State sampling dependence of the Hopfield network inference

The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations. We present the system in the glassy phase with low temperature and high memory load. We find that the inference error is very sensitive to the form of state sampling. When a single state is sampled to compute magnetizations and correlations, the inference error is almost indistinguishable irrespective of the sampled state. However, the error can be greatly reduced if the data is collected with state transitions. Our result holds for different disorder samples and accounts for the previously observed large fluctuations of inference error at low temperatures.Comment: 4 pages, 1 figure, further discussions added and relevant references adde

Collective perspective on advances in Dyson-Schwinger Equation QCD

We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson-Schwinger equations, addressing: aspects of confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small- to large-Q^2; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.Comment: 56 pages. Summary of lectures delivered by the authors at the "Workshop on AdS/CFT and Novel Approaches to Hadron and Heavy Ion Physics," 2010-10-11 to 2010-12-03, hosted by the Kavli Institute for Theoretical Physics, China, at the Chinese Academy of Science