Search results for: Zhenyu Gu

Authors: Min Sun, Zhenyu Liu

Abstract:

In this paper, a new descent-projection method with a new search direction for monotone structured variational inequalities is proposed. The method is simple, which needs only projections and some function evaluations, so its computational load is very tiny. Under mild conditions on the problem-s data, the method is proved to converges globally. Some preliminary computational results are also reported to illustrate the efficiency of the method.

Keywords: variational inequalities, monotone function, global convergence.

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Authors: Ou Xie, Zhenyu Zhao

Abstract:

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.

Keywords: Ill-posed problem, Unknown source, Poisson equation, Tikhonov regularization method, Discrepancy principle

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Authors: Zhenyu Zhao, Lei You

Abstract:

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords: Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.

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Authors: Lei Zhang, Tingting Xu, Jun He, Zhenyu Yan, Roger Brooks

Abstract:

Email marketing is one of the most important segments of online marketing. Email content is vital to customers. Different customers may have different familiarity with a product, so a successful marketing strategy must personalize email content based on individual customers’ product affinity. In this study, we build our personalized email marketing strategy with three types of emails: nurture, promotion, and conversion. Each type of emails has a different influence on customers. We investigate this difference by analyzing customers’ open rates, click rates and opt-out rates. Feature importance from response models is also analyzed. The goal of the marketing strategy is to improve the click rate on conversion-type emails. To build the personalized strategy, we formulate the problem as a reinforcement learning problem and adopt a Q-learning algorithm with variations. The simulation results show that our model-based strategy outperforms the current marketer’s strategy.

Keywords: Email marketing, email content, reinforcement learning, machine learning, Q-learning.

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Authors: Zhenyu Zhang, Qingbin Gao

Abstract:

Low-resolution digital encoder (LRDE) is commonly adopted as a position sensor in low-cost and resource-constraint applications. Traditionally, a digital encoder is modeled as a quantizer without considering the initial position of the LRDE. However, it cannot be applied to extreme LRDE for which stroke of angular motion is only a few times of resolution of the encoder. Besides, the actual angular motion is substantially distorted by this extreme LRDE so that the encoder reading does not faithfully represent the actual angular motion. This paper presents a modeling method for extreme LRDE by taking into account the initial position of the LRDE. For a control system with sinusoidal reference signal and extreme LRDE, this paper analyzes the characteristics of angular motion. Specifically, two descriptors of sinusoidal angular motion are studied, which essentially sheds light on the actual angular motion from extreme LRDE.

Keywords: Low resolution digital encoder, resource-constraint control system, sinusoidal reference signal, servo motion control.

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Authors: Zhepeng Rui, Zhenyu Gu, Caitilin de Bérigny

Abstract:

In the current study, we designed an interactive meditation and brain painting application to cultivate users’ creativity, promote meditation, reduce stress, and improve cognition while attempting to learn a foreign language. User tests and data analyses were conducted on 42 male and 42 female participants to better understand sex-associated psychological and aesthetic differences. Our method utilized brain-computer interfaces to import meditation and attention data to create artwork in meditation-based applications. Female participants showed statistically significantly different language learning outcomes following three meditation paradigms. The art style of brain painting helped females with language memory. Our results suggest that the most ideal methods for promoting memory attention were meditation methods and brain painting exercises contributing to language learning, memory concentration promotion, and foreign word memorization. We conclude that a short period of meditation practice can help in learning a foreign language. These findings provide insights into meditation, creative language education, brain-computer interface, and human-computer interactions.

Keywords: Brain-computer interface, creative thinking, meditation, mental health.

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Authors: Kevin Spencer G. Anglim, Zhenyu Zhang, Qingbin Gao

Abstract:

Reusable launch vehicles (RLVs) present a more environmentally-friendly approach to accessing space when compared to traditional launch vehicles that are discarded after each flight. This paper studies the recyclable nature of RLVs by presenting a solution method for determining minimum-fuel optimal trajectories using principles from optimal control theory and particle swarm optimization (PSO). This problem is formulated as a minimum-landing error powered descent problem where it is desired to move the RLV from a fixed set of initial conditions to three different sets of terminal conditions. However, unlike other powered descent studies, this paper considers the highly nonlinear effects caused by atmospheric drag, which are often ignored for studies on the Moon or on Mars. Rather than optimizing the controls directly, the throttle control is assumed to be bang-off-bang with a predetermined thrust direction for each phase of flight. The PSO method is verified in a one-dimensional comparison study, and it is then applied to the two-dimensional cases, the results of which are illustrated.

Keywords: Minimum-fuel optimal trajectory, particle swarm optimization, reusable rocket, SpaceX.

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