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 "bounding the bethe and the degree m bethe permanents"):
  Abstract: It was recently conjectured that the permanent of a ${P}$-lifting $\theta^{\uparrow{P}}$ of a matrix $\theta$ of degree $M$ is less than or equal to the $M$th power of the permanent perm$(\theta)$, i.e., perm$(\theta^{\uparrow{P}})\leq(\text{perm}(\theta))^M$ and, consequently, that the degree-$M$ Bethe permanent $\text{perm}_{M,\mathrm{B}} (\theta)$ of a matrix $\theta$ is less than or equal to the permanent perm$(\theta)$ of $\theta$, i.e., perm$_{M, \mathrm{B}} (\theta)\leq \text{perm}(\theta)$. In this paper, we prove these related conjectures and show in addition a few properties of the permanent of block matrices that are lifts of a matrix. As a corollary, we obtain an alternative proof of the inequality perm$_{\mathrm{B}} (\theta)\leq \text{perm}(\theta)$ on the Bethe permanent of the base matrix $\theta$ that uses only the combinatorial definition of the Bethe permanent.

Includes members:
  Member "hierarchical and high girth qc ldpc codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "multi dimensional spatially coupled code design enhancing the cycle properties")
  Member "the bethe permanent of a nonnegative matrix":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")
  Member "design of multiple edge protographs for qc ldpc codes avoiding short inevitable cycles":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a new multi edge metric constrained peg algorithm for designing binary ldpc code with improved cycle structure")
  Member "bounds on the minimum distance of punctured quasi cyclic ldpc codes":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "characterization and efficient search of non elementary trapping sets of ldpc codes with applications to stopping sets")
  Member "quasi cyclic ldpc codes influence of proto and tanner graph structure on minimum hamming distance upper bounds":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "multi dimensional spatially coupled code design enhancing the cycle properties")
  Member "the bethe partition function of log supermodular graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "lifted hybrid variational inference")
  Member "computing the permanent with belief propagation":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "the bethe permanent of a nonnegative matrix")
  Member "absdet pseudo codewords and perm pseudo codewords definitions and properties":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "the bethe permanent of a nonnegative matrix")

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)