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 "weak stability of ell_1 minimization methods in sparse data reconstruction"):
  Abstract: As one of the most plausible convex optimization methods for sparse data reconstruction, $\ell_1$-minimization plays a fundamental role in the development of sparse optimization theory. The stability of this method has been addressed in the literature under various assumptions such as restricted isometry property (RIP), null space property (NSP), and mutual coherence. In this paper, we propose a unified means to develop the so-called weak stability theory for $\ell_1$-minimization methods under the condition called weak range space property of a transposed design matrix, which turns out to be a necessary and sufficient condition for the standard $\ell_1$-minimization method to be weakly stable in sparse data reconstruction. The reconstruction error bounds established in this paper are measured by the so-called Robinson's constant. #R##N#We also provide a unified weak stability result for standard $\ell_1$-minimization under several existing compressed-sensing matrix properties. In particular, the weak stability of $\ell_1$-minimization under the constant-free range space property of order $k$ of the transposed design matrix is established for the first time in this paper. Different from the existing analysis, we utilize the classic Hoffman's Lemma concerning the error bound of linear systems as well as the Dudley's theorem concerning the polytope approximation of the unit $\ell_2$-ball to show that $\ell_1$-minimization is robustly and weakly stable in recovering sparse data from inaccurate measurements.

Includes members:
  Member "the gap between the null space property and the restricted isometry property":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "preserving injectivity under subgaussian mappings and its application to compressed sensing")
  Member "1 bit compressive sensing reformulation and rrsp based sign recovery theory":
    also connected through other hyperedges:
      (none)
  Member "sparse representation of a polytope and recovery of sparse signals and low rank matrices":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the importance of phase in complex compressive sensing")
  Member "one condition for solution uniqueness and robustness of both l1 synthesis and l1 analysis minimizations":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "exact matrix completion based on low rank hankel structure in the fourier domain")
  Member "sharp rip bound for sparse signal and low rank matrix recovery":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a deterministic convergence framework for exact non convex phase retrieval")
  Member "new bounds for restricted isometry constants":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "the use of mutual coherence to prove ell 1 ell 0 equivalence in classification problems")
  Member "on polar polytopes and the recovery of sparse representations":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "relaxed recovery conditions for omp ols by exploiting both coherence and decay")

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)