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: "a complete dichotomy rises from the capture of vanishing signatures"
  Abstract: We prove a complexity dichotomy theorem for Holant problems over an arbitrary set of complex-valued symmetric constraint functions F on Boolean variables. This extends and unifies all previous dichotomies for Holant problems on symmetric constraint functions (taking values without a finite modulus). We define and characterize all symmetric vanishing signatures. They turned out to be essential to the complete classification of Holant problems. The dichotomy theorem has an explicit tractability criterion expressible in terms of holographic transformations. A Holant problem defined by a set of constraint functions F is solvable in polynomial time if it satisfies this tractability criterion, and is #P-hard otherwise. The tractability criterion can be intuitively stated as follows: A set F is tractable if (1) every function in F has arity at most two, or (2) F is transformable to an affine type, or (3) F is transformable to a product type, or (4) F is vanishing, combined with the right type of binary functions, or (5) F belongs to a special category of vanishing type Fibonacci gates. The proof of this theorem utilizes many previous dichotomy theorems on Holant problems and Boolean #CSP. Holographic transformations play an indispensable role as both a proof technique and in the statement of the tractability criterion.

Connected through hyperedge HE-1 (induced by source paper "zeros and approximations of holant polynomials on the complex plane"):
  with members:
    - "fast algorithms at low temperatures via markov chains"
    - "counting perfect matchings and the eight vertex model"
    - "counting independent sets and colorings on random regular bipartite graphs"
    - "algorithms for bis hard problems on expander graphs"
    - "zeros of holant problems locations and algorithms"
    - "the complexity of approximating the matching polynomial in the complex plane"
    - "algorithmic pirogov sinai theory"
    - "approximability of the six vertex model"

Connected through hyperedge HE-2 (induced by source paper "complexity of counting weighted eulerian orientations with ars"):
  with members:
    - "dichotomy for real holant c problems"
    - "holographic algorithm with matchgates is universal for planar csp over boolean domain"
    - "the complexity of holant problems over boolean domain with non negative weights"
    - "the complexity of weighted and unweighted csp"
    - "the complexity of planar boolean csp with complex weights"
    - "complexity of counting csp with complex weights"
    - "an effective dichotomy for the counting constraint satisfaction problem"
    - "the complexity of weighted boolean csp"

Connected through hyperedge HE-3 (induced by source paper "perfect matchings rank of connection tensors and graph homomorphisms"):
  with members:
    - "holographic algorithm with matchgates is universal for planar csp over boolean domain"
    - "a holant dichotomy is the fkt algorithm universal"
    - "counting homomorphisms and partition functions"
    - "complexity of counting csp with complex weights"
    - "an effective dichotomy for the counting constraint satisfaction problem"
    - "graph homomorphisms with complex values a dichotomy theorem"
    - "a complexity dichotomy for partition functions with mixed signs"

Connected through hyperedge HE-4 (induced by source paper "clifford gates in the holant framework"):
  with members:
    - "dichotomy for real holant c problems"
    - "the complexity of holant problems over boolean domain with non negative weights"
    - "basis collapse for holographic algorithms over all domain sizes"
    - "a holant dichotomy is the fkt algorithm universal"
    - "base collapse of holographic algorithms"
    - "holographic algorithms beyond matchgates"

Connected through hyperedge HE-5 (induced by source paper "dichotomy for real holant c problems"):
  with members:
    - "holographic algorithm with matchgates is universal for planar csp over boolean domain"
    - "complexity of counting csp with complex weights"
    - "the complexity of weighted boolean csp"

Connected through hyperedge HE-6 (induced by source paper "counting hypergraph matchings up to uniqueness threshold"):
  with members:
    - "bis hardness for 2 spin systems on bipartite bounded degree graphs in the tree non uniqueness region"
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"
    - "counting independent sets in hypergraphs when strong spatial mixing fails"
    - "fptas for hardcore and ising models on hypergraphs"
    - "the complexity of approximately counting in 2 spin systems on k uniform bounded degree hypergraphs"
    - "approximation via correlation decay when strong spatial mixing fails"
    - "fptas for weighted fibonacci gates and its applications"
    - "a simple fptas for counting edge covers"

Connected through hyperedge HE-7 (induced by source paper "block interpolation a framework for tight exponential time counting complexity"):
  with members:
    - "fine grained dichotomies for the tutte plane and boolean csp"
    - "on problems as hard as cnf sat"
    - "exponential time complexity of the permanent and the tutte polynomial"
    - "the complexity of computing the sign of the tutte polynomial"
    - "complexity of counting csp with complex weights"
    - "exponential time complexity of weighted counting of independent sets"
    - "the exponential time complexity of computing the probability that a graph is connected"
    - "inapproximability of the tutte polynomial"

Connected through hyperedge HE-8 (induced by source paper "holographic algorithms beyond matchgates"):
  with members:
    - "the complexity of planar boolean csp with complex weights"
    - "dichotomy for holant problems with a function on domain size 3"
    - "complexity of counting csp with complex weights"
    - "gadgets and anti gadgets leading to a complexity dichotomy"
    - "an effective dichotomy for the counting constraint satisfaction problem"
    - "holographic algorithms with matchgates capture precisely tractable planar csp"
    - "from holant to csp and back dichotomy for holant c problems"
    - "a decidable dichotomy theorem on directed graph homomorphisms with non negative weights"

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.CC(Computational Complexity)