Recently updated notes
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Michael Reed1980no dateCited in Intensity Dot Product Graphs as a standard reference for compact operator theory (Chapter VI), grounding the use of Hilbert-Schmidt operators when the heat map is recast as an integral kernel.
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Hans Sagan1994no dateFootnote citation in Intensity Dot Product Graphs pointing readers to Sagan's monograph for Hilbert's cube-filling curve, illustrating that measurable bijections between segments and higher-dimensional regio…
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Patrick Billingsley1995no dateReferenced in Intensity Dot Product Graphs as the source for Fubini's theorem, justifying iterated integration over the product intensity when computing expected edge counts in the appendix derivations.
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Timothée Poisot2016no dateCited in Intensity Dot Product Graphs to acknowledge prior recognition that food webs should be treated as probabilistic objects, supporting the framing of classic food webs as statistical summaries of an un…
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Giulio V. Dalla Riva2016no dateRecognized in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities as the first application of RDPG to ecological networks, showing that latent positions capture evolutionary signatures in food webs and grounding the ecological motiva…
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Bernard W Silverman2018no dateInvoked in Intensity Dot Product Graphs as the canonical reference for density estimation, the second stage of IDPG inference where embedded node positions are treated as a point cloud to recover the latent…
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Avanti Athreya2018no dateWe anchor Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities in the RDPG framework via this survey, which catalogs the spectral estimation theory and applications to connectome analysis and social network inference that we build on.…
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Mu Zhu2006no dateCited in Intensity Dot Product Graphs alongside other singular-value thresholding methods as one approach to selecting an embedding dimension from the singular value sequence of the adjacency matrix during I…
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Matan Gavish2014no dateListed in Intensity Dot Product Graphs as an example of optimal singular value truncation for choosing the latent dimension during the spectral embedding step of IDPG inference.
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Sourav Chatterjee2015no dateReferenced in Intensity Dot Product Graphs as a matrix estimation technique for selecting an appropriate dimension from the singular values of the adjacency matrix when fitting an IDPG.
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Patrick Rubin-Delanchy2022no dateWe invoke the generalised RDPG interpretation alongside the Sankhya limit theorem in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities to record that per-vertex covariances depend on the edge variance profile, a fact our Fisher inf…
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Stephen J Young2007no dateCited alongside the Athreya survey to mark the original RDPG model, providing the foundational definition that Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities extends to the dynamical setting where latent positions evolve in time…
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Edoardo M Airoldi2008no dateListed among the established families that fix the node set and randomize edges, with mixed-membership stochastic blockmodels standing in for the broader SBM literature. Intensity Dot Product Graphs groups i…
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Günter Last2017no datePaired with Daley and Vere-Jones as a modern textbook on the Poisson process, providing the technical apparatus (Mecke formulae, intensity measures) on which the IDPG construction in Intensity Dot Product Graphs…
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A. Kechris1995no dateUsed in Intensity Dot Product Graphs for Kuratowski's theorem (Thm. 15.6), supplying the Borel isomorphism between any uncountable Polish space and [0,1] that lets the latent space Omega be relabeled to the…
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John Frank Charles Kingman1993no dateCited in Intensity Dot Product Graphs as a source for Campbell's formula, which underwrites the derivation of expected edge counts under the Poisson point process foundation of the IDPG model.
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Diana Cai2016no dateCited in Intensity Dot Product Graphs for the directed analogue of exchangeable-graph priors, providing the digraphon-specific weak-isomorphism machinery that Theorem 5 (no regular equivalent digraphon) reli…
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Peter Orbanz2014no dateCited in Intensity Dot Product Graphs as the foundational reference for exchangeable arrays and graphon priors, grounding the weak-isomorphism representation theorem that lifts the regularity obstruction fro…
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Frank Morgan2016no dateInvoked in Intensity Dot Product Graphs (Sec. 3.2) for the geometric-measure-theory fact that rectifiable curves have Hausdorff dimension at most one, supplying the dimensional ceiling that drives the BV and…
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Bogdan Nica2018no dateCited in Intensity Dot Product Graphs for the classic graph Laplacian L = D - A and Cheeger-type spectral interpretations, providing the discrete template that the measure-theoretic Laplacian generalizes.
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Joseph J. Rotman1995no dateCited as the standard reference for the theory of point processes, supplying the mathematical backbone for the Poisson-point-process latent population that Intensity Dot Product Graphs places on its Euclidea…
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Vladimir I. Bogachev and Oleg G. Smolyanov2020no dateUsed in Intensity Dot Product Graphs alongside Reed-Simon for the spectral theory of compact operators (Chapter 28), supporting both the Schmidt decomposition and the Mercer-theorem reduction in the symmetri…
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Zhong-Zhi Bai and Jian-Yu Pan2021no dateCited in Intensity Dot Product Graphs (Chapter 3) as the matrix-analysis reference accompanying Weyl's inequality, supplying the finite-dimensional version applied to adjacency and probability matrices.
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Sergei Ovchinnikov2021no dateCited in Intensity Dot Product Graphs (chapter 15, sec 5) for the existence of a measure-preserving Borel isomorphism between [0,1] with Lebesgue measure and Omega with the normalized intensity, upgrading Ku…
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Penny Roberts2025no dateCited at the opening as the canonical reference for the dominant network-modeling paradigm, in which nodes are fixed and only edges are stochastic. Intensity Dot Product Graphs uses Newman's textbook to anch…