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: "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 $\lambda<\lambda_c(\Delta)$.

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"
    - "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"
    - "improved bounds on the phase transition for the hard core model in 2 dimensions"
    - "correlation decay up to uniqueness in spin systems"

Connected through hyperedge HE-2 (induced by source paper "fast sampling and counting k sat solutions in the local lemma regime"):
  with members:
    - "algorithms for bis hard problems on expander graphs"
    - "algorithmic pirogov sinai theory"
    - "counting hypergraph colorings in the local lemma regime"
    - "a faster approximation algorithm for the gibbs partition function"
    - "approximate counting the lovasz local lemma and inference in graphical models"
    - "parallel algorithms and concentration bounds for the lovasz local lemma via witness dags"
    - "approximation via correlation decay when strong spatial mixing fails"
    - "new constructive aspects of the lovasz local lemma"

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"
    - "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"
    - "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-4 (induced by source paper "fast algorithms at low temperatures via markov chains"):
  with members:
    - "counting independent sets and colorings on random regular bipartite graphs"
    - "algorithms for bis hard problems on expander graphs"
    - "algorithmic pirogov sinai theory"
    - "fptas for bis with degree bounds on one side"

Connected through hyperedge HE-5 (induced by source paper "dynamic mcmc sampling"):
  with members:
    - "uniform sampling through the lov asz local lemma"
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"
    - "correlation decay up to uniqueness in spin systems"

Connected through hyperedge HE-6 (induced by source paper "dynamic sampling from graphical models"):
  with members:
    - "distributed symmetry breaking in sampling optimal distributed randomly coloring with fewer colors"
    - "a simple parallel and distributed sampling technique local glauber dynamics"
    - "tight bounds for popping algorithms"
    - "sublogarithmic distributed algorithms for lov asz local lemma and the complexity hierarchy"
    - "what can be sampled locally"
    - "a polynomial time approximation algorithm for all terminal network reliability"
    - "uniform sampling through the lov asz local lemma"
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"

Connected through hyperedge HE-7 (induced by source paper "algorithms for bis hard problems on expander graphs"):
  with members:
    - "markov chains for the hard core model via polymer models"
    - "counting independent sets and colorings on random regular bipartite graphs"
    - "sampling in uniqueness from the potts and random cluster models on random regular graphs"
    - "algorithmic pirogov sinai theory"
    - "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"
    - "random cluster dynamics for the ising model is rapidly mixing"
    - "fptas for bis with degree bounds on one side"

Connected through hyperedge HE-8 (induced by source paper "distributed symmetry breaking in sampling optimal distributed randomly coloring with fewer colors"):
  with members:
    - "on local distributed sampling and counting"
    - "a simple parallel and distributed sampling technique local glauber dynamics"
    - "what can be sampled locally"
    - "sampling random colorings of sparse random graphs"
    - "on the complexity of local distributed graph problems"
    - "the locality of distributed symmetry breaking"
    - "deterministic distributed vertex coloring in polylogarithmic time"

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)