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Model-free reinforcement learning is a promising approach for autonomously solving challenging robotics control problems, but faces exploration difficulty without information of the robot's kinematics and dynamics morphology. The under-exploration of multiple modalities with symmetric states leads to behaviors that are often unnatural and sub-optimal. This issue becomes particularly pronounced in the context of robotic systems with morphological symmetries, such as legged robots for which the resulting asymmetric and aperiodic behaviors compromise performance, robustness, and transferability to real hardware. To mitigate this challenge, we can leverage symmetry to guide and improve the exploration in policy learning via equivariance/invariance constraints. In this paper, we investigate the efficacy of two approaches to incorporate symmetry: modifying the network architectures to be strictly equivariant/invariant, and leveraging data augmentation to approximate equivariant/invariant actor-critics. We implement the methods on challenging loco-manipulation and bipedal locomotion tasks and compare with an unconstrained baseline. We find that the strictly equivariant policy consistently outperforms other methods in sample efficiency and task performance in simulation. In addition, symmetry-incorporated approaches exhibit better gait quality, higher robustness and can be deployed zero-shot in real-world experiments.

This paper investigates the significance of consumer opinions in relation to value in China's A-share market. By analyzing a large dataset comprising over 18 million product reviews by customers on JD.com, we demonstrate that sentiments expressed in consumer reviews can influence stock returns, indicating that consumer opinions contain valuable information that can impact the stock market. Our findings show that Customer Negative Sentiment Tendency (CNST) and One-Star Tendency (OST) have a negative effect on expected stock returns, even after controlling for firm characteristics such as market risk, illiquidity, idiosyncratic volatility, and asset growth. Further analysis reveals that the predictive power of CNST is stronger in firms with high sentiment conditions, growth companies, and firms with lower accounting transparency. We also find that CNST negatively predicts revenue surprises, earnings surprises, and cash flow shocks. These results suggest that online satisfaction derived from big data analysis of customer reviews contains novel information about firms' fundamentals., Comment: 29 pages, 9 tables

Non-relativistic quantum chromodynamics (NRQCD) factorization formulism is an important approach to investigate the production of the heavy quarkonium. In this paper, we study the production of the $\Omega_{ccc}$ and $\Omega_{bbb}$ at the $e^+e^-$ collider, using the NRQCD factorization formulism. We calculate the total and differential cross sections exactly of the processes, $e^+e^-\rightarrow \gamma^*/Z^*\rightarrow \Omega_{ccc}\bar{c}\bar{c}\bar{c}$ and $e^+e^-\rightarrow \gamma^*/Z^*\rightarrow \Omega_{bbb}\bar{b}\bar{b}\bar{b}$, in the leading order at the $e^+e^-$ colliders with different energies. The results show that it is hard to observe them at the $e^+e^-$ collider directly.

In this note, we present a new method to investigate the positronium states in ${\rm{QED_3}}$. According to the $\rm{K\ddot{a}ll\acute{e}n-Lehmann}$ spectral representation, the energy eigenvalues of bound states are poles of the correlation function. Using the chain approximation, we obtain the energy eigenvalues of the vector positronium states by taking into account the single-valued branches of multi-valued function. Using the same method, we also find the electron physical mass at some single-valued branch of multi-value function. Our results are agreement with the known ones., Comment: 11 pages, 11 figures

Surface dielectric barrier discharge (SDBD) actuators driven by the Pulsed-DC voltages are analyzed. The Pulsed-DC SDBD studied in this work is equivalent to a classical SDBD driven by a tailored Fast-Rise-Slow-Decay (FRSD) voltage waveform. The plasma channel formation and charge production process in the voltage rising stage are studied at different slopes using a classical 2D fluid model, the thrust generated in the voltage decaying stage is studied based on an analytical approach taking 2D model results as the input. A thrust pulse is generated in the trailing edge of the voltage waveform and reaches maximum when the voltage decreases by approximately the value of cathode voltage fall~($\approx$600~V). The time duration of the rising and trailing edge, the decay rate and the amplitude of applied voltage are the main factors affecting the performance of the actuator. Analytical expressions are formulated for the value and time moment of peak thrust, the upper limit of thrust is also estimated. Higher voltage rising rate leads to higher charge density in the voltage rising stage thus higher thrust. Shorter voltage trailing edge, in general, results in higher value and earlier appearance of the peak thrust. The detailed profile of the trailing edge also affects the performance. Results in this work allow us to flexibly design the FRSD waveforms for an SDBD actuator according to the requirements of active flow control in different application conditions.