Partially Explicit Generalized Multiscale Method for Poroelasticity Problem

We develop a partially explicit time discretization based on the framework of constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for the problem of linear poroelasticity with high contrast. Firstly, dominant basis functions generated by the CEM-GMsFEM approach are used to capture important degrees of freedom and it is known to give contrast-independent convergence that scales with the mesh size. In typical situation, one has very few degrees of freedom in dominant basis functions. This part is treated implicitly. Secondly, we design and introduce an additional space in the complement space and these degrees are treated explicitly. We also investigate the CFL-type stability restriction for this problem, and the restriction for the time step is contrast independent.Comment: 23 Pages,61 figures. arXiv admin note: text overlap with arXiv:2208.0554

Five-S-isotope evidence of two distinct mass-independent sulfur isotope effects and implications for the modern and Archean atmospheres.

The signature of mass-independent fractionation of quadruple sulfur stable isotopes (S-MIF) in Archean rocks, ice cores, and Martian meteorites provides a unique probe of the oxygen and sulfur cycles in the terrestrial and Martian paleoatmospheres. Its mechanistic origin, however, contains some uncertainties. Even for the modern atmosphere, the primary mechanism responsible for the S-MIF observed in nearly all tropospheric sulfates has not been identified. Here we present high-sensitivity measurements of a fifth sulfur isotope, stratospherically produced radiosulfur, along with all four stable sulfur isotopes in the same sulfate aerosols and a suite of chemical species to define sources and mechanisms on a field observational basis. The five-sulfur-isotope and multiple chemical species analysis approach provides strong evidence that S-MIF signatures in tropospheric sulfates are concomitantly affected by two distinct processes: an altitude-dependent positive 33S anomaly, likely linked to stratospheric SO2 photolysis, and a negative 36S anomaly mainly associated with combustion. Our quadruple stable sulfur isotopic measurements in varying coal samples (formed in the Carboniferous, Permian, and Triassic periods) and in SO2 emitted from combustion display normal 33S and 36S, indicating that the observed negative 36S anomalies originate from a previously unknown S-MIF mechanism during combustion (likely recombination reactions) instead of coal itself. The basic chemical physics of S-MIF in both photolytic and thermal reactions and their interplay, which were not explored together in the past, may be another ingredient for providing deeper understanding of the evolution of Earth's atmosphere and life's origin

Towards Privacy-Preserving and Verifiable Federated Matrix Factorization

Recent years have witnessed the rapid growth of federated learning (FL), an emerging privacy-aware machine learning paradigm that allows collaborative learning over isolated datasets distributed across multiple participants. The salient feature of FL is that the participants can keep their private datasets local and only share model updates. Very recently, some research efforts have been initiated to explore the applicability of FL for matrix factorization (MF), a prevalent method used in modern recommendation systems and services. It has been shown that sharing the gradient updates in federated MF entails privacy risks on revealing users' personal ratings, posing a demand for protecting the shared gradients. Prior art is limited in that they incur notable accuracy loss, or rely on heavy cryptosystem, with a weak threat model assumed. In this paper, we propose VPFedMF, a new design aimed at privacy-preserving and verifiable federated MF. VPFedMF provides for federated MF guarantees on the confidentiality of individual gradient updates through lightweight and secure aggregation. Moreover, VPFedMF ambitiously and newly supports correctness verification of the aggregation results produced by the coordinating server in federated MF. Experiments on a real-world moving rating dataset demonstrate the practical performance of VPFedMF in terms of computation, communication, and accuracy

Elucidating the Exposure Bias in Diffusion Models

Diffusion models have demonstrated impressive generative capabilities, but their 'exposure bias' problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically investigate the exposure bias problem in diffusion models by first analytically modelling the sampling distribution, based on which we then attribute the prediction error at each sampling step as the root cause of the exposure bias issue. Furthermore, we discuss potential solutions to this issue and propose an intuitive metric for it. Along with the elucidation of exposure bias, we propose a simple, yet effective, training-free method called Epsilon Scaling to alleviate the exposure bias. We show that Epsilon Scaling explicitly moves the sampling trajectory closer to the vector field learned in the training phase by scaling down the network output (Epsilon), mitigating the input mismatch between training and sampling. Experiments on various diffusion frameworks (ADM, DDPM/DDIM, EDM, LDM), unconditional and conditional settings, and deterministic vs. stochastic sampling verify the effectiveness of our method. For example, our ADM-ES, as a SOTA stochastic sampler, obtains 2.17 FID on CIFAR-10 dataset under 100-step unconditional generation. The code is available at \url{https://github.com/forever208/ADM-ES} and \url{https://github.com/forever208/EDM-ES}.Comment: under revie

Modal nudging in nonlinear elasticity: tailoring the elastic post-buckling behaviour of engineering structures

The buckling and post-buckling behaviour of slender structures is increasingly being harnessed for smart functionalities. Equally, the post-buckling regime of many traditional engineering structures is not being used for design and may therefore harbour latent load-bearing capacity for further structural efficiency. Both applications can benefit from a robust means of modifying and controlling the post-buckling behaviour for a specific purpose. To this end, we introduce a structural design paradigm termed modal nudging, which can be used to tailor the post-buckling response of slender engineering structures without any significant increase in mass. Modal nudging uses deformation modes of stable post-buckled equilibria to perturb the undeformed baseline geometry of the structure imperceptibly, thereby favouring the seeded post-buckling response over potential alternatives. The benefits of this technique are enhanced control over the post-buckling behaviour, such as modal differentiation for smart structures that use snap-buckling for shape adaptation, or alternatively, increased load-carrying capacity, increased compliance or a shift from imperfection sensitivity to imperfection insensitivity. Although these concepts are, in theory, of general applicability, we concentrate here on planar frame structures analysed using the nonlinear finite element method and numerical continuation procedures. Using these computational techniques, we show that planar frame structures may exhibit isolated regions of stable equilibria in otherwise unstable post-buckling regimes, or indeed stable equilibria entirely disconnected from the natural structural response. In both cases, the load-carrying capacity of these isolated stable equilibria is greater than the natural structural response of the frames. Using the concept of modal nudging it is possible to “nudge” the frames onto these equilibrium paths of greater load-carrying capacity. Due to the scale invariance of modal nudging, these findings may impact the design of structures from the micro- to the macro-scale

Synthesis and characterization of zeolite-Y using Ficus exasperata leaf: A preliminary study

In this study, Ficus exasperata (Fe) leaf (sand paper leaf) raw sample was characterized using proximate and ultimate analysis and the ash was characterized using X-ray fluorescence (XRF), X-ray diffraction (XRD), Scanning Electron Microscopy (SEM) and Fourier Transform Infrared (FTIR) spectroscopy. XRF analysis showed that Alumina (Al2 O3) and Silica (SiO2) were 6.50% and 67.50%, Energy Dispersive X-ray (EDX) analysis showed high presence of silica (42.40%), alumina (15.00%) and Oxygen (20.80%). FTIR unveiled peaks with zeolite-Y patterns. SEM analysis indicates good surface morphology and hexagonal shaped crystal lattice in comparison with commercial zeolite-Y

Baichuan 2: Open Large-scale Language Models

Large language models (LLMs) have demonstrated remarkable performance on a variety of natural language tasks based on just a few examples of natural language instructions, reducing the need for extensive feature engineering. However, most powerful LLMs are closed-source or limited in their capability for languages other than English. In this technical report, we present Baichuan 2, a series of large-scale multilingual language models containing 7 billion and 13 billion parameters, trained from scratch, on 2.6 trillion tokens. Baichuan 2 matches or outperforms other open-source models of similar size on public benchmarks like MMLU, CMMLU, GSM8K, and HumanEval. Furthermore, Baichuan 2 excels in vertical domains such as medicine and law. We will release all pre-training model checkpoints to benefit the research community in better understanding the training dynamics of Baichuan 2.Comment: Baichuan 2 technical report. Github: https://github.com/baichuan-inc/Baichuan