Behavior of different numerical schemes for population genetic drift problems

In this paper, we focus on numerical methods for the genetic drift problems, which is governed by a degenerated convection-dominated parabolic equation. Due to the degeneration and convection, Dirac singularities will always be developed at boundary points as time evolves. In order to find a \emph{complete solution} which should keep the conservation of total probability and expectation, three different schemes based on finite volume methods are used to solve the equation numerically: one is a upwind scheme, the other two are different central schemes. We observed that all the methods are stable and can keep the total probability, but have totally different long-time behaviors concerning with the conservation of expectation. We prove that any extra infinitesimal diffusion leads to a same artificial steady state. So upwind scheme does not work due to its intrinsic numerical viscosity. We find one of the central schemes introduces a numerical viscosity term too, which is beyond the common understanding in the convection-diffusion community. Careful analysis is presented to prove that the other central scheme does work. Our study shows that the numerical methods should be carefully chosen and any method with intrinsic numerical viscosity must be avoided.Comment: 17 pages, 8 figure

Tacchi: A Pluggable and Low Computational Cost Elastomer Deformation Simulator for Optical Tactile Sensors

Simulation is widely applied in robotics research to save time and resources. There have been several works to simulate optical tactile sensors that leverage either a smoothing method or Finite Element Method (FEM). However, elastomer deformation physics is not considered in the former method, whereas the latter requires a massive amount of computational resources like a computer cluster. In this work, we propose a pluggable and low computational cost simulator using the Taichi programming language for simulating optical tactile sensors, named as Tacchi . It reconstructs elastomer deformation using particles, which allows deformed elastomer surfaces to be rendered into tactile images and reveals contact information without suffering from high computational costs. Tacchi facilitates creating realistic tactile images in simulation, e.g., ones that capture wear-and-tear defects on object surfaces. In addition, the proposed Tacchi can be integrated with robotics simulators for a robot system simulation. Experiment results showed that Tacchi can produce images with better similarity to real images and achieved higher Sim2Real accuracy compared to the existing methods. Moreover, it can be connected with MuJoCo and Gazebo with only the requirement of 1G memory space in GPU compared to a computer cluster applied for FEM. With Tacchi, physical robot simulation with optical tactile sensors becomes possible. All the materials in this paper are available at https://github.com/zixichen007115/Tacchi .Comment: 8 pages, 6 figures, accepted by IEEE Robotics and Automation Letter

Multivariate analysis and optimal configuration of wind-photovoltaic complementary power generation system

Advantages of wind-solar complementary power generation system to utilize solar and wind energy in the aspect of resource and technical economy have been reviewed tersely. Convenience of entering and exiting generating equipment and load from DC as well as AC bus are interpreted briefly. The factors that affect the electrical power output of the system were analyzed and studied. Based on the law of energy conservation, the energetic matching algorithm was proposed which forms the foundation of optimal configuration of system. Finally, the intelligent control and on-line monitoring of wind-solar complementary power generation system were discussed

Prenatal diagnosis of fetal intracranial medulloepithelioma: a case report

Intracranial medulloepithelioma is a very rare and highly malignant tumor that is typically diagnosed in childhood and has an inferior prognosis. In the current report, we described a case of fetal intracranial medulloepithelioma that was detected during the third trimester by prenatal ultrasonography, which displayed homogenous echogenicity with well-circumscribed margins and abundant blood flow. On magnetic resonance imaging, it was hyperintense on both T1- and T2-weighted magnetic resonance imaging. The fetal intracranial tumor was progressive, with rapid expansion within 3 weeks. The report aimed to provide knowledge on the clinical characteristics of fetal intracranial medulloepithelioma in prenatal diagnosis, particularly the radiological features