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: "improved bounds on the phase transition for the hard core model in 2 dimensions"
  Abstract: For the hard-core lattice gas model defined on independent sets weighted by an activity $\lambda$, we study the critical activity $\lambda_c(\mathbb{Z}^2)$ for the uniqueness/non-uniqueness threshold on the 2-dimensional integer lattice $\mathbb{Z}^2$. The conjectured value of the critical activity is approximately $3.796$. Until recently, the best lower bound followed from algorithmic results of Weitz (2006). Weitz presented an FPTAS for approximating the partition function for graphs of constant maximum degree $\Delta$ when $\lambda 2.388$. In this paper, we establish an upper bound for this approach, by showing that, for all $\sigma$, SSM does not hold on $T_{\mathrm{saw}}^\sigma(\mathbb{Z}^2)$ when $\lambda>3.4$. We also present a refinement of the approach of Restrepo et al. which improves the lower bound to $\lambda_c(\mathbb{Z}^2)>2.48$.

Connected through hyperedge HE-1 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model"):
  with members:
    - "improved analysis of higher order random walks and applications"
    - "log concave polynomials ii high dimensional walks and an fpras for counting bases of a matroid"
    - "high dimensional random walks and colorful expansion"
    - "convergence of mcmc and loopy bp in the tree uniqueness region for the hard core model"
    - "computing the independence polynomial from the tree threshold down to the roots"
    - "spatial mixing and the connective constant optimal bounds"
    - "spatial mixing and approximation algorithms for graphs with bounded connective constant"
    - "correlation decay up to uniqueness in spin systems"

Connected through hyperedge HE-2 (induced by source paper "convergence of mcmc and loopy bp in the tree uniqueness region for the hard core model"):
  with members:
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"
    - "fptas for bis with degree bounds on one side"
    - "a simple fptas for counting edge covers"
    - "spatial mixing and the connective constant optimal bounds"
    - "loopy belief propagation for approximate inference an empirical study"
    - "spatial mixing and approximation algorithms for graphs with bounded connective constant"
    - "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs"
    - "correlation decay up to uniqueness in spin systems"

Connected through hyperedge HE-3 (induced by source paper "counting hypergraph matchings up to uniqueness threshold"):
  with members:
    - "bis hardness for 2 spin systems on bipartite bounded degree graphs in the tree non uniqueness region"
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"
    - "counting independent sets in hypergraphs when strong spatial mixing fails"
    - "fptas for hardcore and ising models on hypergraphs"
    - "the complexity of approximately counting in 2 spin systems on k uniform bounded degree hypergraphs"
    - "approximation via correlation decay when strong spatial mixing fails"
    - "fptas for weighted fibonacci gates and its applications"
    - "a simple fptas for counting edge covers"

Connected through hyperedge HE-4 (induced by source paper "spatial mixing and the connective constant optimal bounds"):
  with members:
    - "mcmc sampling colourings and independent sets of g n d n near the uniqueness threshold"
    - "spatial mixing and approximation algorithms for graphs with bounded connective constant"
    - "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs"
    - "correlation decay up to uniqueness in spin systems"
    - "approximate counting via correlation decay in spin systems"
    - "improved inapproximability results for counting independent sets in the hard core model"
    - "computational transition at the uniqueness threshold"

Connected through hyperedge HE-5 (induced by source paper "approximate capacities of two dimensional codes by spatial mixing"):
  with members:
    - "fptas for counting monotone cnf"
    - "spatial mixing and approximation algorithms for graphs with bounded connective constant"
    - "approximate counting via correlation decay on planar graphs"
    - "correlation decay up to uniqueness in spin systems"
    - "approximate counting via correlation decay in spin systems"

Connected through hyperedge HE-6 (induced by source paper "spatial mixing and approximation algorithms for graphs with bounded connective constant"):
  with members:
    - "mcmc sampling colourings and independent sets of g n d n near the uniqueness threshold"
    - "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs"
    - "correlation decay up to uniqueness in spin systems"
    - "approximate counting via correlation decay in spin systems"
    - "computational transition at the uniqueness threshold"

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)