Enumeration of spanning trees in a pseudofractal scale-free web

Spanning trees are an important quantity characterizing the reliability of a network, however, explicitly determining the number of spanning trees in networks is a theoretical challenge. In this paper, we study the number of spanning trees in a small-world scale-free network and obtain the exact expressions. We find that the entropy of spanning trees in the studied network is less than 1, which is in sharp contrast to previous result for the regular lattice with the same average degree, the entropy of which is higher than 1. Thus, the number of spanning trees in the scale-free network is much less than that of the corresponding regular lattice. We present that this difference lies in disparate structure of the two networks. Since scale-free networks are more robust than regular networks under random attack, our result can lead to the counterintuitive conclusion that a network with more spanning trees may be relatively unreliable.Comment: Definitive version accepted for publication in EPL (Europhysics Letters

Finding Influencers in Complex Networks: An Effective Deep Reinforcement Learning Approach

Maximizing influences in complex networks is a practically important but computationally challenging task for social network analysis, due to its NP- hard nature. Most current approximation or heuristic methods either require tremendous human design efforts or achieve unsatisfying balances between effectiveness and efficiency. Recent machine learning attempts only focus on speed but lack performance enhancement. In this paper, different from previous attempts, we propose an effective deep reinforcement learning model that achieves superior performances over traditional best influence maximization algorithms. Specifically, we design an end-to-end learning framework that combines graph neural network as the encoder and reinforcement learning as the decoder, named DREIM. Trough extensive training on small synthetic graphs, DREIM outperforms the state-of-the-art baseline methods on very large synthetic and real-world networks on solution quality, and we also empirically show its linear scalability with regard to the network size, which demonstrates its superiority in solving this problem

Dirichlet Boundary Value Problems for Second Order pp-Laplacian Difference Equations

In this paper, the solutions to second order Dirichlet boundary value problems of $p$-Laplacian difference equations are investigated. By using critical point theory, existence and multiplicity results are obtained. The proof is based on the Mountain Pass Lemma in combination with variational techniques

Why do supply chain technologies sometimes fail to improve a firm’s performance?

Successful implementation depends on the reason why the technology was adopted in the first place, write Zhongzhi Liu, Daniel Prajogo, and Adegoke Ok

swTVM: Exploring the Automated Compilation for Deep Learning on Sunway Architecture

The flourish of deep learning frameworks and hardware platforms has been demanding an efficient compiler that can shield the diversity in both software and hardware in order to provide application portability. Among the exiting deep learning compilers, TVM is well known for its efficiency in code generation and optimization across diverse hardware devices. In the meanwhile, the Sunway many-core processor renders itself as a competitive candidate for its attractive computational power in both scientific and deep learning applications. This paper combines the trends in these two directions. Specifically, we propose swTVM that extends the original TVM to support ahead-of-time compilation for architecture requiring cross-compilation such as Sunway. In addition, we leverage the architecture features during the compilation such as core group for massive parallelism, DMA for high bandwidth memory transfer and local device memory for data locality, in order to generate efficient code for deep learning application on Sunway. The experimental results show the ability of swTVM to automatically generate code for various deep neural network models on Sunway. The performance of automatically generated code for AlexNet and VGG-19 by swTVM achieves 6.71x and 2.45x speedup on average than hand-optimized OpenACC implementations on convolution and fully connected layers respectively. This work is the first attempt from the compiler perspective to bridge the gap of deep learning and high performance architecture particularly with productivity and efficiency in mind. We would like to open source the implementation so that more people can embrace the power of deep learning compiler and Sunway many-core processor

The Barcelona ionospheric mapping function (BIMF) and its application to northern mid-latitudes

This is a post-peer-review, pre-copyedit version of an article published in Gps solutions. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10291-018-0731-0A simple way of improving the Global Navigation Satellite Systems (GNSS) slant ionospheric correction from Vertical Total Electron Content (VTEC) models is presented. In many GNSS applications, a mapping function is required to convert from VTEC, which may be provided in Global Ionospheric Maps (GIMs), to Slant TEC (STEC). Typical approaches assume a single ionospheric shell with constant height, which is unrealistic, especially for low-elevation signals. To reduce the associated conversion error, we propose the Barcelona Ionospheric Mapping Function and its first implementation at northern mid-latitudes (BIMF-nml). BIMF is based on a climatic prediction of the distribution of the topside vertical electron content fraction of VTEC (hereinafter µ2). BIMF is convenient to be applied since no external data are required in practice. To evaluate its performance, we use as independent reference the STEC difference (so-called dSTEC) values directly measured from mid-latitude dual-frequency Global Positioning System (GPS) receivers that have not been used in the computation of the VTEC GIMs under assessment. It is shown that the use of BIMF improves the GIM STEC estimation compared to the single-layer assumptions. This is the case for the mapping functions used by the International GNSS Service (IGS) and Satellite-Based Augmentation Systems (SBAS). This improvement is valid not only for the UPC GIMs, up to 15% for the year 2014, but especially for the GIMs of other analysis centers, such as those produced by CODE and JPL, up to 32 and 29%, respectively.Peer ReviewedPostprint (author's final draft

Multiple Sampling Fast Correlation Attack on Small State Stream Ciphers with Limited Round Key Period

The fast correlation attack (FCA) is a powerful cryptanalysis technique that targets stream ciphers based on linear feedback shift registers (LFSRs). Several FCAs were applied to small state stream ciphers (SSCs). In this paper, the idea of multiple sampling is proposed to use the available keystream bits more efficiently and decrease the data complexity of the attacks. This idea helps to overcome the limitation of SSCs on the number of output keystream bits. Moreover, we classify the parity check equations obtained from the different sampling rounds into different groups to ensure that the round keys used in these equations are the same. Our attack is applied to the Fruit-80 and reduces the data complexity from 2^56.82 to 2^49.82. This modified FCA can be applied to all SSCs with limited round key periods. Finally, we suggest a new design idea to strengthen SSCs against FCAs