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 "directed information on abstract spaces properties and variational equalities"):
  Abstract: Directed information or its variants are utilized extensively in the characterization of the capacity of channels with memory and feedback, nonanticipative lossy data compression, and their generalizations to networks. In this paper, we derive several functional and topological properties of directed information for general abstract alphabets (complete separable metric spaces) using the topology of weak convergence of probability measures. These include convexity of the set of consistent distributions, which uniquely define causally conditioned distributions, convexity and concavity of directed information with respect to the sets of consistent distributions, weak compactness of these sets of distributions, their joint distributions and their marginals. Furthermore, we show lower semicontinuity of directed information, and under certain conditions we also establish continuity of directed information. Finally, we derive variational equalities for directed information, including sequential versions. These may be viewed as the analogue of the variational equalities of mutual information (utilized in Blahut-Arimoto algorithm). #R##N#In summary, we extend the basic functional and topological properties of mutual information to directed information. These properties are discussed in the context of extremum problems of directed information.

Includes members:
  Member "sequential necessary and sufficient conditions for capacity achieving distributions of channels with memory and feedback":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a connection between feedback capacity and kalman filter for colored gaussian noises")
  Member "capacity achieving distributions information lossless randomized strategies for feedback channels with memory the lqg theory of directed information part ii":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "sequential necessary and sufficient conditions for capacity achieving distributions of channels with memory and feedback")
  Member "optimal nonanticipative estimation schemes for time varying gauss markov processes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "filtering with fidelity for time varying gauss markov processes")
  Member "capacity of binary state symmetric channel with and without feedback and transmission cost":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "single letter expression of capacity for a class of channels with memory")
  Member "information nonanticipative rate distortion function and its applications":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "transfer entropy in mdps with temporal logic specifications")
  Member "information structures for feedback capacity of channels with memory and transmission cost stochastic optimal control variational equalities part i":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "single letter expression of capacity for a class of channels with memory")
  Member "nonanticipative rate distortion function and relations to filtering theory":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "zero delay rate distortion via filtering for vector valued gaussian sources")
  Member "capacity of a post channel with and without feedback":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "computing the feedback capacity of finite state channels using reinforcement learning")

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)