Authored lecture exposition. Theorem14 states that the image of the first fixed point above the critical point does not belong to the transitive target; Theorem12 recalls omega-Jónsson functions.

Second edition author manuscript. Sections7D.5–7D.6 give the coding lemmas; Section7D.19 constructs coding games using ordinal codes.

Author’s preprint. The recursively inseparable-set construction preceding Theorem2.8 uses overspill to obtain an internally coded nonrecursive standard set.

Authored lecture notes by Jaap van Oosten, Utrecht University. Theorem0.11, printed pp.x–xii, states the adjoint lifting theorem and constructs the lifted adjoint from reflexive presentations. Theorem1.16 applies lifting to logical functors through power-object monadicity.

By Daniel Jurafsky and James H. Martin. Author-hosted third-edition draft, appendix A, Hidden Markov Models, dated 19 August 2026.

Official PDF: web.stanford.edu/~jurafsky/slp3/A.pdf

Appendix A.2, pp. 2–3, specifies initial, transition and emission distributions and the Markov/output-independence assumptions. Appendix A.3 gives the forward algorithm.

Arthur Gretton coauthored an exposition of Reproducing kernel Hilbert spaces with Dino Sejdinovic. Their notes explain how a positive-definite kernel determines a Hilbert space and how Mercer's theorem supplies an eigenfunction expansion under compactness assumptions. This makes it possible to represent functions through kernel evaluations or spectral coordinates.^[ref]

Dino Sejdinovic coauthored notes on Reproducing kernel Hilbert spaces with Arthur Gretton. They develop the correspondence between positive-definite kernels and Hilbert spaces of functions, including Mercer's theorem. The reproducing property turns point evaluation into an inner product, connecting function-space geometry with computable kernel values.^[ref]

Carlo Mantegazza coauthored a proof of compactness for special functions of bounded variation with Giovanni Alberti. The theorem combines control of gradients with control of jump discontinuities. It allows limits of suitably bounded sequences to remain in the same function class, supporting existence arguments for variational models with interfaces.^[ref]

Giovanni Alberti coauthored a compactness theorem for special functions of bounded variation with Carlo Mantegazza. The result controls sequences that may contain jump discontinuities, using bounds on variation, gradients and jump sets. Such compactness is essential in calculus of variations problems where minimizing configurations can develop cracks or interfaces.^[ref]

Martin Burger coauthored an exposition of regularization of an inverse problem with Martin Benning. Their treatment of inverse problems connects nonlinear penalties, prior information and stability of reconstruction. The framework distinguishes exact inversion from a controlled approximation that remains meaningful when measurements contain noise or the inverse map is discontinuous.^[ref]

Martin Benning coauthored an account of modern regularization of an inverse problem for inverse problems with Martin Burger. It explains how prior information and stabilizing penalties make ill-posed inversion tractable, including nonlinear regularization for linear forward maps. Existence depends on conditions such as compactness and lower semicontinuity, not merely on writing down a minimization problem.^[ref]

Yonina C. Eldar coauthored a study of Fourier phase retrieval with Tamir Bendory and Robert Beinert. It compares basic magnitude measurements with richer designs such as masks or short-time measurements. Extra measurement structure can remove ambiguities that persist in the simplest model, linking experimental design with mathematical identifiability.^[ref]

Robert Beinert coauthored an account of Fourier phase retrieval with Tamir Bendory and Yonina C. Eldar. Their analysis separates uniqueness questions from reconstruction algorithms and records the symmetries invisible to Fourier-magnitude measurements. This clarifies why an algorithm producing a signal is insufficient unless the measurement design also makes the signal identifiable.^[ref]

Tamir Bendory coauthored a study of Fourier phase retrieval with Robert Beinert and Yonina C. Eldar. It examines reconstruction from Fourier magnitudes and distinguishes unavoidable ambiguities from genuine uniqueness failures. Global phase, translation and conjugate reflection already preserve basic magnitude data, so meaningful recovery claims must account for these symmetries.^[ref]