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: "semidefinite programs on sparse random graphs and their application to community detection"
  Abstract: Denote by $A$ the adjacency matrix of an Erdos-Renyi graph with bounded average degree. We consider the problem of maximizing $\langle A-E\{A\},X\rangle$ over the set of positive semidefinite matrices $X$ with diagonal entries $X_{ii}=1$. We prove that for large (bounded) average degree $d$, the value of this semidefinite program (SDP) is --with high probability-- $2n\sqrt{d} + n\, o(\sqrt{d})+o(n)$. For a random regular graph of degree $d$, we prove that the SDP value is $2n\sqrt{d-1}+o(n)$, matching a spectral upper bound. Informally, Erdos-Renyi graphs appear to behave similarly to random regular graphs for semidefinite programming. #R##N#We next consider the sparse, two-groups, symmetric community detection problem (also known as planted partition). We establish that SDP achieves the information-theoretically optimal detection threshold for large (bounded) degree. Namely, under this model, the vertex set is partitioned into subsets of size $n/2$, with edge probability $a/n$ (within group) and $b/n$ (across). We prove that SDP detects the partition with high probability provided $(a-b)^2/(4d)> 1+o_{d}(1)$, with $d= (a+b)/2$. By comparison, the information theoretic threshold for detecting the hidden partition is $(a-b)^2/(4d)> 1$: SDP is nearly optimal for large bounded average degree. #R##N#Our proof is based on tools from different research areas: $(i)$ A new `higher-rank' Grothendieck inequality for symmetric matrices; $(ii)$ An interpolation method inspired from statistical physics; $(iii)$ An analysis of the eigenvectors of deformed Gaussian random matrices.

Connected through hyperedge HE-1 (induced by source paper "computational hardness of certifying bounds on constrained pca problems"):
  with members:
    - "mean field approximation convex hierarchies and the optimality of correlation rounding a unified perspective"
    - "heterogeneous multireference alignment a single pass approach"
    - "community detection in hypergraphs spiked tensor models and sum of squares"
    - "the lov asz theta function for random regular graphs and community detection in the hard regime"
    - "the power of sum of squares for detecting hidden structures"
    - "bayesian estimation from few samples community detection and related problems"
    - "sum of squares lower bounds for refuting any csp"
    - "a nearly tight sum of squares lower bound for the planted clique problem"

Connected through hyperedge HE-2 (induced by source paper "local statistics semidefinite programming and community detection"):
  with members:
    - "a tight degree 4 sum of squares lower bound for the sherrington kirkpatrick hamiltonian"
    - "vector colorings of random ramanujan and large girth irregular graphs"
    - "computational hardness of certifying bounds on constrained pca problems"
    - "the lov asz theta function for random regular graphs and community detection in the hard regime"
    - "learning from untrusted data"
    - "avoiding imposters and delinquents adversarial crowdsourcing and peer prediction"
    - "exact recovery in the stochastic block model"
    - "community detection thresholds and the weak ramanujan property"

Connected through hyperedge HE-3 (induced by source paper "the sdp value for random two eigenvalue csps"):
  with members:
    - "the threshold for sdp refutation of random regular nae 3sat"
    - "the lov asz theta function for random regular graphs and community detection in the hard regime"
    - "sum of squares lower bounds for refuting any csp"
    - "the backtracking survey propagation algorithm for solving random k sat problems"
    - "strongly refuting random csps below the spectral threshold"
    - "a composition theorem for parity kill number"
    - "spectral redemption in clustering sparse networks"
    - "community detection thresholds and the weak ramanujan property"

Connected through hyperedge HE-4 (induced by source paper "lifting sum of squares lower bounds degree 2 to degree 4"):
  with members:
    - "extended formulation lower bounds for refuting random csps"
    - "the threshold for sdp refutation of random regular nae 3sat"
    - "the power of sum of squares for detecting hidden structures"
    - "sum of squares lower bounds for refuting any csp"
    - "a nearly tight sum of squares lower bound for the planted clique problem"
    - "strongly refuting random csps below the spectral threshold"
    - "improved sum of squares lower bounds for hidden clique and hidden submatrix problems"

Connected through hyperedge HE-5 (induced by source paper "a tight degree 4 sum of squares lower bound for the sherrington kirkpatrick hamiltonian"):
  with members:
    - "computational hardness of certifying bounds on constrained pca problems"
    - "bayesian estimation from few samples community detection and related problems"
    - "a statistical model for tensor pca"
    - "sum of squares proofs and the quest toward optimal algorithms"

Connected through hyperedge HE-6 (induced by source paper "revisiting clustering as matrix factorisation on the stiefel manifold"):
  with members:
    - "dimensionality reduction for k means clustering and low rank approximation"

Connected through hyperedge HE-7 (induced by source paper "message passing algorithms for synchronization problems over compact groups"):
  with members:
    - "finite sample analysis of approximate message passing algorithms"
    - "the projected power method an efficient algorithm for joint alignment from pairwise differences"
    - "mutual information in rank one matrix estimation"
    - "mutual information for symmetric rank one matrix estimation a proof of the replica formula"
    - "phase transitions in sparse pca"
    - "non unique games over compact groups and orientation estimation in cryo em"
    - "mmse of probabilistic low rank matrix estimation universality with respect to the output channel"
    - "information theoretically optimal sparse pca"

Connected through hyperedge HE-8 (induced by source paper "information theoretic thresholds from the cavity method"):
  with members:
    - "planting colourings silently"
    - "mutual information in rank one matrix estimation"
    - "the condensation phase transition in random graph coloring"
    - "asymptotic mutual information for the two groups stochastic block model"
    - "conditioning and covariance on caterpillars"
    - "chasing the k colorability threshold"
    - "on the complexity of random satisfiability problems with planted solutions"
    - "community detection thresholds and the weak ramanujan property"

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)