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: "critical points and gr obner bases the unmixed case"
  Abstract: We consider the problem of computing critical points of the restriction of a polynomial map to an algebraic variety. This is of first importance since the global minimum of such a map is reached at a critical point. Thus, these points appear naturally in non-convex polynomial optimization which occurs in a wide range of scientific applications (control theory, chemistry, economics,...). Critical points also play a central role in recent algorithms of effective real algebraic geometry. Experimentally, it has been observed that Gr\"obner basis algorithms are efficient to compute such points. Therefore, recent software based on the so-called Critical Point Method are built on Gr\"obner bases engines. Let $f_1,..., f_p$ be polynomials in $ \Q[x_1,..., x_n]$ of degree $D$, $V\subset\C^n$ be their complex variety and $\pi_1$ be the projection map $(x_1,.., x_n)\mapsto x_1$. The critical points of the restriction of $\pi_1$ to $V$ are defined by the vanishing of $f_1,..., f_p$ and some maximal minors of the Jacobian matrix associated to $f_1,..., f_p$. Such a system is algebraically structured: the ideal it generates is the sum of a determinantal ideal and the ideal generated by $f_1,..., f_p$. We provide the first complexity estimates on the computation of Gr\"obner bases of such systems defining critical points. We prove that under genericity assumptions on $f_1,..., f_p$, the complexity is polynomial in the generic number of critical points, i.e. $D^p(D-1)^{n-p}{{n-1}\choose{p-1}}$. More particularly, in the quadratic case D=2, the complexity of such a Gr\"obner basis computation is polynomial in the number of variables $n$ and exponential in $p$. We also give experimental evidence supporting these theoretical results.

Connected through hyperedge HE-1 (induced by source paper "solving determinantal systems using homotopy techniques"):
  with members:
    - "critical point computations on smooth varieties degree and complexity bounds"
    - "a polyhedral method to compute all affine solution sets of sparse polynomial systems"
    - "a nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets"
    - "probabilistic algorithm for polynomial optimization over a real algebraic set"
    - "on the complexity of the generalized minrank problem"

Connected through hyperedge HE-2 (induced by source paper "bit complexity for multi homogeneous polynomial system solving application to polynomial minimization"):
  with members:
    - "solving rank constrained semidefinite programs in exact arithmetic"
    - "symbolic numeric tools for analytic combinatorics in several variables"
    - "powers of tensors and fast matrix multiplication"
    - "a nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets"
    - "on the complexity of the multivariate resultant"
    - "intrinsic complexity estimates in polynomial optimization"
    - "probabilistic algorithm for polynomial optimization over a real algebraic set"
    - "multihomogeneous resultant formulae for systems with scaled support"

Connected through hyperedge HE-3 (induced by source paper "determinantal sets singularities and application to optimal control in medical imagery"):
  with members:
    - "data discriminants of likelihood equations"
    - "real root finding for low rank linear matrices"
    - "real root finding for rank defects in linear hankel matrices"
    - "real root finding for determinants of linear matrices"
    - "on the complexity of the generalized minrank problem"

Connected through hyperedge HE-4 (induced by source paper "critical point computations on smooth varieties degree and complexity bounds"):
  with members:
    - "a nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets"
    - "probabilistic algorithm for polynomial optimization over a real algebraic set"
    - "on the complexity of the generalized minrank problem"

Connected through hyperedge HE-5 (induced by source paper "computing small certificates of inconsistency of quadratic fewnomial systems"):
  with members:
    - "a nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets"
    - "probabilistic algorithm for polynomial optimization over a real algebraic set"
    - "on the complexity of the generalized minrank problem"

Connected through hyperedge HE-6 (induced by source paper "real root finding for low rank linear matrices"):
  with members:
    - "sparse fglm algorithms"
    - "determinantal sets singularities and application to optimal control in medical imagery"
    - "bit complexity for multi homogeneous polynomial system solving application to polynomial minimization"
    - "real root finding for rank defects in linear hankel matrices"
    - "real root finding for determinants of linear matrices"
    - "polynomial systems solving by fast linear algebra"
    - "a nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets"
    - "probabilistic algorithm for polynomial optimization over a real algebraic set"

Connected through hyperedge HE-7 (induced by source paper "real root finding for rank defects in linear hankel matrices"):
  with members:
    - "real root finding for low rank linear matrices"
    - "real root finding for determinants of linear matrices"
    - "a nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets"
    - "probabilistic algorithm for polynomial optimization over a real algebraic set"

Connected through hyperedge HE-8 (induced by source paper "real root finding for determinants of linear matrices"):
  with members:
    - "sparse fglm algorithms"
    - "polynomial systems solving by fast linear algebra"
    - "a nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets"
    - "on the complexity of the generalized minrank problem"

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)