1,042 research outputs found
Stable, High-Average-Power, Degenerate Optical Parametric Oscillator at 2.1 μm
We describe a degenerate 1.064-μm-pumped pulsed optical parametric oscillator based on MgO:PPLN in compact Littrow-grating cavity configuration, providing 2.7W of average power at 2.1μm with high spectral and power stability in good spatial beam quality.Peer ReviewedPostprint (author's final draft
Degree Heterogeneity in Higher-Order Networks: Inference in the Hypergraph -Model
The -model for random graphs is commonly used for
representing pairwise interactions in a network with degree heterogeneity.
Going beyond pairwise interactions, Stasi et al. (2014) introduced the
hypergraph -model for capturing degree heterogeneity in
networks with higher-order (multi-way) interactions. In this paper we initiate
the rigorous study of the hypergraph -model with multiple
layers, which allows for hyperedges of different sizes across the layers. To
begin with, we derive the rates of convergence of the maximum likelihood (ML)
estimate and establish their minimax rate optimality. We also derive the
limiting distribution of the ML estimate and construct asymptotically valid
confidence intervals for the model parameters. Next, we consider the
goodness-of-fit problem in the hypergraph -model.
Specifically, we establish the asymptotic normality of the likelihood ratio
(LR) test under the null hypothesis, derive its detection threshold, and also
its limiting power at the threshold. Interestingly, the detection threshold of
the LR test turns out to be minimax optimal, that is, all tests are
asymptotically powerless below this threshold. The theoretical results are
further validated in numerical experiments. In addition to developing the
theoretical framework for estimation and inference for hypergraph
-models, the above results fill a number of gaps in the
graph -model literature, such as the minimax optimality of
the ML estimates and the non-null properties of the LR test, which, to the best
of our knowledge, have not been studied before
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