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 "asymptotic divergences and strong dichotomy"):
  Abstract: The Schnorr-Stimm dichotomy theorem concerns finite-state gamblers that bet on infinite sequences of symbols taken from a finite alphabet $\Sigma$. #R##N#In this paper we use the Kullback-Leibler divergence to formulate the $\textit{lower asymptotic divergence}$ $\text{div}(S||\alpha)$ of a probability measure $\alpha$ on $\Sigma$ from a sequence $S$ over $\Sigma$ and the $\textit{upper asymptotic divergence}$ $\text{Div}(S||\alpha)$ of $\alpha$ from $S$ in such a way that a sequence $S$ is $\alpha$-normal (meaning that every string $w$ has asymptotic frequency $\alpha(w)$ in $S$) if and only if $\text{Div}(S||\alpha)=0$. We also use the Kullback-Leibler divergence to quantify the $\textit{total risk }$ $\text{Risk}_G(w)$ that a finite-state gambler $G$ takes when betting along a prefix $w$ of $S$. #R##N#Our main theorem is a $\textit{strong dichotomy theorem}$ that uses the above notions to $\textit{quantify}$ the exponential rates of winning and losing on the two sides of the Schnorr-Stimm dichotomy theorem (with the latter routinely extended from normality to $\alpha$-normality). Modulo asymptotic caveats in the paper, our strong dichotomy theorem says that the following two things hold for prefixes $w$ of $S$. #R##N#(1) The infinitely-often exponential rate of winning is $2^{\text{Div}(S||\alpha)|w|}$. #R##N#(2) The exponential rate of loss is $2^{-\text{Risk}_G(w)}$. #R##N#We also use (1) to show that $1-\text{Div}(S||\alpha)/c$, where $c= \log(1/ \min_{a\in\Sigma}\alpha(a))$, is an upper bound on the finite-state $\alpha$-dimension of $S$ and prove the dual fact that $1-\text{div}(S||\alpha)/c$ is an upper bound on the finite-state strong $\alpha$-dimension of $S$.

Includes members:
  Member "automatic kolmogorov complexity and normality revisited":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "automatic supermartingales acting on sequences")
  Member "computing absolutely normal numbers in nearly linear time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "lempel ziv a one bit catastrophe but not a tragedy")
  Member "a divergence formula for randomness and dimension":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "mutual dimension and random sequences")
  Member "dimensions of copeland erdos sequences":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "finite state dimension and real arithmetic")
  Member "dimension in complexity classes":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the incomputability of computable dimension")
  Member "the dimensions of individual strings and sequences":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "who asked us how the theory of computing answers questions about analysis")

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.IT(Information Theory)