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 "applications of monotone rank to complexity theory"):
  Abstract: Raz's recent result \cite{Raz2010} has rekindled people's interest in the study of \emph{tensor rank}, the generalization of matrix rank to high dimensions, by showing its connections to arithmetic formulas. In this paper, we follow Raz's work and show that \emph{monotone rank}, the monotone variant of tensor rank and matrix rank, has applications in algebraic complexity, quantum computing and communication complexity. This paper differs from Raz's paper in that it leverages existing results to show unconditional bounds while Raz's result relies on some assumptions. #R##N#We show a super-exponential separation between monotone and non-monotone computation in the non-commutative model, and thus provide a strong solution to Nisan's question \cite{Nis1991} in algebraic complexity. More specifically, we exhibit that there exists a homogeneous algebraic function $f$ of degree $d$ ($d$ even) on $n$ variables with the monotone algebraic branching program (ABP) complexity $\Omega(d^2\log n)$ and the non-monotone ABP complexity $O(d^2)$. #R##N#In Bell's theorem\cite{Bel1964, CHSH1969}, a basic assumption is that players have free will, and under such an assumption, local hidden variable theory still cannot predict the correlations produced by quantum mechanics. Using tools from monotone rank, we show that even if we disallow the players to have free will, local hidden variable theory still cannot predict the correlations produced by quantum mechanics. #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 "monotone rank and separations in computational complexity":
    also connected through other hyperedges:
      (none)
  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 "partition arguments in multiparty communication complexity":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "adding a referee to an interconnection network what can not be computed in one round")
  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)