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: "combining the k cnf and xor phase transitions"
  Abstract: The runtime performance of modern SAT solvers on random $k$-CNF formulas is deeply connected with the 'phase-transition' phenomenon seen empirically in the satisfiability of random $k$-CNF formulas. Recent universal hashing-based approaches to sampling and counting crucially depend on the runtime performance of SAT solvers on formulas expressed as the conjunction of both $k$-CNF and XOR constraints (known as $k$-CNF-XOR formulas), but the behavior of random $k$-CNF-XOR formulas is unexplored in prior work. In this paper, we present the first study of the satisfiability of random $k$-CNF-XOR formulas. We show empirical evidence of a surprising phase-transition that follows a linear trade-off between $k$-CNF and XOR constraints. Furthermore, we prove that a phase-transition for $k$-CNF-XOR formulas exists for $k = 2$ and (when the number of $k$-CNF constraints is small) for $k > 2$.

Connected through hyperedge HE-1 (induced by source paper "quantitative verification of neural networks and its security applications"):
  with members:
    - "phase transition behavior of cardinality and xor constraints"
    - "adversarial examples are a natural consequence of test error in noise"
    - "strip a defence against trojan attacks on deep neural networks"
    - "the curse of concentration in robust learning evasion and poisoning attacks from concentration of measure"
    - "formal security analysis of neural networks using symbolic intervals"
    - "a dual approach to scalable verification of deep networks"
    - "the secret sharer measuring unintended neural network memorization extracting secrets"
    - "adversarial spheres"

Connected through hyperedge HE-2 (induced by source paper "graph colouring meets deep learning effective graph neural network models for combinatorial problems"):
  with members:
    - "learning a sat solver from single bit supervision"
    - "machine learning for combinatorial optimization a methodological tour d horizon"
    - "learning to solve np complete problems a graph neural network for decision tsp"
    - "recurrent relational networks for complex relational reasoning"
    - "relational inductive biases deep learning and graph networks"
    - "recurrent relational networks"
    - "neural message passing for quantum chemistry"
    - "very deep convolutional networks for large scale image recognition"

Connected through hyperedge HE-3 (induced by source paper "phase transition behavior of cardinality and xor constraints"):
  with members:
    - "the hard problems are almost everywhere for random cnf xor formulas"
    - "property driven fence insertion using reorder bounded model checking"
    - "distribution aware sampling and weighted model counting for sat"
    - "a scalable approximate model counter"
    - "taming the curse of dimensionality discrete integration by hashing and optimization"
    - "list decoding of polar codes"
    - "probabilistic planning via heuristic forward search and weighted model counting"

Connected through hyperedge HE-4 (induced by source paper "fouriersat a fourier expansion based algebraic framework for solving hybrid boolean constraints"):
  with members:
    - "phase transition behavior of cardinality and xor constraints"
    - "on nonconvex optimization for machine learning gradients stochasticity and saddle points"
    - "variable elimination in the fourier domain"
    - "escaping from saddle points online stochastic gradient for tensor decomposition"
    - "sat modulo monotonic theories"
    - "analysis of boolean functions"

Connected through hyperedge HE-5 (induced by source paper "problem solving at the edge of chaos entropy puzzles and the sudoku freezing transition"):
  with members:
    - "computational red teaming in a sudoku solving context neural network based skill representation and acquisition"
    - "the backtracking survey propagation algorithm for solving random k sat problems"
    - "the condensation phase transition in random graph coloring"
    - "difficulty rating of sudoku puzzles an overview and evaluation"
    - "aspects of statistical physics in computational complexity"
    - "on the role of working memory in trading off skills and situation awareness in sudoku"
    - "there is no 16 clue sudoku solving the sudoku minimum number of clues problem"
    - "view based propagator derivation"

Connected through hyperedge HE-6 (induced by source paper "bit vector model counting using statistical estimation"):
  with members:
    - "the hard problems are almost everywhere for random cnf xor formulas"
    - "sound probabilistic sat with projection"
    - "approximate probabilistic inference via word level counting"
    - "approximate counting in smt and value estimation for probabilistic programs"
    - "a scalable approximate model counter"
    - "the good old davis putnam procedure helps counting models"

Connected through hyperedge HE-7 (induced by source paper "general bounds on satisfiability thresholds for random csps via fourier analysis"):
  with members:
    - "beating the random assignment on constraint satisfaction problems of bounded degree"
    - "analysis of boolean functions"
    - "catching the k naesat threshold"
    - "reconstruction and clustering in 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)