Small-world MCMC and convergence to multi-modal distributions: From slow mixing to fast mixing

We compare convergence rates of Metropolis--Hastings chains to multi-modal target distributions when the proposal distributions can be of ``local'' and ``small world'' type. In particular, we show that by adding occasional long-range jumps to a given local proposal distribution, one can turn a chain that is ``slowly mixing'' (in the complexity of the problem) into a chain that is ``rapidly mixing.'' To do this, we obtain spectral gap estimates via a new state decomposition theorem and apply an isoperimetric inequality for log-concave probability measures. We discuss potential applicability of our result to Metropolis-coupled Markov chain Monte Carlo schemes.Comment: Published at http://dx.doi.org/10.1214/105051606000000772 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

In plane stiffness of multifunctional hierarchical honeycombs with negative Poisson's ratio sub-structures

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Research on The Opportunities and Challenges of Russia's Digital Economy Development

In recent years, Russia's digital economy has made great progress, but there are still some constraints in the development process. This article summarizes the opportunities and challenges of the development of Russia's digital economy, and gives policy suggestions to promote the development of Russia's digital economy

Political and Economic Prerequisites for The Emergence of The Chinese Strategy “Belt and Road” In Asia-Europe

China's Belt and Road Initiative has now become a global, inclusive project. But there are still many problems. The article attempts to find out the motives of China in this project. The article focuses on the motives (prerequisites) that prompted China to create such a capital-intensive global initiative

Forecasting property price indices in Hong Kong based on grey models

The real estate market in Hong Kong plays an important role in its economy. The property prices have been increasing a lot since 2009, which have become a major concern. However, few studies have been done to forecast the property price indices in Hong Kong. In this paper, two grey models, GM(1,1) and GM(0,N), are introduced for the forecasting. The results show that GM(1,1) has a better performance when forecasting with stable trend data, while GM(0,N) is more suitable for forecasting data in fluctuating trend. The sensitivity analysis for GM(0,N) shows that Population(POP) and Best Lending Rate(BLR) are significantly sensitive factors for data in stable trend. While for the fluctuating data, sensitivity of each factor presents uncertainties. This study also compares the forecasting performance of grey models with the ANN model and ARIMA model. The study demonstrates that grey models are more suitable for forecasting the Hong Kong property price indices than others

Estimating the contribution of strong daily export events to total pollutant export from the United States in summer

While the export of pollutants from the United States exhibits notable variability from day to day and is often considered to be “episodic,” the contribution of strong daily export events to total export has not been quantified. We use carbon monoxide (CO) as a tracer of anthropogenic pollutants in the Model of OZone And Related Tracers (MOZART) to estimate this contribution. We first identify the major export pathway from the United States to be through the northeast boundary (24–48°N along 67.5°W and 80–67.5°W along 48°N), and then analyze 15 summers of daily CO export fluxes through this boundary. These daily CO export fluxes have a nearly Gaussian distribution with a mean of 1100 Gg CO day−1 and a standard deviation of 490 Gg CO day−1. To focus on the synoptic variability, we define a “synoptic background” export flux equal to the 15 day moving average export flux and classify strong export days according to their fluxes relative to this background. As expected from Gaussian statistics, 16% of summer days are “strong export days,” classified as those days when the CO export flux exceeds the synoptic background by one standard deviation or more. Strong export days contributes 25% to the total export, a value determined by the relative standard deviation of the CO flux distribution. Regressing the anomalies of the CO export flux through the northeast U.S. boundary relative to the synoptic background on the daily anomalies in the surface pressure field (also relative to a 15 day running mean) suggests that strong daily export fluxes are correlated with passages of midlatitude cyclones over the Gulf of Saint Lawrence. The associated cyclonic circulation and Warm Conveyor Belts (WCBs) that lift surface pollutants over the northeastern United States have been shown previously to be associated with long-range transport events. Comparison with observations from the 2004 INTEX-NA field campaign confirms that our model captures the observed enhancements in CO outflow and resolves the processes associated with cyclone passages on strong export days. “Moderate export days,” defined as days when the CO flux through the northeast boundary exceeds the 15 day running mean by less than one standard deviation, represent an additional 34% of summer days and 40% of total export. These days are also associated with migratory midlatitude cyclones. The remaining 35% of total export occurs on “weak export days” (50% of summer days) when high pressure anomalies occur over the Gulf of Saint Lawrence. Our findings for summer also apply to spring, when the U.S. pollutant export is typically strongest, with similar contributions to total export and associated meteorology on strong, moderate and weak export days. Although cyclone passages are the primary driver for strong daily export events, export during days without cyclone passages also makes a considerable contribution to the total export and thereby to the global pollutant budget

The strain-induced transitions of the piezoelectric, pyroelectric and electrocaloric properties of the CuInP2_2S6_6 films

The low-dimensional ferroelectrics, ferrielectrics and antiferroelectrics are of urgent scientific interest due to their unusual polar, piezoelectric, electrocaloric and pyroelectric properties. The strain engineering and strain control of the ferroelectric properties of layered 2D Van der Waals materials, such as CuInP$_2$(S,Se)$_6$ monolayers, thin films and nanoflakes, are of fundamental interest and especially promising for their advanced applications in nanoscale nonvolatile memories, energy conversion and storage, nano-coolers and sensors. Here, we study the polar, piezoelectric, electrocaloric and pyroelectric properties of thin strained films of a ferrielectric CuInP$_2$S$_6$ covered by semiconducting electrodes and reveal an unusually strong effect of a mismatch strain on these properties. In particular, the sign of the mismatch strain and its magnitude determine the complicated behavior of piezoelectric, electrocaloric and pyroelectric responses. The strain effect on these properties is opposite, i.e., "anomalous", in comparison with many other ferroelectric films, for which the out-of-plane remanent polarization, piezoelectric, electrocaloric and pyroelectric responses increase strongly for tensile strains and decrease or vanish for compressive strains.Comment: 16 pages, 5 figures, to be presented at the VI Lithuanian-Polish Meeting on Physics of Ferroelectric

Bending-induced isostructural transitions in ultrathin layers of van der Waals ferrielectrics

Using Landau-Ginzburg-Devonshire (LGD) phenomenological approach we analyze the bending-induced re-distribution of electric polarization and field, elastic stresses and strains inside ultrathin layers of van der Waals ferrielectrics. We consider a CuInP2S6 (CIPS) thin layer with fixed edges and suspended central part, the bending of which is induced by external forces. The unique aspect of CIPS is the existence of two ferrielectric states, FI1 and FI2, corresponding to big and small polarization values, which arise due to the specific four-well potential of the eighth-order LGD functional. When the CIPS layer is flat, the single-domain FI1 state is stable in the central part of the layer, and the FI2 states are stable near the fixed edges. With an increase of the layer bending below the critical value, the sizes of the FI2 states near the fixed edges decreases, and the size of the FI1 region increases. When the bending exceeds the critical value, the edge FI2 states disappear being substituted by the FI1 state, but they appear abruptly near the inflection regions and expand as the bending increases. The bending-induced isostructural FI1-FI2 transition is specific for the bended van der Waals ferrielectrics described by the eighth (or higher) order LGD functional with consideration of linear and nonlinear electrostriction couplings. The isostructural transition, which is revealed in the vicinity of room temperature, can significantly reduce the coercive voltage of ferroelectric polarization reversal in CIPS nanoflakes, allowing for the curvature-engineering control of various flexible nanodevices.Comment: 26 pages, 7 figures and Appendices A-