Soft bounds on diffusion produce skewed distributions and Gompertz growth

Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the increments of the diffusing variable are subject to configuration-dependent bounds. This work explores theoretically some of the revealing landmarks of such phenomenology, termed "soft bound". At long times, the system reaches a steady state irreversibly (i.e., violating detailed balance), characterized by a skewed "shoulder" in the density distribution, and by a net local probability flux, which has entropic origin. The largest point in the support of the distribution follows a saturating dynamics, expressed by the Gompertz law, in line with empirical observations. Finally, we propose a generic allometric scaling for the origin of soft bounds. These findings shed light on the impact on a system of such "scaling" constraint and on its possible generating mechanisms.Comment: 9 pages, 6 color figure

Quantum Optimization of Fully-Connected Spin Glasses

The Sherrington-Kirkpatrick model with random $\pm1$ couplings is programmed on the D-Wave Two annealer featuring 509 qubits interacting on a Chimera-type graph. The performance of the optimizer compares and correlates to simulated annealing. When considering the effect of the static noise, which degrades the performance of the annealer, one can estimate an improvement on the comparative scaling of the two methods in favor of the D-Wave machine. The optimal choice of parameters of the embedding on the Chimera graph is shown to be associated to the emergence of the spin-glass critical temperature of the embedded problem.Comment: includes supplemental materia

Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management

We present the mapping of a class of simplified air traffic management (ATM) problems (strategic conflict resolution) to quadratic unconstrained boolean optimization (QUBO) problems. The mapping is performed through an original representation of the conflict-resolution problem in terms of a conflict graph, where nodes of the graph represent flights and edges represent a potential conflict between flights. The representation allows a natural decomposition of a real world instance related to wind-optimal trajectories over the Atlantic ocean into smaller subproblems, that can be discretized and are amenable to be programmed in quantum annealers. In the study, we tested the new programming techniques and we benchmark the hardness of the instances using both classical solvers and the D-Wave 2X and D-Wave 2000Q quantum chip. The preliminary results show that for reasonable modeling choices the most challenging subproblems which are programmable in the current devices are solved to optimality with 99% of probability within a second of annealing time.Comment: Paper accepted for publication on: IEEE Transactions on Intelligent Transportation System