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: "an n log n lower bound for fourier transform computation in the well conditioned model"
  Abstract: Obtaining a non-trivial (super-linear) lower bound for computation of the Fourier transform in the linear circuit model has been a long standing open problem for over 40 years. #R##N#An early result by Morgenstern from 1973, provides an $\Omega(n \log n)$ lower bound for the unnormalized Fourier transform when the constants used in the computation are bounded. The proof uses a potential function related to a determinant. The result does not explain why the normalized Fourier transform (of unit determinant) should be difficult to compute in the same model. Hence, the result is not scale insensitive. #R##N#More recently, Ailon (2013) showed that if only unitary 2-by-2 gates are used, and additionally no extra memory is allowed, then the normalized Fourier transform requires $\Omega(n\log n)$ steps. This rather limited result is also sensitive to scaling, but highlights the complexity inherent in the Fourier transform arising from introducing entropy, unlike, say, the identity matrix (which is as complex as the Fourier transform using Morgenstern's arguments, under proper scaling). #R##N#In this work we extend the arguments of Ailon (2013). In the first extension, which is also the main contribution, we provide a lower bound for computing any scaling of the Fourier transform. Our restriction is that, the composition of all gates up to any point must be a well conditioned linear transformation. The lower bound is $\Omega(R^{-1}n\log n)$, where $R$ is the uniform condition number. Second, we assume extra space is allowed, as long as it contains information of bounded norm at the end of the computation. #R##N#The main technical contribution is an extension of matrix entropy used in Ailon (2013) for unitary matrices to a potential function computable for any matrix, using Shannon entropy on "quasi-probabilities".

Connected through hyperedge HE-1 (induced by source paper "paraunitary matrices entropy algebraic condition number and fourier computation"):
  with members:
    - "the complexity of computing a fourier perturbation"
    - "the johnson lindenstrauss lemma is optimal for linear dimensionality reduction"
    - "a lower bound for fourier transform computation in a linear model over 2x2 unitary gates using matrix entropy"

Connected through hyperedge HE-2 (induced by source paper "tighter fourier transform complexity tradeoffs"):
  with members:
    - "a lower bound for fourier transform computation in a linear model over 2x2 unitary gates using matrix entropy"
    - "new and improved johnson lindenstrauss embeddings via the restricted isometry 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.CC(Computational Complexity)