• Publications
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Finding community structure in very large networks.
TLDR
A hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O (md log n) where d is the depth of the dendrogram describing the community structure.
Hierarchical structure and the prediction of missing links in networks
TLDR
This work presents a general technique for inferring hierarchical structure from network data and shows that the existence of hierarchy can simultaneously explain and quantitatively reproduce many commonly observed topological properties of networks.
Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
TLDR
This paper uses the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram of the stochastic block model, a commonly used generative model for social and biological networks, and develops a belief propagation algorithm for inferring functional groups or communities from the topology of the network.
Quantum automata and quantum grammars
TLDR
This work proposes quantum versions of finite-state and push-down automata, and regular and context-free grammars, and finds analogs of several classical theorems, including pumping lemmas, closure properties, rational and algebraic generating functions, and Greibach normal form.
Spectral redemption in clustering sparse networks
TLDR
A way of encoding sparse data using a “nonbacktracking” matrix, and it is shown that the corresponding spectral algorithm performs optimally for some popular generative models, including the stochastic block model.
Mean-field solution of the small-world network model.
TLDR
A mean-field solution for the average path length and for the distribution of path lengths in the small-world network model is presented, which is exact in the limit of large system size and either a large or small number of shortcuts.
Quantum Walks on the Hypercube
TLDR
Two quantum walks on the n-dimensional hypercube are studied, one in discrete time and one in continuous time, showing that the instantaneous mixing time is (π/4)n steps, faster than the Θ(n log n) steps required by the classical walk.
Recursion Theory on the Reals and Continuous-Time Computation
  • C. Moore
  • Computer Science, Mathematics
    Theor. Comput. Sci.
  • 3 August 1996
We define a case of recursive functions on the reals analogous to the classical recursive functions on the natural numbers, corresponding to a conceptual analog computer that operates in continuous
Epidemics and percolation in small-world networks.
  • C. Moore, M. Newman
  • Mathematics, Medicine
    Physical review. E, Statistical physics, plasmas…
  • 30 November 1999
TLDR
The resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network, and are given exact solutions for the position of this threshold in a variety of cases.
The Nature of Computation
TLDR
The authors explain why the P vs. NP problem is so fundamental, and why it is so hard to resolve, and lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing.
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