Path Integral Based Convolution and Pooling for Graph Neural Networks

Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose a path integral based graph neural networks (PAN) for classification and regression tasks on graphs. Specifically, we consider a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It generalizes the graph Laplacian to a new transition matrix we call maximal entropy transition (MET) matrix derived from a path integral formalism. Importantly, the diagonal entries of the MET matrix are directly related to the subgraph centrality, thus providing a natural and adaptive pooling mechanism. PAN provides a versatile framework that can be tailored for different graph data with varying sizes and structures. We can view most existing GNN architectures as special cases of PAN. Experimental results show that PAN achieves state-of-the-art performance on various graph classification/regression tasks, including a new benchmark dataset from statistical mechanics we propose to boost applications of GNN in physical sciences.Comment: 15 pages, 4 figures, 6 tables. arXiv admin note: text overlap with arXiv:1904.1099

Experiments and simulations of MEMS thermal sensors for wall shear-stress measurements in aerodynamic control applications

MEMS thermal shear-stress sensors exploit heat-transfer effects to measure the shear stress exerted by an air flow on its solid boundary, and have promising applications in aerodynamic control. Classical theory for conventional, macroscale thermal shear-stress sensors states that the rate of heat removed by the flow from the sensor is proportional to the 1/3-power of the shear stress. However, we have observed that this theory is inconsistent with experimental data from MEMS sensors. This paper seeks to develop an understanding of MEMS thermal shear-stress sensors through a study including both experimental and theoretical investigations. We first obtain experimental data that confirm the inadequacy of the classical theory by wind-tunnel testing of prototype MEMS shear-stress sensors with different dimensions and materials. A theoretical analysis is performed to identify that this inadequacy is due to the lack of a thin thermal boundary layer in the fluid flow at the sensor surface, and then a two-dimensional MEMS shear-stress sensor theory is presented. This theory incorporates important heat-transfer effects that are ignored by the classical theory, and consistently explains the experimental data obtained from prototype MEMS sensors. Moreover, the prototype MEMS sensors are studied with three-dimensional simulations, yielding results that quantitatively agree with experimental data. This work demonstrates that classical assumptions made for conventional thermal devices should be carefully examined for miniature MEMS devices

Diagnosing the particle transport mechanism in the pulsar halo via X-ray observations

Pulsar halos (also termed 'TeV halo') are a new class of $\gamma$-ray sources in Galaxy, which manifest as extended $\gamma$-ray emission around middle-age pulsars, as discovered around the Geminga pulsar, the Monogem pulsar and PSR~J0622+3749 by HAWC and LHAASO. A consensus has been reached that the TeV emission comes from the inverse Compton scattering of escaping electrons/positrons from the PWN off soft background radiation field, while the particle transport mechanism in the halo is still in dispute. Currently, there are mainly three interpretations, namely, the isotropic, suppressed diffusion model; the isotropic, unsuppressed diffusion model with considering ballistic propagation of newly injected particles; the anisotropic diffusion model. While the predicted gamma-ray surface brightness profiles by all three models can be more or less consistent with the observation, the implication of the three models for cosmic-ray transport mechanisms and the properties of interstellar magnetic field are quite different. In this study, we calculate the anticipated X-ray emission of pulsar halos under the three models. We show that the synchrotron radiation of these escaping electrons can produce a corresponding X-ray halo around the pulsar, and the expected surface brightness profiles are distinct in three models. We suggest that sensitive X-ray detectors of a large field of view (such as eROSITA and Einstein Probe) with a reasonably long exposure time are crucial to understand the formation mechanism of pulsar halos and serve as a probe to the properties of the interstellar turbulence.Comment: 7 figure

Trade-Offs between the Metabolic Rate and Population Density of Plants

The energetic equivalence rule, which is based on a combination of metabolic theory and the self-thinning rule, is one of the fundamental laws of nature. However, there is a progressively increasing body of evidence that scaling relationships of metabolic rate vs. body mass and population density vs. body mass are variable and deviate from their respective theoretical values of 3/4 and −3/4 or −2/3. These findings questioned the previous hypotheses of energetic equivalence rule in plants. Here we examined the allometric relationships between photosynthetic mass (Mp) or leaf mass (ML) vs. body mass (β); population density vs. body mass (δ); and leaf mass vs. population density, for desert shrubs, trees, and herbaceous plants, respectively. As expected, the allometric relationships for both photosynthetic mass (i.e. metabolic rate) and population density varied with the environmental conditions. However, the ratio between the two exponents was −1 (i.e. β/δ = −1) and followed the trade-off principle when local resources were limited. Our results demonstrate for the first time that the energetic equivalence rule of plants is based on trade-offs between the variable metabolic rate and population density rather than their constant allometric exponents

Dark matter search with CMB: a study of foregrounds

The energy injected from dark matter annihilation and decay processes potentially raises the ionisation of the intergalactic medium and leaves visible footprints on the anisotropy maps of the cosmic microwave background (CMB). Galactic foregrounds emission in the microwave bands contaminate the CMB measurement and may affect the search for dark matter's signature. In this paper, we construct a full CMB data and foreground simulation based on the design of the next-generation ground-based CMB experiments. The foreground residual after the components separation on maps is fully considered in our data analysis, accounting for various contamination from the emission of synchrotron, thermal dust, free-free and spinning dust. We analyse the corresponding sensitivity on dark matter parameters from the temperature and polarization maps, and we find that the CMB foregrounds leave a non-zero yet controllable impact on the sensitivity. Comparing with statistics-only analysis, the CMB foreground residual leads to a factor of at most 19% weakening on energy-injection constraints, depending on the specific dark matter process and experimental configuration. Strong limits on dark matter annihilation rate and decay lifetime can be expected after foreground subtraction.Comment: 6 figures, 2 tables. The foreground, mask maps and simulated datasets used in this work are available at https://github.com/Junsong-Cang/DM_CMB_Forecas

Salusin- β

The pathophysiological mechanisms for vascular lesions in diabetes mellitus (DM) are complex, among which endothelial dysfunction plays a vital role. Therapeutic target against endothelial injury may provide critical venues for treatment of diabetic vascular diseases. We recently identified that salusin-β contributed to high glucose-induced endothelial cell apoptosis. However, the roles of salusin-β in DM-induced endothelial dysfunction remain largely elusive. Male C57BL/6J mice were used to induce type 2 diabetes mellitus (T2DM) model. Human umbilical vein endothelial cells (HUVECs) were cultured in high glucose/high fat (HG/HF) medium. We demonstrated increased expression of salusin-β in diabetic aortic tissues and high-glucose/high-fat- (HG/HF-) incubated HUVECs. Disruption of salusin-β by shRNA abrogated the reactive oxygen species (ROS) production, inflammation, and nitrotyrosine content of HUVECs cultured in HG/HF medium. The HG/HF-mediated decrease in peroxisome proliferator-activated receptor γ (PPARγ) expression was restored by salusin-β shRNA, and PPARγ inhibitor T0070907 abolished the protective actions of salusin-β shRNA on endothelial injury in HG/HF-treated HUVECs. Salusin-β silencing obviously improved endothelium-dependent vasorelaxation, oxidative stress, inflammatory response, and nitrative stress in diabetic aorta. Taken together, our results highlighted the essential role of salusin-β in pathological endothelial dysfunction, and salusin-β may be a promising target in treatment of vascular complications of DM