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 "the paulsen problem continuous operator scaling and smoothed analysis"):
  Abstract: The Paulsen problem is a basic open problem in operator theory: Given vectors $u_1, \ldots, u_n \in \mathbb R^d$ that are $\epsilon$-nearly satisfying the Parseval's condition and the equal norm condition, is it close to a set of vectors $v_1, \ldots, v_n \in \mathbb R^d$ that exactly satisfy the Parseval's condition and the equal norm condition? Given $u_1, \ldots, u_n$, the squared distance (to the set of exact solutions) is defined as $\inf_{v} \sum_{i=1}^n \| u_i - v_i \|_2^2$ where the infimum is over the set of exact solutions. Previous results show that the squared distance of any $\epsilon$-nearly solution is at most $O({\rm{poly}}(d,n,\epsilon))$ and there are $\epsilon$-nearly solutions with squared distance at least $\Omega(d\epsilon)$. The fundamental open question is whether the squared distance can be independent of the number of vectors $n$. #R##N#We answer this question affirmatively by proving that the squared distance of any $\epsilon$-nearly solution is $O(d^{13/2} \epsilon)$. Our approach is based on a continuous version of the operator scaling algorithm and consists of two parts. First, we define a dynamical system based on operator scaling and use it to prove that the squared distance of any $\epsilon$-nearly solution is $O(d^2 n \epsilon)$. Then, we show that by randomly perturbing the input vectors, the dynamical system will converge faster and the squared distance of an $\epsilon$-nearly solution is $O(d^{5/2} \epsilon)$ when $n$ is large enough and $\epsilon$ is small enough. To analyze the convergence of the dynamical system, we develop some new techniques in lower bounding the operator capacity, a concept introduced by Gurvits to analyze the operator scaling algorithm.

Includes members:
  Member "operator scaling via geodesically convex optimization invariant theory and polynomial identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "rigorous guarantees for tyler s m estimator via quantum expansion")
  Member "much faster algorithms for matrix scaling":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "flows in almost linear time via adaptive preconditioning")
  Member "matrix scaling and balancing via box constrained newton s method and interior point methods":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "flows in almost linear time via adaptive preconditioning")
  Member "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "rigorous guarantees for tyler s m estimator via quantum expansion")
  Member "operator scaling theory and applications":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "rigorous guarantees for tyler s m estimator via quantum expansion")
  Member "a deterministic polynomial time algorithm for non commutative rational identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "rigorous guarantees for tyler s m estimator via quantum expansion")
  Member "algorithms and hardness for robust subspace recovery":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "list decodable subspace recovery")
  Member "fingerprinting with equiangular tight frames":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "kesten mckay law for random subensembles of paley equiangular tight frames")

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.DS(Data Structures and Algorithms)