human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "sos and planted clique tight analysis of mpw moments at all degrees and an optimal lower bound at degree four"
  Abstract: The problem of finding large cliques in random graphs and its "planted" variant, where one wants to recover a clique of size $\omega \gg \log{(n)}$ added to an \Erdos-\Renyi graph $G \sim G(n,\frac{1}{2})$, have been intensely studied. Nevertheless, existing polynomial time algorithms can only recover planted cliques of size $\omega = \Omega(\sqrt{n})$. By contrast, information theoretically, one can recover planted cliques so long as $\omega \gg \log{(n)}$. In this work, we continue the investigation of algorithms from the sum of squares hierarchy for solving the planted clique problem begun by Meka, Potechin, and Wigderson (MPW, 2015) and Deshpande and Montanari (DM,2015). Our main results improve upon both these previous works by showing: #R##N#1. Degree four SoS does not recover the planted clique unless $\omega \gg \sqrt n poly \log n$, improving upon the bound $\omega \gg n^{1/3}$ due to DM. A similar result was obtained independently by Raghavendra and Schramm (2015). #R##N#2. For $2 < d = o(\sqrt{\log{(n)}})$, degree $2d$ SoS does not recover the planted clique unless $\omega \gg n^{1/(d + 1)} /(2^d poly \log n)$, improving upon the bound due to MPW. #R##N#Our proof for the second result is based on a fine spectral analysis of the certificate used in the prior works MPW,DM and Feige and Krauthgamer (2003) by decomposing it along an appropriately chosen basis. Along the way, we develop combinatorial tools to analyze the spectrum of random matrices with dependent entries and to understand the symmetries in the eigenspaces of the set symmetric matrices inspired by work of Grigoriev (2001). #R##N#An argument of Kelner shows that the first result cannot be proved using the same certificate. Rather, our proof involves constructing and analyzing a new certificate that yields the nearly tight lower bound by "correcting" the certificate of previous works.

Connected through hyperedge HE-1 (induced by source paper "a nearly tight sum of squares lower bound for the planted clique problem"):
  with members:
    - "improved sum of squares lower bounds for hidden clique and hidden submatrix problems"
    - "sum of squares lower bounds for sparse pca"
    - "sum of squares lower bounds from pairwise independence"
    - "sum of squares lower bounds for planted clique"
    - "dictionary learning and tensor decomposition via the sum of squares method"
    - "sum of squares proofs and the quest toward optimal algorithms"
    - "rounding sum of squares relaxations"
    - "hidden cliques and the certification of the restricted isometry property"

Connected through hyperedge HE-2 (induced by source paper "tensor prediction rademacher complexity and random 3 xor"):
  with members:
    - "how to refute a random csp"
    - "tight lower bounds for planted clique in the degree 4 sos program"
    - "dictionary learning and tensor decomposition via the sum of squares method"
    - "sum of squares proofs and the quest toward optimal algorithms"
    - "rounding sum of squares relaxations"
    - "smoothed analysis of tensor decompositions"
    - "from average case complexity to improper learning complexity"
    - "understanding alternating minimization for matrix completion"

Connected through hyperedge HE-3 (induced by source paper "sum of squares lower bounds for sparse pca"):
  with members:
    - "improved sum of squares lower bounds for hidden clique and hidden submatrix problems"
    - "tight lower bounds for planted clique in the degree 4 sos program"
    - "tensor prediction rademacher complexity and random 3 xor"
    - "sum of squares lower bounds for planted clique"
    - "dictionary learning and tensor decomposition via the sum of squares method"
    - "sum of squares proofs and the quest toward optimal algorithms"
    - "rounding sum of squares relaxations"
    - "more data speeds up training time in learning halfspaces over sparse vectors"

Question: Please tell me which class the center node belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.CC(Computational Complexity)