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 "the maximum mutual information between the output of a binary symmetric channel and a boolean function of its input"):
  Abstract: We prove the Courtade-Kumar conjecture, which states that the mutual information between any Boolean function of an $n$-dimensional vector of independent and identically distributed inputs to a memoryless binary symmetric channel and the corresponding vector of outputs is upper-bounded by $1-\operatorname{H}(p)$, where $\operatorname{H}(p)$ represents the binary entropy function. That is, let $\mathbf{X}=[X_1...X_n]$ be a vector of independent and identically distributed Bernoulli($1/2$) random variables, which are the input to a memoryless binary symmetric channel, with the error probability equal to $0 \leq p \leq 1/2$, and $\mathbf{Y}=[Y_1...Y_n]$ the corresponding output. Let $f:\{0,1\}^n \rightarrow \{0,1\}$ be an $n$-dimensional Boolean function. Then, $\operatorname{MI}(f(\mathbf{X}),\mathbf{Y}) \leq 1-\operatorname{H}(p)$. We provide the proof for the most general case of the conjecture, that is for any $n$-dimensional Boolean function $f$ and for any value of the error probability of the binary symmetric channel, $0 \leq p \leq 1/2$. Our proof employs only basic concepts from information theory, probability theory and transformations of random variables and vectors.

Includes members:
  Member "the most informative boolean function conjecture holds for high noise":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "principal inertia components and applications")
  Member "on the entropy of a noisy function":
    also connected through other hyperedges:
      - Hyperedge HE-2 (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-3 (induced by source paper "guessing with a bit of help")
  Member "an exploration of the role of principal inertia components in information theory":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the courtade kumar conjecture for certain classes of boolean functions")

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)