Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov-Arnold-Moser (KAM) theorem--a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt. By contrast, 'non-KAM' chaos switches on and off abruptly at critical values of the perturbation frequency. This type of dynamics has wide-ranging implications in the theory of plasma physics, tokamak fusion, turbulence, ion traps, and quasicrystals. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.

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We investigate chaotic electron transport in the lowest miniband of a semiconductor superlattice with a tilted magnetic field. This experimentally accessible non-Kolmogorov-Arnol'd-Moser system involves only stationary electric and magnetic fields, but is dynamically equivalent to a time-dependent kicked harmonic oscillator. The onset of chaos strongly delocalizes the electron orbits, thus raising the electrical conductivity. When the cyclotron and Bloch frequencies are commensurate, the phase space is threaded by a stochastic web, which produces a further resonant increase in the conductivity.

Multivariate random effects meta-analysis (MRMA) is an appropriate way for synthesizing data from studies reporting multiple correlated outcomes. In a Bayesian framework, it has great potential for integrating evidence from a variety of sources. In this paper, we propose a Bayesian model for MRMA of mixed outcomes, which extends previously developed bivariate models to the trivariate case and also allows for combination of multiple outcomes that are both continuous and binary. We have constructed informative prior distributions for the correlations by using external evidence. Prior distributions for the within-study correlations were constructed by employing external individual patent data and using a double bootstrap method to obtain the correlations between mixed outcomes. The between-study model of MRMA was parameterized in the form of a product of a series of univariate conditional normal distributions. This allowed us to place explicit prior distributions on the between-study correlations, which were constructed using external summary data. Traditionally, independent ‘vague’ prior distributions are placed on all parameters of the model. In contrast to this approach, we constructed prior distributions for the between-study model parameters in a way that takes into account the inter-relationship between them. This is a flexible method that can be extended to incorporate mixed outcomes other than continuous and binary and beyond the trivariate case. We have applied this model to a motivating example in rheumatoid arthritis with the aim of incorporating all available evidence in the synthesis and potentially reducing uncertainty around the estimate of interest. © 2013 The Authors. Statistics inMedicine Published by John Wiley & Sons, Ltd.

BackgroundNetwork meta-analysis (NMA) enables simultaneous comparison of multiple treatments while preserving randomisation. When summarising evidence to inform an economic evaluation, it is important that the analysis accurately reflects the dependency structure within the data, as correlations between outcomes may have implication for estimating the net benefit associated with treatment. A multivariate NMA offers a framework for evaluating multiple treatments across multiple outcome measures while accounting for the correlation structure between outcomes.MethodsThe standard NMA model is extended to multiple outcome settings in two stages. In the first stage, information is borrowed across outcomes as well across studies through modelling the within-study and between-study correlation structure. In the second stage, we make use of the additional assumption that intervention effects are exchangeable between outcomes to predict effect estimates for all outcomes, including effect estimates on outcomes where evidence is either sparse or the treatment had not been considered by any one of the studies included in the analysis. We apply the methods to binary outcome data from a systematic review evaluating the effectiveness of nine home safety interventions on uptake of three poisoning prevention practices (safe storage of medicines, safe storage of other household products, and possession of poison centre control telephone number) in households with children. Analyses are conducted in WinBUGS using Markov Chain Monte Carlo (MCMC) simulations.ResultsUnivariate and the first stage multivariate models produced broadly similar point estimates of intervention effects but the uncertainty around the multivariate estimates varied depending on the prior distribution specified for the between-study covariance structure. The second stage multivariate analyses produced more precise effect estimates while enabling intervention effects to be predicted for all outcomes, including intervention effects on outcomes not directly considered by the studies included in the analysis.ConclusionsAccounting for the dependency between outcomes in a multivariate meta-analysis may or may not improve the precision of effect estimates from a network meta-analysis compared to analysing each outcome separately.

We study the dynamics of Bose-Einstein condensates in an optical lattice and harmonic trap. The condensates are set in motion by displacing the trap and initially follow simple semiclassical paths, shaped by the lowest energy band. Above a critical displacement, the condensate undergoes Bragg reflection. For high atom densities, the first Bragg reflection generates a train of solitons and vortices, which destabilize the condensate and trigger explosive expansion. At lower densities, soliton and vortex formation requires multiple Bragg reflections, and damps the center-of-mass motion.Pacs numbers: 03.75. Fi, 32.80.Pj, 42.50.Vk, 05.45.Yv Optical lattices (OLs) provide unprecedented control of transport through the energy bands of periodic quantum systems. This has led to beautiful experimental demonstrations of Bloch oscillations [1] and quantized Wannier-Stark ladders [2] for non-interacting ultra-cold alkali atoms. There is also great interest in understanding the behavior of Bose-Einstein condensates (BECs), formed from interacting alkali atoms, in OLs [3][4][5][6][7][8][9][10][11][12][13][14][15]. Predictions [4,5] that accelerated condensates will perform Bloch oscillations, whose turning points at the top of the energy band correspond to successive Bragg reflections, have been confirmed in experiments [7,12] on 87 Rb BECs with equilibrium peak densities n 0 < ∼ 10 14 cm −3 . For n 0 > ∼ 10 14 cm −3 , more complex motion has been observed [11,12], which cannot be explained by Bragg reflection or analogous semiclassical models of energy band transport. Previous numerical studies of condensate dynamics in OLs have used the one-dimensional (1D) GrossPitaevskii equation [5,8,11]. They provide invaluable insights for understanding the mean center-of-mass motion of the condensate, but have not related this motion to changes in the internal structure of the condensate, in particular dynamical excitations such as solitons and vortices. Producing such excitations in a controlled way requires state-of-the-art experimental techniques, which involve manipulating the condensate phase and/or density profile [15][16][17][18][19], rotating the confining trap [20,21], moving a laser beam through the atom cloud [13,22,23], or tuning the inter-atomic interactions [24].In this Letter, we show that Bragg reflection provides a new mechanism for generating solitons and vortices in BECs. Moreover, these excitations can have a dramatic effect on the evolution of the atom cloud. At the first Bragg reflection, the condensate wavefunction is a standing wave with nodes at each maximum in the OL potential. At each node, the condensate phase changes abruptly by π. Bragg reflection therefore imprints atom density and phase profiles similar to those used to generate solitons in experiment [15][16][17][18][19]. The effect of this imprinting on the condensate dynamics depends critically on the atom density. For condensates with n 0 > ∼ 10 14 cm −3 , realized in recent experiments [11,12], it leads to the self-assembly of a chain of stationa...

Objectives. To systematically review and meta-analyse evidence on the effectiveness of the TNF-α inhibitors when used sequentially.Methods. Systematic review of comparative and single-arm observational studies. Data were synthesized using random-effects meta-analysis. Treatment effects were estimated using four outcome measures from the included studies: European League Against Rheumatism (EULAR) and ACR20 response rates and mean improvement in disease activity score-28 (DAS-20) and HAQ. The effect of other factors was explored via meta-regression and sub-group analyses.Results. Twenty studies comprising 2705 patients were included in the analysis. All studies were observational and most had no control group. Therefore, our primary analysis considered patient changes from baseline. The mean percentage of ACR20 responders was 60.8% (95% CI 53.8, 67.4), EULAR responders 70.5% (95% CI 63.7, 76.6), mean overall improvement in DAS-28 scores was 1.53 (95% CI 1.25, 1.80) and in HAQ scores was 0.25 (95% CI 0.11, 0.40). Four studies made comparisons with patients who received TNF-α inhibitors for the first time. Response rates associated with sequential TNF-α inhibitor treatment were lower than for first-time use.Conclusions. Sequential TNF-α inhibitor use is likely to lead to treatment benefit in terms of the signs and symptoms of disease and physical function. There is also some evidence to suggest that the probability of achieving a response is lower, and the average magnitude of response is lower than the first use. Further evidence from randomized controlled trials is required to confirm and further quantify the role specific anti-TNF-α agents have when used sequentially.

The MTC approach to synthesis allows the evidence base on clinical effectiveness to be treated as a coherent whole, include more data, and sometimes relax the assumptions made in the pair-wise approaches. However, MTC models are necessarily more complex than those developed for pair-wise meta-analysis and thus could be seen as less transparent. Therefore, it is important that model details and the assumptions made are carefully reported alongside the results.