human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "non shannon information inequalities in four random variables"
  Abstract: Any unconstrained information inequality in three or fewer random variables can be written as a linear combination of instances of Shannon's inequality I(A;B|C) >= 0 . Such inequalities are sometimes referred to as "Shannon" inequalities. In 1998, Zhang and Yeung gave the first example of a "non-Shannon" information inequality in four variables. Their technique was to add two auxiliary variables with special properties and then apply Shannon inequalities to the enlarged list. Here we will show that the Zhang-Yeung inequality can actually be derived from just one auxiliary variable. Then we use their same basic technique of adding auxiliary variables to give many other non-Shannon inequalities in four variables. Our list includes the inequalities found by Xu, Wang, and Sun, but it is by no means exhaustive. Furthermore, some of the inequalities obtained may be superseded by stronger inequalities that have yet to be found. Indeed, we show that the Zhang-Yeung inequality is one of those that is superseded. We also present several infinite families of inequalities. This list includes some, but not all of the infinite families found by Matus. Then we will give a description of what additional information these inequalities tell us about entropy space. This will include a conjecture on the maximum possible failure of Ingleton's inequality. Finally, we will present an application of non-Shannon inequalities to network coding. We will demonstrate how these inequalities are useful in finding bounds on the information that can flow through a particular network called the Vamos network.

Connected through hyperedge HE-1 (induced by source paper "on the storage cost of private information retrieval"):
  with members:
    - "how to use undiscovered information inequalities direct applications of the copy lemma"
    - "breaking the mds pir capacity barrier via joint storage coding"
    - "an open source toolbox for computer aided investigation on the fundamental limits of information systems version 0 1"
    - "capacity achieving private information retrieval codes from mds coded databases with minimum message size"
    - "improved storage for efficient private information retrieval"
    - "the capacity of private information retrieval from uncoded storage constrained databases"
    - "capacity achieving private information retrieval codes with optimal message size and upload cost"
    - "on the capacity of locally decodable codes"

Connected through hyperedge HE-2 (induced by source paper "how to use undiscovered information inequalities direct applications of the copy lemma"):
  with members:
    - "partition symmetrical entropy functions"
    - "entropy region and convolution"
    - "equivalence of two proof techniques for non shannon type inequalities"
    - "improved upper bounds for the information rates of the secret sharing schemes induced by the vamos matroid"

Connected through hyperedge HE-3 (induced by source paper "tropical probability theory and an application to the entropic cone"):
  with members:
    - "on the hardness of entropy minimization and related problems"

Connected through hyperedge HE-4 (induced by source paper "partition symmetrical entropy functions"):
  with members:
    - "conditional information inequalities for entropic and almost entropic points"
    - "on the non robustness of essentially conditional information inequalities"
    - "entropy functions and determinant inequalities"
    - "on essentially conditional information inequalities"
    - "average entropy functions"
    - "information rates of minimal non matroid related access structures"
    - "a projection method for derivation of non shannon type information inequalities"
    - "dualities between entropy functions and network codes"

Connected through hyperedge HE-5 (induced by source paper "explicit polyhedral bounds on network coding rate regions via entropy function region algorithms symmetry and computation"):
  with members:
    - "guessing numbers of odd cycles"
    - "characterizing the rate region of the 4 3 3 exact repair regenerating codes"
    - "achievable rate regions for network coding"
    - "a projection method for derivation of non shannon type information inequalities"

Connected through hyperedge HE-6 (induced by source paper "mapping the region of entropic vectors with support enumeration information geometry"):
  with members:
    - "entropy region and convolution"
    - "equivalence of two proof techniques for non shannon type inequalities"
    - "finite p groups entropy vectors and the ingleton inequality for nilpotent groups"
    - "linear rank inequalities on five or more variables"
    - "mission impossible computing the network coding capacity region"
    - "a projection method for derivation of non shannon type information inequalities"
    - "entropy vectors and network codes"
    - "dualities between entropy functions and network codes"

Connected through hyperedge HE-7 (induced by source paper "index coding capacity how far can one go with only shannon inequalities"):
  with members:
    - "topological interference management through index coding"
    - "on the capacity region for index coding"
    - "interference networks with no csit impact of topology"
    - "local graph coloring and index coding"
    - "an equivalence between network coding and index coding"
    - "index coding an interference alignment perspective"
    - "lexicographic products and the power of non linear network coding"
    - "index coding via linear programming"

Connected through hyperedge HE-8 (induced by source paper "entropy region and convolution"):
  with members:
    - "equivalence of two proof techniques for non shannon type inequalities"
    - "conditional information inequalities for entropic and almost entropic points"
    - "on the ingleton violations in finite groups"
    - "on the non robustness of essentially conditional information inequalities"
    - "on essentially conditional information inequalities"
    - "graph theoretical constructions for graph entropy and network coding based communications"

Question: Please tell me which class the center node 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)