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: "approximating the permanent with fractional belief propagation"
  Abstract: We discuss schemes for exact and approximate computations of permanents, and compare them with each other. Specifically, we analyze the Belief Propagation (BP) approach and its Fractional Belief Propagation (FBP) generalization for computing the permanent of a non-negative matrix. Known bounds and conjectures are verified in experiments, and some new theoretical relations, bounds and conjectures are proposed. The Fractional Free Energy (FFE) functional is parameterized by a scalar parameter $\gamma\in[-1;1]$, where $\gamma=-1$ corresponds to the BP limit and $\gamma=1$ corresponds to the exclusion principle (but ignoring perfect matching constraints) Mean-Field (MF) limit. FFE shows monotonicity and continuity with respect to $\gamma$. For every non-negative matrix, we define its special value $\gamma_*\in[-1;0]$ to be the $\gamma$ for which the minimum of the $\gamma$-parameterized FFE functional is equal to the permanent of the matrix, where the lower and upper bounds of the $\gamma$-interval corresponds to respective bounds for the permanent. Our experimental analysis suggests that the distribution of $\gamma_*$ varies for different ensembles but $\gamma_*$ always lies within the $[-1;-1/2]$ interval. Moreover, for all ensembles considered the behavior of $\gamma_*$ is highly distinctive, offering an emprirical practical guidance for estimating permanents of non-negative matrices via the FFE approach.

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"
    - "a generalization of permanent inequalities and applications in counting and optimization"
    - "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"

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"
    - "a generalization of permanent inequalities and applications in counting and optimization"
    - "nash social welfare matrix permanent and stable polynomials"
    - "the bethe permanent of a nonnegative matrix"
    - "approximating the permanent with belief propagation"

Connected through hyperedge HE-3 (induced by source paper "multiple scan data association by convex variational inference"):
  with members:
    - "a scalable algorithm for tracking an unknown number of targets using multiple sensors"
    - "marginal multi bernoulli filters rfs derivation of mht jipda and association based member"
    - "an efficient variational approximation of the best fitting multi bernoulli filter"
    - "approximate evaluation of marginal association probabilities with belief propagation"
    - "loopy belief propagation for approximate inference an empirical study"
    - "the bethe permanent of a nonnegative matrix"
    - "a new class of upper bounds on the log partition function"
    - "merging belief propagation and the mean field approximation a free energy approach"

Connected through hyperedge HE-4 (induced by source paper "message passing and combinatorial optimization"):
  with members:
    - "augmentative message passing for traveling salesman problem and graph partitioning"
    - "perturbed message passing for constraint satisfaction problems"
    - "revisiting algebra and complexity of inference in graphical models"
    - "on map inference by mwss on perfect graphs"
    - "loopy belief propagation for approximate inference an empirical study"
    - "graphical models for game theory"
    - "message passing algorithms reparameterizations and splittings"
    - "the bethe permanent of a nonnegative matrix"

Connected through hyperedge HE-5 (induced by source paper "approximate evaluation of marginal association probabilities with belief propagation"):
  with members:
    - "loopy belief propagation for approximate inference an empirical study"
    - "the bethe permanent of a nonnegative matrix"
    - "a new class of upper bounds on the log partition function"
    - "approximating the permanent with belief propagation"
    - "max product for maximum weight matching convergence correctness and lp duality"
    - "belief propagation and beyond for particle tracking"

Connected through hyperedge HE-6 (induced by source paper "graphical model approximations of random finite set filters"):
  with members:
    - "the bethe permanent of a nonnegative matrix"
    - "a new class of upper bounds on the log partition function"
    - "message passing for maximum weight independent set"
    - "approximating the permanent with belief propagation"
    - "max product for maximum weight matching convergence correctness and lp duality"
    - "belief propagation and beyond for particle tracking"

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)