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Federico Campagna20251 hours agoI just discovered this beok thanks to an episod of Lepht Hand (this one: https://splitinfinities.substack.com/p/lepht-hand-myth-nostalgia-and-liberation-598 ). I was already open to consider some its…
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Daniel Baumann20222 hours agoWhen I was younger, say between middle- and high-school, I was always in awe with the cosmos. Questions about where "all this" came from, where it was going, and what kept everything together were exc…
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Shoshichi Kobayashi1963no dateKobayashi and Nomizu's treatise supplies the classical principal-bundle machinery we invoke in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities for existence and uniqueness of horizontal lifts and for the Ambrose-Singer theorem li…
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Jakob Uexüll2010no dateBetween interface and truth: Multi-task selection drives ecologically veridical perception takes von Uexkull's Umwelt as a precursor to ecological veridicality, with the separation condition giving a mathematical formalisation of how species-specific perceptual worlds a…
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Elliott Sober2024no dateSober's recent treatment of evolutionary theory reinforces the methodological view, paired with Sober (2008) in Between interface and truth: Multi-task selection drives ecologically veridical perception, that population-level laws need initial conditions and auxiliaries…
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Elliott Sober2008no dateSober's analysis of evidence in evolution frames evidential support as model-comparative. We adopt this stance in Between interface and truth: Multi-task selection drives ecologically veridical perception to read our optimality and convergence theorems as conditional ad…
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Eugene Seneta2006no dateSeneta's treatise supplies the Perron-Frobenius machinery used in Between interface and truth: Multi-task selection drives ecologically veridical perception for reducible nonnegative matrices: the Frobenius block-triangular decomposition, the per-block Perron expansion…
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Massimo Pigliucci2006no datePigliucci and Kaplan argue that adaptationist explanations must be assessed against alternative causal pathways and developmental structure. We invoke this stance in Between interface and truth: Multi-task selection drives ecologically veridical perception to keep our t…
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Donald D. Hoffman2019no dateHoffman's book draws the philosophical conclusion that perception shows icons on a desktop rather than reality. We engage this position in Between interface and truth: Multi-task selection drives ecologically veridical perception as the strong non-veridical reading our…
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Peter Godfrey-Smith2024no dateCited alongside Godfrey-Smith (2009) in Between interface and truth: Multi-task selection drives ecologically veridical perception to support the model-based stance on Darwinian populations, which justifies treating our framework as an idealised map rather than a full b…
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Peter Godfrey-Smith2009no dateFollowing Godfrey-Smith's model-based treatment of Darwinian populations, we frame the apparatus of Between interface and truth: Multi-task selection drives ecologically veridical perception as an idealised map from ecological structure to selective pressure, with no cl…
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Stewart N. Ethier1986no dateWe invoke in Between interface and truth: Multi-task selection drives ecologically veridical perception the density-dependent population-process limit from Chapter 11 of Ethier and Kurtz to show Wright-Fisher trajectories converge in probability to the deterministic rep…
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P.-A. Absil2008no dateWe adopt the metric quotient-manifold framework of Absil, Mahony, and Sepulchre as the geometric backbone for the principal bundle in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities: their Riemannian connection on R*^{n x d}/O(d)…
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Klaus-Jochen Engel2000no dateCited in Intensity Dot Product Graphs for the theory of strongly continuous one-parameter semigroups, supplying the framework needed to ask whether the continuous Laplacian generates a heat semigroup on the…
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Alexander Grigor'yan2009no dateCited in Intensity Dot Product Graphs as the analytic backdrop for heat kernels on manifolds and graphs, providing the tools the authors would extend to verify sectoriality and dissipativity of the continuou…
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László Lovász2012no dateCited as the standard reference for graphon theory, against which Intensity Dot Product Graphs later proves a dimensional obstruction: the one-dimensional label space of Lovasz-style graphons cannot faithful…
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Tosio Kato1995no dateKato's perturbation theory underwrites the small-mutation expansion in Between interface and truth: Multi-task selection drives ecologically veridical perception, giving the analytic first-order correction to the dominant Perron eigenvector around the unperturbed diagon…
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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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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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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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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…