Dark Matter Decay and the Abundance of Ultracompact Minihalos

Ultracompact minihalos would be formed if there are larger density perturbations ($0.0003 < \delta\rho/\rho < 0.3$) in the earlier epoch. The density profile of them is steeper than the standard dark matter halos. If the dark matter can annihilate or decay into the standard particles, e.g., photons, these objects would be the potential astrophysical sources. In order to be consistent with the observations, such as $Fermi$, the abundance of ultracompact minihalos must be constrained. On the other hand, the formation of these objects has very tight relation with the primordial curvature perturbations on smaller scale, so the fraction of ultracompact minihalos is very important for modern cosmology. In previous works, the studies are focused on the dark matter annihilation for these objects. But if the dark matter is not annihilated, the dark matter decay is another important possible case. On the other hand, the abundance of ultracompact minihalos is related to many other parameters, such as the mass of dark matter, the decay channels and the density profile of dark matter halo. One of the important aspects of this work is that we investigate the $\gamma$-ray signals from nearby ultracompact minihalos due to dark matter decay and another important aspect is to study in detail how the different decay channels and density profiles affect the constraints on the abundance of ultracompact minihalos.Comment: 11 pages, 4 figures, 1 table. Comments Welcome!! Some presentations are improved and added, figures are replotted according to the referees' suggestion. The constraints on the primordial curvature perturbations are also given. Accepted for publication in EP

On stability of subelliptic harmonic maps with potential

In this paper, we investigate the stability problem of subelliptic harmonic maps with potential. First, we derive the first and second variation formulas for subelliptic harmonic maps with potential. As a result, it is proved that a subelliptic harmonic map with potential is stable if the target manifold has nonpositive curvature and the Hessian of the potential is nonpositive definite. We also give Leung type results which involve the instability of subelliptic harmonic maps with potential when the target manifold is a sphere of dimension $\geq 3$

Automatic Modeling for Modular Reconfigurable Robotic Systems: Theory and Practice

A modular reconfigurable robot consists of a collection of individual link and joint components that can be assembled into a number of different robot ge-ometries. Compared to a conventional industrial robot with fixed geometry, such a system can provide flexibility to the user to cope with a wide spectru

Learn from Yesterday: A Semi-Supervised Continual Learning Method for Supervision-Limited Text-to-SQL Task Streams

Conventional text-to-SQL studies are limited to a single task with a fixed-size training and test set. When confronted with a stream of tasks common in real-world applications, existing methods struggle with the problems of insufficient supervised data and high retraining costs. The former tends to cause overfitting on unseen databases for the new task, while the latter makes a full review of instances from past tasks impractical for the model, resulting in forgetting of learned SQL structures and database schemas. To address the problems, this paper proposes integrating semi-supervised learning (SSL) and continual learning (CL) in a stream of text-to-SQL tasks and offers two promising solutions in turn. The first solution Vanilla is to perform self-training, augmenting the supervised training data with predicted pseudo-labeled instances of the current task, while replacing the full volume retraining with episodic memory replay to balance the training efficiency with the performance of previous tasks. The improved solution SFNet takes advantage of the intrinsic connection between CL and SSL. It uses in-memory past information to help current SSL, while adding high-quality pseudo instances in memory to improve future replay. The experiments on two datasets shows that SFNet outperforms the widely-used SSL-only and CL-only baselines on multiple metrics.Comment: Accepted by AAAI-202