Self-similar algebraic spiral solution of 2-D incompressible Euler equations

In this paper, we prove the existence of self-similar algebraic spiral solutions for 2-D incompressible Euler equations for the initial vorticity of the form $|y|^{-\frac1\mu}\ \mathring{\omega}(\theta)$ with $\mu>\frac12$ and $\mathring{\omega}\in L^1(\mathbb T)$ satisfying $m$-fold symmetry ($m\geq 2$) and a dominant condition. As an important application, we prove the existence of weak solution when $\mathring{\omega}$ is a Radon measure on $\mathbb T$ with $m$-fold symmetry, which is related to the vortex sheet solution.Comment: 60 pages, 1 figur

Construction of a High-Density Linkage Map and QTL Fine Mapping for Growth- and Sex-Related Traits in Channel Catfish (Ictalurus punctatus)

A high-density genetic linkage map is of particular importance in the fine mapping for important economic traits and whole genome assembly in aquaculture species. The channel catfish (Ictalurus punctatus), a species native to North America, is one of the most important commercial freshwater fish in the world. Outside of the United States, China has become the major producer and consumer of channel catfish after experiencing rapid development in the past three decades. In this study, based on restriction site associated DNA sequencing (RAD-seq), a high-density genetic linkage map of channel catfish was constructed by using single nucleotide polymorphisms (SNPs) in a F1 family composed of 156 offspring and their two parental individuals. A total of 4,768 SNPs were assigned to 29 linkage groups (LGs), and the length of the linkage map reached 2,480.25 centiMorgans (cM) with an average distance of 0.55 cM between loci. Based on this genetic linkage map, 223 genomic scaffolds were anchored to the 29 LGs of channel catfish, and a total length of 704.66 Mb was assembled. Quantitative trait locus (QTL) mapping and genome-wide association analysis identified 10 QTLs of sex-related and six QTLs of growth-related traits at LG17 and LG28, respectively. Candidate genes associated with sex dimorphism, including spata2, spata5, sf3, zbtb38, and fox, were identified within QTL intervals on the LG17. A sex-linked marker with simple sequence repeats (SSR) in zbtb38 gene of the LG17 was validated for practical verification of sex in the channel catfish. Thus, the LG17 was considered as a sex-related LG. Potential growth-related genes were also identified, including important regulators such as megf9, npffr1, and gas1. In a word, we constructed the high-density genetic linkage map and developed the sex-linked marker in channel catfish, which are important genetic resources for future marker-assisted selection (MAS) of this economically important teleost

Efficient and effective extreme learning machine with minimal user intervention

Artificial Neural Networks (ANN) is a dominate machine learning technique inspired by biological neural networks. The data explosion today offers great opportunities for algorithms like ANN that can uncover sophisticated relationships in various applications. However, traditional ANN algorithms like Back-Propagation (BP) have been known to face challenging issues such as specifying learning rate, the number of epochs, stopping criterion and running into local minima. In recent years, an emerging algorithm named Extreme Learning Machine (ELM) has attracted a significant amount of research attentions. ELM is a variant of ANN with a single hidden layer. In contrast to normal tedious tuning procedures, the input weights and biases are randomly generated. Therefore, a lot of computing resources can be saved and high learning efficiency is achieved in ELM, which is also its most salient feature. However, some issues still exist in ELM. For example, although the non-analytical parameter determination procedure improves the learning efficiency, it also causes fluctuating performance of ELM on the same problem with different initial parameters. Thus, the ELM algorithm may appear less stable. To tackle this issue, regularization approaches have been applied in the ELM algorithms, and the most common one is the Regularized Extreme Learning Machine (RELM), which employs the ridge regression. Better generalization performance and higher stability have been reported with RELM, but slower learning efficiency is expected. The original ELM utilizes the batch learning strategy, which faces difficulties when dealing with sequential data. Therefore, many ELM variants that can deal with this issue were created, with the Online Sequential ELM (OS-ELM) being the most notable one. However, an inevitable procedure is the faced by nearly all of ELM and other ANN algorithms, that is parameter tuning. Although the ELM enjoys the benefit of easy implementation because of the randomly generated initial parameters, its performance is still greatly influenced by the size of the hidden layer, i.e., the number of hidden neurons $L$. The optimal choice of $L$ in different tasks typically ranges from several to hundreds, and the issues of underfitting and overfitting are commonly associated with it. Constructive approaches have been extensively proposed to automatically select the $L$. Notable ones include Incremental ELM (I-ELM), Convex incremental ELM (CI-ELM), Error-Minimized ELM (EM-ELM) and Dynamic ELM (D-ELM). However, one fatal flaw is shared among the aforementioned constructive ELMs, that is they all use the expected learning accuracy (training error) as the architecture selection criterion. The training error will keep decreasing until reaching zero with more and more hidden neurons added, therefore specifying an appropriate expected learning accuracy is just another way of choosing $L$, and the performance is highly affected by the choice. In this thesis, we adopt the Leave-One-Out Cross-Validation (LOO-CV) error as the performance metric, which has rarely been used for this purpose because of its extremely slow execution speed. Various techniques have been implemented to make the calculation of LOO-CV error highly efficient. Therefore, we are able to propose a pair of algorithms that can achieve desirable performance with no or minimal user intervention, which is also the central theme of this thesis. Specifically, the Efficient Leave-One-Out Cross-Validation Based Extreme Learning Machine (ELOO-ELM) is proposed to automatically select the optimal $L$ in ELM. To deal with the regularization in RELM, the Efficient Leave-One-Out Cross-Validation Based Regularized Extreme Learning Machine (ELOO-RELM) is also proposed. Both ELOO-ELM and ELOO-RELM utilize LOO-CV error as the selection criterion, and thus the stability can be guaranteed. They all employ a highly efficient formula to calculate the LOO-CV error. Thus, the speed advantage of the ELM can be retained. The complexity of these two algorithms scales linearly with the size of training samples and is very similar to the original ELM. Therefore, they are able to deal with a large amount of data. To find the optimal ridge parameter in a more straightforward manner instead of being searched and compared, Automatic Regularized ELM (AR-ELM) is also introduced. It can achieve even faster learning speed than ELOO-RELM without providing model candidates beforehand, but the stability may not be guaranteed because of the adaptation of the Lawless and Wang formula. The proposed ELOO-ELM, ELOO-RELM, and AR-ELM are all batch learning algorithms. Therefore, the feasibility of extending them to online scenarios is also discussed. Also, a regularized version of the OS-ELM is proposed.Doctor of Philosophy (EEE

Exploration of mini-UAV helicopter implementation

69 p.The research of Miniature Unmanned Aerial Vehicles (UAVs) draws more and more attentions in recent years because of its superior advantages compared to traditional human controlled aircrafts, such as fast response time, less detectable by enemy, zero casualties for combat troops and cheaper price. A wide range of tasks are being researched, which include search and rescue, surveillance, traffic monitoring, border patrol, and reconnaissance, etc. Vertical Takeoff and Landing (VTOL) vehicles have shown great potential in both civilian and military domains.Master of Science (Computer Control and Automation

A survey of inverse reinforcement learning techniques

This purpose of this paper is to provide an overview of the theoretical background and applications of inverse reinforcement learning (IRL). Reinforcement learning (RL) techniques provide a powerful solution for sequential decision making problems under uncertainty. RL uses an agent equipped with a reward function to find a policy through interactions with a dynamic environment. However, one major assumption of existing RL algorithms is that reward function, the most succinct representation of the designer's intention, needs to be provided beforehand. In practice, the reward function can be very hard to specify and exhaustive to tune for large and complex problems, and this inspires the development of IRL, an extension of RL, which directly tackles this problem by learning the reward function through expert demonstrations. In this paper, the original IRL algorithms and its close variants, as well as their recent advances are reviewed and compared. This paper can serve as an introduction guide of fundamental theory and developments, as well as the applications of IRL. This paper surveys the theories and applications of IRL, which is the latest development of RL and has not been done so far

A review of inverse reinforcement learning theory and recent advances

A major challenge faced by machine learning community is the decision making problems under uncertainty. Reinforcement Learning (RL) techniques provide a powerful solution for it. An agent used by RL interacts with a dynamic environment and finds a policy through a reward function, without using target labels like Supervised Learning (SL). However, one fundamental assumption of existing RL algorithms is that reward function, the most succinct representation of the designer's intention, needs to be provided beforehand. In practice, the reward function can be very hard to specify and exhaustive to tune for large and complex problems, and this inspires the development of Inverse Reinforcement Learning (IRL), an extension of RL, which directly tackles this problem by learning the reward function through expert demonstrations. IRL introduces a new way of learning policies by deriving expert's intentions, in contrast to directly learning policies, which can be redundant and have poor generalization ability. In this paper, the original IRL algorithms and its close variants, as well as their recent advances are reviewed and compared

Receding horizon cache and extreme learning machine based reinforcement learning

Function approximators have been extensively used in Reinforcement Learning (RL) to deal with large or continuous space problems. However, batch learning Neural Networks (NN), one of the most common approximators, has been rarely applied to RL. In this paper, possible reasons for this are laid out and a solution is proposed. Specifically, a Receding Horizon Cache (RHC) structure is designed to collect training data for NN by dynamically archiving state-action pairs and actively updating their Q-values, which makes batch learning NN much easier to implement. Together with Extreme Learning Machine (ELM), a new RL with function approximation algorithm termed as RHC and ELM based RL (RHC-ELM-RL) is proposed. A mountain car task was carried out to test RHC-ELM-RL and compare its performance with other algorithms