Connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups

A graph is said to be s-arc-regular if its full automorphism group acts regularly on the set of its s-arcs. In this paper, we investigate connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups. Two suffcient and necessary conditions for such graphs to be 1- or 2-arc-regular are given and based on the conditions, several infinite families of 1-or 2-arc-regular cubic Cayley graphs of alternating groups are constructed.     

Formation of lithium,sodium and potassium complexes with 1,3,5‐triamino‐1,3,5‐trideoxy‐cis‐inositol (taci)

Single crystals of (1,3‐diamino‐5‐azaniumyl‐1,3,5‐trideoxy‐cis‐inositol‐κ³O²,O⁴,O⁶)(1,3,5‐triamino‐1,3,5‐trideoxy‐cis‐inositol‐κ³O²,O⁴,O⁶)lithium(I) diiodide dihydrate, [Li(C₆H₁₆N₃O₃)(C₆H₁₅N₃O₃)]I₂·2H₂O or [Li(Htaci)(taci)]I₂·2H₂O (taci is 1,3,5‐triamino‐1,3,5‐trideoxy‐cis‐inositol), (I), bis(1,3,5‐triamino‐1,3,5‐trideoxy‐cis‐inositol‐κ³O²,O⁴,O⁶)sodium(I) iodide, [Na(C₆H₁₅N₃O₃)₂]I or [Na(taci)₂]I, (II), and bis(1,3,5‐triamino‐1,3,5‐trideoxy‐cis‐inositol‐κ³O²,O⁴,O⁶)potassium(I) iodide, [K(C₆H₁₅N₃O₃)₂]I or [K(taci)₂]I, (III), were grown by diffusion of MeOH into aqueous solutions of the complexes. The structures of the Na and K complexes are isotypic. In all three complexes, the taci ligands adopt a chair conformation with axial hydroxy groups, and the metal cations exhibit exclusive O‐atom coordination. The six O atoms of the resulting MO₆ unit define a centrosymmetric trigonal antiprism with approximate D_3d symmetry. The interligand O...O distances increase significantly in the order Li < Na < K. The structure of (I) exhibits a complex three‐dimensional network of R—NH₂—H...NH₂—R, R—O—H...NH₂—R and R—O—H...O(H)—H...NH₂—R hydrogen bonds. The structures of the Na and K complexes consist of a stack of layers, in which each taci ligand is bonded to three neighbours via pairwise O—H...NH₂ interactions between vicinal HO—CH—CH—NH₂ groups.     

Incompatibility networks as models of scale-free small-world graphs

We make a mapping from Sierpinski fractals to a new class of networks, the incompatibility networks, which are scale-free, small-world, disassortative, and maximal planar graphs. Some relevant characteristics of the networks such as degree distribution, clustering coefficient, average path length, and degree correlations are computed analytically and found to be peculiarly rich. The method of network representation can be applied to some real-life systems making it possible to study the complexity of real networked systems within the framework of complex network theory.     

Perfect 1‐Factorizations of a Family of Cayley Graphs

A 1‐factorization of a graph G is a decomposition of G into edge‐disjoint 1‐factors (perfect matchings), and a perfect 1‐factorization is a 1‐factorization in which the union of any two of the 1‐factors is a Hamilton cycle. We consider the problem of the existence of perfect 1‐factorizations of even order 4‐regular Cayley graphs, with a particular interest in circulant graphs. In this paper, we study a new family of graphs, denoted , which are Cayley graphs if and only if k is even or . By solving the perfect 1‐factorization problem for a large class of graphs, we obtain a new class of 4‐regular bipartite circulant graphs that do not have a perfect 1‐factorization, answering a problem posed in 7 . With further study of graphs, we prove the nonexistence of P1Fs in a class of 4‐regular non‐bipartite circulant graphs, which is further support for a conjecture made in 7 .     

融合图卷积神经网络和注意力机制的PM2.5小时浓度多步预测

PM_2.5小时浓度多为单步预测。为实现PM_2.5小时浓度的多步预测,基于“编码器-解码器”的序列-序列预测（Seq2Seq）模型,集合图卷积神经网络提取非欧式空间数据特征的能力以及注意力机制自适应关注特征的能力,提出了融合图卷积神经网络和注意力机制的PM_2.5小时浓度多步预测（GCN_Attention_Seq2Seq）模型。并与Seq2Seq模型和使用了图卷积神经网络、未使用注意力机制的GCN_Seq2Seq模型进行了对照,以2015—2016年北京市22个空气质量监测站点的空气质量数据为样本进行实例验证,结果表明,Seq2Seq模型和图卷积神经网络（GCN）可对PM_2.5小时浓度数据的时空依赖进行有效建模,注意力机制有助于减缓多步预测中的预测精度衰减,提升PM_2.5小时浓度多步预测的精度。GCN_Attention_Seq2Seq模型可有效应用于多种长度的PM_2.5浓度预测窗口。     

Prediction of Compound Synthesis Accessibility Based on Reaction Knowledge Graph

With the increasing application of deep-learning-based generative models for de novo molecule design, the quantitative estimation of molecular synthetic accessibility (SA) has become a crucial factor for prioritizing the structures generated from generative models. It is also useful for helping in the prioritization of hit/lead compounds and guiding retrosynthesis analysis. In this study, based on the USPTO and Pistachio reaction datasets, a chemical reaction network was constructed for the identification of the shortest reaction paths (SRP) needed to synthesize compounds, and different SRP cut-offs were then used as the threshold to distinguish a organic compound as either an easy-to-synthesize (ES) or hard-to-synthesize (HS) class. Two synthesis accessibility models (DNN-ECFP model and graph-based CMPNN model) were built using deep learning/machine learning algorithms. Compared to other existing synthesis accessibility scoring schemes, such as SYBA, SCScore, and SAScore, our results show that CMPNN (ROC AUC: 0.791) performs better than SYBA (ROC AUC: 0.76), albeit marginally, and outperforms SAScore and SCScore. Our prediction models based on historical reaction knowledge could be a potential tool for estimating molecule SA.     

Topological bulk-edge effects in quantum graph transport

We examine quantum transport in periodic quantum graphs with a vertex coupling non-invariant with respect to time reversal. It is shown that the graph topology may play a decisive role in the conductivity properties illustrating this claim with two examples. In the first, the transport is possible at high energies in the bulk only being suppressed at the sample edges, while in the second one the situation is opposite, the transport is possible at the edge only.     

Neural network representations of quantum many-body states

Machine learning is currently the most active interdisciplinary field having numerous applications;additionally,machine-learning techniques are used to research quantum many-body problems.In this study,we first propose neural network quantum states(NNQSs)with general input observables and explore a few related properties,such as the tensor product and local unitary operation.Second,we determine the necessary and sufficient conditions for the representability of a general graph state using normalized NNQS.Finally,to quantify the approximation degree of a given pure state,we define the best approximation degree using normalized NNQSs.Furthermore,we observe that some 7V-qubit states can be represented by a normalized NNQS,such as separable pure states,Bell states and GHZ states.     

On Symmetric Cayley Graphs of Valency Eleven

A Cayley graph Γ=Cay(G,S)is said to be normal if G is normal in Aut Γ.In this paper,we investigate the normality problem of the connected 11-valent symmetric Cayley graphs Γ of finite nonabelian simple groups G,where the vertex stabilizer Av is soluble for A=Aut Γ and v ∈ VΓ.We prove that either Γ is normal or G=A5,A10,A54,A274,A549 or A1099.Further,11-valent symmetric nonnormal Cayley graphs of A5,A54 and A274 are constructed.This provides some more examples of nonnormal 11-valent symmetric Cayley graphs of finite nonabelian simple groups after the first graph of this kind(of valency 11)was constructed by Fang,Ma and Wang in 2011.