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 "discovering the roots uniform closure results for algebraic classes under factoring"):
  Abstract: Newton iteration (NI) is an almost 350 years old recursive formula that approximates a simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) that approximates all the roots simultaneously. In this form, the process yields a better circuit complexity in the case when the number of roots $r$ is small but the multiplicities are exponentially large. Our method sets up a linear system in $r$ unknowns and iteratively builds the roots as formal power series. For an algebraic circuit $f(x_1,\ldots,x_n)$ of size $s$ we prove that each factor has size at most a polynomial in: $s$ and the degree of the squarefree part of $f$. Consequently, if $f_1$ is a $2^{\Omega(n)}$-hard polynomial then any nonzero multiple $\prod_{i} f_i^{e_i}$ is equally hard for arbitrary positive $e_i$'s, assuming that $\sum_i \text{deg}(f_i)$ is at most $2^{O(n)}$. #R##N#It is an old open question whether the class of poly($n$)-sized formulas (resp. algebraic branching programs) is closed under factoring. We show that given a polynomial $f$ of degree $n^{O(1)}$ and formula (resp. ABP) size $n^{O(\log n)}$ we can find a similar size formula (resp. ABP) factor in randomized poly($n^{\log n}$)-time. Consequently, if determinant requires $n^{\Omega(\log n)}$ size formula, then the same can be said about any of its nonzero multiples. #R##N#As part of our proofs, we identify a new property of multivariate polynomial factorization. We show that under a random linear transformation $\tau$, $f(\tau\overline{x})$ completely factors via power series roots. Moreover, the factorization adapts well to circuit complexity analysis. This with allRootsNI are the techniques that help us make progress towards the old open problems, supplementing the large body of classical results and concepts in algebraic circuit factorization (eg. Zassenhaus, J.NT 1969, Kaltofen, STOC 1985-7 \& Burgisser, FOCS 2001).

Includes members:
  Member "algebraic dependencies and pspace algorithms in approximative complexity":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "constructing faithful homomorphisms over fields of finite characteristic")
  Member "the complexity of factors of multivariate polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "algebraic branching programs border complexity and tangent spaces")
  Member "small hitting sets for tiny arithmetic circuits or how to turn bad designs into good":
    also connected through other hyperedges:
      (none)
  Member "on algebraic branching programs of small width":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "algebraic branching programs border complexity and tangent spaces")
  Member "a pspace construction of a hitting set for the closure of small algebraic circuits":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "algebraic dependencies and pspace algorithms in approximative complexity")
  Member "arithmetic circuits with locally low algebraic rank":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "constructing faithful homomorphisms over fields of finite characteristic")
  Member "proof complexity lower bounds from algebraic circuit complexity":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "semi algebraic proofs ips lower bounds and the tau conjecture can a natural number be negative")
  Member "boundaries of vp and vnp":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "algebraic branching programs border complexity and tangent spaces")

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.CC(Computational Complexity)