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: "precise phase transition of total variation minimization"
  Abstract: Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as $\ell_1$ minimization and nuclear norm minimization are well understood through recent years' research. However, rigorously characterizing the phase transition of total variation (TV) minimization in recovering sparse-gradient signal is still open. In this paper, we fully characterize the phase transition curve of the TV minimization. Our proof builds on Donoho, Johnstone and Montanari's conjectured phase transition curve for the TV approximate message passing algorithm (AMP), together with the linkage between the minmax Mean Square Error of a denoising problem and the high-dimensional convex geometry for TV minimization.

Connected through hyperedge HE-1 (induced by source paper "compressed sensing with 1d total variation breaking sample complexity barriers via non uniform recovery"):
  with members:
    - "total variation minimization in compressed sensing"
    - "ell 1 analysis minimization and generalized co sparsity when does recovery succeed"
    - "convex recovery of a structured signal from independent random linear measurements"
    - "the generalized lasso with non linear observations"
    - "robust analysis l1 recovery from gaussian measurements and total variation minimization"
    - "sharp mse bounds for proximal denoising"
    - "stable image reconstruction using total variation minimization"
    - "stable and robust sampling strategies for compressive imaging"

Connected through hyperedge HE-2 (induced by source paper "living near the edge a lower bound on the phase transition of total variation minimization"):
  with members:
    - "on the error in phase transition computations for compressed sensing"
    - "sample complexity of total variation minimization"
    - "total variation minimization in compressed sensing"
    - "ell 1 analysis minimization and generalized co sparsity when does recovery succeed"
    - "convex recovery of a structured signal from independent random linear measurements"
    - "robust analysis l1 recovery from gaussian measurements and total variation minimization"
    - "corrupted sensing novel guarantees for separating structured signals"
    - "on the effective measure of dimension in the analysis cosparse model"

Connected through hyperedge HE-3 (induced by source paper "on the error in phase transition computations for compressed sensing"):
  with members:
    - "exploiting prior information in block sparse signals"
    - "ell 1 analysis minimization and generalized co sparsity when does recovery succeed"
    - "corrupted sensing novel guarantees for separating structured signals"
    - "living on the edge phase transitions in convex programs with random data"
    - "sharp mse bounds for proximal denoising"
    - "simple bounds for recovering low complexity models"
    - "accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising"
    - "various thresholds for ell_1 optimization in compressed sensing"

Connected through hyperedge HE-4 (induced by source paper "ell 1 analysis minimization and generalized co sparsity when does recovery succeed"):
  with members:
    - "learning co sparse analysis operators with separable structures"
    - "compressive sensing with redundant dictionaries and structured measurements"
    - "robust analysis l1 recovery from gaussian measurements and total variation minimization"
    - "structure dependent sampling in compressed sensing theoretical guarantees for tight frames"
    - "on the effective measure of dimension in the analysis cosparse model"
    - "projection onto the cosparse set is np hard"
    - "analysis operator learning and its application to image reconstruction"
    - "stable image reconstruction using total variation minimization"

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.IT(Information Theory)