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 "broadcasting on random directed acyclic graphs"):
  Abstract: We study the following generalization of the well-known model of broadcasting on trees. Consider an infinite directed acyclic graph (DAG) with a unique source vertex    $X$   . Let the collection of vertices at distance    $k$    from    $X$    be called the    $k$   th layer, and suppose every non-source vertex has indegree    $d \geq 2$   . At layer 0, the source vertex is given a random bit. At layer    $k\geq 1$   , each vertex receives    $d$    bits from its parents in the    $(k-1)$   th layer, which are transmitted along edges that are independent binary symmetric channels (BSCs) with crossover probability    $\delta \in \left({0,\frac {1}{2}}\right)$   . Each vertex combines its    $d$    noisy inputs using a deterministic    $d$   -ary Boolean processing function that generates the value at the vertex. The goal is to be able to reconstruct the original bit    $X$    with probability of error bounded away from    $\frac {1}{2}$    using the values of all vertices at an arbitrarily deep layer    $k$   . This question is closely related to models of reliable computation and storage, and information flow in biological networks. In this paper, we treat the case of randomly constructed DAGs, for which we show that broadcasting is only possible if the BSC noise level    $\delta $    is below a certain (degree and function dependent) critical threshold. For    $d \geq 3$   , and random DAGs with layers of size    $\Omega (\log (k))$    and majority processing functions, we identify the critical threshold. For    $d = 2$   , we establish a similar result for the NAND processing function. We also prove a partial converse result for odd    $d \geq 3$    illustrating that the identified thresholds are impossible to improve by selecting different processing functions if the decoder is restricted to using a single vertex’s value. Finally, for any BSC noise level    $\delta $   , we construct explicit DAGs (using regular bipartite lossless expander graphs) with bounded degree and layers of size    $\Theta (\log (k))$    admitting reconstruction. In particular, we show that the first    $r$    layers of such DAGs can be generated in either deterministic quasi-polynomial time or randomized polylogarithmic time in    $r$   . These results portray a doubly-exponential advantage for storing a bit in bounded degree DAGs compared to trees, where    $d = 1$    but layer sizes need to grow exponentially with depth in order for broadcasting to be possible.

Includes members:
  Member "reliable computation by formulas of noisy and gates and noiseless xor gates with applications to quantum mechanics":
    also connected through other hyperedges:
      (none)
  Member "noise thresholds for amplification quantum foundations from classical fault tolerant computation":
    also connected through other hyperedges:
      (none)
  Member "strong data processing inequalities for channels and bayesian networks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "intelligence physics and information the tradeoff between accuracy and simplicity in machine learning")
  Member "dissipation of information in channels with input constraints":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "accuracy memory tradeoffs and phase transitions in belief propagation")
  Member "reconstruction and clustering in random constraint satisfaction problems":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "information theoretic thresholds from the cavity method")
  Member "noise threshold for universality of 2 input gates":
    also connected through other hyperedges:
      (none)

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)