Topological sampling through windings

We propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional U(1) gauge theory with and without fermion content. This algorithm includes reversible jumps between topological sectors – winding steps – combined with standard HMC steps. The full algorithm is referred to as winding HMC (wHMC), and it shows an improved behaviour of the autocorrelation time towards the continuum limit. We find excellent agreement between the wHMC estimates of the plaquette and topological susceptibility and the analytical predictions in the U(1) pure gauge theory, which are known even at finite $$\beta $$ β . We also study the expectation values in fixed topological sectors using both HMC and wHMC, with and without fermions. Even when topology is frozen in HMC – leading to significant deviations in topological as well as non-topological quantities – the two algorithms agree on the fixed-topology averages. Finally, we briefly compare the wHMC algorithm results to those obtained with master-field simulations of size $$L\sim 8 \times 10^3$$ L ∼ 8 × 10 3 .

Differentially Private Autocorrelation Time-Series Data Publishing Based on Sliding Window

Privacy protection is one of the major obstacles for data sharing. Time-series data have the characteristics of autocorrelation, continuity, and large scale. Current research on time-series data publication mainly ignores the correlation of time-series data and the lack of privacy protection. In this paper, we study the problem of correlated time-series data publication and propose a sliding window-based autocorrelation time-series data publication algorithm, called SW-ATS. Instead of using global sensitivity in the traditional differential privacy mechanisms, we proposed periodic sensitivity to provide a stronger degree of privacy guarantee. SW-ATS introduces a sliding window mechanism, with the correlation between the noise-adding sequence and the original time-series data guaranteed by sequence indistinguishability, to protect the privacy of the latest data. We prove that SW-ATS satisfies ε-differential privacy. Compared with the state-of-the-art algorithm, SW-ATS is superior in reducing the error rate of MAE which is about 25%, improving the utility of data, and providing stronger privacy protection.

Ergodic sampling of the topological charge using the density of states

In lattice calculations, the approach to the continuum limit is hindered by the severe freezing of the topological charge, which prevents ergodic sampling in configuration space. In order to significantly reduce the autocorrelation time of the topological charge, we develop a density of states approach with a smooth constraint and use it to study SU(3) pure Yang Mills gauge theory near the continuum limit. Our algorithm relies on simulated tempering across a range of couplings, which guarantees the decorrelation of the topological charge and ergodic sampling of topological sectors. Particular emphasis is placed on testing the accuracy, efficiency and scaling properties of the method. In their most conservative interpretation, our results provide firm evidence of a sizeable reduction of the exponent z related to the growth of the autocorrelation time as a function of the inverse lattice spacing.

Stochasticity-induced stabilization weakens in diverse communities.

Environmental stochasticity and the temporal variations of demographic rates associated with it are ubiquitous in nature. The ability of these fluctuations to stabilize a coexistence state of competing populations (sometimes known as the storage effect) is a counterintuitive feature that has aroused much interest. Here we consider the performance of environmental stochasticity as a stabilizer in diverse communities. We show that the effect of stochasticity is buffered because of the differential response of populations to environmental variations, and its stabilizing effect disappears as the number of populations increases. Of particular importance is the ratio between the autocorrelation time of the environment and the generation time. Species richness grows with stochasticity only when this ratio is smaller than the inverse of the fundamental biodiversity parameter. When stochasticity impedes coexistence and lowers the species richness, the ratio between the strength of environmental variations and the speciation (or migration) rate governs its effect.

Assessment of spatial and temporal variations in soil moisture from satellite observations and ground-based measurements and their relationship with plant cover

<p>The dynamic processes of mass and energy exchange on the soil surface are mainly influenced by plant cover, soil physical quantities and meteorological conditions. The aims of the research were: (a) to identify spatial and temporal changes in soil moisture (SM) obtained from satellite observations and ground measurements at the regional scale and (b) to determine the temporal variability of soil moisture in the soil profile with and bare soil (reference). The study area included 9 sites in the eastern part of Poland. Agro-meteorological stations in each site allowed monitoring soil moisture (SM). Satellite SM data (time series) for the years 2010–2016 (every week) obtained from the Soil Moisture and Ocean Salinity satellite (SMOS L2 v. 650 datasets) were gridded using the discrete global grid (DGG) with the nodes spaced at 15 km. Seven DGG pixels per each site were considered in a way that the central one (named S0) containing the agrometeorological station was bordered with 6 others (S1÷S6). The measurements of SM were performed at depths of 0.05, 0.1, 0.2, 0.3, 0.4, 0.5 and 0.8 m once a day in April-July in plots of spring barley, rye and bare soil. The temporal dependence of the SMOS surface soil moisture was observed in S0÷S6 with the radius of autocorrelation time from 8.1 to 25.2 weeks. The smallest autocorrelation time (3 weeks ) was found in pixels with dominance of arable lands and the largest one - with dominance of wetlands (16.8 weeks) and forests (from 12 to 15.6 weeks). The autocorrelation times in S0 were much greater for ground-based SM data (11.1 to 43.1 weeks) than those for SMOS SM data. The autocorrelations enabled satisfactory predicting changes in SM forwards and backwards using the kriging method and filling gaps in the SM time series. As to ground measurements the highest autocorrelation times were in the soil below the plough layer under rye (170 days) and the lowest in the surface soil under barley and bare soil (18 and 19 days). In the plot of rye with the highest soil density the autocorrelation radius was over 1.5 months. The fractal dimensions (D0) indicated a large randomness of the surface SMOS SM distribution (D0 1.86–1.95) and the ground SM measurements (D0 1.82–1.92). The D0 values clearly decreased with the depth (from 1.7 to 1.15) in plant-covered soil while in the bare soil they did not change much throughout the profile (D0 1.7–1.8). The D0 values indicated that the temporal distribution of SM in the soil profile was more random in bare than plant-covered soil. The results help to understanding autocorrelation time ranges in surface and deeper soil and spatial changes in soil moisture depending on plant cover.</p><p>Acknowledgements. Research was conducted under the project "Water in soil – satellite monitoring and improving the retention using biochar" no. BIOSTRATEG3/345940/7/NCBR/2017 which was financed by Polish National Centre for Research and Development in the framework of “Environment, agriculture and forestry" – BIOSTRATEG strategic R&D programme.</p>

Large-N SU(N) Yang-Mills theories with milder topological freezing

We simulate 4d SU(N) pure-gauge theories at large N using a parallel tempering scheme that combines simulations with open and periodic boundary conditions, implementing the algorithm originally proposed by Martin Hasenbusch for 2d CPN–1 models. That allows to dramatically suppress the topological freezing suffered from standard local algorithms, reducing the autocorrelation time of Q2 up to two orders of magnitude. Using this algorithm in combination with simulations at non-zero imaginary θ we are able to refine state-of-the-art results for the large-N behavior of the quartic coefficient of the θ-dependence of the vacuum energy b2, reaching an accuracy comparable with that of the large-N limit of the topological susceptibility.

Response theory and phase transitions for the thermodynamic limit of interacting identical systems

We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers–Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker–Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the effect of the mutual interaction between the systems. Such an interaction creates a memory effect. We are able to derive conditions determining the occurrence of phase transitions specifically due to system-to-system interactions. Such phase transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. We clarify that such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. Finally, we show how our results can elucidate the properties of the Desai–Zwanzig model and of the Bonilla–Casado–Morillo model, which feature paradigmatic equilibrium and non-equilibrium phase transitions, respectively.

Quasi-reliable estimates of effective sample size

The efficiency of a Markov chain Monte Carlo algorithm for estimating the mean of a function of interest might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated autocorrelation time. To ensure the reliability of such an estimate, it is suggested that there be an adequate sampling of state space— to the extent that this can be determined from the available samples. A sufficient condition for adequate sampling is derived in terms of the supremum of all possible integrated autocorrelation times, which leads to a more stringent condition for adequate sampling than that simply obtained from integrated autocorrelation times for functions of interest. A method for estimating the supremum of all integrated autocorrelation times, based on approximation in a finite-dimensional subspace, is derived and evaluated empirically.

Does ENSO Regularity Increase in a Warming Climate?

The impact of a warming climate on El Niño–Southern Oscillation (ENSO) is investigated in large-ensemble simulations of the Community Earth System Model (CESM1). These simulations are forced by historical emissions for the past and the RCP8.5-scenario emissions for future projections. The simulated variance of the Niño-3.4 ENSO index increases from 1.4°C2 in 1921–80 to 1.9°C2 in 1981–2040 and 2.2°C2 in 2041–2100. The autocorrelation time scale of the index also increases, consistent with a narrowing of its spectral peak in the 3–7-yr ENSO band, raising the possibility of greater seasonal to interannual predictability in the future. Low-order linear inverse models (LIMs) fitted separately to the three 60-yr periods capture the CESM1 increase in ENSO variance and regularity. Remarkably, most of the increase can be attributed to the increase in the 23-month damping time scale of a single damped oscillatory ENSO eigenmode of these LIMs by 5 months in 1981–2040 and 6 months in 2041–2100. These apparently robust projected increases may, however, be compromised by CESM1 biases in ENSO amplitude and damping time scale. An LIM fitted to the 1921–80 observations has an ENSO eigenmode with a much shorter 8-month damping time scale, similar to that of several other eigenmodes. When the mode’s damping time scale is increased by 5 and 6 months in this observational LIM, a much smaller increase of ENSO variance is obtained than in the CESM1 projections. This may be because ENSO is not as dominated by a single ENSO eigenmode in reality as it is in the CESM1.