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: "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs"
  Abstract: In a seminal paper (Weitz, 2006), Weitz gave a deterministic fully polynomial approximation scheme for count- ing exponentially weighted independent sets (equivalently, approximating the partition function of the hard-core model from statistical physics) on graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the infinite d-regular tree. More recently Sly (Sly, 2010) showed that this is optimal in the sense that if there is an FPRAS for the hard-core partition function on graphs of maximum degree d for activities larger than the critical activity on the infinite d-regular tree then NP = RP. In this paper, we extend Weitz's approach to derive a deterministic fully polynomial approx- imation scheme for the partition function of the anti-ferromagnetic Ising model with arbitrary field on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. This in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al (Restrepo et al, 2011) to the case of the anti-ferromagnetic Ising model with arbitrary field. By a standard correspondence, these results translate to arbitrary two-state anti-ferromagnetic spin systems with soft constraints.

Connected through hyperedge HE-1 (induced by source paper "efficient distance approximation for structured high dimensional distributions via learning"):
  with members:
    - "efficiently learning and sampling interventional distributions from observations"
    - "learning and testing causal models with interventions"
    - "learning graphical models using multiplicative weights"
    - "testing ising models"
    - "square hellinger subadditivity for bayesian networks and its applications to identity testing"
    - "testing bayesian networks"
    - "causal networks semantics and expressiveness"
    - "optimal algorithms for testing closeness of discrete distributions"

Connected through hyperedge HE-2 (induced by source paper "perfect sampling from spatial mixing"):
  with members:
    - "dynamic sampling from graphical models"
    - "on local distributed sampling and counting"
    - "approximately counting bases of bicircular matroids"
    - "improved bounds for randomly sampling colorings via linear programming"
    - "a polynomial time approximation algorithm for all terminal network reliability"
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"
    - "approximate counting via correlation decay on planar graphs"
    - "correlation decay up to uniqueness in spin systems"

Connected through hyperedge HE-3 (induced by source paper "spectral approximate inference"):
  with members:
    - "the mean field approximation information inequalities algorithms and complexity"
    - "the ising partition function zeros and deterministic approximation"
    - "convergence of mcmc and loopy bp in the tree uniqueness region for the hard core model"
    - "variable elimination in the fourier domain"
    - "inapproximability for antiferromagnetic spin systems in the tree non uniqueness region"
    - "a new class of upper bounds on the log partition function"
    - "correlation decay up to uniqueness in spin systems"

Connected through hyperedge HE-4 (induced by source paper "zeros of ferromagnetic 2 spin systems"):
  with members:
    - "zeros of holant problems locations and algorithms"
    - "the ising partition function zeros and deterministic approximation"
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"
    - "uniqueness spatial mixing and approximation for ferromagnetic 2 spin systems"
    - "correlation decay up to uniqueness in spin systems"

Connected through hyperedge HE-5 (induced by source paper "boolean approximate counting csps with weak conservativity and implications for ferromagnetic two spin"):
  with members:
    - "functional clones and expressibility of partition functions"
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"
    - "the complexity of approximating conservative counting csps"
    - "the complexity of ferromagnetic two spin systems with external fields"
    - "the expressibility of functions on the boolean domain with applications to counting csps"
    - "approximating the tutte polynomial of a binary matroid and other related combinatorial polynomials"
    - "correlation decay up to uniqueness in spin systems"
    - "from holant to csp and back dichotomy for holant c problems"

Connected through hyperedge HE-6 (induced by source paper "swendsen wang dynamics for general graphs in the tree uniqueness region"):
  with members:
    - "spatial mixing and non local markov chains"
    - "random cluster dynamics for the ising model is rapidly mixing"
    - "spatial mixing and the connective constant optimal bounds"
    - "correlation decay up to uniqueness in spin systems"
    - "computational transition at the uniqueness threshold"
    - "adaptive simulated annealing a near optimal connection between sampling and counting"

Connected through hyperedge HE-7 (induced by source paper "the ising partition function zeros and deterministic approximation"):
  with members:
    - "a generalization of permanent inequalities and applications in counting and optimization"
    - "convergence of mcmc and loopy bp in the tree uniqueness region for the hard core model"
    - "real stable polynomials and matroids optimization and counting"
    - "random cluster dynamics for the ising model is rapidly mixing"
    - "uniqueness spatial mixing and approximation for ferromagnetic 2 spin systems"
    - "fptas for hardcore and ising models on hypergraphs"
    - "counting hypergraph matchings up to uniqueness threshold"
    - "the complexity of approximately counting in 2 spin systems on k uniform bounded degree hypergraphs"

Connected through hyperedge HE-8 (induced by source paper "bis hardness for 2 spin systems on bipartite bounded degree graphs in the tree non uniqueness region"):
  with members:
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"
    - "the complexity of approximating conservative counting csps"
    - "approximating the partition function of planar two state spin systems"
    - "the complexity of ferromagnetic two spin systems with external fields"
    - "the expressibility of functions on the boolean domain with applications to counting csps"
    - "inapproximability for antiferromagnetic spin systems in the tree non uniqueness region"
    - "inapproximability after uniqueness phase transition in two spin systems"
    - "approximating the partition function of the ferromagnetic potts model"

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)