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 "monotone rank and separations in computational complexity"):
  Abstract: In the paper, we introduce the concept of monotone rank, and using it as a powerful tool, we obtain several important and strong separation results in computational complexity. #R##N#We show a super-exponential separation between monotone and non-monotone computation in the non-commutative model, and thus give the answer to a longstanding open problem posed by Nisan \cite{Nis1991} in algebraic complexity. More specifically, we exhibit a homogeneous algebraic function $f$ of degree $d$ ($d$ even) on $n$ variables with the monotone algebraic branching program (ABP) complexity $\Omega(n^{d/2})$ and the non-monotone ABP complexity $O(d^2)$. #R##N#We propose a relaxed version of the famous Bell's theorem\cite{Bel1964}\cite{CHSH1969}. Bell's theorem basically states that local hidden variable theory cannot predict the correlations produced by quantum mechanics, and therefore is an impossibility result. Bell's theorem heavily relies on the diversity of the measurements. We prove that even if we fix the measurement, infinite amount of local hidden variables will still be needed, though now the prediction of "quantum mechanics" becomes physically feasible. Quantitatively, at least $n$ bits of local hidden variables are needed to simulate the correlations of size $2n$ generated from a 2-qubit Bell state. The bound is asymptotically tight. #R##N#We generalize the log-rank conjecture \cite{LS1988} in communication complexity to the multiparty case, and prove that for super-polynomial parties, there is a super-polynomial separation between the deterministic communication complexity and the logarithm of the rank of the communication tensor. This means that the log-rank conjecture does not hold in "high" dimensions.

Includes members:
  Member "tensor rank some lower and upper bounds":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "learning representations from imperfect time series data via tensor rank regularization")
  Member "homogeneous formulas and symmetric polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "new exponential size lower bounds against depth four circuits of bounded individual degree")
  Member "arithmetic circuits and the hadamard product of polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on explicit branching programs for the rectangular determinant and permanent polynomials")
  Member "on the complexity of nonnegative matrix factorization":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "convergence to second order stationarity for non negative matrix factorization provably and concurrently")

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)