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 "on the most informative boolean functions of the very noisy channel"):
  Abstract: Let $X^n$ be an independently identically distributed Bernoulli $(1/2)$ random variables and let $Y^n$ be the result of passing $X^n$ through a binary symmetric channel (BSC) with crossover probability $\alpha$. For any Boolean function $f: \{0,1\}^n\to\{0,1\}$, Courtade and Kumar postulated that $I(f(X^n);Y^n)\le 1-H(\alpha)$. In this paper, we prove, in a purely mathematical point of view, that the conjecture is true in high noise regime by showing that $H(\alpha)-H(f(X^n)|Y^n)\le1-H(f(X^n))$ holds for $\alpha\in[\frac12-\delta,\frac12+\delta]$, where $\delta>0$ is some universally small constant. We first point out that in high noise regime, a function $f$ is more informative if the second derivative of $H(\alpha)-H(f(X^n)|Y^n)$ has a larger value at $\alpha=\frac12$. Then we show that, the ratio spectrum of $f^{-1}(0)$, an integer sequence which characterizes the structure of $f^{-1}(0)$, is the fundamental metric that determines the second derivative of $H(\alpha)-H(f(X^n)|Y^n)$ evaluated at $\alpha=\frac12$. With $|f^{-1}(0)|$ fixed, lex function is a locally most informative function for the very noisy BSC. The dictator function $f(X^n)=X_i, (1\le i\le n)$, with $i=1$ being a special case of lex function $|f^{-1}(0)|=2^{n-1}$, is the globally most informative function for the very noisy BSC as it is the only type of functions that maximize the second derivative of $H(\alpha)-H(f(X^n)|Y^n)$ evaluated at $\alpha=\frac12$ to $0$ over all possible $|f^{-1}(0)|$.

Includes members:
  Member "how to quantize n outputs of a binary symmetric channel to n 1 bits":
    also connected through other hyperedges:
      (none)
  Member "on the entropy of a noisy function":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "guessing with a bit of help")
  Member "an improved upper bound for the most informative boolean function conjecture":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "guessing with a bit of help")

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)