human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "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.

Includes members:
  Member "improved sum of squares lower bounds for hidden clique and hidden submatrix problems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "broadcast congested clique planted cliques and pseudorandom generators")
  Member "sum of squares lower bounds for sparse pca":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "0 1 phase transitions in sparse spiked matrix estimation")
  Member "sum of squares lower bounds from pairwise independence":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "breaking symmetries to rescue sum of squares the case of makespan scheduling")
  Member "tight lower bounds for planted clique in the degree 4 sos program":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "average case lower bounds for learning sparse mixtures robust estimation and semirandom adversaries")
  Member "decomposing overcomplete 3rd order tensors using sum of squares algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "learning two layer rectified neural networks in polynomial time")
  Member "tensor prediction rademacher complexity and random 3 xor":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "extended formulation lower bounds for refuting random csps")
  Member "sum of squares lower bounds for planted clique":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "broadcast congested clique planted cliques and pseudorandom generators")
  Member "lower bounds on the size of semidefinite programming relaxations":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "lifting with simple gadgets and applications to circuit and proof complexity")

Question: Please tell me which class the source paper 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)