arXiv subjects

Min Dai

Publications and source records attributed to Min Dai.

29 records · Page 2Linked to original sources

arXiv2022

Physical Properties of 29 sdB+dM Eclipsing Binaries in Zwicky Transient Facility

The development of large-scale time-domain surveys provides an opportunity to study the physical properties as well as the evolutionary scenario of B-type subdwarfs (sdB) and M-type dwarfs (dM). Here, we obtained 33 sdB+dM eclipsing binaries based on the Zwicky Transient Facility (ZTF) light curves and $Gaia$ early data release 3 (EDR3) parallaxes. By using the PHOEBE code for light curve analysis, we obtain probability distributions for parameters of 29 sdB+dM. $R_1$, $R_2$, and $i$ are well determined, and the average uncertainty of mass ratio $q$ is 0.08. Our parameters are in good agreement with previous works if a typical mass of sdB is assumed. Based on parameters of 29 sdB+dM, we find that both the mass ratio $q$ and the companion's radius $R_2$ decrease with the shortening of the orbital period. For the three sdB+dMs with orbital periods less than 0.075 days, their companions are all brown dwarfs. The masses and radii of the companions satisfy the mass--radius relation for low-mass stars and brown dwarfs. Companions with radii between $0.12R_\odot$ and $0.15R_\odot$ seem to be missing in the observations. As more short-period sdB+dM eclipsing binaries are discovered and classified in the future with ZTF and $Gaia$, we will have more information to constrain the evolutionary ending of sdB+dM.

astro-ph.SR↗

arXiv2021

Nonparametric inference of stochastic differential equations based on the relative entropy rate

The information detection of complex systems from data is currently undergoing a revolution, driven by the emergence of big data and machine learning methodology. Discovering governing equations and quantifying dynamical properties of complex systems are among central challenges. In this work, we devise a nonparametric approach to learn the relative entropy rate from observations of stochastic differential equations with different drift functions.The estimator corresponding to the relative entropy rate then is presented via the Gaussian process kernel theory. Meanwhile, this approach enables to extract the governing equations. We illustrate our approach in several examples. Numerical experiments show the proposed approach performs well for rational drift functions, not only polynomial drift functions.

math.DS↗

arXiv2021

Bipedal Walking on Constrained Footholds: Momentum Regulation via Vertical COM Control

This paper presents an online walking synthesis methodology to enable dynamic and stable walking on constrained footholds for underactuated bipedal robots. Our approach modulates the change of angular momentum about the foot-ground contact pivot at discrete impact using pre-impact vertical center of mass (COM) velocity. To this end, we utilize the underactuated Linear Inverted Pendulum (LIP) model for approximating the underactuated walking dynamics to provide the desired post-impact angular momentum for each step. Desired outputs are constructed via online optimization combined with closed-form polynomials and tracked via a quadratic program (QP) based controller. This method is demonstrated on two robots, AMBER and 3D Cassie, for which stable walking behaviors with constrained footholds are realized on flat ground, stairs, and randomly located stepping stones.

cs.RO↗

arXiv2021

Episodic Learning for Safe Bipedal Locomotion with Control Barrier Functions and Projection-to-State Safety

This paper combines episodic learning and control barrier functions in the setting of bipedal locomotion. The safety guarantees that control barrier functions provide are only valid with perfect model knowledge; however, this assumption cannot be met on hardware platforms. To address this, we utilize the notion of projection-to-state safety paired with a machine learning framework in an attempt to learn the model uncertainty as it affects the barrier functions. The proposed approach is demonstrated both in simulation and on hardware for the AMBER-3M bipedal robot in the context of the stepping-stone problem, which requires precise foot placement while walking dynamically.

cs.RO↗

arXiv2021

Variational inference of the drift function for stochastic differential equations driven by Lévy processes

In this paper, we consider the nonparametric estimation problem of the drift function of stochastic differential equations driven by $α$-stable Lévy motion. First, the Kullback-Leibler divergence between the path probabilities of two stochastic differential equations with different drift functions is optimized. By using the Lagrangian multiplier, the variational formula based on the stationary Fokker-Planck equation is constructed. Then combined with the data information, the empirical distribution is used to replace the stationary density, and the drift function is estimated non-parametrically from the perspective of the process. In the numerical experiment, the different amounts of data and different $α$ values are studied. The experimental results show that the estimation result of the drift function is related to both. When the amount of data increases, the estimation result will be better, and when the $α$ value increases, the estimation result is also better.

math.ST↗

arXiv2020

Memory-Gated Recurrent Networks

The essence of multivariate sequential learning is all about how to extract dependencies in data. These data sets, such as hourly medical records in intensive care units and multi-frequency phonetic time series, often time exhibit not only strong serial dependencies in the individual components (the "marginal" memory) but also non-negligible memories in the cross-sectional dependencies (the "joint" memory). Because of the multivariate complexity in the evolution of the joint distribution that underlies the data generating process, we take a data-driven approach and construct a novel recurrent network architecture, termed Memory-Gated Recurrent Networks (mGRN), with gates explicitly regulating two distinct types of memories: the marginal memory and the joint memory. Through a combination of comprehensive simulation studies and empirical experiments on a range of public datasets, we show that our proposed mGRN architecture consistently outperforms state-of-the-art architectures targeting multivariate time series.

cs.LG↗

arXiv2020

Real-Time Fault Detection and Process Control Based on Multi-channel Sensor Data Fusion

Sensor signals acquired in the industrial process contain rich information which can be analyzed to facilitate effective monitoring of the process, early detection of system anomalies, quick diagnosis of fault root causes, and intelligent system design and control. In many mechatronic systems, multiple signals are acquired by different sensor channels (i.e. multi-channel data) which can be represented by high-order arrays (tensorial data). The multi-channel data has a high-dimensional and complex cross-correlation structure. It is crucial to develop a method that considers the interrelationships between different sensor channels. This paper proposes a new process monitoring approach based on uncorrelated multilinear discriminant analysis that can effectively model the multi-channel data to achieve a superior monitoring and fault diagnosis performance compared to other competing methods. The proposed method is applied directly to the high-dimensional tensorial data. Features are extracted and combined with multivariate control charts to monitor multi-channel data. The effectiveness of the proposed method in quick detection of process changes is demonstrated with both the simulation and a real-world case study.

eess.SP↗

arXiv2020

Detecting the maximum likelihood transition path from data of stochastic dynamic systems

In recent years, the discovery of complex dynamic systems in various fields through data-driven methods has attracted widespread attention. This method has played the role of data and has become an advantageous tool for us to study complex phenomena. In this work, we propose a framework for detecting the dynamic behavior, such as the maximum likelihood transition path, of stochastic dynamic systems from data. For the stochastic dynamic system, we need to use the Kramers-Moyal formula to convert it into a deterministic form for processing, then use the extended SINDy method to obtain the parameters of stochastic dynamic systems, and finally calculate the maximum likelihood transition path. We give two examples of stochastic dynamical systems driven by additive and multiplicative Gaussian noise, and demonstrate the validity of the method by reproducing the known dynamical system behavior.

math.DS↗

arXiv2020

Maximum Likelihood Estimation of Stochastic Differential Equations with Random Effects Driven by Fractional Brownian Motion

Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by the stochastic differential equations with drift term relying on some random effects. We obtain the Girsanov-type formula of the stochastic differential equation driven by Fractional Brownian Motion through kernel transformation. Under some assumptions of the random effect, we estimate the parameter estimators by the maximum likelihood estimation and give some numerical simulations for the discrete observations. Results show that for the different H, the parameter estimator is closer to the true value as the amount of data increases.

math.ST↗

arXiv2009

Optimal Redeeming Strategy of Stock Loans

A stock loan is a loan, secured by a stock, which gives the borrower the right to redeem the stock at any time before or on the loan maturity. The way of dividends distribution has a significant effect on the pricing of the stock loan and the optimal redeeming strategy adopted by the borrower. We present the pricing models sub ject to various ways of dividend distribution. Since closed-form price formulas are generally not available, we provide a thorough analysis to examine the optimal redeeming strategy. Numerical results are presented as well.

q-fin.PR↗

arXiv2009

Continuous-Time Markowitz's Model with Transaction Costs

A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem,inherently in a finite time horizon. With a series of transformations, the problem is turned into a so-called double obstacle problem, a well studied problem in physics and partial differential equation literature, featuring two time-varying free boundaries. The two boundaries, which define the buy, sell, and no-trade regions, are proved to be smooth in time. This in turn characterizes the optimal strategy, via a Skorokhod problem, as one that tries to keep a certain adjusted bond-stock position within the no-trade region. Several features of the optimal strategy are revealed that are remarkably different from its no-transaction-cost counterpart. It is shown that there exists a critical length in time, which is dependent on the stock excess return as well as the transaction fees but independent of the investment target and the stock volatility, so that an expected terminal return may not be achievable if the planning horizon is shorter than that critical length (while in the absence of transaction costs any expected return can be reached in an arbitrary period of time). It is further demonstrated that anyone following the optimal strategy should not buy the stock beyond the point when the time to maturity is shorter than the aforementioned critical length. Moreover, the investor would be less likely to buy the stock and more likely to sell the stock when the maturity date is getting closer. These features, while consistent with the widely accepted investment wisdom, suggest that the planning horizon is an integral part of the investment opportunities.

q-fin.PM↗