Optimization in random field Ising models by quantum annealing

We investigate the properties of quantum annealing applied to the random field Ising model in one, two and three dimensions. The decay rate of the residual energy, defined as the energy excess from the ground state, is find to be $e_{res}\sim \log(N_{MC})^{-\zeta}$ with $\zeta$ in the range $2...6$, depending on the strength of the random field. Systems with ``large clusters'' are harder to optimize as measured by $\zeta$. Our numerical results suggest that in the ordered phase $\zeta=2$ whereas in the paramagnetic phase the annealing procedure can be tuned so that $\zeta\to6$.Comment: 7 pages (2 columns), 9 figures, published with minor changes, one reference updated after the publicatio

Elastic lines on splayed columnar defects studied numerically

We investigate by exact optimization method properties of two- and three-dimensional systems of elastic lines in presence of splayed columnar disorder. The ground state of many lines is separable both in 2d and 3d leading to a random walk -like roughening in 2d and ballistic behavior in 3d. Furthermore, we find that in the case of pure splayed columnar disorder in contrast to point disorder there is no entanglement transition in 3d. Entanglement can be triggered by perturbing the pure splay system with point defects.Comment: 9 pages, 11 figures. Accepted for publication in PR

Maximum likelihood reconstruction for Ising models with asynchronous updates

We describe how the couplings in an asynchronous kinetic Ising model can be inferred. We consider two cases, one in which we know both the spin history and the update times and one in which we only know the spin history. For the first case, we show that one can average over all possible choices of update times to obtain a learning rule that depends only on spin correlations and can also be derived from the equations of motion for the correlations. For the second case, the same rule can be derived within a further decoupling approximation. We study all methods numerically for fully asymmetric Sherrington-Kirkpatrick models, varying the data length, system size, temperature, and external field. Good convergence is observed in accordance with the theoretical expectations

Network inference using asynchronously updated kinetic Ising Model

Network structures are reconstructed from dynamical data by respectively naive mean field (nMF) and Thouless-Anderson-Palmer (TAP) approximations. For TAP approximation, we use two methods to reconstruct the network: a) iteration method; b) casting the inference formula to a set of cubic equations and solving it directly. We investigate inference of the asymmetric Sherrington- Kirkpatrick (S-K) model using asynchronous update. The solutions of the sets cubic equation depend of temperature T in the S-K model, and a critical temperature Tc is found around 2.1. For T < Tc, the solutions of the cubic equation sets are composed of 1 real root and two conjugate complex roots while for T > Tc there are three real roots. The iteration method is convergent only if the cubic equations have three real solutions. The two methods give same results when the iteration method is convergent. Compared to nMF, TAP is somewhat better at low temperatures, but approaches the same performance as temperature increase. Both methods behave better for longer data length, but for improvement arises, TAP is well pronounced.Comment: 6 pages, 4 figure

Complex networks created by aggregation

We study aggregation as a mechanism for the creation of complex networks. In this evolution process vertices merge together, which increases the number of highly connected hubs. We study a range of complex network architectures produced by the aggregation. Fat-tailed (in particular, scale-free) distributions of connections are obtained both for networks with a finite number of vertices and growing networks. We observe a strong variation of a network structure with growing density of connections and find the phase transition of the condensation of edges. Finally, we demonstrate the importance of structural correlations in these networks.Comment: 12 pages, 13 figure

Estimating informal care inputs associated with EQ-5D for use in economic evaluation.

OBJECTIVES: This paper estimates informal care need using the health of the patient. The results can be used to predict changes in informal care associated with changes in the health of the patient measured using EQ-5D. METHODS: Data was used from a prospective survey of inpatients containing 59,512 complete responses across 44,494 individuals. The number of days a friend or relative has needed to provide care or help with normal activities in the last 6 weeks was estimated using the health of the patient measured by EQ-5D, ICD chapter and other health and sociodemographic data. A variety of different regression models were estimated that are appropriate for the distribution of the informal care dependent variable, which has large spikes at 0 (zero informal care) and 42 days (informal care every day). RESULTS: The preferred model that most accurately predicts the distribution of the data is the zero-inflated negative binomial with variable inflation. The results indicate that improving the health of the patient reduces informal care need. The relationship between ICD chapter and informal care need is not as clear. CONCLUSIONS: The preferred zero-inflated negative binomial with variable inflation model can be used to predict changes in informal care associated with changes in the health of the patient measured using EQ-5D and these results can be applied to existing datasets to inform economic evaluation. Limitations include recall bias and response bias of the informal care data, and restrictions of the dataset to exclude some patient groups

The effect of thresholding on temporal avalanche statistics

We discuss intermittent time series consisting of discrete bursts or avalanches separated by waiting or silent times. The short time correlations can be understood to follow from the properties of individual avalanches, while longer time correlations often present in such signals reflect correlations between triggerings of different avalanches. As one possible source of the latter kind of correlations in experimental time series, we consider the effect of a finite detection threshold, due to e.g. experimental noise that needs to be removed. To this end, we study a simple toy model of an avalanche, a random walk returning to the origin or a Brownian bridge, in the presence and absence of superimposed delta-correlated noise. We discuss the properties after thresholding of artificial timeseries obtained by mixing toy avalanches and waiting times from a Poisson process. Most of the resulting scalings for individual avalanches and the composite timeseries can be understood via random walk theory, except for the waiting time distributions when strong additional noise is added. Then, to compare with a more complicated case we study the Manna sandpile model of self-organized criticality, where some further complications appear.Comment: 15 pages, 12 figures, submitted to J. Stat. Mech., special issue of the UPoN2008 conferenc

Measuring functional renormalization group fixed-point functions for pinned manifolds

Exact numerical minimization of interface energies is used to test the functional renormalization group (FRG) analysis for interfaces pinned by quenched disorder. The fixed-point function R(u) (the correlator of the coarse-grained disorder) is computed. In dimensions D=d+1, a linear cusp in R''(u) is confirmed for random bond (d=1,2,3), random field (d=0,2,3), and periodic (d=2,3) disorders. The functional shocks that lead to this cusp are seen. Small, but significant, deviations from 1-loop FRG results are compared to 2-loop corrections. The cross-correlation for two copies of disorder is compared with a recent FRG study of chaos.Comment: 4 pages, 4 figure

Fluctuations and scaling in creep deformation

The spatial fluctuations of deformation are studied in creep in the Andrade's power-law and the logarithmic phases, using paper samples. Measurements by the Digital Image Correlation technique show that the relative strength of the strain rate fluctuations increases with time, in both creep regimes. In the Andrade creep phase characterized by a power law decay of the strain rate $\epsilon_t \sim t^{-\theta}$, with $\theta \approx 0.7$, the fluctuations obey $\Delta \epsilon_t \sim t^{-\gamma}$, with $\gamma \approx 0.5$. The local deformation follows a data collapse appropriate for an absorbing state/depinning transition. Similar behavior is found in a crystal plasticity model, with a jamming or yielding phase transition

1/f1/f noise and avalanche scaling in plastic deformation

We study the intermittency and noise of dislocation systems undergoing shear deformation. Simulations of a simple two-dimensional discrete dislocation dynamics model indicate that the deformation rate exhibits a power spectrum scaling of the type $1/f^{\alpha}$. The noise exponent is far away from a Lorentzian, with $\alpha \approx 1.5$. This result is directly related to the way the durations of avalanches of plastic deformation activity scale with their size.Comment: 6 pages, 5 figures, submitted to Phys. Rev.