265 research outputs found

    Logarithmic Sobolev inequalities for non-equilibrium steady states

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    We consider two methods to establish log-Sobolev inequalities for the invariant measure of a diffusion process when its density is not explicit and the curvature is not positive everywhere. In the first approach, based on the Holley-Stroock and Aida-Shigekawa perturbation arguments [16, 1], the control on the (non-explicit) perturbation is obtained by stochastic control methods, following the comparison technique introduced by Conforti [7]. The second method combines the Wasserstein-22 contraction method, used in [24] to prove a Poincar\'e inequality in some non-equilibrium cases, with Wang's hypercontractivity results [29].Comment: 22 page

    Uniform-in-time propagation of chaos for mean field Langevin dynamics

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    We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the LpL^p-convergence of the marginal distributions towards the unique invariant measure for the mean field dynamics. Furthermore, we prove the uniform-in-time propagation of chaos in both the L2L^2-Wasserstein metric and relative entropy.Comment: 66 pages, 3 figures and 1 table. Contains corrections and enhancements to arXiv:2212.03050v

    PETformer: Long-term Time Series Forecasting via Placeholder-enhanced Transformer

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    Recently, the superiority of Transformer for long-term time series forecasting (LTSF) tasks has been challenged, particularly since recent work has shown that simple models can outperform numerous Transformer-based approaches. This suggests that a notable gap remains in fully leveraging the potential of Transformer in LTSF tasks. Consequently, this study investigates key issues when applying Transformer to LTSF, encompassing aspects of temporal continuity, information density, and multi-channel relationships. We introduce the Placeholder-enhanced Technique (PET) to enhance the computational efficiency and predictive accuracy of Transformer in LTSF tasks. Furthermore, we delve into the impact of larger patch strategies and channel interaction strategies on Transformer's performance, specifically Long Sub-sequence Division (LSD) and Multi-channel Separation and Interaction (MSI). These strategies collectively constitute a novel model termed PETformer. Extensive experiments have demonstrated that PETformer achieves state-of-the-art performance on eight commonly used public datasets for LTSF, surpassing all existing models. The insights and enhancement methodologies presented in this paper serve as valuable reference points and sources of inspiration for future research endeavors

    Disability-Free Life Expectancy among People Over 60 Years Old by Sex, Urban and Rural Areas in Jiangxi Province, China

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    Objective: To estimate and compare age trends and the disability-free life expectancy (DFLE) of the population over 60 years old in 2018 in Jiangxi Province, China, by sex and urban–rural areas. Methods: The model life table was employed to estimate the age-specific mortality rate by sex and urban–rural areas, based on the Summary of Health Statistics of Jiangxi Province in 2018 and the Sixth National Health Service survey of Jiangxi Province. DFLE and its ratio to life expectancy (LE) were obtained by the Sullivan method. Results: In 2018, the DFLE among people over 60 is 17.157 years for men and is 19.055 years for women, accounting for 89.7% and 86.5% of their LE respectively. The DFLE/LE of men is higher than that of women at all ages. LE and DFLE are higher for the population in urban areas than in rural areas. For women, DFLE/LE is higher in urban areas than in rural areas (except at ages 75 and 80). Urban men have a higher DFLE/LE than rural men (except at age 85). The difference in DFLE between men and women over 60 years is 1.898 years, of which 2.260 years are attributable to the mortality rate, and 0.362 years are due to the disability-free prevalence. In addition, the difference in DFLE between urban–rural elderly over 60 years old is mostly attributed to the mortality rate by gender (male: 0.902/1.637; female: 0.893/1.454), but the impact of the disability-free rate cannot be ignored either (male: 0.735/1.637; female: 0.561/1.454). Conclusions: The increase in DFLE is accompanied by the increase in LE, but with increased age, DFLE/LE gradually decreases. With advancing age, the effect of disability on elderly people becomes more severe. The government administration must implement some preventive actions to improve health awareness and the life quality of the elderly. Rural elderly; rural women in particular, need to be paid more attention and acquire more health care

    Machine learning approach for analysing and predicting the modulus response of the structural epoxy adhesive at elevated temperatures

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    For bonded Fibre Reinforced Polymer (FRP) strengthening systems in civil engineering projects, the adhesive joint performance is a key factor in the effectiveness of the strengthening; however, it is known that the material properties of structural epoxy adhesives change with temperature. This present paper examines the implied relationship between the curing regimes and the storage modulus response of the adhesive using a Machine Learning (ML) approach. A dataset containing 157 experimental data collected from the scientific papers and academic theses was used for training and testing an Artificial Neural Network (ANN) model. The sensitivity analysis reveals that the curing conditions have a significant effect on the glass transition temperatures (Tg) of the adhesive, and consequently on the storage modulus response at elevated temperatures. Curing at an extremely high temperature for a long time does not, however, guarantee a better thermal performance. For the studied adhesive, curing in a warm (≄ 45°C) and dry (near 0 % RH) environment for 21 days is recommended for practical applications. A software with a Graphical User Interface (GUI) was established, which can predict the storage modulus response of the adhesive, plot the corresponding response curve, and estimate the optimum curing condition.</p