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: "on the concentration of the number of solutions of random satisfiability formulas"
  Abstract: Let $Z(F)$ be the number of solutions of a random $k$-satisfiability formula $F$ with $n$ variables and clause density $\alpha$. Assume that the probability that $F$ is unsatisfiable is $O(1/\log(n)^{1+\e})$ for $\e>0$. We show that (possibly excluding a countable set of `exceptional' $\alpha$'s) the number of solutions concentrate in the logarithmic scale, i.e., there exists a non-random function $\phi(\alpha)$ such that, for any $\delta>0$, $(1/n)\log Z(F)\in [\phi-\delta,\phi+\delta]$ with high probability. In particular, the assumption holds for all $\alpha<1$, which proves the above concentration claim in the whole satisfiability regime of random $2$-SAT. We also extend these results to a broad class of constraint satisfaction problems. The proof is based on an interpolation technique from spin-glass theory, and on an application of Friedgut's theorem on sharp thresholds for graph properties.

Connected through hyperedge HE-1 (induced by source paper "counting solutions to random cnf formulas"):
  with members:
    - "counting independent sets and colorings on random regular bipartite graphs"
    - "counting hypergraph colorings in the local lemma regime"
    - "sampling random colorings of sparse random graphs"
    - "approximate counting the lovasz local lemma and inference in graphical models"
    - "approximation via correlation decay when strong spatial mixing fails"
    - "new constructive aspects of the lovasz local lemma"
    - "deterministic algorithms for the lovasz local lemma"
    - "a constructive proof of the general lovasz local lemma"

Connected through hyperedge HE-2 (induced by source paper "combining the k cnf and xor phase transitions"):
  with members:
    - "constrained sampling and counting universal hashing meets sat solving"
    - "aspects of statistical physics in computational complexity"
    - "distribution aware sampling and weighted model counting for sat"
    - "balancing scalability and uniformity in sat witness generator"
    - "a scalable approximate model counter"
    - "a scalable and nearly uniform generator of sat witnesses"

Connected through hyperedge HE-3 (induced by source paper "threshold saturation in spatially coupled constraint satisfaction problems"):
  with members:
    - "a simple proof of threshold saturation for coupled scalar recursions"
    - "spatially coupled ensembles universally achieve capacity under belief propagation"
    - "lossy source coding via spatially coupled ldgm ensembles"
    - "chains of mean field models"
    - "wave like solutions of general one dimensional spatially coupled systems"
    - "information theoretically optimal compressed sensing via spatial coupling and approximate message passing"
    - "threshold saturation via spatial coupling why convolutional ldpc ensembles perform so well over the bec"
    - "coupled graphical models and their thresholds"

Connected through hyperedge HE-4 (induced by source paper "frozen variables in random boolean constraint satisfaction problems"):
  with members:
    - "on independent sets in random graphs"
    - "the set of solutions of random xorsat formulae"
    - "catching the k naesat threshold"
    - "the solution space geometry of random linear equations"
    - "reconstruction and clustering in random constraint satisfaction problems"
    - "tight thresholds for cuckoo hashing via xorsat"
    - "decay of correlations for sparse graph error correcting codes"
    - "on the solution space geometry of random constraint satisfaction problems"

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)