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

The Sensitivity of Ligo to a Stochastic Background, and its Dependance on the Detector Orientations

We analyze the sensitivity of a network of interferometer gravitational-wave detectors to the gravitational-wave stochastic background, and derive the dependence of this sensitivity on the orientations of the detector arms. We build on and extend the recent work of Christensen, but our conclusion for the optimal choice of orientations of a pair of detectors differs from his. For a pair of detectors (such as LIGO) that subtends an angle at the center of the earth of \,\alt 70^\circ, we find that the optimal configuration is for each detector to have its arms make an angle of $45^\circ$ (modulo $90^\circ$) with the arc of the great circle that joins them. For detectors that are farther separated, each detector should instead have one arm aligned with this arc. We also describe in detail the optimal data-analysis algorithm for searching for the stochastic background with a detector network, which is implicit in earlier work of Michelson. The LIGO pair of detectors will be separated by $\sim 3000 \, {\rm km}$. The minimum detectable stochastic energy-density for these detectors with their currently planned orientations is $\sim 3\%$ greater than what it would be if the orientations were optimal.Comment: 56 pages, 10 figures, Caltech preprint GRP-347, submitted to Phys Rev D, uses revtex macro

Gravitational Radiation From Cosmological Turbulence

An injection of energy into the early Universe on a given characteristic length scale will result in turbulent motions of the primordial plasma. We calculate the stochastic background of gravitational radiation arising from a period of cosmological turbulence, using a simple model of isotropic Kolmogoroff turbulence produced in a cosmological phase transition. We also derive the gravitational radiation generated by magnetic fields arising from a dynamo operating during the period of turbulence. The resulting gravitational radiation background has a maximum amplitude comparable to the radiation background from the collision of bubbles in a first-order phase transition, but at a lower frequency, while the radiation from the induced magnetic fields is always subdominant to that from the turbulence itself. We briefly discuss the detectability of such a signal.Comment: 20 pages. Corrections for an errant factor of 2 in all the gravity wave characteristic amplitudes. Accepted for publication in Phys. Rev.

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