2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)最新文献

{"title":"Unstructured Hardness to Average-Case Randomness","authors":"Lijie Chen, R. Rothblum, R. Tell","doi":"10.1109/FOCS54457.2022.00048","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00048","url":null,"abstract":"The leading technical approach in uniform hardness-to-randomness in the last two decades faced several well-known barriers that caused results to rely on overly strong hardness assumptions, and yet still yield suboptimal conclusions. In this work we show uniform hardness-to-randomness results that simultaneously break through all of the known barriers. Specifically, consider any one of the following three assumptions:1)For some $epsilon>0$ there exists a function f computable by uniform circuits of size $2^{O(n)}$ and depth $2^{o(n)}$ such that f is hard for probabilistic time $2^{epsilon n}$.2)For every $cin mathbb{N}$ there exists a function f computable by logspace-uniform circuits of polynomial size and depth n2 such that every probabilistic algorithm running in time nc fails to compute f on $mathrm{a}(1/n)$-fraction of the inputs.3)For every $cin mathbb{N}$ there exists a logspace-uniform family of arithmetic formulas of degree n2 over a field of size poly $(n)$ such that no algorithm running in probabilistic time nc can evaluate the family on a worst-case input. Assuming any of these hypotheses, where the hardness is for every sufficiently large input length $nin mathbb{N}$, we deduce that $mathcal{R}mathcal{P}$ can be derandomized in polynomial time and on all input lengths, on average. Furthermore, under the first assumption we also show that $mathcal{B}mathcal{P}mathcal{P}$ can be derandomized in polynomial time, on average and on all input lengths, with logarithmically many advice bits. On the way to these results we also resolve two related open problems. First, we obtain an optimal worst-case to average-case reduction for computing problems in linear space by uniform probabilistic algorithms; this result builds on a new instance checker based on the doubly efficient proof system of Goldwasser, Kalai, and Rothblum (J. ACM, 2015). Secondly, we resolve the main open problem in the work of Carmosino, Impagliazzo and Sabin (ICALP 2018), by deducing derandomization from weak and general fine-grained hardness hypotheses. The full version of this paper is available online [5].","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128496609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hardness Self-Amplification from Feasible Hard-Core Sets","authors":"Shuichi Hirahara, Nobutaka Shimizu","doi":"10.1109/FOCS54457.2022.00058","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00058","url":null,"abstract":"We consider the question of hardness self-amplification: Given a Boolean function f that is hard to compute on an o (1)-fraction of inputs drawn from some distribution, can we prove that f is hard to compute on a $(displaystyle frac{1}{2}-o(1))$-fraction of inputs drawn from the same distribution? We prove hardness self-amplification results for natural distributional problems studied in fine-grained average-case complexity, such as the problem of counting the number of the triangles modulo 2 in a random tripartite graph and the online vector-matrix-vector multiplication problem over $mathbb{F}_{2}$. More generally, we show that any problem that can be decomposed into \"computationally disjoint\" subsets of inputs admits hardness self-amplification. This is proved by generalizing the security proof of the NisanWigderson pseudorandom generator, in which case nearly disjoint subsets of inputs are considered. At the core of our proof techniques is a new notion of feasible hard-core set, which generalizes Impagliazzo’s hard-core set [Impagliazzo, FOCS’95]. We show that any weak average-case hard function f has a feasible hard-core set H: any small H-oracle circuit (that is allowed to make queries q to H if $f(q)$ can be computed without the oracle) fails to compute f on a $(displaystyle frac{1}{2}-o(1))$-fraction of inputs in H.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125445182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Indistinguishability Obfuscation via Mathematical Proofs of Equivalence","authors":"Abhishek Jain, Zhengzhong Jin","doi":"10.1109/FOCS54457.2022.00100","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00100","url":null,"abstract":"Over the last decade, indistinguishability obfuscation (iO) has emerged as a seemingly omnipotent primitive with numerous applications to cryptography and beyond. Moreover, recent breakthrough work has demonstrated that iO can be realized from well-founded assumptions. A thorn to all this remarkable progress is a limitation of all known constructions of general-purpose iO: the security reduction incurs a loss that is exponential in the input length of the function. This “input-length barrier” to iO stems from the non-falsifiability of the iO definition and is discussed in folklore as being possibly inherent. It has many negative consequences; notably, constructing iO for programs with inputs of unbounded length remains elusive due to this barrier. We present a new framework aimed towards overcoming the input-length barrier. Our approach relies on short mathematical proofs of functional equivalence of circuits (and Turing machines) to avoid the brute-force “input-by-input” check employed in prior works.– We show how to obfuscate circuits that have efficient proofs of equivalence in Propositional Logic with a security loss independent of input length.– Next, we show how to obfuscate Turing machines with unbounded length inputs, whose functional equivalence can be proven in Cook’s Theory PV.– Finally, we demonstrate applications of our results to succinct non-interactive arguments and witness encryption, and provide guidance on using our techniques for building new applications.To realize our approach, we depart from prior work and develop a new gate-by-gate obfuscation template that preserves the topology of the input circuit.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125888902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deterministic Small Vertex Connectivity in Almost Linear Time","authors":"Thatchaphol Saranurak, Sorrachai Yingchareonthawornchai","doi":"10.1109/FOCS54457.2022.00080","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00080","url":null,"abstract":"In the vertex connectivity problem, given an undirected n-vertex m-edge graph G, we need to compute the minimum number of vertices that can disconnect G after removing them. This problem is one of the most well-studied graph problems. From 2019, a new line of work [Nanongkai et al. STOC’19;SODA’20;STOC’21] has used randomized techniques to break the quadratic-time barrier and, very recently, culminated in an almost-linear time algorithm via the recently announced maxflow algorithm by Chen et al. In contrast, all known deterministic algorithms are much slower. The fastest algorithm [Gabow FOCS’00] takes $O(m(n+min{c^{5/2}, cn^{3/4}}))$ time where c is the vertex connectivity. It remains open whether there exists a subquadratic-time deterministic algorithm for any constant c > 3. In this paper, we give the first deterministic almost-linear time vertex connectivity algorithm for all constants c. Our running time is $m^{1+o(1)}2^{O(c^{2})}$ time, which is almost-linear for all $c=o(sqrt{log n})$. This is the first deterministic algorithm that breaks the $O(n^{2})$-time bound on sparse graphs where $m=O(n)$, which is known for more than 50 years ago [Kleitman’69]. Towards our result, we give a new reduction framework to vertex expanders which in turn exploits our new almost-linear time construction of mimicking network for vertex connectivity. The previous construction by Kratsch and Wahlström [FOCS’12] requires large polynomial time and is randomized.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130076998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Error Correcting Codes that Achieve BSC Capacity Against Channels that are Poly-Size Circuits","authors":"Ronen Shaltiel, Jad Silbak","doi":"10.1109/FOCS54457.2022.00009","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00009","url":null,"abstract":"Guruswami and Smith (J. ACM 2016) considered codes for channels that are poly-size circuits which modify at most a p-fraction of the bits of the codeword. This class of channels is significantly stronger than Shannon’s binary symmetric channel (BSC), but weaker than Hamming’s channels which are computationally unbounded. Guruswami and Smith gave an explicit Monte-Carlo construction of codes with optimal rate of R(p) = 1 − H(p) that achieve list-decoding in this scenario. Here, “explicit Monte-Carlo” means that both encoding and decoding algorithms run in polynomial time. However, the encoding and decoding algorithms also receive a uniformly chosen string of polynomial length (which is chosen and published, once and for all, in a pre-processing stage) and their correctness is guaranteed w.h.p. over this random choice. Guruswami and Smith asked whether it is possible to obtain uniquely decodable codes for poly-size channels with rate that beats the Gilbert-Varshamov bound $R^{GV}(p)=1-H(2p)$. We give an affirmative answer, Specifically:•For every $0leq pltfrac{1}{4}$, we give an explicit Monte-Carlo construction of uniquely-decodable codes with optimal rate R(p) = 1 − H(p). This matches the rate achieved by Guruswami and Smith for the easier task of list-decoding, and also matches the capacity of binary symmetric channels. Moreover, this rate is strictly larger than that of codes for the standard coding scenario (namely, uniquely-decodable codes for Hamming channels).•Even ignoring explicitness, our result implies a characterization of the capacity of poly-size channels, which was not previously understood.Our technique builds on the earlier list-decodable codes of Guruswami and Smith, achieving unique-decoding by extending and modifying the construction so that we can identify the correct message in the list. For this purpose we use ideas from coding theory and pseudorandomness, specifically:•We construct codes for binary symmetric channels that beat the Gilbert-Varshamov bound, and are “evasive” in the sense that a poly-size circuit that receives a random (or actually pseudorandom) string, cannot find a codeword within relative distance 2p. This notion of evasiveness is inspired by the recent work of Shaltiel and Silbak (STOC 2021) on codes for space bounded channels.•We develop a methodology (that is inspired by proofs of t-wise independent tail inequalities, and may be of independent interest) to analyze random codes, in scenarios where the success of the channel is measured in an additional random experiment (as in the evasiveness experiment above).•We introduce a new notion of “small-set non-malleable codes” that is tailored for our application, and may be of independent interest.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121595148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Range Avoidance Problem for Circuits","authors":"Hanlin Ren, R. Santhanam, Zhikun Wang","doi":"10.1109/FOCS54457.2022.00067","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00067","url":null,"abstract":"We consider the range avoidance problem (called Avoid): given the description of a circuit with more output gates than input gates, find a string that is not in the range of the circuit. This problem is complete for the class APEPP that corresponds to explicit constructions of objects whose existence follows from the probabilistic method (Korten, FOCS 2021). Motivated by applications in explicit constructions and complexity theory, we initiate the study of the range avoidance problem for weak circuit classes, and obtain the following results: 1)Generalising Williams’s connections between circuitanalysis algorithms and circuit lower bounds (J. ACM 2014), we present a framework for solving $mathscr{C}$-Avoid in FPNP using circuit-analysis data structures for $mathscr{C}$, for “typical” multi-output circuit classes $mathscr{C}$. As an application, we present a non-trivial FPNP range avoidance algorithm for De Morgan formulas./inlp>An important technical ingredient is a construction of rectangular PCPs of proximity, building on the rectangular PCPs by Bhangale, Harsha, Paradise, and Tal (FOCS 2020).2)Using the above framework, we show that circuit lower bounds for ENP are equivalent to circuit-analysis algorithms with ENP preprocessing. This is the first equivalence result regarding circuit lower bounds for ENP. Our equivalences have the additional advantages that they work in both infinitely-often and almost-everywhere settings, and that they also hold for larger (e.g., subexponential) size bounds.3)Complementing the above results, we show that in some settings, solving $mathscr{C}$-Avoid would imply breakthrough lower bounds, even for very weak circuit classes $mathscr{C}$. In particular, an algorithm for AC0-Avoid with polynomial stretch implies lower bounds against NC1, and an algorithm for $NC_{4}^{0}$-Avoid with very small stretch implies lower bounds against NC1 and branching programs.4)We show that Avoid is in FNP if and only if there is a propositional proof system that breaks every non-uniform proof complexity generator. This result connects the study of range avoidance with fundamental questions in proof complexity.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129141881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rate-1 Non-Interactive Arguments for Batch-NP and Applications","authors":"Lalita Devadas, Rishab Goyal, Y. Kalai, V. Vaikuntanathan","doi":"10.1109/FOCS54457.2022.00103","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00103","url":null,"abstract":"We present a rate-1 construction of a publicly verifiable non-interactive argument system for batch-NP (also called a BARG), under the LWE assumption. Namely, a proof corresponding to a batch of k NP statements each with an m-bit witness, has size $m+poly(lambda, log k)$.In contrast, prior work either relied on non-standard knowledge assumptions, or produced proofs of size m. poly $(lambda, log k)$ (Choudhuri, Jain, and Jin, STOC 2021, following Kalai, Paneth, and Yang 2019).We show how to use our rate-l BARG scheme to obtain the following results, all under the LWE assumption:•A multi-hop BARG scheme for NP.•A multi-hop aggregate signature scheme (in the standard model).•An incrementally verifiable computation (IVC) scheme for arbitrary T-time deterministic computations with proof size poly $(lambda, log T)$.Prior to this work, multi-hop BARGs were only known under non-standard knowledge assumptions or in the random oracle model; aggregate signatures were only known under indistinguishability obfuscation (and RSA) or in the random oracle model; IVC schemes with proofs of size poly $(lambda, T^{epsilon})$ were known under a bilinear map assumption, and with proofs of size poly $(lambda, log T)$ under non-standard knowledge assumptions or in the random oracle model.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126872783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fooling polynomials using invariant theory*","authors":"H. Derksen, Emanuele Viola","doi":"10.1109/FOCS54457.2022.00045","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00045","url":null,"abstract":"We revisit the problem of constructing explicit pseudorandom generators that fool with error ϵ degree-d polynomials in n variables over the field Fq, in the case of large q. Previous constructions either have seed length $geq 2^{d}log q$, and thus are only non-trivial when $dlt log n$, or else rely on a seminal reduction by Bogdanov (STOC 2005). This reduction yields seed length not less than $d^{4}log n+log q$ and requires fields of size $qgeq d^{6}/epsilon^{2}$; and explicit generators meeting such bounds are known.Departing from Bogdanov’s reduction, we develop an algebraic analogue of the Bogdanov-Viola paradigm (FOCS 2007, SICOMP 2010) of summing generators for degree-one polynomials. Whereas previous analyses of the paradigm are restricted to degree $dlt log n$, we give a new analysis which handles large degrees. A main new idea is to show that the construction preserves indecomposability of polynomials. Apparently for the first time in the area, the proof uses invariant theory.Our approach in particular yields several new pseudorandom generators. In particular, for large enough fields we obtain seed length $O(dlog n+log q)$ which is optimal up to constant factors. We also construct generators for fields of size as small as $O(d^{4})$. Further reducing the field size requires a significant change in techniques: Most or all generators for large-degree polynomials rely on Weil bounds; but such bounds are only applicable when $qgt d^{4}$","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"38 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121005428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometry of Secure Two-party Computation","authors":"S. Basu, H. A. Khorasgani, H. K. Maji, H. Nguyen","doi":"10.1109/FOCS54457.2022.00101","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00101","url":null,"abstract":"What is the round and communication complexity of secure computation? The seminal results of Chor-Kushilevitz-Beaver (STOC-1989, FOCS-1989, DIMACS-1989) answer this question for computations with deterministic output. However, this question has remained unanswered for computations with randomized output. Our work answers this question for two-party secure function evaluation functionalities. We introduce a geometric encoding of all candidate secure protocols for a given computation as points in a high-dimensional space. The following results follow by analyzing the properties of these sets of points.1)It is decidable to determine if a given computation has a secure protocol within round or communication constraints.2)We construct one such protocol if it exists.3)Otherwise, we present an obstruction to achieving security.Our technical contributions imply new information complexity bounds for secure computation.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116361481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Separated borders: Exponential-gap fanin-hierarchy theorem for approximative depth-3 circuits","authors":"P. Dutta, Nitin Saxena","doi":"10.1109/FOCS54457.2022.00026","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00026","url":null,"abstract":"Mulmuley and Sohoni (2001) proposed an ambitious program, the Geometric Complexity Theory (GCT), to prove $Pneq NP$ and related conjectures using algebraic geometry and representation theory. Gradually, GCT has introduced new structures and questions in complexity. GCT tries to capture the algebraic/geometric notion of ’approximation’ by defining border classes. Surprisingly, (Kumar ToCT’20) proved the universal power of the border of top-fanin- 2 depth-3 circuits $(overline{Sigma^{[2]}PiSigma})$; which is in complete contrast to its classical model. Recently, (Dutta,Dwivedi,Saxena, FOCS’21) put an upper bound, by showing that bounded-top-fanin border depth-3 circuits $(overline{Sigma^{[k]}PiSigma}$ for constant $k)$ can be computed by a polynomial-size algebraic branching program (ABP). It was left open to show an exponential separation between the class of ABPs and $overline{Sigma^{[k]}PiSigma}$. In this article, we show a strongly-exponential separation between any two consecutive border classes, $overline{Sigma^{[k]}PiSigma}$ and $Sigma^{[k+1]}PiSigma$, establishing an optimal hierarchy of constant topfanin border depth- 3 circuits. Put in GCT language: we prove an exponential-hierarchy for padded- k-th-secant-varieties of the Chow variety of $mathbb{F}^{n+1} $. This positively answers [Open question 2 of Dutta,Dwivedi,Saxena FOCS’21] and [Problem 8.10 with constant r, of Landsberg, Annal.Ferrara’15]. Full version: https://www.cse.iitk.ac.in/users/nitin/papers/exphierarchy.pdf","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116005695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}