The multidimensional dependence of halo bias in the eye of a machine: a tale of halo structure, assembly and environment

We develop a novel approach in exploring the joint dependence of halo bias on multiple halo properties using Gaussian process regression. Using a $\Lambda$CDM $N$-body simulation, we carry out a comprehensive study of the joint bias dependence on halo structure, formation history and environment. We show that the bias is a multivariate function of halo properties that falls into three regimes. For massive haloes, halo mass explains the majority of bias variation. For early-forming haloes, bias depends sensitively on the recent mass accretion history. For low-mass and late-forming haloes, bias depends more on the structure of a halo such as its shape and spin. Our framework enables us to convincingly prove that $V_\mathrm{max}/V_\mathrm{vir}$ is a lossy proxy of formation time for bias modelling, whereas the mass, spin, shape and formation time variables are non-redundant with respect to each other. Combining mass and formation time largely accounts for the mass accretion history dependence of bias. Combining all the internal halo properties fully accounts for the density profile dependence inside haloes, and predicts the clustering variation of individual haloes to a $20\%$ level at $\sim 10\mathrm{Mpc}h^{-1}$. When an environmental density is measured outside $1\mathrm{Mpc}h^{-1}$ from the halo centre, it outperforms and largely accounts for the bias dependence on the internal halo structure, explaining the bias variation above a level of $30\%$.Comment: MNRAS accepte

Robust Discontinuity Indicators for High-Order Reconstruction of Piecewise Smooth Functions

In many applications, piecewise continuous functions are commonly interpolated over meshes. However, accurate high-order manipulations of such functions can be challenging due to potential spurious oscillations known as the Gibbs phenomena. To address this challenge, we propose a novel approach, Robust Discontinuity Indicators (RDI), which can efficiently and reliably detect both C^{0} and C^{1} discontinuities for node-based and cell-averaged values. We present a detailed analysis focusing on its derivation and the dual-thresholding strategy. A key advantage of RDI is its ability to handle potential inaccuracies associated with detecting discontinuities on non-uniform meshes, thanks to its innovative discontinuity indicators. We also extend the applicability of RDI to handle general surfaces with boundaries, features, and ridge points, thereby enhancing its versatility and usefulness in various scenarios. To demonstrate the robustness of RDI, we conduct a series of experiments on non-uniform meshes and general surfaces, and compare its performance with some alternative methods. By addressing the challenges posed by the Gibbs phenomena and providing reliable detection of discontinuities, RDI opens up possibilities for improved approximation and analysis of piecewise continuous functions, such as in data remap.Comment: 37 pages, 37 figures, submitted to Computational and Applied Mathematics (COAM

Measuring the Angular Velocity of a Propeller with Video Camera Using Electronic Rolling Shutter

Noncontact measurement for rotational motion has advantages over the traditional method which measures rotational motion by means of installing some devices on the object, such as a rotary encoder. Cameras can be employed as remote monitoring or inspecting sensors to measure the angular velocity of a propeller because of their commonplace availability, simplicity, and potentially low cost. A defect of the measurement with cameras is to process the massive data generated by cameras. In order to reduce the collected data from the camera, a camera using ERS (electronic rolling shutter) is applied to measure angular velocities which are higher than the speed of the camera. The effect of rolling shutter can induce geometric distortion in the image, when the propeller rotates during capturing an image. In order to reveal the relationship between the angular velocity and the image distortion, a rotation model has been established. The proposed method was applied to measure the angular velocities of the two-blade propeller and the multiblade propeller. The experimental results showed that this method could detect the angular velocities which were higher than the camera speed, and the accuracy was acceptable

Integration modes, global networks, and knowledge diffusion in overseas M&As by emerging market firms

Purpose This paper aims to examine how integration modes impact the acquirer knowledge diffusion capacity of overseas mergers and acquisitions (M&As) effected by emerging market firms and the role played by the global innovation network position of the acquiring firms in affecting this relationship. Design/methodology/approach Through the use of structural equation modelling and bootstrap testing, the hypotheses are tested by drawing upon a sample of 102 overseas M&As effected by listed Chinese manufacturing companies. Findings The results show that acquirers from emerging countries are unable to increase the knowledge diffusion capacity unless they choose the right post-merger integration mode. This paper also finds that the relationship between integration mode and knowledge diffusion is channelled through the centrality and structural holes of acquirers in the global innovation networks. When considering the combinations of different resource similarities and complementarities of the acquired firms, differences emerge in the integration model and network embedded path of acquirers in emerging countries. Practical implications Emerging market multinational enterprises should consider post-merger integration as a crucial facilitator to the crafting of global innovation network positions that promote knowledge diffusion. The choices of integration mode and brand management autonomy should be matched with the resource similarities and complementarities that exist between the acquirer and target firms. Originality/value Based on the resource orchestration theory and by focussing on network centrality and structural hole as the crucial links, this study provides a nuanced understanding of the relationship between post-merger integration and knowledge diffusion and sheds light on latecomer firms from emerging countries