On the Whitney disks in Heegaard Floer homology theory

The Whitney disks play a central role in defining Heegaard Floer homology of a $3$-dimensional manifold. We use Nielsen theory to a simple criterion to the existence of Whitney disks, connecting two given intersections

Persistence of sub-chain groups

In this work, we present a generalization of extended persistent homology to filtrations of graded sub-groups by defining relative homology in this setting. Our work provides a more comprehensive and flexible approach to get an algebraic invariant overcoming the limitations of the standard approach. The main contribution of our work is the development of a stability theorem for extended persistence modules using an extension of the definition of interleaving and the rectangle measure. This stability theorem is a crucial property for the application of mathematical tools in data analysis. We apply the stability theorem to extended persistence modules obtained from extended path homology of directed graphs and extended homology of hypergraphs, which are two important examples in topological data analysis

Photochemical characteristics of diclofenac and its photodegradation of inclusion complexes with β-cyclodextrins

Diclofenac is one of most frequently detected compounds in the water cycle. In this work, the effect of initial concentration, liquid inclusion complexes with β-Cyclodextrins (β-CDs) on the photodegradation of diclofenac were studied. Six phototransformation products were detected by HPLC chromatograms. UV-absorption spectra of diclofenac and phototransformation products were determined. One of the phototransformation products was identified. The degradation followed pseudo-first-order kinetics. The experiment showed that irradiation of diclofenac in the presence of β-CDs increase photodegradation rate and determined the optimal molar ratio of diclofenac to β-CDs as 1:2. The reduced photohaemolytic activity of diclofenac in the presence of β-CDs may be attributed to the sequestering and stabilizing of the radical intermediates and /or photoproducts by complexation

Design of 2 μm Wavelength Polarization Mode Controllers

A single-slot waveguide for transverse electric (TE) to transverse magnetic (TM) mode conversion operating at wavelengths around 2 μm is proposed based on an InGaSb/AlGaAsSb quantum well structure. The polarization mode convertor has a deep-etched ridge waveguide and a single shallow-etched slot, and can be fabricated in a single stage of dry-etching. The dependence of polarization conversion efficiency on slot width, slot position, slot depth and waveguide length was investigated, and a design that was insensitive to fabrication tolerances was identified. A TE-TM mode conversion efficiency of more than 97% can be obtained in a 2141-μm-long waveguide

BGM-Net: Boundary-Guided Multiscale Network for Breast Lesion Segmentation in Ultrasound.

Automatic and accurate segmentation of breast lesion regions from ultrasonography is an essential step for ultrasound-guided diagnosis and treatment. However, developing a desirable segmentation method is very difficult due to strong imaging artifacts e.g., speckle noise, low contrast and intensity inhomogeneity, in breast ultrasound images. To solve this problem, this paper proposes a novel boundary-guided multiscale network (BGM-Net) to boost the performance of breast lesion segmentation from ultrasound images based on the feature pyramid network (FPN). First, we develop a boundary-guided feature enhancement (BGFE) module to enhance the feature map for each FPN layer by learning a boundary map of breast lesion regions. The BGFE module improves the boundary detection capability of the FPN framework so that weak boundaries in ambiguous regions can be correctly identified. Second, we design a multiscale scheme to leverage the information from different image scales in order to tackle ultrasound artifacts. Specifically, we downsample each testing image into a coarse counterpart, and both the testing image and its coarse counterpart are input into BGM-Net to predict a fine and a coarse segmentation maps, respectively. The segmentation result is then produced by fusing the fine and the coarse segmentation maps so that breast lesion regions are accurately segmented from ultrasound images and false detections are effectively removed attributing to boundary feature enhancement and multiscale image information. We validate the performance of the proposed approach on two challenging breast ultrasound datasets, and experimental results demonstrate that our approach outperforms state-of-the-art methods

Mounting a screwdriver onto a screw using hybrid control

Many peg-hole-insertion strategies have been developed for autonomous assembly tasks. Unfortunately, none of them appear applicable to the simple task of mounting a screwdriver, which has a thin tip, onto a screw, whose small head and narrow drive significantly limit the work space. The task has thus remained a challenging test for a robot's dexterity. In this thesis, we have developed a mounting strategy for a robotic arm that proceeds in two phases: a) screwdriver tip localization relative to the screw's drive via sliding and b) tip insertion into the slot via rotation. During the entire operation, the contact between the screwdriver's tip and the screw head is maintained with a sequence of three hybrid controllers. The hybrid controller has two goals---motion tracking and force regulating. As long as these two goals are not mutually exclusive, they can be decoupled in some way. In this thesis, we make use of the smooth and invertible mapping from the joint space to the task space to decouple the two control goals and design controllers separately. The traditional motion controller in the task space is used for motion control, while the force controller is designed through manipulating the desired trajectory to regulate the force indirectly. Two case studies---contour tracking/polishing surfaces and grabbing boxes with two robotic arms---are presented to show the efficacy of the hybrid controller, and simulations with physics engines are carried out to validate the efficacy of the proposed method. The mounting strategy using hybrid control is simulated on the same platform for demonstration as well

Nanopositioning with piezoelectric actuators: Modeling, control, and applications

Nanopositioning is critical for applications in microscale or nanoscale, such as investigation and manipulation of biological, chemical or physical processes/materials, and usually realized with piezoelectric actuators (PEA). However, due to the nonlinearities, it is challenging to achieve high-accuracy and broad-bandwidth control of PEAs. In this dissertation, we investigate how to improve the control accuracy and bandwidth. In addition, we apply the proposed controllers on two applications based on atomic force microscopes (AFMs). In Chapter 2, we combine iterative learning control (ILC) with predictive control (MPC) forming IL-MPC. It avoids the inversion model compared to inversion-based ILC and also has low tracking errors in the first iteration. The convergence condition of IL-MPC is derived. In particular, we studied the performance of IL-MPC when the reference trajectory is varying both theoretically and experimentally. Although IL-MPC can be used for high-accuracy and broad-bandwidth control of PEAs, it is not a real-time controller, the design of which is the focus of Chapters 3-6. The key idea is to accurately model the PEA dynamics over a broad bandwidth with recurrent neural networks (RNNs) and design predictive controllers based on the resulted models. In Chapter 3, RNN is used to model the PEA dynamics and combined with a linear model to improve the modeling accuracy. Then a nonlinear predictive controller is designed with the augmented RNN model. To improve the computation efficiency of the controller, the gradient is computed analytically for the optimization problem. Nevertheless, the computation efficiency hinders the usage of large sampling frequency which is necessary for many applications. This issue is alleviated in Chapter 4 in which the nonlinear model is linearized with Koopman operators. However, as the RNN becomes more complex, the computation efficiency is still a problem even with linearization. An alternative is to model the inversion dynamics with RNNs, which leads to the control approach in Chapter 5. The inversion model based on RNNs can compensate for most of the nonlinearities; then, a linear model was used to capture the residual dynamics. Furthermore, how to reduce the modeling errors when incorporating the linear model with the RNN inversion model is investigated in Chapter 6. Finally, with regard to the applications, we applied IL-MPC for high-speed AFM imaging and the proposed real-time controller for polymer indentation control, which further validate the proposed methods.</p

Mounting a screwdriver onto a screw using hybrid control

Many peg-hole-insertion strategies have been developed for autonomous assembly tasks. Unfortunately, none of them appear applicable to the simple task of mounting a screwdriver, which has a thin tip, onto a screw, whose small head and narrow drive significantly limit the work space. The task has thus remained a challenging test for a robot's dexterity. In this thesis, we have developed a mounting strategy for a robotic arm that proceeds in two phases: a) screwdriver tip localization relative to the screw's drive via sliding and b) tip insertion into the slot via rotation. During the entire operation, the contact between the screwdriver's tip and the screw head is maintained with a sequence of three hybrid controllers. The hybrid controller has two goals---motion tracking and force regulating. As long as these two goals are not mutually exclusive, they can be decoupled in some way. In this thesis, we make use of the smooth and invertible mapping from the joint space to the task space to decouple the two control goals and design controllers separately. The traditional motion controller in the task space is used for motion control, while the force controller is designed through manipulating the desired trajectory to regulate the force indirectly. Two case studies---contour tracking/polishing surfaces and grabbing boxes with two robotic arms---are presented to show the efficacy of the hybrid controller, and simulations with physics engines are carried out to validate the efficacy of the proposed method. The mounting strategy using hybrid control is simulated on the same platform for demonstration as well.</p