Optimal Actuator Location of the Minimum Norm Controls for Stochastic Heat Equations

In this paper, we study the approximate controllability for the stochastic heat equation over measurable sets, and the optimal actuator location of the minimum norm controls. We formulate a relaxed optimization problem for both actuator location and its corresponding minimum norm control into a two-person zero sum game problem and develop a sufficient and necessary condition for the optimal solution via Nash equilibrium. At last, we prove that the relaxed optimal solution is an optimal actuator location for the classical problem

Observability Inequality of Backward Stochastic Heat Equations for Measurable Sets and Its Applications

This paper aims to provide directly the observability inequality of backward stochastic heat equations for measurable sets. As an immediate application, the null controllability of the forward heat equations is obtained. Moreover, an interesting relaxed optimal actuator location problem is formulated, and the existence of its solution is proved. Finally, the solution is characterized by a Nash equilibrium of the associated game problem

Multi-stage Suture Detection for Robot Assisted Anastomosis based on Deep Learning

In robotic surgery, task automation and learning from demonstration combined with human supervision is an emerging trend for many new surgical robot platforms. One such task is automated anastomosis, which requires bimanual needle handling and suture detection. Due to the complexity of the surgical environment and varying patient anatomies, reliable suture detection is difficult, which is further complicated by occlusion and thread topologies. In this paper, we propose a multi-stage framework for suture thread detection based on deep learning. Fully convolutional neural networks are used to obtain the initial detection and the overlapping status of suture thread, which are later fused with the original image to learn a gradient road map of the thread. Based on the gradient road map, multiple segments of the thread are extracted and linked to form the whole thread using a curvilinear structure detector. Experiments on two different types of sutures demonstrate the accuracy of the proposed framework.Comment: Submitted to ICRA 201

Collapse Transition of Two-Dimensional Flexible and Semiflexible Polymers

The nature of the globule-coil transition of surface-confined polymers has been an issue of debate. Here this 2D collapse transition is studied through a partially directed lattice model. In the general case of polymers with positive bending stiffness ($\Delta>0$), the collapse transition is {\em first-order}; it becomes {\em second-order} only in the limiting case of zero bending stiffness ($\Delta\equiv 0$). These analytical results are confirmed by Monte Carlo simulations. We also suggest some possible future experiments.Comment: 4 pages, 3 figure

Norm and time optimal control problems of stochastic heat equations

This paper investigates the norm and time optimal control problems for stochastic heat equations. We begin by presenting a characterization of the norm optimal control, followed by a discussion of its properties. We then explore the equivalence between the norm optimal control and time optimal control, and subsequently establish the bang-bang property of the time optimal control. These problems, to the best of our knowledge, are among the first to discuss in the stochastic case