纵横扩张的优化

得到了最小折数纵横扩张的判别准则．针对4-正则图的平面嵌入的纵横扩张的特殊性，给出了它的最小折数纵横扩张判别准则．     

谱半径前六位的n阶单圈图

恰含一个圈的简单连通图称为单圈图。Cn记n个顶点的圈。△（i,j,κ）记C3的三个顶点上分别接出i,j,κ条悬挂边所得的图，其中i≥j≥κ≥0.Sl^n-l记Cl的某一顶点上接出n-l条悬挂边所得到的图。△（n-4 1,0,0)记△（n-4,0,0)的某个悬挂点上接出一条悬挂边所得到的图。本文证明了：若把所有n(n≥12）阶单圈图按其最大特征值从大到小的顺序排列，则排在前六位的依次是S3^n-3，△（n-4,1,0),△（n-4 1,0,0),S4^n-4,△（n-5,2,0),△（n-5,1,1)。     

Infinitesimal obstructions to weakly mixing

Let ^t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M ⁿ , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d ^t and, for each x M, we define a smooth real function _x (t) : (1 + _i (t)), where the _i(t) are the eigenvalues of AA ^T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d^2t , restricted to v at the point _x ^-t M ⁿ.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that _x ^' (t) 0 for all x M and real t; then, if _x ^t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.     

The traveling salesman problem in graphs with some excluded minors

Given a graph and a length function defined on its edge-set, the Traveling Salesman Problem can be described as the problem of finding a family of edges (an edge may be chosen several times) which forms a spanning Eulerian subgraph of minimum length. In this paper we characterize those graphs for which the convex hull of all solutions is given by the nonnegativity constraints and the classical cut constraints. This characterization is given in terms of excluded minors. A constructive characterization is also given which uses a small number of basic graphs.     

The adsorption of CO on evaporated iridium films,studied with infrared reflection-absorption spectroscopy

The adsorption of ^12CO on Ir films evaporated under ultrahigh vacuum (UHV) conditions was studied using infrared reflection-absorption spectroscopy (IRAS). Only a single absorption band was observed at 300 K, shifting continuously from the “singleton” value ~2010 cm^?1 at very low coverages to 2093 cm^?1 at saturation coverage. This band is attributed to CO adsorbed on top of the surface atoms. Synchronously with this shift the bandwidth at half maximum intensity $\text{Δv}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ decreases from ~30 to 8 cm^?1. The integrated peak area increases linearly with coverage up to a relative coverage (θ_r) of approximately 0.4, then the increase levels off and a maximum is observed. Upon continuing adsorption the intensity decreases slightly. In addition results are presented on adsorption at 300 K of ¹²CO?¹³CO isotopic mixtures. The coverage induced frequency shift is discussed in terms of a dipole-dipole coupling mechanism and it is concluded that intermolecular coupling can explain the shift (~83 cm^?1) observed. The decrease in intensity at coverages > 0.4 is attributed to the formation of a compressed overlayer with part of the CO molecules adsorbed in a multicentre position with different spectral properties. No infrared bands of nitrogen adsorbed at 78 K could be detected at pressures up to 6.7 kPa (1 Pa = 0.0075 Torr, 1 Torr = 133.32 Pa).     

Multi-Scale Aggregation Graph Neural Networks Based on Feature Similarity for Semi-Supervised Learning

The problem of extracting meaningful data through graph analysis spans a range of different fields, such as social networks, knowledge graphs, citation networks, the World Wide Web, and so on. As increasingly structured data become available, the importance of being able to effectively mine and learn from such data continues to grow. In this paper, we propose the multi-scale aggregation graph neural network based on feature similarity (MAGN), a novel graph neural network defined in the vertex domain. Our model provides a simple and general semi-supervised learning method for graph-structured data, in which only a very small part of the data is labeled as the training set. We first construct a similarity matrix by calculating the similarity of original features between all adjacent node pairs, and then generate a set of feature extractors utilizing the similarity matrix to perform multi-scale feature propagation on graphs. The output of multi-scale feature propagation is finally aggregated by using the mean-pooling operation. Our method aims to improve the model representation ability via multi-scale neighborhood aggregation based on feature similarity. Extensive experimental evaluation on various open benchmarks shows the competitive performance of our method compared to a variety of popular architectures.     

FTRLIM: Distributed Instance Matching Framework for Large-Scale Knowledge Graph Fusion

Instance matching is a key task in knowledge graph fusion, and it is critical to improving the efficiency of instance matching, given the increasing scale of knowledge graphs. Blocking algorithms selecting candidate instance pairs for comparison is one of the effective methods to achieve the goal. In this paper, we propose a novel blocking algorithm named MultiObJ, which constructs indexes for instances based on the Ordered Joint of Multiple Objects’ features to limit the number of candidate instance pairs. Based on MultiObJ, we further propose a distributed framework named Follow-the-Regular-Leader Instance Matching (FTRLIM), which matches instances between large-scale knowledge graphs with approximately linear time complexity. FTRLIM has participated in OAEI 2019 and achieved the best matching quality with significantly efficiency. In this research, we construct three data collections based on a real-world large-scale knowledge graph. Experiment results on the constructed data collections and two real-world datasets indicate that MultiObJ and FTRLIM outperform other state-of-the-art methods.     

Nonequilibrium free energy and information flow of a double quantum-dot system with Coulomb coupling

We build a double quantum-dot system with Coulomb coupling and aim at studying connections among the entropy production, free energy, and information flow. By utilizing concepts in stochastic thermodynamics and graph theory analysis, Clausius and nonequilibrium free energy inequalities are built to interpret local second law of thermodynamics for subsystems. A fundamental set of cycle fluxes and affinities is identified to decompose two inequalities by using Schnakenberg's network theory. Results show that the thermodynamic irreversibility has energy-related and information-related contributions. A global cycle associated with the feedback-induced information flow would pump electrons against the bias voltage, which implements a Maxwell demon.     

Enhanced Directed Random Walk for the Identification of Breast Cancer Prognostic Markers from Multiclass Expression Data

Artificial intelligence in healthcare can potentially identify the probability of contracting a particular disease more accurately. There are five common molecular subtypes of breast cancer: luminal A, luminal B, basal, ERBB2, and normal-like. Previous investigations showed that pathway-based microarray analysis could help in the identification of prognostic markers from gene expressions. For example, directed random walk (DRW) can infer a greater reproducibility power of the pathway activity between two classes of samples with a higher classification accuracy. However, most of the existing methods (including DRW) ignored the characteristics of different cancer subtypes and considered all of the pathways to contribute equally to the analysis. Therefore, an enhanced DRW (eDRW+) is proposed to identify breast cancer prognostic markers from multiclass expression data. An improved weight strategy using one-way ANOVA (F-test) and pathway selection based on the greatest reproducibility power is proposed in eDRW+. The experimental results show that the eDRW+ exceeds other methods in terms of AUC. Besides this, the eDRW+ identifies 294 gene markers and 45 pathway markers from the breast cancer datasets with better AUC. Therefore, the prognostic markers (pathway markers and gene markers) can identify drug targets and look for cancer subtypes with clinically distinct outcomes.     

Personal Interest Attention Graph Neural Networks for Session-Based Recommendation

Session-based recommendations aim to predict a user’s next click based on the user’s current and historical sessions, which can be applied to shopping websites and APPs. Existing session-based recommendation methods cannot accurately capture the complex transitions between items. In addition, some approaches compress sessions into a fixed representation vector without taking into account the user’s interest preferences at the current moment, thus limiting the accuracy of recommendations. Considering the diversity of items and users’ interests, a personalized interest attention graph neural network (PIA-GNN) is proposed for session-based recommendation. This approach utilizes personalized graph convolutional networks (PGNN) to capture complex transitions between items, invoking an interest-aware mechanism to activate users’ interest in different items adaptively. In addition, a self-attention layer is used to capture long-term dependencies between items when capturing users’ long-term preferences. In this paper, the cross-entropy loss is used as the objective function to train our model. We conduct rich experiments on two real datasets, and the results show that PIA-GNN outperforms existing personalized session-aware recommendation methods.