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 "convergence of mcmc and loopy bp in the tree uniqueness region for the hard core model"):
  Abstract: We study the hard-core model defined on independent sets of an input graph where the independent sets are weighted by a parameter $\lambda>0$. For constant $\Delta$, previous work of Weitz (2006) established an FPTAS for the partition function for graphs of maximum degree $\Delta$ when $\lambda \lambda_c(\Delta)$. The running time of Weitz's algorithm is exponential in $\log(\Delta)$. Here we present an FPRAS for the partition function whose running time is $O^*(n^2)$. We analyze the simple single-site Glauber dynamics for sampling from the associated Gibbs distribution. We prove there exists a constant $\Delta_0$ such that for all graphs with maximum degree $\Delta\geq\Delta_0$ and girth $\geq 7$, the mixing time of the Glauber dynamics is $O(n\log(n))$ when $\lambda<\lambda_c(\Delta)$. Our work complements that of Weitz which applies for constant $\Delta$ whereas our work applies for all $\Delta \geq \Delta_0$. #R##N#We utilize loopy BP (belief propagation), a widely-used inference algorithm. A novel aspect of our work is using the principal eigenvector for the BP operator to design a distance function which contracts in expectation for pairs of states that behave like the BP fixed point. We also prove that the Glauber dynamics behaves locally like loopy BP. As a byproduct we obtain that the Glauber dynamics converges, after a short burn-in period, close to the BP fixed point, and this implies that the fixed point of loopy BP is a close approximation to the Gibbs distribution. Using these connections we establish that loopy BP quickly converges to the Gibbs distribution when the girth $\geq 6$ and $\lambda<\lambda_c(\Delta)$.

Includes members:
  Member "inapproximability of the partition function for the antiferromagnetic ising and hard core models":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "lower bounds for testing graphical models colorings and antiferromagnetic ising models")
  Member "fptas for bis with degree bounds on one side":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "counting independent sets and colorings on random regular bipartite graphs")
  Member "a simple fptas for counting edge covers":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "zeros and approximations of holant polynomials on the complex plane")
  Member "spatial mixing and the connective constant optimal bounds":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "loopy belief propagation for approximate inference an empirical study":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "analyzing differentiable fuzzy logic operators")
  Member "spatial mixing and approximation algorithms for graphs with bounded connective constant":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "improved bounds on the phase transition for the hard core model in 2 dimensions":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "efficient distance approximation for structured high dimensional distributions via learning")

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.DM(Discrete Mathematics)