Computationally Tractable Pairwise Complexity Profile

Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the information to describe a system as a function of the scale at which it is observed. We present a new formulation of the complexity profile, which expands its possible application to high-dimensional real-world and mathematically defined systems. The new method is constructed from the pairwise dependencies between components of the system. The pairwise approach may serve as both a formulation in its own right and a computationally feasible approximation to the original complexity profile. We compare it to the original complexity profile by giving cases where they are equivalent, proving properties common to both methods, and demonstrating where they differ. Both formulations satisfy linear superposition for unrelated systems and conservation of total degrees of freedom (sum rule). The new pairwise formulation is also a monotonically non-increasing function of scale. Furthermore, we show that the new formulation defines a class of related complexity profile functions for a given system, demonstrating the generality of the formalism.Comment: 18 pages, 3 figure

Two tribunals and an appeal in Seychelles : monitoring and enforcement of legal ethics in a small jurisdiction

On paper, the legal profession in Seychelles does appear to be governed by ethical rules of conduct backed up by appropriate mechanisms for enforcement. However, on closer inspection, it appears that in practice these mechanisms function erratically, if at all. This paper examines the regulatory gap between theory and practice, focusing on recent examples of enforcement actions against lawyers and judges in the jurisdiction. It goes on to discuss possible reasons for this gap, including a lack of ethical education, lack of peer pressure or other incentive to maintain ethical standards, and deficiencies in independence and impartiality of disciplinary tribunals. These reasons are discussed in the context of the small scale of the legal profession in a micro-jurisdiction.peer-reviewe

Multi-hadron-state contamination in nucleon observables from chiral perturbation theory

Multi-particle states with additional pions are expected to be a non-negligible source of the excited-state contamination in lattice simulations at the physical point. It is shown that baryon chiral perturbation theory (ChPT) can be employed to calculate the contamination due to two-particle nucleon-pion states in various nucleon observables. Results to leading order are presented for the nucleon axial, tensor and scalar charge and three Mellin moments of parton distribution functions: the average quark momentum fraction, the helicity and the transversity moment. Taking into account experimental and phenomenological results for the charges and moments the impact of the nucleon-pion-states on lattice estimates for these observables can be estimated. The nucleon-pion-state contribution leads to an overestimation of all charges and moments obtained with the plateau method. The overestimation is at the 5-10% level for source-sink separations of about 2 fm. Existing lattice data is not in conflict with the ChPT predictions, but the comparison suggests that significantly larger source-sink separations are needed to compute the charges and moments with few-percent precision.Comment: 17 pages, 8 figures. Talk given at the 35th International Symposium on Lattice Field Theory, 18 - 24 June 2017, Granada, Spai