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: "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.

Connected through hyperedge HE-1 (induced by source paper "rigorous guarantees for tyler s m estimator via quantum expansion"):
  with members:
    - "spectral analysis of matrix scaling and operator scaling"
    - "operator scaling via geodesically convex optimization invariant theory and polynomial identity testing"
    - "efficient algorithms for tensor scaling quantum marginals and moment polytopes"
    - "alternating minimization scaling algorithms and the null cone problem from invariant theory"
    - "maximum entropy distributions bit complexity and stability"
    - "computing maximum entropy distributions everywhere"
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "a deterministic polynomial time algorithm for non commutative rational identity testing"

Connected through hyperedge HE-2 (induced by source paper "spectral analysis of matrix scaling and operator scaling"):
  with members:
    - "operator scaling via geodesically convex optimization invariant theory and polynomial identity testing"
    - "testing halfspaces over rotation invariant distributions"
    - "much faster algorithms for matrix scaling"
    - "matrix scaling and balancing via box constrained newton s method and interior point methods"
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "a deterministic polynomial time algorithm for non commutative rational identity testing"
    - "algorithms and hardness for robust subspace recovery"
    - "perfect matchings in o n 1 5 time in regular bipartite graphs"

Connected through hyperedge HE-3 (induced by source paper "subspace arrangements graph rigidity and derandomization through submodular optimization"):
  with members:
    - "bipartite perfect matching is in quasi nc"
    - "progress on polynomial identity testing ii"
    - "deterministic polynomial time algorithms for matrix completion problems"

Connected through hyperedge HE-4 (induced by source paper "on a weighted linear matroid intersection algorithm by deg det computation"):
  with members:
    - "constructive noncommutative rank computation in deterministic polynomial time over fields of arbitrary characteristics"

Connected through hyperedge HE-5 (induced by source paper "operator scaling via geodesically convex optimization invariant theory and polynomial identity testing"):
  with members:
    - "alternating minimization scaling algorithms and the null cone problem from invariant theory"
    - "algorithms based on algebras and their applications to isomorphism of polynomials with one secret group isomorphism and polynomial identity testing"
    - "the paulsen problem continuous operator scaling and smoothed analysis"
    - "much faster algorithms for matrix scaling"
    - "matrix scaling and balancing via box constrained newton s method and interior point methods"
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "constructive noncommutative rank computation in deterministic polynomial time over fields of arbitrary characteristics"
    - "non commutative edmonds problem and matrix semi invariants"

Connected through hyperedge HE-6 (induced by source paper "efficient algorithms for tensor scaling quantum marginals and moment polytopes"):
  with members:
    - "operator scaling via geodesically convex optimization invariant theory and polynomial identity testing"
    - "alternating minimization scaling algorithms and the null cone problem from invariant theory"
    - "membership in moment polytopes is in np and conp"
    - "on vanishing of kronecker coefficients"
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "constructive noncommutative rank computation is in deterministic polynomial time"
    - "a deterministic polynomial time algorithm for non commutative rational identity testing"
    - "computing multiplicities of lie group representations"

Connected through hyperedge HE-7 (induced by source paper "recent progress on scaling algorithms and applications"):
  with members:
    - "the paulsen problem continuous operator scaling and smoothed analysis"
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "constructive noncommutative rank computation is in deterministic polynomial time"
    - "non commutative edmonds problem and matrix semi invariants"
    - "explicit lower bounds via geometric complexity theory"
    - "geometric complexity theory and tensor rank"

Connected through hyperedge HE-8 (induced by source paper "alternating minimization scaling algorithms and the null cone problem from invariant theory"):
  with members:
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "non commutative edmonds problem and matrix semi invariants"
    - "understanding alternating minimization for matrix completion"
    - "explicit lower bounds via geometric complexity theory"
    - "geometric complexity theory v equivalence between blackbox derandomization of polynomial identity testing and derandomization of noether s normalization lemma"

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.CC(Computational Complexity)