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: "higher order derivatives in costa s entropy power inequality"
  Abstract: Let $X$ be an arbitrary continuous random variable and $Z$ be an independent Gaussian random variable with zero mean and unit variance. For $t~>~0$, Costa proved that $e^{2h(X+\sqrt{t}Z)}$ is concave in $t$, where the proof hinged on the first and second order derivatives of $h(X+\sqrt{t}Z)$. Specifically, these two derivatives are signed, i.e., $\frac{\partial}{\partial t}h(X+\sqrt{t}Z) \geq 0$ and $\frac{\partial^2}{\partial t^2}h(X+\sqrt{t}Z) \leq 0$. In this paper, we show that the third order derivative of $h(X+\sqrt{t}Z)$ is nonnegative, which implies that the Fisher information $J(X+\sqrt{t}Z)$ is convex in $t$. We further show that the fourth order derivative of $h(X+\sqrt{t}Z)$ is nonpositive. Following the first four derivatives, we make two conjectures on $h(X+\sqrt{t}Z)$: the first is that $\frac{\partial^n}{\partial t^n} h(X+\sqrt{t}Z)$ is nonnegative in $t$ if $n$ is odd, and nonpositive otherwise; the second is that $\log J(X+\sqrt{t}Z)$ is convex in $t$. The first conjecture can be rephrased in the context of completely monotone functions: $J(X+\sqrt{t}Z)$ is completely monotone in $t$. The history of the first conjecture may date back to a problem in mathematical physics studied by McKean in 1966. Apart from these results, we provide a geometrical interpretation to the covariance-preserving transformation and study the concavity of $h(\sqrt{t}X+\sqrt{1-t}Z)$, revealing its connection with Costa's EPI.

Connected through hyperedge HE-1 (induced by source paper "convexity of mutual information along the ornstein uhlenbeck flow"):
  with members:
    - "convexity of mutual information along the heat flow"
    - "information and estimation in fokker planck channels"
    - "a concavity property for the reciprocal of fisher information and its consequences on costa s epi"
    - "information theoretic proofs of entropy power inequalities"
    - "estimation in gaussian noise properties of the minimum mean square error"
    - "generalized entropy power inequalities and monotonicity properties of information"
    - "mutual information and minimum mean square error in gaussian channels"

Connected through hyperedge HE-2 (induced by source paper "convexity of mutual information along the heat flow"):
  with members:
    - "convexity of mutual information along the ornstein uhlenbeck flow"
    - "information and estimation in fokker planck channels"
    - "a strengthened entropy power inequality for log concave densities"
    - "mutual information and minimum mean square error in gaussian channels"

Connected through hyperedge HE-3 (induced by source paper "information and estimation in fokker planck channels"):
  with members:
    - "generalization of the de bruijn s identity to general phi entropies and phi fisher informations"
    - "pointwise relations between information and estimation in gaussian noise"
    - "mutual information relative entropy and estimation in the poisson channel"
    - "mutual information and minimum mean square error in gaussian channels"

Connected through hyperedge HE-4 (induced by source paper "a concavity property for the reciprocal of fisher information and its consequences on costa s epi"):
  with members:
    - "a strengthened entropy power inequality for log concave densities"
    - "the concavity of renyi entropy power"
    - "an information theoretic proof of nash s inequality"
    - "information theoretic proofs of entropy power inequalities"
    - "mutual information and minimum mean square error in gaussian channels"

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)