In the area of large-scale graph data representation and semi-supervised learning, deep graph-based convolutional neural networks have been widely applied. However, typical graph convolutional network (GCN) aggregates information of neighbor nodes based on binary neighborhood similarity (adjacency matrix). It treats all neighbor nodes of one node equally, which does not suppress the influence of dissimilar neighbor nodes. In this paper, we investigate GCN based on similarity matrix instead of adjacency matrix of graph nodes. Gaussian heat kernel similarity in Euclidean space is first adopted, which is named EGCN. Then biologically inspired manifold similarity is trained in reproducing kernel Hilbert space (RKHS), based on which a manifold GCN (named MGCN) is proposed for graph data representation and semi-supervised learning with four different kernel types. The proposed method is evaluated with extensive experiments on four benchmark document citation network datasets. The objective function of manifold similarity learning converges very quickly on different datasets using various kernel functions. Compared with state-of-the-art methods, our method is very competitive in terms of graph node recognition accuracy. In particular, the recognition rates of MGCN (Gaussian kernel) and MGCN (Polynomial Kernel) outperform that of typical GCN about 3.8% on Cora dataset, 3.5% on Citeseer dataset, 1.3% on Pubmed dataset and 4% on Cora_ML dataset, respectively. Although the proposed MGCN is relatively simple and easy to implement, it can discover local manifold structure by manifold similarity learning and suppress the influence of dissimilar neighbor nodes, which shows the effectiveness of the proposed MGCN.
Conservation laws are considered to be fundamental laws of nature. It has
broad applications in many fields, including physics, chemistry, biology, geology, and
engineering. Solving the differential equations associated with conservation laws is a
major branch in computational mathematics. The recent success of machine learning,
especially deep learning in areas such as computer vision and natural language processing, has attracted a lot of attention from the community of computational mathematics and inspired many intriguing works in combining machine learning with traditional methods. In this paper, we are the first to view numerical PDE solvers as an
MDP and to use (deep) RL to learn new solvers. As proof of concept, we focus on
1-dimensional scalar conservation laws. We deploy the machinery of deep reinforcement learning to train a policy network that can decide on how the numerical solutions should be approximated in a sequential and spatial-temporal adaptive manner.
We will show that the problem of solving conservation laws can be naturally viewed
as a sequential decision-making process, and the numerical schemes learned in such a
way can easily enforce long-term accuracy. Furthermore, the learned policy network
is carefully designed to determine a good local discrete approximation based on the
current state of the solution, which essentially makes the proposed method a meta-learning approach. In other words, the proposed method is capable of learning how to
discretize for a given situation mimicking human experts. Finally, we will provide details on how the policy network is trained, how well it performs compared with some
state-of-the-art numerical solvers such as WENO schemes, and supervised learning
based approach L3D and PINN, and how well it generalizes. 相似文献
Although 40% of adolescent idiopathic scoliosis (AIS) patients present with chronic back pain, the pathophysiology and underlying pain mechanisms remain poorly understood. We hypothesized that development of chronic pain syndrome in AIS is associated with alterations in pain modulatory mechanisms.
PURPOSE
To identify the presence of sensitization in nociceptive pathways and to assess the efficacy of the diffuse noxious inhibitory control in patients with AIS presenting with chronic back pain.
STUDY DESIGN
Cross-sectional study.
PATIENT SAMPLE
Ninety-four patients diagnosed with AIS and chronic back pain.
OUTCOME MEASURES
Quantitative sensory testing (QST) assessed pain modulation and self-reported questionnaires were used to assess pain burden and health-related quality of life.
METHODS
Patients underwent a detailed pain assessment using a standard and validated quantitative sensory testing (QST) protocol. The measurements included mechanical detection thresholds (MDT), pain pressure threshold (PPT), heat pain threshold (HPT), heat tolerance threshold (HTT), and a conditioned pain modulation (CPM) paradigm. Altogether, these tests measured changes in regulation of the neurophysiology underlying the nociceptive processes based on the patient's pain perception. Funding was provided by The Louise and Alan Edwards Foundation and The Shriners Hospitals for Children.
RESULTS
Efficient pain inhibitory response was observed in 51.1% of patients, while 21.3% and 27.7% had sub-optimal and inefficient CPM, respectively. Temporal summation of pain was observed in 11.7% of patients. Significant correlations were observed between deformity severity and pain pressure thresholds (p=.023) and CPM (p=.017), neuropathic pain scores and pain pressure thresholds (p=.015) and temporal summation of pain (p=.047), and heat temperature threshold and pain intensity (p=.048).
CONCLUSIONS
Chronic back pain has an impact in the quality of life of adolescents with idiopathic scoliosis. We demonstrated a high prevalence of impaired pain modulation in this group. The association between deformity severity and somatosensory dysfunction may suggest that spinal deformity can be a trigger for abnormal neuroplastic changes in this population contributing to chronic pain syndrome. 相似文献