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Additinal file 1: Appendix table A. Mesh sensitivity test.

In 1979, Hartley and Kawauchi proved that the Conway polynomial of a strongly negative amphichiral knot factors as $f(z)f(-z)$. In this paper, we normalize the factor $f(z)$ to define the half-Conway polynomial. First, we prove that the half-Conway polynomial satisfies an equivariant skein relation, giving the first feasible computational method, which we use to compute the half-Conway polynomial for knots with 12 or fewer crossings. This skein relation also leads to a diagrammatic interpretation of the degree-one coefficient, from which we obtain a lower bound on the equivariant unknotting number. Second, we completely characterize polynomials arising as half-Conway polynomials of knots in $S^3$, answering a problem of Hartley-Kawauchi. As a special case, we construct the first examples of non-slice strongly negative amphichiral knots with determinant one, answering a question of Manolescu. The double branched covers of these knots provide potentially non-trivial torsion elements in the homology cobordism group.

High attack rate in a Tong Lau house outbreak of COVID-19 with subdivided units in Hong Kong

Based on the 1–3 identical high-rise buildings with pile-raft foundation, a series of building-site two-dimensional finite element analysis models with different building spacings is established. Then, considering the nonlinear characteristics of soil and structure, the static-dynamic coupled numerical simulations are conducted to study the structure-soil-structure interaction (SSSI) under different ground motion. The results show that: 1) Adjacent high-rise buildings have the most unfavorable impact on the peak acceleration of the 1/4–1/2 height floors of the middle building, and increase the normalized response acceleration spectra value of acceleration near the second natural period of the structure; 2) Adjacent high-rise buildings have the most significant impact on the inter-story drift of the top, bottom and basement of the middle building; 3) Adjacent high-rise buildings redistribute the total horizontal shear force of the pile top of the middle building among the pile foundations, so that the peak value of the pile top shear force of each pile changes significantly, which is extremely unfavorable to the seismic safety of the structure. It should be taken seriously in the seismic design of structures. In addition, the structure spacing that results in favorable or unfavorable effects is discussed, and the reasons for the impact are analyzed.

Collaboration between heterogeneous robots promises increased robustness and efficiency of tasks with great potential in applications, such as manufacturing, search and rescue. In this paper, we present a collaboration system based on an edge computing framework, a mobile robot named “StellaX” and a manipulator. The robot StellaX is assembled by a three-wheel omnidirectional platform, a LIDAR scanner for indoor autonomous navigation, and a stereo camera which can capture objects' images. The information of objects, which can be used for grasping, is stored and shared with the manipulator through the edge computing framework with Docker and ROS. Finally, we test the collaboration system by conducting an object recognition experiment and a navigation experiment. The experimental results demonstrate the system effectiveness and prove that the system yields better real-time performance and reduces total task execution time than a cloud computing-based scenario.

Crack detection and crack sealing are challenging tasks which have been researched for decades due to the complicated roadway conditions in real world. Especially, crack sealing is an important procedure used to extend the life of road pavement. This paper develops and implements a kind of manipulator system for roadway crack sealing, which consists of a six-degree-of-freedom(6-DoF) manipulator with a novel crack sealing end-effector, a stereo camera, an air pump, a glue barrel and a laptop. The paper presents the hardware construction and working schematic of the manipulation system. Before crack sealing, a supervised method based on deep learning is used to detect the cracks and obtain the cracks' image information, which can be merged with depth information to acquire the accurate location information of cracks. We validate the feasibility of the crack sealing end-effector which can be applied to seal cracks on uneven road surface by indoor simulation tests.

In this paper, we develop and implement a kind of mobile manipulator named Jupiter, which consists of a six-degree-of-freedom(DOF) manipulator and an omnidirectional mobile platform with four actively steerable wheels. In contrast to the omnidirectional mobile manipulator with Mecanum wheels, the proposed mobile manipulator can be adopted in rough terrains. Two laser scanners and a stereo camera are mounted in the system to perceive the environment. With the IMU and odometry data, Jupiter is capable of doing SLAM by Hector SLAM method and path planning. A manipulation frameworks with a single shot multibox detector (SSD) approach is used to detect and grasp the objects. Combining the two function, both the manipulator and the platform are integrated into a system which can execute mobile manipulation tasks autonomously. Our contribution includes a complete hardware construction and software pipeline of the mobile manipulator which is capable of autonomously doing SLAM, navigation, detecting and grasping objects. The performance of the system are tested and proved by autonomously executing an mobile manipulation mission including autonomous navigation with multi-sensors and apples grasping and placing.

In this paper, a novel Attitude and Heading Reference System(AHRS) algorithm for real time controlling of various mobile robots is presented. Such a control system is essential for real time mobile robots control applications, such as entertainment, business activities, industrial, domestic assistant and etc. New angles and vectors definition, system specification and Momentum Correction Factor(MCF) are proposed to compensate the motion time delay during an inertial action. A dedicated experimental setup is established to test the algorithm. Experimental results show that the proposed algorithm is able to maintain an accurate and delay-free motion control.

This paper presents a global 3D feature descriptor for object recognition and grasping. The proposed descriptor stems from the clustered viewpoint feature histogram (CVFH) feature descriptor. Since the CVFH feature descriptor relies on shape information only, it obtains a poor performance when recognizing the objects with similar shapes. In order to improve the robustness and accuracy of object recognition, we extend CVFH feature descriptor with color information. Then this new global 3D feature descriptor is tested for multiple classes of 3D object classification by using support vector machines (SVM), and it is evaluated with a public dataset and real scenes respectively. The experimental results show that the proposed descriptor outperforms the CVFH feature descriptor in terms of recognition rate. Finally we utilize the proposed descriptor on our grasping system to recognize and grasp the objects, showing that the grasping system can accomplish the tasks well.

Fox conjectured the Alexander polynomial of an alternating knot is trapezoidal, i.e. the coefficients first increase, then stabilize and finally decrease in a symmetric way. Recently, Hirasawa and Murasugi further conjectured a relation between the number of the stable coefficients in the Alexander polynomial and the signature invariant. In this paper we prove the Hirasawa-Murasugi conjecture for two-bridge knots., Comment: minor errors corrected

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