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: "essentially optimal interactive certificates in linear algebra"
  Abstract: Certificates to a linear algebra computation are additional data structures for each output, which can be used by a---possibly randomized---verification algorithm that proves the correctness of each output. The certificates are essentially optimal if the time (and space) complexity of verification is essentially linear in the input size $N$, meaning $N$ times a factor $N^{o(1)}$, i.e., a factor $N^{\eta(N)}$ with $\lim_{N\to \infty} \eta(N)$ $=$ $0$. We give algorithms that compute essentially optimal certificates for the positive semidefiniteness, Frobenius form, characteristic and minimal polynomial of an $n\times n$ dense integer matrix $A$. Our certificates can be verified in Monte-Carlo bit complexity $(n^2 \lognormA)^{1+o(1)}$, where $\lognormA$ is the bit size of the integer entries, solving an open problem in [Kaltofen, Nehring, Saunders, Proc.\ ISSAC 2011] subject to computational hardness assumptions. Second, we give algorithms that compute certificates for the rank of sparse or structured $n\times n$ matrices over an abstract field, whose Monte Carlo verification complexity is $2$ matrix-times-vector products $+$ $n^{1+o(1)}$ arithmetic operations in the field. For example, if the $n\times n$ input matrix is sparse with $n^{1+o(1)}$ non-zero entries, our rank certificate can be verified in $n^{1+o(1)}$ field operations. This extends also to integer matrices with only an extra $||A||^{1+o(1)}$ factor. All our certificates are based on interactive verification protocols with the interaction removed by a Fiat-Shamir identification heuristic. The validity of our verification procedure is subject to standard computational hardness assumptions from cryptography.

Connected through hyperedge HE-1 (induced by source paper "elimination based certificates for triangular equivalence and rank profiles"):
  with members:
    - "fast computation of the rank profile matrix and the generalized bruhat decomposition"
    - "linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix"
    - "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 "lu factorization with errors"):
  with members:
    - "error correction in fast matrix multiplication and inverse"
    - "what can and can t we do with sparse polynomials"
    - "certificates for triangular equivalence and rank profiles"
    - "linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix"
    - "efficiently correcting matrix products"
    - "powers of tensors and fast matrix multiplication"
    - "parallel computation of echelon forms"
    - "simultaneous computation of the row and column rank profiles"

Connected through hyperedge HE-3 (induced by source paper "error correction in fast matrix multiplication and inverse"):
  with members:
    - "certificates for triangular equivalence and rank profiles"
    - "linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix"
    - "efficiently correcting matrix products"
    - "powers of tensors and fast matrix multiplication"
    - "faster sparse multivariate polynomial interpolation of straight line programs"
    - "faster polynomial multiplication over finite fields"
    - "faster algorithms for rectangular matrix multiplication"
    - "fast matrix rank algorithms and applications"

Connected through hyperedge HE-4 (induced by source paper "certification of minimal approximant bases"):
  with members:
    - "certificates for triangular equivalence and rank profiles"
    - "fast computation of minimal interpolation bases in popov form for arbitrary shifts"
    - "linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix"
    - "powers of tensors and fast matrix multiplication"

Connected through hyperedge HE-5 (induced by source paper "certificates for triangular equivalence and rank profiles"):
  with members:
    - "fast computation of the rank profile matrix and the generalized bruhat decomposition"
    - "linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix"
    - "computing the rank profile matrix"
    - "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-6 (induced by source paper "linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix"):
  with members:
    - "time optimal interactive proofs for circuit evaluation"

Connected through hyperedge HE-7 (induced by source paper "selecting algorithms for black box matrices checking for matrix properties that can simplify computations"):
  with members:
    - "linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix"

Connected through hyperedge HE-8 (induced by source paper "interactive certificate for the verification of wiedemann s krylov sequence application to the certification of the determinant the minimal and the characteristic polynomials of sparse matrices"):
  with members:
    - "time optimal interactive proofs for circuit evaluation"

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)