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 "kruskal katona for convex sets with applications"):
  Abstract: The well-known Kruskal-Katona theorem in combinatorics says that (under mild conditions) every monotone Boolean function $f: \{0,1\}^n \to \{0,1\}$ has a nontrivial "density increment." This means that the fraction of inputs of Hamming weight $k+1$ for which $f=1$ is significantly larger than the fraction of inputs of Hamming weight $k$ for which $f=1.$ #R##N#We prove an analogous statement for convex sets. Informally, our main result says that (under mild conditions) every convex set $K \subset \mathbb{R}^n$ has a nontrivial density increment. This means that the fraction of the radius-$r$ sphere that lies within $K$ is significantly larger than the fraction of the radius-$r'$ sphere that lies within $K$, for $r'$ suitably larger than $r$. For centrally symmetric convex sets we show that our density increment result is essentially optimal. #R##N#As a consequence of our Kruskal-Katona type theorem, we obtain the first efficient weak learning algorithm for convex sets under the Gaussian distribution. We show that any convex set can be weak learned to advantage $\Omega(1/n)$ in $\mathsf{poly}(n)$ time under any Gaussian distribution and that any centrally symmetric convex set can be weak learned to advantage $\Omega(1/\sqrt{n})$ in $\mathsf{poly}(n)$ time. We also give an information-theoretic lower bound showing that the latter advantage is essentially optimal for $\mathsf{poly}(n)$ time weak learning algorithms. As another consequence of our Kruskal-Katona theorem, we give the first nontrivial Gaussian noise stability bounds for convex sets at high noise rates. Our results extend the known correspondence between monotone Boolean functions over $ \{0,1\}^n$ and convex bodies in Gaussian space.

Includes members:
  Member "learning geometric concepts with nasty noise":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "learning halfspaces with massart noise under structured distributions")
  Member "beyond talagrand functions new lower bounds for testing monotonicity and unateness":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "almost optimal testers for concise representations")
  Member "a polynomial lower bound for testing monotonicity":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "almost optimal testers for concise representations")
  Member "analysis of boolean functions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "coarse grained complexity for dynamic algorithms")
  Member "boolean function monotonicity testing requires almost n 1 2 non adaptive queries":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "almost optimal testers for concise representations")
  Member "an invariance principle for polytopes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "fooling polytopes")
  Member "nearly optimal solutions for the chow parameters problem and low weight approximation of halfspaces":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "nearly tight bounds for robust proper learning of halfspaces with a margin")
  Member "average sensitivity and noise sensitivity of polynomial threshold functions":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "approximating the noise sensitivity of a monotone boolean function")

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)