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 extrapolation of analytic functions"):
  Abstract: This paper examines the problem of extrapolation of an analytic function for $x > 1$ given perturbed samples from an equally spaced grid on $[-1,1]$. Mathematical folklore states that extrapolation is in general hopelessly ill-conditioned, but we show that a more precise statement carries an interesting nuance. For a function $f$ on $[-1,1]$ that is analytic in a Bernstein ellipse with parameter $\rho > 1$, and for a uniform perturbation level $\epsilon$ on the function samples, we construct an asymptotically best extrapolant $e(x)$ as a least squares polynomial approximant of degree $M^*$ given explicitly. We show that the extrapolant $e(x)$ converges to $f(x)$ pointwise in the interval $I_\rho\in[1,(\rho+\rho^{-1})/2)$ as $\epsilon \to 0$, at a rate given by a $x$-dependent fractional power of $\epsilon$. More precisely, for each $x \in I_{\rho}$ we have #R##N#\[ #R##N#|f(x) - e(x)| = \mathcal{O}\left( \epsilon^{-\log r(x) / \log\rho} \right), \qquad\qquad r(x) = \frac{x+\sqrt{x^2-1}}{\rho}, #R##N#\] up to log factors, provided that the oversampling conditioning is satisfied. That is, #R##N#\[ #R##N#M^* \leq \frac{1}{2} \sqrt{N}, #R##N#\] which is known to be needed from approximation theory. In short, extrapolation enjoys a weak form of stability, up to a fraction of the characteristic smoothness length. The number of function samples, $N+1$, does not bear on the size of the extrapolation error provided that it obeys the oversampling condition. We also show that one cannot construct an asymptotically more accurate extrapolant from $N+1$ equally spaced samples than $e(x)$, using any other linear or nonlinear procedure. The proofs involve original statements on the stability of polynomial approximation in the Chebyshev basis from equally spaced samples and these are expected to be of independent interest.

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 "super resolution via superset selection and pruning":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "compressive spectral estimation with single snapshot esprit stability and resolution")
  Member "towards a mathematical theory of super resolution":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "approximate support recovery of atomic line spectral estimation a tale of resolution and precision")

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)