On A Parabolic Equation in MEMS with An External Pressure

The parabolic problem $u_t-\Delta u=\frac{\lambda f(x)}{(1-u)^2}+P$ on a bounded domain $\Omega$ of $R^n$ with Dirichlet boundary condition models the microelectromechanical systems(MEMS) device with an external pressure term. In this paper, we classify the behavior of the solution to this equation. We first show that under certain initial conditions, there exists critical constants $P^*$ and $\lambda_P^*$ such that when $0\leq P\leq P^*$, $0<\lambda\leq \lambda_P^*$, there exists a global solution, while for $0\leq P\leq P^*,\lambda>\lambda_P^*$ or $P>P^*$, the solution quenches in finite time. The estimate of voltage $\lambda_P^*$, quenching time $T$ and pressure term $P^*$ are investigated. The quenching set $\Sigma$ is proved to be a compact subset of $\Omega$ with an additional condition, provided $\Omega\subset R^n$ is a convex bounded set. In particular, if $\Omega$ is radially symmetric, then the origin is the only quenching point. Furthermore, we not only derive the two-side bound estimate for the quenching solution, but also study the asymptotic behavior of the quenching solution in finite time.Comment: 35 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1402.0066 by other author

Multi-Phase Multi-Objective Dexterous Manipulation with Adaptive Hierarchical Curriculum

Dexterous manipulation tasks usually have multiple objectives, and the priorities of these objectives may vary at different phases of a manipulation task. Varying priority makes a robot hardly or even failed to learn an optimal policy with a deep reinforcement learning (DRL) method. To solve this problem, we develop a novel Adaptive Hierarchical Reward Mechanism (AHRM) to guide the DRL agent to learn manipulation tasks with multiple prioritized objectives. The AHRM can determine the objective priorities during the learning process and update the reward hierarchy to adapt to the changing objective priorities at different phases. The proposed method is validated in a multi-objective manipulation task with a JACO robot arm in which the robot needs to manipulate a target with obstacles surrounded. The simulation and physical experiment results show that the proposed method improved robot learning in task performance and learning efficiency.Comment: Accepted by the Journal of Intelligent & Robotic System

Stable In-hand Manipulation with Finger Specific Multi-agent Shadow Reward

Deep Reinforcement Learning has shown its capability to solve the high degrees of freedom in control and the complex interaction with the object in the multi-finger dexterous in-hand manipulation tasks. Current DRL approaches prefer sparse rewards to dense rewards for the ease of training but lack behavior constraints during the manipulation process, leading to aggressive and unstable policies that are insufficient for safety-critical in-hand manipulation tasks. Dense rewards can regulate the policy to learn stable manipulation behaviors with continuous reward constraints but are hard to empirically define and slow to converge optimally. This work proposes the Finger-specific Multi-agent Shadow Reward (FMSR) method to determine the stable manipulation constraints in the form of dense reward based on the state-action occupancy measure, a general utility of DRL that is approximated during the learning process. Information Sharing (IS) across neighboring agents enables consensus training to accelerate the convergence. The methods are evaluated in two in-hand manipulation tasks on the Shadow Hand. The results show FMSR+IS converges faster in training, achieving a higher task success rate and better manipulation stability than conventional dense reward. The comparison indicates FMSR+IS achieves a comparable success rate even with the behavior constraint but much better manipulation stability than the policy trained with a sparse reward

Curriculum-based Sensing Reduction in Simulation to Real-World Transfer for In-hand Manipulation

Simulation to Real-World Transfer allows affordable and fast training of learning-based robots for manipulation tasks using Deep Reinforcement Learning methods. Currently, Sim2Real uses Asymmetric Actor-Critic approaches to reduce the rich idealized features in simulation to the accessible ones in the real world. However, the feature reduction from the simulation to the real world is conducted through an empirically defined one-step curtail. Small feature reduction does not sufficiently remove the actor's features, which may still cause difficulty setting up the physical system, while large feature reduction may cause difficulty and inefficiency in training. To address this issue, we proposed Curriculum-based Sensing Reduction to enable the actor to start with the same rich feature space as the critic and then get rid of the hard-to-extract features step-by-step for higher training performance and better adaptation for real-world feature space. The reduced features are replaced with random signals from a Deep Random Generator to remove the dependency between the output and the removed features and avoid creating new dependencies. The methods are evaluated on the Allegro robot hand in a real-world in-hand manipulation task. The results show that our methods have faster training and higher task performance than baselines and can solve real-world tasks when selected tactile features are reduced

A Novel Center-based Deep Contrastive Metric Learning Method for the Detection of Polymicrogyria in Pediatric Brain MRI

Polymicrogyria (PMG) is a disorder of cortical organization mainly seen in children, which can be associated with seizures, developmental delay and motor weakness. PMG is typically diagnosed on magnetic resonance imaging (MRI) but some cases can be challenging to detect even for experienced radiologists. In this study, we create an open pediatric MRI dataset (PPMR) with PMG and controls from the Children's Hospital of Eastern Ontario (CHEO), Ottawa, Canada. The differences between PMG MRIs and control MRIs are subtle and the true distribution of the features of the disease is unknown. This makes automatic detection of cases of potential PMG in MRI difficult. We propose an anomaly detection method based on a novel center-based deep contrastive metric learning loss function (cDCM) which enables the automatic detection of cases of potential PMG. Additionally, based on our proposed loss function, we customize a deep learning model structure that integrates dilated convolution, squeeze-and-excitation blocks and feature fusion for our PPMR dataset. Despite working with a small and imbalanced dataset our method achieves 92.01% recall at 55.04% precision. This will facilitate a computer aided tool for radiologists to select potential PMG MRIs. To the best of our knowledge, this research is the first to apply machine learning techniques to identify PMG from MRI only.Comment: 24 pages, 13 figure

Late Gas accretion onto Primordial Minihalos: a Model for Leo T, Dark Galaxies and Extragalactic High-Velocity Clouds

In this letter we revisit the idea of reionization feedback on dwarf galaxy formation. We show that primordial minihalos with v_cir<20 km/s stop accreting gas after reionization, as it is usually assumed, but in virtue of their increasing concentration and the decreasing temperature of the intergalactic medium as redshift decreases below z=3, they have a late phase of gas accretion and possibly star formation. We expect that pre-reionization fossils that evolved on the outskirts of the Milky Way or in isolation show a bimodal star formation history with 12 Gyr old and <10 Gyr old population of stars. Leo T fits with this scenario. Another prediction of the model is the possible existence of a population of gas rich minihalos that never formed stars. More work is needed to understand whether a subset of compact high-velocity clouds can be identified as such objects or whether an undiscovered population exists in the voids between galaxies.Comment: 5 pages, 4 figures, accepted version MNRAS 392, L4