Contraction conditions with perturbed linear operators and applications

In this paper, we present some new fixed point theorems for both single-valued and multi-valued maps controlled by the contraction conditions with perturbed linear operators in continuous function spaces. Our results can be applied to various integral operators. Some previous results are generalized in this literature. As applications, the existence and uniqueness of solutions of impulsive periodic boundary value problems and functional differential inclusions are exhibited in the last section

Steve-Eye: Equipping LLM-based Embodied Agents with Visual Perception in Open Worlds

Recent studies have presented compelling evidence that large language models (LLMs) can equip embodied agents with the self-driven capability to interact with the world, which marks an initial step toward versatile robotics. However, these efforts tend to overlook the visual richness of open worlds, rendering the entire interactive process akin to "a blindfolded text-based game." Consequently, LLM-based agents frequently encounter challenges in intuitively comprehending their surroundings and producing responses that are easy to understand. In this paper, we propose Steve-Eye, an end-to-end trained large multimodal model designed to address this limitation. Steve-Eye integrates the LLM with a visual encoder which enables it to process visual-text inputs and generate multimodal feedback. In addition, we use a semi-automatic strategy to collect an extensive dataset comprising 850K open-world instruction pairs, empowering our model to encompass three essential functions for an agent: multimodal perception, foundational knowledge base, and skill prediction and planning. Lastly, we develop three open-world evaluation benchmarks, then carry out extensive experiments from a wide range of perspectives to validate our model's capability to strategically act and plan. Codes and datasets will be released.Comment: 19 pages, 19 figure

Trajectory Planning with Pose Feedback for a Dual-Arm Space Robot

In order to obtain high precision path tracking for a dual-arm space robot, a trajectory planning method with pose feedback is proposed to be introduced into the design process in this paper. Firstly, pose error kinematic models are derived from the related kinematics and desired pose command for the end-effector and the base, respectively. On this basis, trajectory planning with pose feedback is proposed from a control perspective. Theoretical analyses show that the proposed trajectory planning algorithm can guarantee that pose error converges to zero exponentially for both the end-effector and the base when the robot is out of singular configuration. Compared with the existing algorithms, the proposed algorithm can lead to higher precision path tracking for the end-effector. Furthermore, the algorithm renders the system good anti-interference property for the base. Simulation results demonstrate the effectiveness of the proposed trajectory planning algorithm

Evidence of Environmental Quenching at Redshift z ~ 2

We report evidence of environmental quenching among galaxies at redshift ~ 2, namely the probability that a galaxy quenches its star formation activity is enhanced in the regions of space in proximity of other quenched, more massive galaxies. The effect is observed as strong clustering of quiescent galaxies around quiescent galaxies on angular scales \theta < 20 arcsec, corresponding to a proper(comoving) scale of 168 (502) kpc at z = 2. The effect is observed only for quiescent galaxies around other quiescent galaxies; the probability to find star-forming galaxies around quiescent or around star-forming ones is consistent with the clustering strength of galaxies of the same mass and at the same redshift, as observed in dedicated studies of galaxy clustering. The effect is mass dependent in the sense that the quenching probability is stronger for galaxies of smaller mass ($\rm{M_*<10^{10} Msun}$) than for more massive ones, i.e. it follows the opposite trend with mass relative to gravitational galaxy clustering. The spatial scale where the effect is observed suggests these environments are massive halos, in which case the observed effect would likely be satellite quenching. The effect is also redshift dependent in that the clustering strength of quiescent galaxies around other quiescent galaxies at z = 1.6 is ~ 1.7 times larger than that of the galaxies with the same stellar mass at z = 2.6. This redshift dependence allows for a crude estimate of the time scale of environmental quenching of low-mass galaxies, which is in the range 1.5 - 4 Gyr, in broad agreement with other estimates and with our ideas on satellite quenching.Comment: 12 pages, 9 figures, Accepted for publication in Ap

LLaMA Rider: Spurring Large Language Models to Explore the Open World

Recently, various studies have leveraged Large Language Models (LLMs) to help decision-making and planning in environments, and try to align the LLMs' knowledge with the world conditions. Nonetheless, the capacity of LLMs to continuously acquire environmental knowledge and adapt in an open world remains uncertain. In this paper, we propose an approach to spur LLMs to explore the open world, gather experiences, and learn to improve their task-solving capabilities. In this approach, a multi-round feedback-revision mechanism is utilized to encourage LLMs to actively select appropriate revision actions guided by feedback information from the environment. This facilitates exploration and enhances the model's performance. Besides, we integrate sub-task relabeling to assist LLMs in maintaining consistency in sub-task planning and help the model learn the combinatorial nature between tasks, enabling it to complete a wider range of tasks through training based on the acquired exploration experiences. By evaluation in Minecraft, an open-ended sandbox world, we demonstrate that our approach LLaMA-Rider enhances the efficiency of the LLM in exploring the environment, and effectively improves the LLM's ability to accomplish more tasks through fine-tuning with merely 1.3k instances of collected data, showing minimal training costs compared to the baseline using reinforcement learning.Comment: 18 page