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 "dual polynomials and communication complexity of textsf xor functions"):
  Abstract: We show a new duality between the polynomial margin complexity of $f$ and the discrepancy of the function $f \circ \textsf{XOR}$, called an $\textsf{XOR}$ function. Using this duality, we develop polynomial based techniques for understanding the bounded error ($\textsf{BPP}$) and the weakly-unbounded error ($\textsf{PP}$) communication complexities of $\textsf{XOR}$ functions. We show the following. #R##N#A weak form of an interesting conjecture of Zhang and Shi (Quantum Information and Computation, 2009) (The full conjecture has just been reported to be independently settled by Hatami and Qian (Arxiv, 2017). However, their techniques are quite different and are not known to yield many of the results we obtain here). Zhang and Shi assert that for symmetric functions $f : \{0, 1\}^n \rightarrow \{-1, 1\}$, the weakly unbounded-error complexity of $f \circ \textsf{XOR}$ is essentially characterized by the number of points $i$ in the set $\{0,1, \dots,n-2\}$ for which $D_f(i) \neq D_f(i+2)$, where $D_f$ is the predicate corresponding to $f$. The number of such points is called the odd-even degree of $f$. We show that the $\textsf{PP}$ complexity of $f \circ \textsf{XOR}$ is $\Omega(k/ \log(n/k))$. #R##N#We resolve a conjecture of a different Zhang characterizing the Threshold of Parity circuit size of symmetric functions in terms of their odd-even degree. #R##N#We obtain a new proof of the exponential separation between $\textsf{PP}^{cc}$ and $\textsf{UPP}^{cc}$ via an $\textsf{XOR}$ function. #R##N#We provide a characterization of the approximate spectral norm of symmetric functions, affirming a conjecture of Ada et al. (APPROX-RANDOM, 2012) which has several consequences. #R##N#Additionally, we prove strong $\textsf{UPP}$ lower bounds for $f \circ \textsf{XOR}$, when $f$ is symmetric and periodic with period $O(n^{1/2-\epsilon})$, for any constant $\epsilon > 0$.

Includes members:
  Member "a nearly optimal lower bound on the approximate degree of ac 0":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "near optimal lower bounds on the threshold degree and sign rank of ac 0")
  Member "spectral norm of symmetric functions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "near log convexity of measured heat in discrete time and consequences")

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)