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: "some closure results for polynomial factorization and applications"
  Abstract: In a sequence of seminal results in the 80's, Kaltofen showed that the complexity class VP is closed under taking factors. A natural question in this context is to understand if other natural classes of multivariate polynomials, for instance, arithmetic formulas, algebraic branching programs, bounded depth arithmetic circuits or the class VNP, are closed under taking factors. #R##N#In this paper, we show that all factors of degree at most $\log^a n$ of polynomials with poly(n) size depth $k$ circuits have poly(n) size circuits of depth at most $O(k + a)$. This partially answers a question of Shpilka-Yehudayoff and has applications to hardness-randomness tradeoffs for bounded depth arithmetic circuits. More precisely, this shows that a superpolynomial lower bound for bounded depth arithmetic circuits, for a family of explicit polynomials of degree poly$(\log n)$ implies deterministic sub-exponential time algorithms for polynomial identity testing (PIT) for bounded depth arithmetic circuits. This is incomparable to a beautiful result of Dvir et al., where they showed that super-polynomial lower bounds for constant depth arithmetic circuits for any explicit family of polynomials (of potentially high degree) implies sub-exponential time deterministic PIT for bounded depth circuits of bounded individual degree. Thus, we remove the "bounded individual degree" condition in [DSY09] at the cost of strengthening the hardness assumption to hold for polynomials of low degree. #R##N#As direct applications of our techniques, we also show that the complexity class VNP is closed under taking factors, thereby confirming a conjecture of B\"urgisser and get an alternate proof of the fact (first shown by Dutta et al.) that if a polynomial $Q$ of degree at most $d$ divides a polynomial $P$ computable by a formula of size $s$, then $Q$ has a formula of size at most poly$(s, d^{\log d}, deg(P))$.

Connected through hyperedge HE-1 (induced by source paper "schur polynomials do not have small formulas if the determinant doesn t"):
  with members:
    - "closure of vp under taking factors a short and simple proof"
    - "discovering the roots uniform closure results for algebraic classes under factoring"
    - "rectangular kronecker coefficients and plethysms in geometric complexity theory"
    - "homogeneous formulas and symmetric polynomials"

Connected through hyperedge HE-2 (induced by source paper "closure of vp under taking factors a short and simple proof"):
  with members:
    - "the complexity of factors of multivariate polynomials"
    - "discovering the roots uniform closure results for algebraic classes under factoring"

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.CC(Computational Complexity)