Nonlinear repulsive force between two solids with axial symmetry

We modify the formulation of Hertz contact theory between two elastic half-solids with axial symmetry and show that these modifications to Hertz’s original framework allow the development of force laws of the form F∝z^n, 10 to describe any aspect ratio in the two bodies, all being valid near the contact surface. We let the x-y plane be the contact surface with an averaged pressure across the same as opposed to a pressure profile that depends on the contact area of a nonconformal contact as originally used by Hertz. We let the z axis connect the centers of the masses and define z_(1,2) = x^(α)/R_(1,2)^(α-1) + y^(α)/(mR_(1,2))^(α-1), where z_(1,2)≥0 refers to the compression of bodies 1, 2, α>1, m>0, x,y≥0. The full cross section can be generated by appropriate reflections using the first quadrant part of the area. We show that the nonlinear repulsive force is F=az^n, where n≡1+(1/α), and z≡z_1 + z_2 is the overlap and we present an expression for a=f(E,σ,m,α,R_(1),R_(2)) with E and σ as Young’s modulus and the Poisson ratio, respectively. For α=2,∞, to similar geometry-dependent constants, we recover Hertz’s law and the linear law, describing the repulsion between compressed spheres and disks, respectively. The work provides a connection between the contact geometry and the nonlinear repulsive law via α and m

Schwarzschild-de Sitter Metric and Inertial Beltrami Coordinates

Under consideration of coordinate conditions, we get the Schwarzschild-Beltrami-de Sitter (S-BdS) metric solution of the Einstein field equations with a cosmological constant $\Lambda$. A brief review to the de Sitter invariant special relativity (dS-SR), and de Sitter general relativity (dS-GR, or GR with a $\Lambda$) is presented. The Beltrami metric $B_{\mu\nu}$ provides inertial reference frame for the dS-spacetime. By examining the Schwarzschild-de Sitter (S-dS) metric $g_{\mu\nu}^{(M)}$ existed in literatures since 1918, we find that the existed S-dS metric $g_{\mu\nu}^{(M)}$ describes some mixing effects of gravity and inertial-force, instead of a pure gravity effect arisen from "solar mass" $M$ in dS-GR. In this paper, we solve the vacuum Einstein equation of dS-GR, with the requirement of gravity-free metric $g_{\mu\nu}^{(M)}|_{M\rightarrow 0}=B_{\mu\nu}$. In this way we find S-BdS solution of dS-GR, written in inertial Beltrami coordinates. This is a new form of S-dS metric. Its physical meaning and possible applications are discussed.Comment: 16 pages, 1 figur

DABS: Data-Agnostic Backdoor attack at the Server in Federated Learning

Federated learning (FL) attempts to train a global model by aggregating local models from distributed devices under the coordination of a central server. However, the existence of a large number of heterogeneous devices makes FL vulnerable to various attacks, especially the stealthy backdoor attack. Backdoor attack aims to trick a neural network to misclassify data to a target label by injecting specific triggers while keeping correct predictions on original training data. Existing works focus on client-side attacks which try to poison the global model by modifying the local datasets. In this work, we propose a new attack model for FL, namely Data-Agnostic Backdoor attack at the Server (DABS), where the server directly modifies the global model to backdoor an FL system. Extensive simulation results show that this attack scheme achieves a higher attack success rate compared with baseline methods while maintaining normal accuracy on the clean data.Comment: Accepted by Backdoor Attacks and Defenses in Machine Learning (BANDS) Workshop at ICLR 202

Multidimensional Taylor Network Optimal Control of MIMO Nonlinear Systems without Models for Tracking by Output Feedback

The actual controlled objects are generally multi-input and multioutput (MIMO) nonlinear systems with imprecise models or even without models, so it is one of the hot topics in the control theory. Due to the complex internal structure, the general control methods without models tend to be based on neural networks. However, the neuron of neural networks includes the exponential function, which contributes to the complexity of calculation, making the neural network control unable to meet the real-time requirements. The newly developed multidimensional Taylor network (MTN) requires only addition and multiplication, so it is easy to realize real-time control. In the present study, the MTN approach is extended to MIMO nonlinear systems without models to realize adaptive output feedback control. The MTN controller is proposed to guarantee the stability of the closed-loop system. Our experimental results show that the output signals of the system are bounded and the tracking error goes nearly to zero. The MTN optimal controller is proven to promise far better real-time dynamic performance and robustness than the BP neural network self-adaption reconstitution controller

Quasar Factor Analysis -- An Unsupervised and Probabilistic Quasar Continuum Prediction Algorithm with Latent Factor Analysis

Since their first discovery, quasars have been essential probes of the distant Universe. However, due to our limited knowledge of its nature, predicting the intrinsic quasar continua has bottlenecked their usage. Existing methods of quasar continuum recovery often rely on a limited number of high-quality quasar spectra, which might not capture the full diversity of the quasar population. In this study, we propose an unsupervised probabilistic model, \textit{Quasar Factor Analysis} (QFA), which combines factor analysis (FA) with physical priors of the intergalactic medium (IGM) to overcome these limitations. QFA captures the posterior distribution of quasar continua through generatively modeling quasar spectra. We demonstrate that QFA can achieve the state-of-the-art performance, $\sim 2\%$ relative error, for continuum prediction in the Ly$\alpha$ forest region compared to previous methods. We further fit 90,678 $22$ quasar spectra from Sloan Digital Sky Survey Data Release 16 and found that for $\sim 30\%$ quasar spectra where the continua were ill-determined with previous methods, QFA yields visually more plausible continua. QFA also attains $\lesssim 1\%$ error in the 1D Ly$\alpha$ power spectrum measurements at $\mathrm{z}\sim 3$ and $\sim 4\%$ in $\mathrm{z}\sim 2.4$. In addition, QFA determines latent factors representing more physically motivated than PCA. We investigate the evolution of the latent factors and report no significant redshift or luminosity dependency except for the Baldwin effect. The generative nature of QFA also enables outlier detection robustly; we showed that QFA is effective in selecting outlying quasar spectra, including damped Ly$\alpha$ systems and potential Type II quasar spectra.Comment: Main body is 23 pages with 14 figures. Much more detailed exposition of the method originally presented in the short conference workshop paper arXiv:2207.02788 . All source codes are made publicly available at https://github.com/ZechangSun/QFA . Submitted to ApJS. Comments are welcome

Linking Forests and Economic Well-being: A Four Quadrant Approach

This paper has three main objectives: (1) to investigate whether the four-quadrant approach introduced by Maini (2003) reveals a useful typology for grouping countries by GDP and forest cover per capita, (2) to determine if the framework can enhance our understanding of the relationship between forest cover and GDP per capita, and (3) to investigate why countries in the four-quadrant world occupy different quadrants, and to determine the principal factors affecting country-movement across and within the individual quadrants. The examination reveals that countries can be classified into four broad categories, and that GDP and forest cover per capita have a low but consistent level of negative association. After regressing economic, institutional, social capital and other variables on a country’s occupancy and movement in the four-quadrant world, the results suggest that countries in each quadrant share different characteristics and that factors underlying country-movement varies according to the quadrant being observed. Overall, countries with less corruption and higher education are likely to experience increases in both forest cover and GDP per capita, while countries exporting a significant proportion of forest products have a reduced probability of increasing both variables.Economic well-being, forest cover, institutions, corruption, education

Active thermal management for Interior Permanent Magnet Synchronous Machine (IPMSM) drives based on model predictive control

This paper proposes an active thermal management scheme for Interior Permanent Magnet Synchronous Machine (IPMSM) drives based on the model predictive control concept. The proposed control scheme can adaptively set torque limit based on the thermal state of the machine to limit the machine winding and end-winding temperatures. The proposed control scheme is assessed by experiments on a laboratory machine drive system and simulated for traction drives over Worldwide Harmonized Light-duty Test Cycle (WLTC). Compared with conventional traction control scheme, the proposed scheme can effectively reduce peak temperature and hence thermal stress of the machine for improving its lifetime

Fast full-color computational imaging with single-pixel detectors

Single-pixel detectors can be used as imaging devices by making use of structured illumination. These systems work by correlating a changing incident light field with signals measured on a photodiode to derive an image of an object. In this work we demonstrate a system that utilizes a digital light projector to illuminate a scene with approximately 1300 different light patterns every second and correlate these with the back scattered light measured by three spectrally-filtered single-pixel photodetectors to produce a full-color high-quality image in a few seconds of data acquisition. We utilize a differential light projection method to self normalize the measured signals, improving the reconstruction quality whilst making the system robust to external sources of noise. This technique can readily be extended for imaging applications at non-visible wavebands