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Local algorithms for maximum cut and minimum bisection on locally treelike regular graphs of large degree 大次局部树状正则图的最大切和最小分的局部算法
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2021-11-12 DOI: 10.1002/rsa.21149
A. Alaoui, A. Montanari, Mark Sellke
{"title":"Local algorithms for maximum cut and minimum bisection on locally treelike regular graphs of large degree","authors":"A. Alaoui, A. Montanari, Mark Sellke","doi":"10.1002/rsa.21149","DOIUrl":"https://doi.org/10.1002/rsa.21149","url":null,"abstract":"Given a graph G$$ G $$ of degree k$$ k $$ over n$$ n $$ vertices, we consider the problem of computing a near maximum cut or a near minimum bisection in polynomial time. For graphs of girth 2L$$ 2L $$ , we develop a local message passing algorithm whose complexity is O(nkL)$$ O(nkL) $$ , and that achieves near optimal cut values among all L$$ L $$ ‐local algorithms. Focusing on max‐cut, the algorithm constructs a cut of value nk/4+nP⋆k/4+err(n,k,L)$$ nk/4+n{P}_{star}sqrt{k/4}+mathsf{err}left(n,k,Lright) $$ , where P⋆≈0.763166$$ {P}_{star}approx 0.763166 $$ is the value of the Parisi formula from spin glass theory, and err(n,k,L)=on(n)+nok(k)+nkoL(1)$$ mathsf{err}left(n,k,Lright)={o}_n(n)+n{o}_kleft(sqrt{k}right)+nsqrt{k}{o}_L(1) $$ (subscripts indicate the asymptotic variables). Our result generalizes to locally treelike graphs, that is, graphs whose girth becomes 2L$$ 2L $$ after removing a small fraction of vertices. Earlier work established that, for random k$$ k $$ ‐regular graphs, the typical max‐cut value is nk/4+nP⋆k/4+on(n)+nok(k)$$ nk/4+n{P}_{star}sqrt{k/4}+{o}_n(n)+n{o}_kleft(sqrt{k}right) $$ . Therefore our algorithm is nearly optimal on such graphs. An immediate corollary of this result is that random regular graphs have nearly minimum max‐cut, and nearly maximum min‐bisection among all regular locally treelike graphs. This can be viewed as a combinatorial version of the near‐Ramanujan property of random regular graphs.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82572542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
A generalization of Faudree–Lehel conjecture holds almost surely for random graphs Faudree-Lehel猜想的推广对随机图几乎成立
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2021-11-07 DOI: 10.1002/rsa.21058
J. Przybylo
{"title":"A generalization of Faudree–Lehel conjecture holds almost surely for random graphs","authors":"J. Przybylo","doi":"10.1002/rsa.21058","DOIUrl":"https://doi.org/10.1002/rsa.21058","url":null,"abstract":"The irregularity strength of a simple graph G=(V,E) , denoted s(G) is a certain measure of the level of irregularity of a graph. It indicates how hard it is to make an irregular multigraph of G via multiplication of its selected edges. It is however more commonly set forth through k‐weightings, that is, mappings ω:E→{1,2,…,k} , assigning every vertex v∈V the weighted degree σ(v):=∑e∋vω(e) . In this setting, s(G) is precisely defined as the least k admitting a k‐weighting of G which attributes pairwise distinct weighted degrees to all vertices of G. It is known that s(G)>n/d in the case of d‐regular graphs with order n and d>1 . An open conjecture of Faudree and Lehel from the 1980s states that s(G)≤n/d+c in turn for some finite constant c independent of d. It is believed that the natural strengthening of this conjecture toward all graphs where d is substituted by the minimum degree δ should also hold. We confirm this supposition in the case of random graphs. Namely, we show that asymptotically almost surely the generalization of Faudree‐Lehel Conjecture holds for a random graph G∈𝒢(n,p) for any constant p, that is, that s(G) takes one of the three values: ⌈n/δ⌉ , ⌈n/δ⌉+1 , or ⌈n/δ⌉+2 . This is implied by the fact that a.a.s. p−1","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85413733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Broadcasting‐induced colorings of preferential attachment trees 广播诱导的优先依恋树着色
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2021-10-28 DOI: 10.1002/rsa.21142
Colin Desmarais, Cecilia Holmgren, S. Wagner
{"title":"Broadcasting‐induced colorings of preferential attachment trees","authors":"Colin Desmarais, Cecilia Holmgren, S. Wagner","doi":"10.1002/rsa.21142","DOIUrl":"https://doi.org/10.1002/rsa.21142","url":null,"abstract":"We consider random two‐colorings of random linear preferential attachment trees, which includes recursive trees, plane‐oriented recursive trees, binary search trees, and a class of d‐ary trees. The random coloring is defined by assigning the root the color red or blue with equal probability, and all other vertices are assigned the color of their parent with probability p$$ p $$ and the other color otherwise. These colorings have been previously studied in other contexts, including Ising models and broadcasting, and can be considered as generalizations of bond percolation. With the help of Pólya urns, we prove limiting distributions, after proper rescalings, for the number of vertices, monochromatic subtrees, and leaves of each color, as well as the number of fringe subtrees with two‐colorings. Using methods from analytic combinatorics, we also provide precise descriptions of the limiting distribution after proper rescaling of the size of the root cluster; the largest monochromatic subtree containing the root.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81606556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Growing uniform planar maps face by face 逐面生成统一的平面地图
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2021-10-27 DOI: 10.1002/rsa.21165
Alessandra Caraceni, Alexandre O. Stauffer
{"title":"Growing uniform planar maps face by face","authors":"Alessandra Caraceni, Alexandre O. Stauffer","doi":"10.1002/rsa.21165","DOIUrl":"https://doi.org/10.1002/rsa.21165","url":null,"abstract":"We provide “growth schemes” for inductively generating uniform random 2p$$ 2p $$ ‐angulations of the sphere with n$$ n $$ faces, as well as uniform random simple triangulations of the sphere with 2n$$ 2n $$ faces. In the case of 2p$$ 2p $$ ‐angulations, we provide a way to insert a new face at a random location in a uniform 2p$$ 2p $$ ‐angulation with n$$ n $$ faces in such a way that the new map is precisely a uniform 2p$$ 2p $$ ‐angulation with n+1$$ n+1 $$ faces. Similarly, given a uniform simple triangulation of the sphere with 2n$$ 2n $$ faces, we describe a way to insert two new adjacent triangles so as to obtain a uniform simple triangulation of the sphere with 2n+2$$ 2n+2 $$ faces. The latter is based on a new bijective presentation of simple triangulations that relies on a construction by Poulalhon and Schaeffer.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89210355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of stationary ballistic deposition on the infinite lattice 无限晶格上静止弹道沉积的存在性
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2021-10-19 DOI: 10.1002/rsa.21116
S. Chatterjee
{"title":"Existence of stationary ballistic deposition on the infinite lattice","authors":"S. Chatterjee","doi":"10.1002/rsa.21116","DOIUrl":"https://doi.org/10.1002/rsa.21116","url":null,"abstract":"Ballistic deposition is one of the many models of interface growth that are believed to be in the KPZ universality class, but have so far proved to be largely intractable mathematically. In this model, blocks of size one fall independently as Poisson processes at each site on the d$$ d $$ ‐dimensional lattice, and either attach themselves to the column growing at that site, or to the side of an adjacent column, whichever comes first. It is not hard to see that if we subtract off the height of the column at the origin from the heights of the other columns, the resulting interface process is Markovian. The main result of this article is that this Markov process has at least one invariant probability measure. We conjecture that the invariant measure is not unique, and provide some partial evidence.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91331791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hypergraph regularity and random sampling 超图正则性与随机抽样
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2021-10-04 DOI: 10.1002/rsa.21126
Felix Joos, Jaehoon Kim, Daniela Kühn, Deryk Osthus
{"title":"Hypergraph regularity and random sampling","authors":"Felix Joos, Jaehoon Kim, Daniela Kühn, Deryk Osthus","doi":"10.1002/rsa.21126","DOIUrl":"https://doi.org/10.1002/rsa.21126","url":null,"abstract":"Suppose that a k ‐uniform hypergraph H satisfies a certain regularity instance (that is, there is a partition of H given by the hypergraph regularity lemma into a bounded number of quasirandom subhypergraphs of prescribed densities). We prove that with high probability a large enough uniform random sample of the vertex set of H also admits the same regularity instance. Here the crucial feature is that the error term measuring the quasirandomness of the subhypergraphs requires only an arbitrarily small additive correction. This has applications to combinatorial property testing. The graph case of the sampling result was proved by Alon, Fischer, Newman and Shapira.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76835867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
IMPLEMENTASI METODE CLUSTERING K-MEANS UNTUK REKOMENDASI PENGADAAN STOCK LAMPU PADA PT GLOBAL LIGHTING INDONESIA PT GLOBAL LIGHTING印度尼西亚股票供应建议的对k -的实现
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2021-09-27 DOI: 10.31253/algor.v3i1.628
Prayogo Putra Tjaya, R. Rino, Hartana Wijaya
{"title":"IMPLEMENTASI METODE CLUSTERING K-MEANS UNTUK REKOMENDASI PENGADAAN STOCK LAMPU PADA PT GLOBAL LIGHTING INDONESIA","authors":"Prayogo Putra Tjaya, R. Rino, Hartana Wijaya","doi":"10.31253/algor.v3i1.628","DOIUrl":"https://doi.org/10.31253/algor.v3i1.628","url":null,"abstract":"PT Global Lighting Indonesia salah satu perusahaan lampu yang sedang berkembang di Indonesia. Dalam suatu usaha perdagangan, jumlah permintaan dari konsumen yang tidak menentu mengakibatkan stok yang disiapkan menjadi tidak stabil. Pengadaan stok lampu di PT Global Lighting Indonesia hanya berdasarkan perkiraan. Hal ini disebabkan karena pemilik perusahaan tidak ingin terjadinya kekurangan stok lampu pada saat permintaan konsumen dalam jumlah besar, maka perusahaan mengambil langkah yaitu melakukan pemesanan barang lebih besar dari sebelumnya. Berdasarkan permasalahan diatas maka di butuhkan sistem dan metode yang mampu mengelompokan produk berdasarkan merk atau model tertentu sehingga memudahkan saat pembuatan laporan dan pengadaan produk, sehingga bisa lebih mengefisiensi waktu, tenag serta biaya. Juga untuk menghindari resiko pengambilan stok lampu yang kurang laku terambil kembali, sehingga berpengaruh terhadap tinggi rendahnya angka penjualan di perusahaan dan terjadinya penumpukan stok lampu yang mengakibatkan barang menjadi rusak dan tidak dapat terjual lagi. Pada penelitian ini, peneliti akan membuat sebuah aplikasi menggunakan metode Clustering K-means untuk mengolah data transaksi yang masuk sehingga akan memudahkan pemilik dan karyawan PT Global Lighting Indonesia dalam memanajemen stok lampu","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74612519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Perancangan Aplikasi Kamus Istilah Komputer Dengan Metode Algoritma Boyer Moore Berbasis Android 以Android为基础的Boyer Moore算法设计计算机术语词典应用程序
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2021-09-27 DOI: 10.31253/algor.v3i1.660
Billy Gozali, Yo Ceng Giap, Desiyanna Lasut
{"title":"Perancangan Aplikasi Kamus Istilah Komputer Dengan Metode Algoritma Boyer Moore Berbasis Android","authors":"Billy Gozali, Yo Ceng Giap, Desiyanna Lasut","doi":"10.31253/algor.v3i1.660","DOIUrl":"https://doi.org/10.31253/algor.v3i1.660","url":null,"abstract":"Kebutuhan masyarakat terhadap perkembangan teknologi inovasi pada kini dapat memberikan manfaat yang penting bagi kegiatan manusia. Perkembangan teknologi informasi itupun sudah dapat dirasakan pemanfaatannya dalam kehidupan manusia, khususnya komputer dan smartphone telah mempengaruhi perkembangannya dan kini telah diminati oleh kehidupan masyarakat. Proses pencarian pun sangatlah penting untuk melakukan proses pencarian pada aplikasi kamus, walaupun saat melakukan proses pencarian pun bisa saja lambat. Untuk mempermudah proses pencarian, diperlukan suatu algoritma yang nantinya akan melakukan suatu pencarian suata kata. Metode yang digunakan oleh peneliti adalah algoritma boyer-moore merupakan metode algoritma pencarian dengan membandingkan tipe data string pada proses pencarian pattern dari penyimpanan basis data. Penelitian ini berfokus terhadap implementasi pada sebuah aplikasi kamus yang nantinya akan membantu pengguna dalam menerjemahkan istilah komputer yang dapat disimpan secara database dalam smartphone. Aplikasi ini dijalankan pada platform android secara offline yang dapat diakses kapanpun dan dimanapun. Untuk membuat aplikasi ini peneliti menggunakan android studio dengan database SQLite dan analisis berorientasi objek melalui sistem flowchart. Aplikasi ini nantinya dapat memberikan tampilan hasil pencarian sebuah istilah berupa media terhadap pencarian istilah komputer pada ponsel smartphone. Berdasarkan hasil pengujian dari 17 responden, aplikasi kamus isitlah komputer memperoleh tingkat presentase sebesar 91,29% yang artinya aplikasi ini tergolong dalam kategori baik. Sehingga dengan adanya aplikasi kamus istilah komputer diharapkan dapat membantu bagi khususnya mahasiswa ilmu komputer ingin memahami sebuah istilah-istilah komputer yang biasa sering ditemui.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83144308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PERANCANGAN APLIKASI E-COMMERCE PADA PT.EXXA BERBASIS WEB MENGGUNAKAN METODE USER CENTERED DESIGN
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2021-09-27 DOI: 10.31253/algor.v3i1.710
Junaedi Lim
{"title":"PERANCANGAN APLIKASI E-COMMERCE PADA PT.EXXA BERBASIS WEB MENGGUNAKAN METODE USER CENTERED DESIGN","authors":"Junaedi Lim","doi":"10.31253/algor.v3i1.710","DOIUrl":"https://doi.org/10.31253/algor.v3i1.710","url":null,"abstract":"Pesatnya pertumbuhan pasar e-commerce di Indonesia memang sudah tidak bisa diragukan lagi. Website e-commerce merupakan media untuk menjual suatu produk atau barang dengan online. Penggunaan website e-commerce mengalami perkembangan yang luar biasa khususnya dalam bidang bisnis jual beli online. Sejak munculnya website e-commerce penggunaannya meluas karena dipandang memberikan manfaat yang besar bagi kelancaran proses transaksi jual beli online. Berdasarkan permasalahan yang ada di PT. EXXA dibutuhkan website e-commerce yang luar biasa untuk memperluas daerah pemasaran produknya. Website e-commerce yang dibutuhkan mampu memberikan informasi seputar produk-produk yang ditawarkan oleh perusahaan serta memberikan kemudahan dalam pengelolaan produk dan transaksi. Penelitian ini bertujuan untuk merancang suatu website e-commerce yang interaktif sehingga user dapat melihat produk yang dijual. Website e-commerce ini disusun dengan menggunakan Aplikasi XAMPP Version 3.2.2 yang merangkum Web Server Apache, Web scripting PHP, MySQL dan juga HTML (Hyper Text Markup Language), CSS (Cascading Style Sheet), JavaScript serta menggunakan Text Editor Sublime Text Version 3.0.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81376796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Perancangan Aplikasi Web Dengan Menggunakan Algoritma Apriori Pada Data Mining Untuk Mengetahui Pola Pembelian Konsumen PT Cipta Tunggal Elektronik
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2021-09-27 DOI: 10.31253/algor.v3i1.640
Freddie Freddie, Yusuf Kurnia, Rudy Arijanto, Yakub Yakub
{"title":"Perancangan Aplikasi Web Dengan Menggunakan Algoritma Apriori Pada Data Mining Untuk Mengetahui Pola Pembelian Konsumen PT Cipta Tunggal Elektronik","authors":"Freddie Freddie, Yusuf Kurnia, Rudy Arijanto, Yakub Yakub","doi":"10.31253/algor.v3i1.640","DOIUrl":"https://doi.org/10.31253/algor.v3i1.640","url":null,"abstract":"PT. Cipta Tunggal Elektronik merupakan perusahaan yang bergerak dibidang distribusi sound system yang membutuhkan strategi promosi dalam penjualannya. Analisa pola pembelian konsumen dapat membantu perusahaan dalam membentuk paket penjualan agar promosi yang dilakukan tepat sasaran. Proses menganalisa pola pembelian konsumen yang dilakukan secara manual tentu akan membutuhkan waktu dan tenaga yang lebih besar. Oleh karena itu, maka dilakukan penelitian serta perancangan sebuah aplikasi yang dapat mengetahui pola pembelian konsumen dengan metode asosiasi, serta menggunakan apriori sebagai algoritmanya. Oleh karena itu, maka diperlukan sebuah rancangan aplikasi berbasis web dengan algoritma apriori. Hasil dari penelitian ini adalah dibuatnya sebuah aplikasi berbasis web yang dapat melakukan analisa pola pembelian dari data transaksi yang dimasukkan, dengan cara menentukan rentang tanggal pada data yang ingin dianalisa, serta memasukkan nilai minimum support dan minimum confidence yang diinginkan.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76155518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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