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: "fast computation of the rank profile matrix and the generalized bruhat decomposition"
  Abstract: The row (resp. column) rank profile of a matrix describes the stair-case shape of its row (resp. column) echelon form. We here propose a new matrix invariant, the rank profile matrix, summarizing all information on the row and column rank profiles of all the leading sub-matrices. We show that this normal form exists and is unique over any ring, provided that the notion of McCoy's rank is used, in the presence of zero divisors. We then explore the conditions for a Gaussian elimination algorithm to compute all or part of this invariant, through the corresponding PLUQ decomposition. This enlarges the set of known Elimination variants that compute row or column rank profiles. As a consequence a new Crout base case variant significantly improves the practical efficiency of previously known implementations over a finite field. With matrices of very small rank, we also generalize the techniques of Storjohann and Yang to the computation of the rank profile matrix, achieving an $(r^\omega+mn)^{1+o(1)}$ time complexity for an $m \times  n$ matrix of rank $r$, where $\omega$ is the exponent of matrix multiplication. Finally, by give connections to the Bruhat decomposition, and several of its variants and generalizations. Thus, our algorithmic improvements for the PLUQ factorization, and their implementations, directly apply to these decompositions. In particular, we show how a PLUQ decomposition revealing the rank profile matrix also reveals both a row and a column echelon form of the input matrix or of any of its leading sub-matrices, by a simple post-processing made of row and column permutations.

Connected through hyperedge HE-1 (induced by source paper "elimination based certificates for triangular equivalence and rank profiles"):
  with members:
    - "linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix"
    - "essentially optimal interactive certificates in linear algebra"
    - "simultaneous computation of the row and column rank profiles"
    - "fast matrix rank algorithms and applications"
    - "rank profile revealing gaussian elimination and the cup matrix decomposition"

Connected through hyperedge HE-2 (induced by source paper "symmetric indefinite triangular factorization revealing the rank profile matrix"):
  with members:
    - "computing the rank profile matrix"

Connected through hyperedge HE-3 (induced by source paper "certificates for triangular equivalence and rank profiles"):
  with members:
    - "linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix"
    - "computing the rank profile matrix"
    - "essentially optimal interactive certificates in linear algebra"
    - "simultaneous computation of the row and column rank profiles"
    - "fast matrix rank algorithms and applications"
    - "rank profile revealing gaussian elimination and the cup matrix decomposition"

Connected through hyperedge HE-4 (induced by source paper "time and space efficient generators for quasiseparable matrices"):
  with members:
    - "computing with quasiseparable matrices"
    - "computing the rank profile matrix"
    - "powers of tensors and fast matrix multiplication"
    - "simultaneous computation of the row and column rank profiles"
    - "rank profile revealing gaussian elimination and the cup matrix decomposition"
    - "fast generalized bruhat decomposition"

Connected through hyperedge HE-5 (induced by source paper "computing with quasiseparable matrices"):
  with members:
    - "computing the rank profile matrix"
    - "simultaneous computation of the row and column rank profiles"
    - "fast generalized bruhat decomposition"

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.SC(Symbolic Computation)