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 "an entropy inequality for symmetric random variables"):
  Abstract: We establish a lower bound on the entropy of weighted sums of (possibly dependent) random variables $(X_1, X_2, \dots, X_n)$ possessing a symmetric joint distribution. Our lower bound is in terms of the joint entropy of $(X_1, X_2, \dots, X_n)$. We show that for $n \geq 3$, the lower bound is tight if and only if $X_i$'s are i.i.d.\ Gaussian random variables. For $n=2$ there are numerous other cases of equality apart from i.i.d.\ Gaussians, which we completely characterize. Going beyond sums, we also present an inequality for certain linear transformations of $(X_1, \dots, X_n)$. Our primary technical contribution lies in the analysis of the equality cases, and our approach relies on the geometry and the symmetry of the problem.

Includes members:
  Member "a counterexample to the vector generalization of costa s epi and partial resolution":
    also connected through other hyperedges:
      (none)
  Member "strengthening the entropy power inequality":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "sum rate capacity for symmetric gaussian multiple access channels with feedback")
  Member "entropy jumps for radially symmetric random vectors":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "wasserstein stability of the entropy power inequality for log concave densities")
  Member "monotonicity of entropy and fisher information a quick proof via maximal correlation":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "maximal correlation and the rate of fisher information convergence in the central limit theorem")
  Member "beyond the entropy power inequality via rearrangements":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "two remarks on generalized entropy power inequalities")
  Member "information theoretic proofs of entropy power inequalities":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "vector gaussian successive refinement with degraded side information")
  Member "information inequalities for joint distributions with interpretations and applications":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "dual loomis whitney inequalities via information theory")
  Member "generalized entropy power inequalities and monotonicity properties of information":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "two remarks on generalized entropy power inequalities")

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.IT(Information Theory)