Global ETD Search
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Showing 1 to 12 of 12 for “"ambient space"”.
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A-infinity algebras for Lagrangians via polyfold theory for Morse trees with holomorphic disks
For a Lagrangian submanifold, we define a moduli space of trees of holomorphic disk maps with Morse flow lines as edges, and construct an ambient space around it which we call the quotient space of disk trees. We show that this ambient space is an M-polyfold with boundary and corners by combining …
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Immersions of Positively Curved Manifolds Into Manifolds With Curvature Bounded Above
… curvature is isometrically immersed in some ambient space, N, what is the radius of the smallest ball in which its image lies? Additionally, when can the knowledge that the image lies inside a ball of restricted size be used to conclude that the immersion is an imbedding whose image bounds a …
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Two-Component Link Symmetries
… knot is a closed curve in a three-dimensional space that does not intersect itself, while a link is two or more such curves that do not intersect each other. We consider the ``intrinsic'' symmetry group of a two-component link L which records directly whether L is isotopic to a link obtained by …
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Better embeddings for Planar Earth-Mover Distance over sparse sets
… of the Planar Earth-Mover Distance (EMD) into lp spaces. EMD is a popular measure of dissimilarity between sets of points, e.g., bags of geometric features. We present a collection of embeddings with the property that their distortion and/or host-space dimension are parametrized by the size (or …
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Algebraic, geometric and numerical methods for Tensor Network Varieties
… the strict containment of the linear span in the ambient space as long as the number of sites is at least quadratic in the bond dimension, improving the state of the art. Finally, based on dimensional considerations, we propose a variation of the nonlinear conjugate gradient method used to …
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Topics in harmonic analysis and partial differential equations: extension theorems and geometric maximum principles
… subset of a geometrically doubling quasi-metric space which satisfies a Hölder-type condition may be extended to the entire space with preservation of regularity. The proof proceeds along the lines of the original work of Whitney in 1934 and yields a linear extension operator. A similar extension …
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In search of better proximity
Given a set of points in a metric space, a fundamental problem is to preprocess these points for answering nearest-neighbor queries on them. Proximity search is the problem of answering more general queries that need the first, second, or further closest neighbors of a query point, possibly in …
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Topological and geometric inference of data
… is to determine the structure of the subspace on which a distribution is supported, given only a finite noisy sample thereof. The special case in which the subspace is an embedded manifold is given particular attention owing to its conceptual elegance, and asymptotic bounds are obtained …
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Potential-based analysis of social, communication, and distributed networks
… of termination time from the dimension of the ambient space. The approach adopted here can also be leveraged to connect the rate of increase of a so-called kinetic-s-energy associated with multi-agent systems to the spectral gap of their underlying dynamics. We describe a richer class of …
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Semi-Open Space and Micro-Environmental Control for Improving Thermal Comfort, Indoor Air Quality, and Building Energy Efficiency
… heating, and cooling combined with local space partition and confinement (called semi-open space or SOS) have the potential to provide micro-environment that is tailored to the individual preference of the occupants, and hence increase the percentage of satisfied occupancy from currently …
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Upper and Lower Complexity Bounds for Some Problems in Elementary Geometry
… ≤ h. For the case of polyhedra defined by 2n halfspaces in Rn , we prove that the set I (2n,n) of parameters describing non-empty polyhedra, has an exponential number of limiting hypersurfaces. From this geometric result we obtain, as a corollary, the existence of a constant c > 1 such that, if …
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Topics in Weyl geometry and quantum anomalies
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms