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: "formal proofs for nonlinear optimization"
  Abstract: We present a formally verified global optimization framework. Given a semialgebraic or transcendental function $f$ and a compact semialgebraic domain $K$, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of $f$ over $K$. This method allows to bound in a modular way some of the constituents of $f$ by suprema of quadratic forms with a well chosen curvature. Thus, we reduce the initial goal to a hierarchy of semialgebraic optimization problems, solved by sums of squares relaxations. Our implementation tool interleaves semialgebraic approximations with sums of squares witnesses to form certificates. It is interfaced with Coq and thus benefits from the trusted arithmetic available inside the proof assistant. This feature is used to produce, from the certificates, both valid underestimators and lower bounds for each approximated constituent. The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of multivariate transcendental inequalities. We illustrate the performance of our formal framework on some of these inequalities as well as on examples from the global optimization literature.

Connected through hyperedge HE-1 (induced by source paper "exact optimization via sums of nonnegative circuits and sums of am gm exponentials"):
  with members:
    - "on exact polya hilbert artin and putinar s representations"
    - "on exact polya and putinar s representations"
    - "realcertify a maple package for certifying non negativity"
    - "certified roundoff error bounds using semidefinite programming"

Connected through hyperedge HE-2 (induced by source paper "algorithms for weighted sums of squares decomposition of non negative univariate polynomials"):
  with members:
    - "symbolic numeric tools for analytic combinatorics in several variables"
    - "probabilistic algorithm for polynomial optimization over a real algebraic set"
    - "from approximate factorization to root isolation with application to cylindrical algebraic decomposition"
    - "univariate real root isolation in an extension field"

Connected through hyperedge HE-3 (induced by source paper "piece wise quadratic approximations of arbitrary error functions for fast and robust machine learning"):
  with members:
    - "smoothed low rank and sparse matrix recovery by iteratively reweighted least squares minimization"
    - "vidaexpert user friendly tool for nonlinear visualization and analysis of multidimensional vectorial data"
    - "principal manifolds and graphs in practice from molecular biology to dynamical systems"
    - "principal graphs and manifolds"
    - "robust principal component analysis"
    - "topological grammars for data approximation"

Connected through hyperedge HE-4 (induced by source paper "certified roundoff error bounds using semidefinite programming"):
  with members:
    - "nlcertify a tool for formal nonlinear optimization"
    - "formal verification of nonlinear inequalities with taylor interval approximations"
    - "a logical product approach to zonotope intersection"
    - "certification of bounds on expressions involving rounded operators"
    - "the octagon abstract domain"
    - "a static analyzer for large safety critical software"

Connected through hyperedge HE-5 (induced by source paper "certifying solutions to overdetermined and singular polynomial systems over q"):
  with members:
    - "deflation and certified isolation of singular zeros of polynomial systems"

Connected through hyperedge HE-6 (induced by source paper "nlcertify a tool for formal nonlinear optimization"):
  with members:
    - "formal verification of nonlinear inequalities with taylor interval approximations"

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.LO(Logic in Computer Science)