Optimal Exploration is no harder than Thompson Sampling

Given a set of arms $\mathcal{Z}\subset \mathbb{R}^d$ and an unknown parameter vector $\theta_\ast\in\mathbb{R}^d$, the pure exploration linear bandit problem aims to return $\arg\max_{z\in \mathcal{Z}} z^{\top}\theta_{\ast}$, with high probability through noisy measurements of $x^{\top}\theta_{\ast}$ with $x\in \mathcal{X}\subset \mathbb{R}^d$. Existing (asymptotically) optimal methods require either a) potentially costly projections for each arm $z\in \mathcal{Z}$ or b) explicitly maintaining a subset of $\mathcal{Z}$ under consideration at each time. This complexity is at odds with the popular and simple Thompson Sampling algorithm for regret minimization, which just requires access to a posterior sampling and argmax oracle, and does not need to enumerate $\mathcal{Z}$ at any point. Unfortunately, Thompson sampling is known to be sub-optimal for pure exploration. In this work, we pose a natural question: is there an algorithm that can explore optimally and only needs the same computational primitives as Thompson Sampling? We answer the question in the affirmative. We provide an algorithm that leverages only sampling and argmax oracles and achieves an exponential convergence rate, with the exponent being the optimal among all possible allocations asymptotically. In addition, we show that our algorithm can be easily implemented and performs as well empirically as existing asymptotically optimal methods

Estimate of Saturation Pressures of Crude Oil by Using Ensemble-Smoother-Assisted Equation of State

The equation of state (EOS) has been extensively used to evaluate the saturation pressures of petroleum fluids. However, the accurate determination of empirical parameters in the EOS is challenging and time-consuming, especially when multiple measurements are involved in the regression process. In this work, an ensemble smoother (ES) -assisted EOS method has been proposed to compute the saturation pressure by intelligently optimizing the to-be-tuned parameters. To be specific, the to-be-tuned parameters for the Peng–Robinson EOS (PR EOS) are integrated into a model input matrix and the measured saturation pressures are collected into a model output matrix. The model input matrix is then integrally and iteratively updated with respect to the model output matrix by using the iterative ES algorithm. For convenience, an in-house module is compiled to implement the ES-assisted EOS for determining the saturation pressures of crude oils. Subsequently, the experimentally measured saturation pressures of 45 mixtures of heavy oil and solvents are used to validate the performance of the in-house module. In addition, 130 measured saturation pressures of worldwide light oil samples are collected to verify the applicability of the developed ES-assisted EOS method. The in-house module is found to be competent by not only matching 45 measured saturation pressures with a better agreement than a commercial simulator but also providing a quantitative means to analyze the uncertainties associated with the estimated model parameters and the saturation pressure. Moreover, the application of the ES-assisted EOS to 130 light oil samples distinctly demonstrates that the new method greatly improves the accuracy and reliability of the EOS regression. Consequently, the in-house module representing the ES-assisted EOS is proven as an efficient and flexible tool to determine the saturation pressure under various conditions and implement uncertain analyses associated with the saturation pressure

Research on residual drift response of steel frames under strong earthquakes

Steel frames designed to the current codes will undergo an unrecoverable plastic deformation under strong earthquakes. The structures subjected to excessive deformations after earthquakes cannot be desirably repaired to their serviceable state, and can only be demolished, which brings about a serious direct and indirect economic loss. Thus, it is of great significance to predict the residual drift for the performance evaluation and control of structures after earthquakes. In order to investigate the residual drift response of steel frames under strong earthquakes, steel frames between 2 and 10 stories in height are designed according to Code for seismic design of buildings (GB50011-2010) and Code for design of steel structures (GB50017-2003) in this study. The designed structures are investigated numerically by pushover analysis and elasto-plastic time history analysis. Furthermore, the peak drifts, residual drifts and drift concentration factors are reasonably obtained under the action of moderate earthquakes and major earthquakes. The results indicate that the scatter in the residual drift results is a bit large. On the basis of analysis results, the calculation formulae are proposed to estimate the residual drifts of steel frames as a function of the expected peak drift, the initial recoverable elastic drift, and the drift concentration factor of steel frames

Average skew information-based coherence and its typicality for random quantum states

We study the average skew information-based coherence for both random pure and mixed states. The explicit formulae of the average skew information-based coherence are derived and shown to be the functions of the dimension N of the state space. We demonstrate that as N approaches to infinity, the average coherence is 1 for random pure states, and a positive constant less than 1/2 for random mixed states. We also explore the typicality of average skew information-based coherence of random quantum states. Furthermore, we identify a coherent subspace such that the amount of the skew information-based coherence for each pure state in this subspace can be bounded from below almost always by a fixed number that is arbitrarily close to the typical value of coherence.Comment: 24page

Coherence and complementarity based on modified generalized skew information

We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalized Wigner-Yanase-Dyson (MWGWYD) skew information. By revisiting state-channel interaction based on MGWYD skew information, a family of coherence measures with respect to quantum channels is proposed. Furthermore, explicit analytical expressions of these coherence measures of qubit states are derived with respect to different quantum channels. Moreover, complementarity relations based on MGWYD skew information and MWGWYD skew information are also presented. Specifically, the conservation relations are investigated, while two interpretations of them including symmetry-asymmetry complementarity and wave-particle duality have been proposed.Comment: 20page

SD-MVS: Segmentation-Driven Deformation Multi-View Stereo with Spherical Refinement and EM optimization

In this paper, we introduce Segmentation-Driven Deformation Multi-View Stereo (SD-MVS), a method that can effectively tackle challenges in 3D reconstruction of textureless areas. We are the first to adopt the Segment Anything Model (SAM) to distinguish semantic instances in scenes and further leverage these constraints for pixelwise patch deformation on both matching cost and propagation. Concurrently, we propose a unique refinement strategy that combines spherical coordinates and gradient descent on normals and pixelwise search interval on depths, significantly improving the completeness of reconstructed 3D model. Furthermore, we adopt the Expectation-Maximization (EM) algorithm to alternately optimize the aggregate matching cost and hyperparameters, effectively mitigating the problem of parameters being excessively dependent on empirical tuning. Evaluations on the ETH3D high-resolution multi-view stereo benchmark and the Tanks and Temples dataset demonstrate that our method can achieve state-of-the-art results with less time consumption.Comment: 10 pages, 9 figures, published to AAAI202

Uncertainty Relations Based on Modified Wigner-Yanase-Dyson Skew Information

Uncertainty relation is a core issue in quantum mechanics and quantum information theory. We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalizedWigner-Yanase-Dyson (MWGWYD) skew information, and establish new uncertainty relations in terms of the MGWYD skew information and MWGWYD skew information.Comment: 16 page

Association between high-density lipoprotein cholesterol and type 2 diabetes mellitus: dual evidence from NHANES database and Mendelian randomization analysis

BackgroundLow levels of high-density lipoprotein cholesterol (HDL-C) are commonly seen in patients with type 2 diabetes mellitus (T2DM). However, it is unclear whether there is an independent or causal link between HDL-C levels and T2DM. This study aims to address this gap by using the The National Health and Nutrition Examination Survey (NHANES) database and Mendelian randomization (MR) analysis.Materials and methodsData from the NHANES survey (2007-2018) with 9,420 participants were analyzed using specialized software. Logistic regression models and restricted cubic splines (RCS) were used to assess the relationship between HDL-C and T2DM incidence, while considering covariates. Genetic variants associated with HDL-C and T2DM were obtained from genome-wide association studies (GWAS), and Mendelian randomization (MR) was used to evaluate the causal relationship between HDL-C and T2DM. Various tests were conducted to assess pleiotropy and outliers.ResultsIn the NHANES study, all groups, except the lowest quartile (Q1: 0.28-1.09 mmol/L], showed a significant association between HDL-C levels and reduced T2DM risk (all P < 0.001). After adjusting for covariates, the Q2 [odds ratio (OR) = 0.67, 95% confidence interval (CI): (0.57, 0.79)], Q3 [OR = 0.51, 95% CI: (0.40, 0.65)], and Q4 [OR = 0.29, 95% CI: (0.23, 0.36)] groups exhibited average reductions in T2DM risk of 23%, 49%, and 71%, respectively. In the sensitivity analysis incorporating other lipid levels, the Q4 group still demonstrates a 57% reduction in the risk of T2DM. The impact of HDL-C levels on T2DM varied with age (P for interaction = 0.006). RCS analysis showed a nonlinear decreasing trend in T2DM risk with increasing HDL-C levels (P = 0.003). In the MR analysis, HDL-C levels were also associated with reduced T2DM risk (OR = 0.69, 95% CI = 0.52-0.82; P = 1.41 × 10-13), and there was no evidence of pleiotropy or outliers.ConclusionThis study provides evidence supporting a causal relationship between higher HDL-C levels and reduced T2DM risk. Further research is needed to explore interventions targeting HDL-C levels for reducing T2DM risk