Glauber Critical Dynamics: Exact Solution of the Kinetic Gaussian Model

In this paper, we have exactly solved Glauber critical dynamics of the Gaussian model on three dimensions. Of course, it is much easy to apply to low dimensional case. The key steps are that we generalize the spin change mechanism from Glauber's single-spin flipping to single-spin transition and give a normalized version of the transition probability . We have also investigated the dynamical critical exponent and found surprisingly that the dynamical critical exponent is highly universal which refer to that for one- two- and three-dimensions they have same value independent of spatial dimensionality in contrast to static (equilibrium) critical exponents.Comment: 9 page

Solvable Kinetic Gaussian Model in External Field

In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic lattice Gaussian spin system with Fourier's transformation method. We obtain exactly the local magnetization and the equal-time pair correlation function. The critical characteristics of the dynamical, the complex susceptibility, and the dynamical response are discussed. The results show that the time evolution of the dynamical quantities and the dynamical responses of the system strongly depend on the frequency and the wave vector of the external field.Comment: 11 page

Interplay between quasi-periodicity and disorder in quantum spin chains in a magnetic field

We study the interplay between disorder and a quasi periodic coupling array in an external magnetic field in a spin-1/2 XXZ chain. A simple real space decimation argument is used to estimate the magnetization values where plateaux show up. The latter are in good agreement with exact diagonalization results on fairly long XX chains. Spontaneous susceptibility properties are also studied, finding a logarithmic behaviour similar to the homogeneously disordered case.Comment: 5 RevTeX pages, 5 Postscript figures include

Counterfactual Evaluation of Slate Recommendations with Sequential Reward Interactions

Users of music streaming, video streaming, news recommendation, and e-commerce services often engage with content in a sequential manner. Providing and evaluating good sequences of recommendations is therefore a central problem for these services. Prior reweighting-based counterfactual evaluation methods either suffer from high variance or make strong independence assumptions about rewards. We propose a new counterfactual estimator that allows for sequential interactions in the rewards with lower variance in an asymptotically unbiased manner. Our method uses graphical assumptions about the causal relationships of the slate to reweight the rewards in the logging policy in a way that approximates the expected sum of rewards under the target policy. Extensive experiments in simulation and on a live recommender system show that our approach outperforms existing methods in terms of bias and data efficiency for the sequential track recommendations problem

Kinetics of a non-glauberian Ising model: global observables and exact results

We analyse the spin-flip dynamics in kinetic Ising chains with Kimball-Deker-Haake (KDH) transition rates, and evaluate exactly the evolution of global quantities like magnetisation and its fluctuations, and the two-time susceptibilities and correlations of the global spin and the global three-spin. Information on the ageing behaviour after a quench to zero temperature is extracted

Universal Critical Behavior of Aperiodic Ferromagnetic Models

We investigate the effects of geometric fluctuations, associated with aperiodic exchange interactions, on the critical behavior of $q$-state ferromagnetic Potts models on generalized diamond hierarchical lattices. For layered exchange interactions according to some two-letter substitutional sequences, and irrelevant geometric fluctuations, the exact recursion relations in parameter space display a non-trivial diagonal fixed point that governs the universal critical behavior. For relevant fluctuations, this fixed point becomes fully unstable, and we show the apperance of a two-cycle which is associated with a novel critical behavior. We use scaling arguments to calculate the critical exponent $\alpha$ of the specific heat, which turns out to be different from the value for the uniform case. We check the scaling predictions by a direct numerical analysis of the singularity of the thermodynamic free-energy. The agreement between scaling and direct calculations is excellent for stronger singularities (large values of $q$). The critical exponents do not depend on the strengths of the exchange interactions.Comment: 4 pages, 1 figure (included), RevTeX, submitted to Phys. Rev. E as a Rapid Communicatio

Quasi-periodic spin chains in a magnetic field

We study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin-1/2 XXZ chain. A new class of magnetization plateaux are obtained by means of Abelian bosonization methods which give rise to a sufficient quantization condition. The investigation of magnetic phase diagrams via exact diagonalization of finite clusters finds a complete agreement with the continuum treatment in a variety of situations.Comment: 4 pages RevTeX, 5 PostScript figures included. Final version to appear in PR

New Dynamic Monte Carlo Renormalization Group Method

The dynamical critical exponent of the two-dimensional spin-flip Ising model is evaluated by a Monte Carlo renormalization group method involving a transformation in time. The results agree very well with a finite-size scaling analysis performed on the same data. The value of $z = 2.13 \pm 0.01$ is obtained, which is consistent with most recent estimates

Nonequilibrium relaxation of the two-dimensional Ising model: Series-expansion and Monte Carlo studies

We study the critical relaxation of the two-dimensional Ising model from a fully ordered configuration by series expansion in time t and by Monte Carlo simulation. Both the magnetization (m) and energy series are obtained up to 12-th order. An accurate estimate from series analysis for the dynamical critical exponent z is difficult but compatible with 2.2. We also use Monte Carlo simulation to determine an effective exponent, z_eff(t) = - {1/8} d ln t /d ln m, directly from a ratio of three-spin correlation to m. Extrapolation to t = infinity leads to an estimate z = 2.169 +/- 0.003.Comment: 9 pages including 2 figure

International variation in oesophageal and gastric cancer survival 2012–2014: differences by histological subtype and stage at diagnosis (an ICBP SURVMARK-2 population-based study)

Objective To provide the first international comparison of oesophageal and gastric cancer survival by stage at diagnosis and histological subtype across high-income countries with similar access to healthcare. Methods As part of the ICBP SURVMARK-2 project, data from 28 923 patients with oesophageal cancer and 25 946 patients with gastric cancer diagnosed during 2012–2014 from 14 cancer registries in seven countries (Australia, Canada, Denmark, Ireland, New Zealand, Norway and the UK) were included. 1-year and 3-year age-standardised net survival were estimated by stage at diagnosis, histological subtype (oesophageal adenocarcinoma (OAC) and oesophageal squamous cell carcinoma (OSCC)) and country. Results Oesophageal cancer survival was highest in Ireland and lowest in Canada at 1 (50.3% vs 41.3%, respectively) and 3 years (27.0% vs 19.2%) postdiagnosis. Survival from gastric cancer was highest in Australia and lowest in the UK, for both 1-year (55.2% vs 44.8%, respectively) and 3-year survival (33.7% vs 22.3%). Most patients with oesophageal and gastric cancer had regional or distant disease, with proportions ranging between 56% and 90% across countries. Stage-specific analyses showed that variation between countries was greatest for localised disease, where survival ranged between 66.6% in Australia and 83.2% in the UK for oesophageal cancer and between 75.5% in Australia and 94.3% in New Zealand for gastric cancer at 1-year postdiagnosis. While survival for OAC was generally higher than that for OSCC, disparities across countries were similar for both histological subtypes. Conclusion Survival from oesophageal and gastric cancer varies across high-income countries including within stage groups, particularly for localised disease. Disparities can partly be explained by earlier diagnosis resulting in more favourable stage distributions, and distributions of histological subtypes of oesophageal cancer across countries. Yet, differences in treatment, and also in cancer registration practice and the use of different staging methods and systems, across countries may have impacted the comparisons. While primary prevention remains key, advancements in early detection research are promising and will likely allow for additional risk stratification and survival improvements in the future