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 "operator scaling theory and applications"):
  Abstract: In this paper we present a deterministic polynomial time algorithm for testing if a symbolic matrix in non-commuting variables over $\mathbb{Q}$ is invertible or not. The analogous question for commuting variables is the celebrated polynomial identity testing (PIT) for symbolic determinants. In contrast to the commutative case, which has an efficient probabilistic algorithm, the best previous algorithm for the non-commutative setting required exponential time (whether or not randomization is allowed). The algorithm efficiently solves the "word problem" for the free skew field, and the identity testing problem for arithmetic formulae with division over non-commuting variables, two problems which had only exponential-time algorithms prior to this work. #R##N#The main contribution of this paper is a complexity analysis of an existing algorithm due to Gurvits, who proved it was polynomial time for certain classes of inputs. We prove it always runs in polynomial time. The main component of our analysis is a simple (given the necessary known tools) lower bound on central notion of capacity of operators (introduced by Gurvits). We extend the algorithm to actually approximate capacity to any accuracy in polynomial time, and use this analysis to give quantitative bounds on the continuity of capacity (the latter is used in a subsequent paper on Brascamp-Lieb inequalities). #R##N#Symbolic matrices in non-commuting variables, and the related structural and algorithmic questions, have a remarkable number of diverse origins and motivations. They arise independently in (commutative) invariant theory and representation theory, linear algebra, optimization, linear system theory, quantum information theory, approximation of the permanent and naturally in non-commutative algebra. We provide a detailed account of some of these sources and their interconnections.

Includes members:
  Member "bipartite perfect matching is in quasi nc":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "from independent sets and vertex colorings to isotropic spaces and isotropic decompositions")
  Member "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "rigorous guarantees for tyler s m estimator via quantum expansion")
  Member "constructive noncommutative rank computation in deterministic polynomial time over fields of arbitrary characteristics":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on a weighted linear matroid intersection algorithm by deg det computation")
  Member "constructive noncommutative rank computation is in deterministic polynomial time":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "general linear group action on tensors a candidate for post quantum cryptography")
  Member "non commutative edmonds problem and matrix semi invariants":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "from independent sets and vertex colorings to isotropic spaces and isotropic decompositions")
  Member "generalized wong sequences and their applications to edmonds problems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "from independent sets and vertex colorings to isotropic spaces and isotropic decompositions")
  Member "explicit noether normalization for simultaneous conjugation via polynomial identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "a generalized sylvester gallai type theorem for quadratic polynomials")
  Member "quasipolynomial time identity testing of non commutative and read once oblivious algebraic branching programs":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "derandomization and absolute reconstruction for sums of powers of linear forms")

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.CC(Computational Complexity)