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AbstractIn 2021, the East Bay Permanent Real Estate Cooperative (EB PREC) purchased Esther's Orbit Room—the last remaining venue of Oakland's West Coast blues scene—to build a haven for Black culture and livelihood. As a novel system of land ownership inspired by land trusts, cooperatives, and social movements, EB PREC orchestrates local, collective governance to harness the staying power of ownership and resist its commodification. EB PREC's complex institutional structure is mirrored in the manifold enclosures of the Orbit Room property, which expands, contracts, and subdivides an ever-contested form of parcelization. As an architectural designer and member of EB PREC, the author combines an analysis of the Orbit Room's as-built conditions with an institutional portrait of EB PREC. This article asks how alignment and misalignment between ownership and property lines can enable—and preclude—the decommodification of property and transform it into an enduring source of power for those so long excluded from it.

We discuss resonances for a nonrelativistic and spinless quantum particle confined to a two- or three-dimensional Riemannian manifold to which a finite number of semiinfinite leads is attached. Resolvent and scattering resonances are shown to coincide in this situation. Next we consider the resonances together with embedded eigenvalues and ask about the high-energy asymptotics of such a family. For the case when all the halflines are attached at a single point we prove that all resonances are in the momentum plane confined to a strip parallel to the real axis, in contrast to the analogous asymptotics in some metric quantum graphs; we illustrate this on several simple examples. On the other hand, the resonance behaviour can be influenced by a magnetic field. We provide an example of such a 'hedgehog' manifold at which a suitable Aharonov-Bohm flux leads to absence of any true resonance, i.e. that corresponding to a pole outside the real axis.

"Trained to extract actionable information from large volumes of high-dimensional data, engineers and scientists often have trouble isolating meaningful low-dimensional structures hidden in their high-dimensional observations. Manifold learning, a groundbreaking technique designed to tackle these issues of dimensionality reduction, finds widespread application in machine learning, neural networks, pattern recognition, image processing, and computer vision. Filling a void in the literature, Manifold Learning Theory and Applications incorporates state-of-the-art techniques in manifold learning with a solid theoretical and practical treatment of the subject. Comprehensive in its coverage, this pioneering work explores this novel modality from algorithm creation to successful implementation--offering examples of applications in medical, biometrics, multimedia, and computer vision. Emphasizing implementation, it highlights the various permutations of manifold learning in industry including manifold optimization, large scale manifold learning, semidefinite programming for embedding, manifold models for signal acquisition, compression and processing, and multi scale manifold. Beginning with an introduction to manifold learning theories and applications, the book includes discussions on the relevance to nonlinear dimensionality reduction, clustering, graph-based subspace learning, spectral learning and embedding, extensions, and multi-manifold modeling. It synergizes cross-domain knowledge for interdisciplinary instructions, offers a rich set of specialized topics contributed by expert professionals and researchers from a variety of fields. Finally, the book discusses specific algorithms and methodologies using case studies to apply manifold learning for real-world problems"--Provided by publisher

Trabajo presentado en la IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), celebrada de forma virtual del 19 al 25 de junio de 2021 ; Very recently, the Neural Cellular Automata (NCA) has been proposed to simulate the morphogenesis process with deep networks. NCA learns to grow an image starting from a fixed single pixel. In this work, we show that the neural network (NN) architecture of the NCA can be encapsulated in a larger NN. This allows us to propose a new model that encodes a manifold of NCA, each of them capable of generating a distinct image. Therefore, we are effectively learning an embedding space of CA, which shows generalization capabilities. We accomplish this by introducing dynamic convolutions inside an Auto-Encoder architecture, for the first time used to join two different sources of information, the encoding and cell¿s environment information. In biological terms, our approach would play the role of the transcription factors, modulating the mapping of genes into specific proteins that drive cellular differentiation, which occurs right before the morphogenesis. We thoroughly evaluate our approach in a dataset of synthetic emojis and also in real images of CIFAR-10. Our model introduces a general- purpose network, which can be used in a broad range of problems beyond image generation. ; This work has been partially funded by the Spanish government with the project HuMoUR TIN2017-90086-R and Maria de Maeztu Seal of Excellence MDM-2016-0656.

The concept of the intrinsic geometry of a nonholonomic Kenmotsu manifold M is introduced. It is understood as the set of those properties of the manifold that depend only on the framing of the D^ distribution D of the manifold M, on the parallel transformation of vectors belonging to the distribution D along curves tangent to this distribution. The invariants of the intrinsic geometry of the nonholonomic Kenmotsu manifold are: the Schouten curvature tensor; 1-form η generating the distribution D; the Lie derivative of the metric tensor g along the vector field ; Schouten — Wagner tensor field P, whose components in adapted coordinates are expressed using the equalities . It is proved that, as in the case of the Kenmotsu manifold, the Schouten — Wagner tensor of the manifold M vanishes. It follows that the Schouten tensor of a nonholonomic Kenmotsu manifold has the same formal properties as the Riemann curvature tensor. It is proved that the alternation of the Ricci — Schouten tensor coincides with the differential of the structural form. This property of the Ricci — Schouten tensor is used in the proof of the main result of the article: a nonholonomic Kenmotsu manifold cannot carry the structure of an η-Einstein manifold.