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 "the theory of the interleaving distance on multidimensional persistence modules"):
  Abstract: In 2009, Chazal et al. introduced $$\epsilon $$∈-interleavings of persistence modules. $$\epsilon $$∈-interleavings induce a pseudometric $$d_\mathrm{I}$$dI on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $$\epsilon $$∈-interleavings and $$d_\mathrm{I}$$dI generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view toward applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $$d_\mathrm{I}$$dI is equal to the bottleneck distance $$d_\mathrm{B}$$dB. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $$\epsilon $$∈-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $$\epsilon $$∈-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $$d_\mathrm{I}$$dI satisfies a universality property. This universality result is the central result of the paper. It says that $$d_\mathrm{I}$$dI satisfies a stability property generalizing one which $$d_\mathrm{B}$$dB is known to satisfy, and that in addition, if $$d$$d is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $$d\le d_\mathrm{I}$$d≤dI. We also show that a variant of this universality result holds for $$d_\mathrm{B}$$dB, over arbitrary fields. Finally, we show that $$d_\mathrm{I}$$dI restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.

Includes members:
  Member "categorified reeb graphs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "intrinsic interleaving distance for merge trees")
  Member "classification of hepatic lesions using the matching metric":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "end to end discriminative deep network for liver lesion classification")
  Member "natural pseudo distance and optimal matching between reduced size functions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the coherent matching distance in 2d persistent homology")
  Member "towards persistence based reconstruction in euclidean spaces":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "time series featurization via topological data analysis")

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.CG(Computational Geometry)