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: "a generalization of permanent inequalities and applications in counting and optimization"
  Abstract: A polynomial $p\in\mathbb{R}[z_1,\dots,z_n]$ is real stable if it has no roots in the upper-half complex plane. Gurvits's permanent inequality gives a lower bound on the coefficient of the $z_1z_2\dots z_n$ monomial of a real stable polynomial $p$ with nonnegative coefficients. This fundamental inequality has been used to attack several counting and optimization problems. #R##N#Here, we study a more general question: Given a stable multilinear polynomial $p$ with nonnegative coefficients and a set of monomials $S$, we show that if the polynomial obtained by summing up all monomials in $S$ is real stable, then we can lowerbound the sum of coefficients of monomials of $p$ that are in $S$. We also prove generalizations of this theorem to (real stable) polynomials that are not multilinear. We use our theorem to give a new proof of Schrijver's inequality on the number of perfect matchings of a regular bipartite graph, generalize a recent result of Nikolov and Singh, and give deterministic polynomial time approximation algorithms for several counting problems.

Connected through hyperedge HE-1 (induced by source paper "gauges loops and polynomials for partition functions of graphical models"):
  with members:
    - "the ising partition function zeros and deterministic approximation"
    - "belief propagation bethe approximation and polynomials"
    - "how to calculate partition functions using convex programming hierarchies provable bounds for variational methods"
    - "a faster approximation algorithm for the gibbs partition function"
    - "the bethe permanent of a nonnegative matrix"
    - "counting in graph covers a combinatorial characterization of the bethe entropy function"
    - "a cluster cumulant expansion at the fixed points of belief propagation"
    - "the bethe partition function of log supermodular graphical models"

Connected through hyperedge HE-2 (induced by source paper "a tight analysis of bethe approximation for permanent"):
  with members:
    - "log concave polynomials i entropy and a deterministic approximation algorithm for counting bases of matroids"
    - "approximate profile maximum likelihood"
    - "belief propagation bethe approximation and polynomials"
    - "approximating the permanent of a random matrix with vanishing mean"
    - "nash social welfare matrix permanent and stable polynomials"
    - "the bethe permanent of a nonnegative matrix"
    - "approximating the permanent with fractional belief propagation"
    - "approximating the permanent with belief propagation"

Connected through hyperedge HE-3 (induced by source paper "stability and complexity of mixed discriminants"):
  with members:
    - "an efficient tree decomposition method for permanents and mixed discriminants"
    - "on the complexity of constrained determinantal point processes"

Connected through hyperedge HE-4 (induced by source paper "the ising partition function zeros and deterministic approximation"):
  with members:
    - "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"
    - "the kadison singer problem for strongly rayleigh measures and applications to asymmetric tsp"

Connected through hyperedge HE-5 (induced by source paper "belief propagation bethe approximation and polynomials"):
  with members:
    - "real stable polynomials and matroids optimization and counting"
    - "effective resistance reducing flows spectrally thin trees and asymmetric tsp"
    - "the bethe permanent of a nonnegative matrix"
    - "entropy optimization and counting"
    - "counting in graph covers a combinatorial characterization of the bethe entropy function"
    - "the bethe partition function of log supermodular graphical models"
    - "partition functions of normal factor graphs"
    - "belief propagation and loop calculus for the permanent of a non negative matrix"

Connected through hyperedge HE-6 (induced by source paper "maximum entropy distributions bit complexity and stability"):
  with members:
    - "fair and diverse dpp based data summarization"
    - "much faster algorithms for matrix scaling"
    - "matrix scaling and balancing via box constrained newton s method and interior point methods"
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "on the complexity of constrained determinantal point processes"
    - "real stable polynomials and matroids optimization and counting"
    - "entropy optimization and counting"

Connected through hyperedge HE-7 (induced by source paper "subdeterminant maximization via nonconvex relaxations and anti concentration"):
  with members:
    - "how to be fair and diverse"
    - "on the complexity of constrained determinantal point processes"
    - "real stable polynomials and matroids optimization and counting"
    - "analysis of boolean functions"
    - "on largest volume simplices and sub determinants"
    - "randomized rounding for the largest simplex problem"
    - "a robust khintchine inequality and algorithms for computing optimal constants in fourier analysis and high dimensional geometry"

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.DS(Data Structures and Algorithms)