human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "stable super resolution limit and smallest singular value of restricted fourier matrices"):
  Abstract: Super-resolution refers to the process of recovering the locations and amplitudes of a collection of point sources, represented as a discrete measure, given $M+1$ of its noisy low-frequency Fourier coefficients. The recovery process is highly sensitive to noise whenever the distance $\Delta$ between the two closest point sources is less than $1/M$. This paper studies the {\it fundamental difficulty of super-resolution} and the {\it performance guarantees of a subspace method called MUSIC} in the regime that $\Delta<1/M$. #R##N#The most important quantity in our theory is the minimum singular value of the Vandermonde matrix whose nodes are specified by the source locations. Under the assumption that the nodes are closely spaced within several well-separated clumps, we derive a sharp and non-asymptotic lower bound for this quantity. Our estimate is given as a weighted $\ell^2$ sum, where each term only depends on the configuration of each individual clump. This implies that, as the noise increases, the super-resolution capability of MUSIC degrades according to a power law where the exponent depends on the cardinality of the largest clump. Numerical experiments validate our theoretical bounds for the minimum singular value and the resolution limit of MUSIC. #R##N#When there are $S$ point sources located on a grid with spacing $1/N$, the fundamental difficulty of super-resolution can be quantitatively characterized by a min-max error, which is the reconstruction error incurred by the best possible algorithm in the worst-case scenario. We show that the min-max error is closely related to the minimum singular value of Vandermonde matrices, and we provide a non-asymptotic and sharp estimate for the min-max error, where the dominant term is $(N/M)^{2S-1}$.

Includes members:
  Member "the recoverability limit for superresolution via sparsity":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "resolution limit for line spectral estimation theory and algorithm")
  Member "music for single snapshot spectral estimation stability and super resolution":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on the stable resolution limit of total variation regularization for spike deconvolution")
  Member "super resolution extremal functions and the condition number of vandermonde matrices":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "resolution limit for line spectral estimation theory and algorithm")
  Member "near minimax line spectral estimation":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "approximate support recovery of atomic line spectral estimation a tale of resolution and precision")
  Member "towards a mathematical theory of super resolution":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximate support recovery of atomic line spectral estimation a tale of resolution and precision")
  Member "mismatch and resolution in compressive imaging":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "resolution limit for line spectral estimation theory and algorithm")
  Member "coherence pattern guided compressive sensing with unresolved grids":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "conditioning of restricted fourier matrices and super resolution of music")

Question: Please tell me which class the source paper 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.IT(Information Theory)