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 "near log convexity of measured heat in discrete time and consequences"):
  Abstract: Let $u,v \in \mathbb{R}^\Omega_+$ be positive unit vectors and $S\in\mathbb{R}^{\Omega\times\Omega}_+$ be a symmetric substochastic matrix. For an integer $t\ge 0$, let $m_t = \smash{\left\langle v,S^tu\right\rangle}$, which we view as the heat measured by $v$ after an initial heat configuration $u$ is let to diffuse for $t$ time steps according to $S$. Since $S$ is entropy improving, one may intuit that $m_t$ should not change too rapidly over time. We give the following formalizations of this intuition. #R##N#We prove that $m_{t+2} \ge m_t^{1+2/t}\!,$ an inequality studied earlier by Blakley and Dixon (also Erdős and Simonovits) for $u=v$ and shown true under the restriction $m_t\ge e^{-4t}$. Moreover we prove that for any $\epsilon>0$, a stronger inequality $m_{t+2} \ge t^{1-\epsilon}\cdot \smash{m_t^{1+2/t}}$ holds unless $m_{t+2}m_{t-2}\ge \delta m_t^2$ for some $\delta$ that depends on $\epsilon$ only. Phrased differently, $\forall \epsilon> 0, \exists \delta> 0$ such that $\forall S,u,v$ \begin{equation*} \frac{m_{t+2}}{m_{t}^{1+2/t}}\ge \min\left\{t^{1-\epsilon}, \delta\frac{m_t^{1-2/t}}{m_{t-2}}\right\}, \quad \forall t \ge 2, \end{equation*} which can be viewed as a truncated log-convexity statement. #R##N#Using this inequality, we answer two related open questions in complexity theory: Any property tester for $k$-linearity requires $\Omega(k\log k)$ queries and the randomized communication complexity of the $k$-Hamming distance problem is $\Omega(k\log k)$. Further we show that any randomized parity decision tree computing $k$-Hamming weight has size $\exp\left(\Omega(k\log k)\right)$.

Includes members:
  Member "on the communication complexity of sparse set disjointness and exists equal problems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the communication complexity of set intersection and multiple equality testing")
  Member "the non adaptive query complexity of testing k parities":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "an exponential speedup in parallel running time for submodular maximization without loss in approximation")
  Member "spectral norm of symmetric functions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "dual polynomials and communication complexity of textsf xor functions")
  Member "lower bounds on information complexity via zero communication protocols and applications":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "query to communication lifting using low discrepancy gadgets")
  Member "an optimal lower bound on the communication complexity of gap hamming distance":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximate mathbb f _2 sketching of valuation 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.CC(Computational Complexity)