human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "discrete geometric analysis of message passing algorithm on graphs"
  Abstract: We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.

Connected through hyperedge HE-1 (induced by source paper "loop calculus for non binary alphabets using concepts from information geometry"):
  with members:
    - "the bethe permanent of a nonnegative matrix"
    - "the matching polytope has exponential extension complexity"
    - "counting in graph covers a combinatorial characterization of the bethe entropy function"
    - "beyond the bethe free energy of ldpc codes via polymer expansions"
    - "new generalizations of the bethe approximation via asymptotic expansion"
    - "primal view on belief propagation"
    - "connection between annealed free energy and belief propagation on random factor graph ensembles"
    - "partition functions of normal factor graphs"

Connected through hyperedge HE-2 (induced by source paper "new generalizations of the bethe approximation via asymptotic expansion"):
  with members:
    - "counting in graph covers a combinatorial characterization of the bethe entropy function"
    - "central approximation in statistical physics and information theory"
    - "partition functions of normal factor graphs"
    - "loop calculus and belief propagation for q ary alphabet loop tower"

Connected through hyperedge HE-3 (induced by source paper "loopy belief propagation bethe free energy and graph zeta function"):
  with members:
    - "map estimation linear programming and belief propagation with convex free energies"
    - "graph zeta function in the bethe free energy and loopy belief propagation"
    - "bayesian compressive sensing via belief propagation"
    - "sufficient conditions for convergence of the sum product algorithm"

Question: Please tell me which class the center node 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.DM(Discrete Mathematics)