Network autoregression model with grouped factor structures

Network autoregression and factor model are effective methods for modeling network time series data.In this study,we propose a network autoregression model with a factor structure that incorporates a latent group structure to address nodal heterogeneity within the network.An iterative algorithm is employed to minimize a least-squares objective function,allowing for simultaneous estimation of both the parameters and the group structure.To determine the unknown number of groups and factors,a PIC criterion is introduced.Additionally,statistical inference of the estimated parameters is presented.To assess the validity of the proposed estimation and inference procedures,we conduct extensive numerical studies.We also demonstrate the utility of our model using a stock dataset obtained from the Chinese A-Share stock market.

The Influence of Primitive Subgroups on the Structure of Finite Groups

A subgroup H of a group G is said to be primitive if it is a proper subgroup of the intersection of all subgroups of G containing H as its proper subgroup. The purpose of this note is to go further into the influence of primitive subgroups on the structure of finite groups. Some new results are obtained.

THE CONTROL OF POLYMETHACRYLATE MOLECULAR STRUCTURE BY GROUP TRANSFER POLYMERIZATION

INTRODUCTION Group transfer polymerization (GTP) is a method for controlling the structure of acrylic polymers in which reactive chain ends are covalentiy bound to a trimethylsilyl group. In the presence of a catalyst, monomer inserts into these chain ends between the silyl group and the last monomer unit. The process is illustrated by equation (1) for methyl methacrylate. GTP is a living polymerization, i. e., there is little or no chain termination and no chain transfer. A significant advantage of GTP is that it

Bromine-contained and Modified with Amino Group, D-π-A α-Cyanostilbenzene Derivative：Synthesis, Crystal Structure and Photoluminescence

A novel D-π-A type α-cyanostilbenzene derivative,（Z）-2-（4-aminophenyl）-3-（4-bromophenyl）-acrylonitrile（ABAN）, was designed and synthesized, by introducing an electrondonating amino group and a heavy atom. The structure of ABAN was confirmed by FT-IR, 1H NMR, 13 C NMR spectra and single-crystal X-ray diffraction analysis. The ABAN is of orthorhombic system, space group P212121, with a = 8.6100（14）, b = 9.6923（16）, c = 15.705（3） , Mr = 299.17, V = 1310.6（4） 3, Z = 4, Dc = 1.516 g/cm-3, μ = 3.119 mm-1, F（000） = 600, Rint = 0.038, R（I 〉 2σ（I）） = 0.0276, w R（I 〉 2σ（I）） = 0.0628, R（all data） = 0.0324, wR（all data） = 0.0646, completeness to theta = 25.00 was 99.8% and GOOF = 1.04. In the crystal structure, ABAN molecules were linked with each other through intermolecular C–H···π interactions and N–H···N hydrogen bonds, by which the 1D chain, 2D plane and 3D stacking structures were constructed. The photophysical properties and calculation results confirmed that ABAN possessed an intramolecular charge transfer（ICT） process. ABAN could be applied into the optoelectronic material field due to good solvent-tuned photophysical properties and highly thermal stability.

Finite Abelian Group of | A(G) |= 27pq

we have discussed structures of Abelian group G by order |A(G) |of automoorphism group and have obtained all types of finite Abelian grooup G when the order of A(G) equals 27pq(p,q are odd primmes).

Genetic Diversity and Genetic Structure of Maize Inbred Lines from Yunnan Revealed by SNP Chips

[Objectives]The genetic diversity and population genetic structure of 107 inbred lines of maize in Yunnan were analyzed,in order to provide technical support for maize germplasm innovation,genetic improvement of germplasm resources,variety management,and lay a solid foundation for exploring genes related to fine traits in the future.[Methods]The 107 maize inbred lines generalized in Yunnan were selected,and 45 backbone inbred lines commonly used in China were used as reference for heterotic group classification.On Axiom Maize 56K SNP Array platform,maize SNP chips(56K)were used to scan the whole maize genome,and the NJ-tree model of Treebest was used to construct a phylogenetic tree.Principal component analysis(PCA)was conducted by GCTA(genome-wide complex trait analysis)to reveal the genetic diversity and population genetic structure.[Results]In the 107 Yunnan local inbred lines,5533 uniformly distributed high-quality SNP marker sites were finally detected.Based on the analysis of these SNP marker sites,Nei s gene diversity index(H)of 107 maize germplasm genes was 0.2981-0.5000 with an average value being 0.4832,and polymorphism information content(PIC)values were 0.2536-0.3750 with an average value being 0.3662.The minimum allele frequency value was 0.5000-0.8178 with an average value being 0.5744.The analysis of population genetic structure showed that when K=6,the maximum value of△K was the maximum,which meant that the inbred lines used in this study could be divided into six groups.They were Tangsi Pingtou blood relationship group,PB blood relationship group,335 female blood relationship group,Zi 330 and the Lüda Honggu blood relationship group,unknown group 1 and unknown group 2.No inbred lines were divided into other heterotic groups.Among them,37 inbred lines from the 2 unknown groups could not be classified into the same group as the 10 known heterotic groups in China.The results of principal component analysis showed that the 107 maize inbred lines generalized in Yunnan could be clearly distinguished from the backbone maize inbred lines commonly used in China.Most of the maize inbred lines in Yunnan were concentrated near the reference backbone inbred lines.But some Yunnan inbred lines were far away from the reference inbred lines commonly used in China.[Conclusions]The maize germplasm resources in Yunnan area were rich in genetic diversity,including multiple heterotic groups,and there was a rich genetic basis of breeding parents.They could be clearly distinguished from the backbone inbred lines commonly used in China,and some of them had a long genetic distance from the backbone inbred lines.The resources which have good application potential can be used to create new heterotic groups.

K2SbB3O8： A Novel Boroantimonate)with Isolated [B3O8]^7- Groups

A new boroantimonate K2SbB3O8 has been synthesized by high-temperature solidstate reactions, and its crystals have been obtained by the flux method. The crystal structure has been determined from single-crystal X-ray diffraction analysis. The compound crystallizes in the monoclinic space group P21/c with a = 5.8890（2）, b = 11.0512（4）, c = 10.8951（4）A, β =103.200（4）°, V = 690.32（4） A^3, Z = 4, F（000） = 672, ρc = 3.467 g/cm^3, Mr = 360.38 and μ = 5.215mm^-1. Its structure feature is a three-dimensional framework composed of SbO6 octahedra and isolated [B3O8]^7- groups with K＋ cations residing in the one-dimensional tunnels along the a-axis.Interestingly, the isolated [B3O8]^7- groups are distinct from the known [B3O8]^7- groups, which always connect to each other. The UV-vis-NIR absorption, thermal stability and infrared spectrum are also discussed in this paper.

Crystal Structure of Natural Non-metamict Ti- and Fe^(2+)-rich Chevkinite-(Ce)

The crystal structure of non-metamict Ti- and Fe2+-rich chevkinite-(Ce) has been redetermined with the single -crystal sample collected from Bayan Obo, Inner Mongolia, China. The chemical formula of the sample is Ce4Fe2Ti3Si4O22. The crystals are monoclinic with the unit cell parameters a = 13.4656(15) ?, b = 5.7356(6) ?, c = 11.0977(12) ?, β= 100.636(2)o, V = 842.39 (16) ?3 and Z = 2. The structures of Ti- and Fe2+-rich chevkinite-(Ce) were refined with space groups P21/a and C2/m. Least-squares refinement results show that both structural models of Ti- and Fe2+-rich chevkinite-(Ce) are very good, R[F2>2σ(F2)] =0.027 with P21/a and R[F2>2σ(F2)] =0.021 with C2/m. In order to illustrate the relationship between the two space groups P21/a and C2/m, the distribution of diffraction intensities was inspected. Pseudo extinction was found, i.e., reflections with h+k=2n are systematically strong, while those with h+k=2n+1 are weak. By neglecting the systematically weak (h+k=2n+1) reflections the space group becomes C2/m. There is a mirror plane in the C2/m perpendicular to the b axis. However, oxygen atoms in the P21/a model are of a symmetrical relationship with the corresponding pseudo mirror plane. It is concluded that the crystal structure of non-metamict Ti- and Fe2+-rich chevkinite-(Ce) is a superstructure with the space group of P21/a, which is of pseudo symmetry corresponding to the space group C2/m.

A sliding-mode triboelectric nanogenerator with chemical group grated structure by shadow mask reactive ion etching

With the support by the National Natural Science Foundation of China,a collaboration by the research groups led by Prof.Cheng Gang(程纲)from Henan University and Prof.Wang Zhonglin(王中林)from Beijing Institute of Nanoenergy and Nanosystems,Chinese Academy of Sciences,invents'a sliding-mode triboelectric nanogenerator with chemical group grated structure by shadow mask reactive ion etching',which was published in ACS Nano(2017,11(9):8796-8803).

A Result on Character Degrees and Conjugacy Class Sizes in Finite Groups

Let G be a finite group and π be a set of primes including at least two elements. We write cd（G） and cs（G） to denote the set of complex irreducible character degrees and conjugacy class sizes of G , respectively, and write π（m）to denote the set of all prime divisors of a positive integer m . For any 1≠m∈cd（G） and 1≠m∈cs（G）, in this note, we shall present the corresponding group structures of finite group G in the case π（m）=π , respectively, which generalizes the result of finite groups with character degrees of two distinct primes. Furthermore, we shall see that the influence of the two sets on the group structure is analogous.

Grouping of amino acids and recognition of protein structurally conserved regions by reduced alphabets of amino acids

Sequence alignment is a common method for finding protein structurally conserved/similar regions. However, sequence alignment is often not accurate if sequence identities between to-be-aligned se- quences are less than 30%. This is because that for these sequences, different residues may play similar structural roles and they are incorrectly aligned during the sequence alignment using substitu- tion matrix consisting of 20 types of residues. Based on the similarity of physicochemical features, residues can be clustered into a few groups. Using such simplified alphabets, the complexity of protein sequences is reduced and at the same time the key information encoded in the sequences remains. As a result, the accuracy of sequence alignment might be improved if the residues are properly clustered. Here, by using a database of aligned protein structures (DAPS), a new clustering method based on the substitution scores is proposed for the grouping of residues, and substitution matrices of residues at different levels of simplification are constructed. The validity of the reduced alphabets is confirmed by relative entropy analysis. The reduced alphabets are applied to recognition of protein structurally conserved/similar regions by sequence alignment. The results indicate that the accuracy or efficiency of sequence alignment can be improved with the optimal reduced alphabet with N around 9.