perspective on complexity. I argue that complex systems can be beautiful and can the object of artification - the neologism refers to processes in which something that is not regarded as art in the traditional sense of the word is changed into art. Complex systems and networks are powerful sources of inspiration for the generative designer, for the artful data visualizer, as well as for the traditional artist. I finally discuss the benefits of a cross-fertilization between science and art

Anomalous diffusion in a symbolic model

We address this work to investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following a power law probability density. In this analysis, we consider that the sum of n symbols represents the position of a particle in erratic movement. This approach revealed a rich diffusive scenario characterized by non-Gaussian distributions and, depending on the power law exponent and also on the procedure used to build the walker, we may have superdiffusion, subdiffusion or usual diffusion. Additionally, we use the continuous-time random walk framework to compare with the numerical data, finding a good agreement. Because of its simplicity and flexibility, this model can be a candidate to describe real systems governed by power laws probabilities densities.Comment: Accepted for publication in Physica Script