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 fourier entropy influence conjecture for extremal classes"):
  Abstract: The Fourier Entropy-Influence (FEI) Conjecture of Friedgut and Kalai states that ${\bf H}[f] \leq C \cdot {\bf I}[f]$ holds for every Boolean function $f$, where ${\bf H}[f]$ denotes the spectral entropy of $f$, ${\bf I}[f]$ is its total influence, and $C > 0$ is a universal constant. Despite significant interest in the conjecture it has only been shown to hold for some classes of Boolean functions such as symmetric functions and read-once formulas. #R##N#In this work, we prove the conjecture for extremal cases, functions with small influence and functions with high entropy. Specifically, we show that: #R##N#* FEI holds for the class of functions with ${\bf I}[f] \leq 2^{-cn}$ with the constant $C = 4 \cdot \frac{c+1}{c}$. Furthermore, proving FEI for a class of functions with ${\bf I}[f] \leq 2^{-s(n)}$ for some $s(n) = o(n)$ will imply FEI for the class of all Boolean functions. #R##N#* FEI holds for the class of functions with ${\bf H}[f] \geq cn$ with the constant $C = \frac{1 + c}{h^{-1}(c^2)}$. Furthermore, proving FEI for a class of functions with ${\bf H}[f] \geq s(n)$ for some $s(n) = o(n)$ will imply FEI for the class of all Boolean functions. #R##N#Additionally, we show that FEI holds for the class of functions with constant $\|\widehat{f}\|_1$, completing the results of Chakhraborty et al. that bounded the entropy of such functions. We also improve the result of Wan et al. for read-k decision trees, from ${\bf H}[f] \leq O(k) \cdot {\bf I}[f]$ to ${\bf H}[f] \leq O(\sqrt{k}) \cdot {\bf I}[f]$. Finally, we suggest a direction for proving FEI for read-k DNFs, and prove the Fourier Min-Entropy/Influence (FMEI) Conjecture for regular read-k DNFs.

Includes members:
  Member "degree and sensitivity tails of two distributions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "alternation sparsity and sensitivity bounds and exponential gaps")
  Member "analysis of boolean functions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "coarse grained complexity for dynamic algorithms")
  Member "a composition theorem for the fourier entropy influence conjecture":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "revisiting bourgain kalai and fourier entropies")

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)