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 "near optimal lower bounds on the threshold degree and sign rank of ac 0"):
  Abstract: The threshold degree of a Boolean function $f\colon\{0,1\}^n\to\{0,1\}$ is the minimum degree of a real polynomial $p$ that represents $f$ in sign: $\mathrm{sgn}\; p(x)=(-1)^{f(x)}.$ A related notion is sign-rank, defined for a Boolean matrix $F=[F_{ij}]$ as the minimum rank of a real matrix $M$ with $\mathrm{sgn}\; M_{ij}=(-1)^{F_{ij}}$. Determining the maximum threshold degree and sign-rank achievable by constant-depth circuits ($\text{AC}^{0}$) is a well-known and extensively studied open problem, with complexity-theoretic and algorithmic applications. #R##N#We give an essentially optimal solution to this problem. For any $\epsilon>0,$ we construct an $\text{AC}^{0}$ circuit in $n$ variables that has threshold degree $\Omega(n^{1-\epsilon})$ and sign-rank $\exp(\Omega(n^{1-\epsilon})),$ improving on the previous best lower bounds of $\Omega(\sqrt{n})$ and $\exp(\tilde{\Omega}(\sqrt{n}))$, respectively. Our results subsume all previous lower bounds on the threshold degree and sign-rank of $\text{AC}^{0}$ circuits of any given depth, with a strict improvement starting at depth $4$. As a corollary, we also obtain near-optimal bounds on the discrepancy, threshold weight, and threshold density of $\text{AC}^{0}$, strictly subsuming previous work on these quantities. Our work gives some of the strongest lower bounds to date on the communication complexity of $\text{AC}^{0}$.

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 "approximate degree secret sharing and concentration phenomena")
  Member "dual lower bounds for approximate degree and markov bernstein inequalities":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "approximate degree secret sharing and concentration phenomena")
  Member "hardness amplification and the approximate degree of constant depth circuits":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "approximate degree secret sharing and concentration phenomena")
  Member "strong direct product theorems for quantum communication and query complexity":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a new minimax theorem for randomized algorithms")
  Member "the intersection of two halfspaces has high threshold degree":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "sign rank can increase under intersection")
  Member "a note on the sign degree of formulas":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "a nearly optimal lower bound on the approximate degree of ac 0")
  Member "optimal bounds for sign representing the intersection of two halfspaces by polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "sign rank can increase under intersection")
  Member "a dual polynomial for or":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "a nearly optimal lower bound on the approximate degree of ac 0")

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)