How Powerful are Graph Neural Networks?

Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance

SoReC: A Social-Relation Based Centrality Measure in Mobile Social Networks

Mobile Social Networks (MSNs) have been evolving and enabling various fields in recent years. Recent advances in mobile edge computing, caching, and device-to-device communications, can have significant impacts on 5G systems. In those settings, identifying central users is crucial. It can provide important insights into designing and deploying diverse services and applications. However, it is challenging to evaluate the centrality of nodes in MSNs with dynamic environments. In this paper, we propose a Social-Relation based Centrality (SoReC) measure, in which social network information is used to quantify the influence of each user in MSNs. We first introduce a new metric to estimate direct social relations among users via direct contacts, and then extend the metric to explore indirect social relations among users bridging by the third parties. Based on direct and indirect social relations, we detect the influence spheres of users and quantify their influence in the networks. Simulations on real-world networks show that the proposed measure can perform well in identifying future influential users in MSNs.Comment: The paper was accepted by ICT201

Delay-Aware Flow Migration for Embedded Services in 5G Core Networks

Service-oriented virtual network deployment is based on statistical resource demands of different services, while data traffic from each service fluctuates over time. In this paper, a delay-aware flow migration problem for embedded services is studied to meet end-to-end (E2E) delay requirement with time-varying traffic. A non-convex multi-objective mixed integer optimization problem is formulated, addressing the trade-off between maximum load balancing and minimum reconfiguration overhead due to flow migrations, under processing and transmission resource constraints and QoS requirement constraints. Since the original problem is non-solvable in optimization solvers due to unsupported types of quadratic constraints, it is transformed to a tractable mixed integer quadratically constrained programming (MIQCP) problem. The optimality gap between the two problems is proved to be zero, so we can obtain the optimum of the original problem through solving the MIQCP problem with some post-processing. Numerical results are presented to demonstrate the aforementioned trade-off, as well as the benefit from flow migration in terms of E2E delay performance guarantee.Comment: 6 pages, 6 figures, ICC 201

Preparation and quantitative magnetic studies of single-domain nickel cylinders

For a complete experimental and theoretical explanation of the magnetic processes in an interacting collection of submicron magnetic particles, a fundamental understanding of the magnetic properties of individual single-domain particles must first be achieved. We have prepared elongated Ni columns ranging in diameter from 0.15 to 1.0 µm by electroplating into specially prepared Al2O3 and glass channeled pore membranes. We have also prepared controlled arrays of Ni columns using e-beam lithography, subsequently electroplating into the written patterns. Using transmission electron microscopy, we have characterized the shape, size, morphology, and crystal structure of the columns. Magnetic force microscopy has been used to determine the switching field Hs versus the applied field angle of the columns. Although the switching field data can be fit to the functional form for nucleation by curling in an infinite cylinder, the observed weak dependence of Hs on column diameter is inconsistent with that expected for curling, particularly for columns of diameter 0.3 µm

DeepMetabolism: A Deep Learning System to Predict Phenotype from Genome Sequencing

Life science is entering a new era of petabyte-level sequencing data. Converting such big data to biological insights represents a huge challenge for computational analysis. To this end, we developed DeepMetabolism, a biology-guided deep learning system to predict cell phenotypes from transcriptomics data. By integrating unsupervised pre-training with supervised training, DeepMetabolism is able to predict phenotypes with high accuracy (PCC>0.92), high speed (100 GB data using a single GPU), and high robustness (tolerate up to 75% noise). We envision DeepMetabolism to bridge the gap between genotype and phenotype and to serve as a springboard for applications in synthetic biology and precision medicine

L\'evy walk revisited: Hermite polynomial expansion approach

Integral transform method (Fourier or Laplace transform, etc) is more often effective to do the theoretical analysis for the stochastic processes. However, for the time-space coupled cases, e.g., L\'evy walk or nonlinear cases, integral transform method may fail to be so strong or even do not work again. Here we provide Hermite polynomial expansion approach, being complementary to integral transform method. Some statistical observables of general L\'evy walks are calculated by the Hermite polynomial expansion approach, and the comparisons are made when both the integral transform method and the newly introduced approach work well.Comment: 14 pages, 9 figure

L\'{e}vy walk dynamics in mixed potentials from the perspective of random walk theory

L\'evy walk process is one of the most effective models to describe superdiffusion, which underlies some important movement patterns and has been widely observed in the micro and macro dynamics. From the perspective of random walk theory, here we investigate the dynamics of L\'evy walks under the influences of the constant force field and the one combined with harmonic potential. Utilizing Hermite polynomial approximation to deal with the spatiotemporally coupled analysis challenges, some striking features are detected, including non Gaussian stationary distribution, faster diffusion, and still strongly anomalous diffusion, etc.Comment: 13 pages, 10 figure

Continuous time random walks and L\'{e}vy walks with stochastic resetting

Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. This paper builds up the theory of intermittent continuous time random walk (CTRW) and L\'{e}vy walk, in which the particles are stochastically reset to a given position with a resetting rate $r$. The mean squared displacements of the CTRW and L\'{e}vy walks with stochastic resetting are calculated, uncovering that the stochastic resetting always makes the CTRW process localized and L\'{e}vy walk diffuse slower. The asymptotic behaviors of the probability density function of L\'evy walk with stochastic resetting are carefully analyzed under different scales of $x$, and a striking influence of stochastic resetting is observed.Comment: 10 pages, 5 figure

Hybrid-aligned nematic liquid-crystal modulators fabricated on VLSI circuits

A new method for fabricating analog light modulators on VLSI devices is described. The process is fully compatible with devices fabricated by commercial VLSI foundries, and the assembly of the modulator structures requires a small number of simple processing steps. The modulators are capable of analog amplitude or phase modulation and can operate at video rates and at low voltages (2.2 V). The modulation mechanism and the process yielding the modulator structures are described. Experimental data are presented

The geometry and environment of repeating FRBs

We propose a geometrical explanation for periodically and nonperiodically repeating fast radio bursts (FRBs) under neutron star (NS)-companion systems. We suggest a constant critical binary separation, $r_{\rm c}$, within which the interaction between the NS and companion can trigger FRB bursts. For an elliptic orbit with the minimum and maximum binary separations, $r_{\rm min}$ and $r_{\rm max}$, a periodically repeating FRB with an active period could be reproduced if $r_{\rm min}<r_{\rm c}<r_{\rm max}$. However, if $r_{\rm max}<r_{\rm c}$, the modulation of orbital motion will not work due to persistent interaction, and this kind of repeating FRBs should be non-periodic. We test relevant NS-companion binary scenarios on the basis of FRB 180916.J0158+65 and FRB 121102 under this geometrical frame. It is found that the pulsar-asteroid belt impact model is more suitable to explain these two FRBs since this model is compatible with different companions (e.g., massive stars and black holes). At last, we point out that FRB 121102-like samples are potential objects which can reveal the evolution of star-forming region.Comment: 7 pages, 2 figures, MNRAS submitte