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Market fluctuations caused by overtrading are important components of systemic market risk. This study examines the effect of investor sentiment on intraday overtrading activities in the Chinese A-share market. Employing high-frequency sentiment indices inferred from social media posts on the Eastmoney forum Guba, the research focuses on constituents of the CSI 300 and CSI 500 indices over a period from 01/01/2018, to 12/30/2022. The empirical analysis indicates that investor sentiment exerts a significantly positive impact on intraday overtrading, with the influence being more pronounced among institutional investors relative to individual traders. Moreover, sentiment-driven overtrading is found to be more prevalent during bull markets as opposed to bear markets. Additionally, the effect of sentiment on overtrading is observed to be more pronounced among individual investors in large-cap stocks compared to small- and mid-cap stocks.

The rapid pace of development in quantum computing technology has sparked a proliferation of benchmarks for assessing the performance of quantum computing hardware and software. Good benchmarks empower scientists, engineers, programmers, and users to understand a computing system's power, but bad benchmarks can misdirect research and inhibit progress. In this Perspective, we survey the science of quantum computer benchmarking. We discuss the role of benchmarks and benchmarking, and how good benchmarks can drive and measure progress towards the long-term goal of useful quantum computations, i.e., "quantum utility". We explain how different kinds of benchmark quantify the performance of different parts of a quantum computer, we survey existing benchmarks, critically discuss recent trends in benchmarking, and highlight important open research questions in this field.

We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on Gaussian priors, leading to convenient conjugate formulae for posterior inference. We review recent results providing theoretical guarantees on the quality of the resulting posterior-based estimation and uncertainty quantification, and we discuss the application of the theory to the important classes of Gaussian series priors defined on the Dirichlet-Laplacian eigenbasis and Mat\'ern process priors. We provide an implementation of posterior inference for both classes of priors, and investigate its performance in a numerical simulation study.

A common method for estimating the Hessian operator from random samples on a low-dimensional manifold involves locally fitting a quadratic polynomial. Although widely used, it is unclear if this estimator introduces bias, especially in complex manifolds with boundaries and nonuniform sampling. Rigorous theoretical guarantees of its asymptotic behavior have been lacking. We show that, under mild conditions, this estimator asymptotically converges to the Hessian operator, with nonuniform sampling and curvature effects proving negligible, even near boundaries. Our analysis framework simplifies the intensive computations required for direct analysis.

The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several numerical method families. The paper provides the discretisation and proves the convergence of the approximate schemes using a compactness argument that works under natural assumptions on data. We also investigate, using a finite volume method, known as the hybrid mixed mimetic (HMM) approach, the effects of multiplicative noise on the dynamics of the travelling waves in the excitable media displayed by the model. Particularly, we consider how sufficiently high noise can cause waves to backfire or fail to propagate.

Error control by means of a posteriori error estimators or indica-tors and adaptive discretizations, such as adaptive mesh refinement, have emerged in the late seventies. Since then, numerous theoretical developments and improvements have been made, as well as the first attempts to introduce them into real-life industrial applications. The present introductory chapter provides an overview of the subject, highlights some of the achievements to date and discusses possible perspectives.

We prove the convergence of a damped Newton's method for the nonlinear system resulting from a discretization of the second boundary value problem for the Monge-Ampere equation. The boundary condition is enforced through the use of the notion of asymptotic cone. The differential operator is discretized based on a discrete analogue of the subdifferential.

In the finite difference approximation of the fractional Laplacian the stiffness matrix is typically dense and needs to be approximated numerically. The effect of the accuracy in approximating the stiffness matrix on the accuracy in the whole computation is analyzed and shown to be significant. Four such approximations are discussed. While they are shown to work well with the recently developed grid-over finite difference method (GoFD) for the numerical solution of boundary value problems of the fractional Laplacian, they differ in accuracy, economics to compute, performance of preconditioning, and asymptotic decay away from the diagonal line. In addition, two preconditioners based on sparse and circulant matrices are discussed for the iterative solution of linear systems associated with the stiffness matrix. Numerical results in two and three dimensions are presented.

Conventional intelligent systems based on deep neural network (DNN) models encounter challenges in achieving human-like continual learning due to catastrophic forgetting. Here, we propose a metaplasticity model inspired by human working memory, enabling DNNs to perform catastrophic forgetting-free continual learning without any pre- or post-processing. A key aspect of our approach involves implementing distinct types of synapses from stable to flexible, and randomly intermixing them to train synaptic connections with different degrees of flexibility. This strategy allowed the network to successfully learn a continuous stream of information, even under unexpected changes in input length. The model achieved a balanced tradeoff between memory capacity and performance without requiring additional training or structural modifications, dynamically allocating memory resources to retain both old and new information. Furthermore, the model demonstrated robustness against data poisoning attacks by selectively filtering out erroneous memories, leveraging the Hebb repetition effect to reinforce the retention of significant data.