Stability and Oscillation of θ-methods for Differential Equation with Piecewise Constant Arguments

This paper studies the numerical properties of θ-methods for the alternately advanced and retarded differential equation u′(t) = au(t)+bu(2[(t+1)/2]). Using two classes of θ-methods, namely the linear θ-method and the one-leg θ-method, the stability regions of numerical methods are determined, and the conditions of oscillation for the θ-methods are derived. Moreover, we give the conditions under which the numerical stability regions contain the analytical stability regions. It is shown that the θ-methods preserve the oscillation of the analytic solution. In addition, the relationships between stability and oscillation are presented. Several numerical examples are given

Size dependent electronic properties of silicon quantum dots - an analysis with hybrid, screened hybrid and local density functional theory

We use an efficient projection scheme for the Fock operator to analyze the size dependence of silicon quantum dots (QDs) electronic properties. We compare the behavior of hybrid, screened hybrid and local density functionals as a function of the dot size up to $\sim$800 silicon atoms and volume of up to $\sim$20nm$^3$. This allows comparing the calculations of hybrid and screened hybrid functionals to experimental results over a wide range of QD sizes. We demonstrate the size dependent behavior of the band gap, density of states, ionization potential and HOMO level shift after ionization. Those results are compared to experiment and to other theoretical approaches, such as tight-binding, empirical pseudopotentials, TDDFT and GW

DPFormer: Learning Differentially Private Transformer on Long-Tailed Data

The Transformer has emerged as a versatile and effective architecture with broad applications. However, it still remains an open problem how to efficiently train a Transformer model of high utility with differential privacy guarantees. In this paper, we identify two key challenges in learning differentially private Transformers, i.e., heavy computation overhead due to per-sample gradient clipping and unintentional attention distraction within the attention mechanism. In response, we propose DPFormer, equipped with Phantom Clipping and Re-Attention Mechanism, to address these challenges. Our theoretical analysis shows that DPFormer can reduce computational costs during gradient clipping and effectively mitigate attention distraction (which could obstruct the training process and lead to a significant performance drop, especially in the presence of long-tailed data). Such analysis is further corroborated by empirical results on two real-world datasets, demonstrating the efficiency and effectiveness of the proposed DPFormer

Towards Grouping in Large Scenes with Occlusion-aware Spatio-temporal Transformers

Group detection, especially for large-scale scenes, has many potential applications for public safety and smart cities. Existing methods fail to cope with frequent occlusions in large-scale scenes with multiple people, and are difficult to effectively utilize spatio-temporal information. In this paper, we propose an end-to-end framework,GroupTransformer, for group detection in large-scale scenes. To deal with the frequent occlusions caused by multiple people, we design an occlusion encoder to detect and suppress severely occluded person crops. To explore the potential spatio-temporal relationship, we propose spatio-temporal transformers to simultaneously extract trajectory information and fuse inter-person features in a hierarchical manner. Experimental results on both large-scale and small-scale scenes demonstrate that our method achieves better performance compared with state-of-the-art methods. On large-scale scenes, our method significantly boosts the performance in terms of precision and F1 score by more than 10%. On small-scale scenes, our method still improves the performance of F1 score by more than 5%. The project page with code can be found at http://cic.tju.edu.cn/faculty/likun/projects/GroupTrans.Comment: 11 pages, 5 figure

Industrial Robot Trajectory Accuracy Evaluation Maps for Hybrid Manufacturing Process based on Joint Angle Error Analysis

Industrial robots have been widely used in various fields. The joint angle error is the main factor that affects the accuracy performance of the robot. It is important to notice that these kinematic parameters error cannot be eliminated from the robot system completely. Even after calibration, these errors still exist and will be fluctuated during the robot system running. This paper proposed a new method of finding the best position and orientation to perform a specific working path based on the current accuracy capacity of the robot system. By analyzing the robot forward/inverse kinematic and the angle error sensitivity of different joint in the serial manipulator system, a new evaluation formulation is established for mapping the trajectory accuracy within the robot’s working volume. The influence of different position and orientation on the movement accuracy of the end effector has been verified by experiments and discussed thoroughly. Finally, a visualized evaluation map can be obtained to describe the accuracy difference of a robotic laser deposition working path at different positions and orientations. This method is helpful for making the maximum usage of the robot’s current accuracy ability rather than blindly pursuing the higher accuracy of the robot system

Exploring the key factors affecting the seasonal variation of phytoplankton in the coastal Yellow Sea

Marine phytoplankton play crucial roles in the ocean’s biological pump and have great impacts on global biogeochemical cycles, yet the knowledge of environmental variables controlling their seasonal dynamics needs to be improved further, especially in the coastal ecosystems. In order to explore the determinants affecting the seasonal variation of phytoplankton, here we conducted three surveys during spring, summer and autumn along the coastal Yellow Sea. Among the phytoplankton community, 49 species of diatoms and 9 species of dinoflagellates were observed in spring, 63 species of diatoms and 10 species of dinoflagellates in summer, and 62 species of diatoms and 11 species of dinoflagellates in autumn. These results thus suggested that there were obvious differences in the number of species across the three seasons, of which diatoms were the most diverse group, followed by dinoflagellates. Additionally, diatoms were the most dominant species of the phytoplankton community and varied largely during different seasons. According to the redundancy analysis, the abundance of phytoplankton community was mainly related to water temperature and dissolved inorganic nitrogen (DIN) during the three seasons, indicating that water temperature and DIN could be the key factors controlling the seasonal variability of phytoplankton community along the coastal Yellow Sea. Also, significant correlations were observed between phytoplankton abundance and heavy metals Zn, As, and Hg during the three seasons, suggesting that these metals also had potential influences on the seasonal dynamics of phytoplankton community in the coastal Yellow Sea

A sensor-based screening tool for identifying high pelvic mobility in patients due to undergo total hip arthroplasty

There is increasing evidence that pelvic mobility is a critical factor to consider in implant alignment during total hip arthroplasty (THA). Here, we test the feasibility of using an inertial sensor fitted across the sacrum to measure change in pelvic tilt, and hence screen for patients with high pelvic mobility. Patients (n = 32, mean age: 57.4 years) due to receive THA surgery participated in the study. Measures of pelvic tilt were captured simultaneously using the device and radiograph in three functional positions: Standing, flexed-seated, and step-up. We found a strong correlation between the device and radiograph measures for the change in pelvic tilt measure from standing to flexed-seated position (R2 = 0.911); 75% of absolute errors were under 5 degrees. We demonstrated that the device can be used as a screening tool to rapidly identify patients who would benefit from more detailed surgical planning of implant positioning to reduce future risks of impingement and dislocation