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Raynaud and Gruson showed that there is a reasonable algebro-geometric notion of family of discrete (infinite-dimensional) vector spaces. The author introduces a notion of family of Tate spaces ("Tate" means "locally linearly compact") and…

Algebraic Geometry · Mathematics 2007-05-23 Vladimir Drinfeld

\v{C}ech complexes reveal valuable topological information about point sets at a certain scale in arbitrary dimensions, but the sheer size of these complexes limits their practical impact. While recent work introduced approximation…

Computational Geometry · Computer Science 2013-07-15 Michael Kerber , R. Sharathkumar

We define functorial isomorphisms of parallel transport along etale paths for a class of vector bundles on a p-adic curve. All bundles of degree zero whose reduction is strongly semistable belong to this class. In particular, they give rise…

Algebraic Geometry · Mathematics 2007-05-23 Christopher Deninger , Annette Werner

\v{C}ech complexes are useful simplicial complexes for computing and analyzing topological features of data that lies in Euclidean space. Unfortunately, computing these complexes becomes prohibitively expensive for large-sized data sets…

Computational Geometry · Computer Science 2018-12-13 Aruni Choudhary , Michael Kerber , Sharath Raghvendra

Frames in finite-dimensional vector spaces are spanning sets of vectors which provide redundant representations of signals. The Parseval frames are particularly useful and important, since they provide a simple reconstruction scheme and are…

Differential Geometry · Mathematics 2025-05-30 Samuel A. Ballas , Tom Needham , Clayton Shonkwiler

We discuss algebraic vector bundles on smooth k-schemes X contractible from the standpoint of A^1-homotopy theory; when k = C, the smooth manifolds X(C) are contractible as topological spaces. The integral algebraic K-theory and integral…

Algebraic Geometry · Mathematics 2007-10-22 Aravind Asok , Brent Doran

This article is devoted to a study of flat orbifold vector bundles. We construct a bijection between the isomorphic classes of proper flat orbifold vector bundles and the equivalence classes of representations of the orbifold fundamental…

Differential Geometry · Mathematics 2022-12-20 Shu Shen , Jianqing Yu

We define and study a certain category of vector bundles on a p-adic curve to which we can associate in a functorial way finite dimensional p-adic representations of the geometric fundamental group. Among other things we investigate two…

Number Theory · Mathematics 2007-05-23 C. Deninger , A. Werner

The key to VI is the selection of a tractable density to approximate the Bayesian posterior. For large and complex models a common choice is to assume independence between multivariate blocks in a partition of the parameter space. While…

Machine Learning · Statistics 2025-10-07 Yu Fu , Michael Stanley Smith , Anastasios Panagiotelis

In this paper, we propose a family of label recovery problems on weighted Euclidean random graphs. The vertices of a graph are embedded in $\mathbb{R}^d$ according to a Poisson point process, and are assigned to a discrete community label.…

Social and Information Networks · Computer Science 2025-01-15 Julia Gaudio , Charlie Guan , Xiaochun Niu , Ermin Wei

The tree reconstruction problem is to find an embedded straight-line tree that approximates a given cloud of unorganized points in $\mathbb{R}^m$ up to a certain error. A practical solution to this problem will accelerate a discovery of new…

Computational Geometry · Computer Science 2020-07-20 Yury Elkin , Di Liu , Vitaliy Kurlin

In the first part of this paper we study a best approximation of a vector in Euclidean space R^n with respect to a closed semi-algebraic set C and a given semi-algebraic norm. Assuming that the given norm and its dual norm are…

Algebraic Geometry · Mathematics 2013-11-08 Shmuel Friedland , Malgorzata Stawiska

The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…

q-alg · Mathematics 2009-10-30 Eli Hawkins

We prove an equivariant analogue of Grothendieck's theorem for vector bundles on the one dimensional projective space over complex numbers.

Algebraic Geometry · Mathematics 2007-05-23 Shrawan Kumar

We prove the existence of extremal, non-csc, K\"ahler metrics on certain unstable projectivised vector bundles $\P (E) \to M$ over a cscK-manifold $M$ with discrete holomorphic automorphism group, in certain adiabatic K\"ahler classes. In…

Differential Geometry · Mathematics 2015-11-03 Till Brönnle

In this paper we contribute to the construction of families of arithmetically Cohen-Macaulay (aCM) indecomposable vector bundles on a wide range of polarized surfaces $(X,\Oo_X(1))$ for $\Oo_X(1)$ an ample line bundle. In many cases, we…

Algebraic Geometry · Mathematics 2018-07-25 Edoardo Ballico , Sukmoon Huh , Joan Pons-Llopis

We give a $2^{n+o(n)}$-time and space randomized algorithm for solving the exact Closest Vector Problem (CVP) on $n$-dimensional Euclidean lattices. This improves on the previous fastest algorithm, the deterministic…

Data Structures and Algorithms · Computer Science 2019-01-28 Divesh Aggarwal , Daniel Dadush , Noah Stephens-Davidowitz

We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…

Computational Geometry · Computer Science 2026-05-28 Hamid Shafieasl , Jeff M. Phillips

We present equivalences between certain categories of vector bundles on projective varieties, namely cokernel bundles, Steiner bundles, syzygy bundles, and monads, and full subcategories of representations of certain quivers. As an…

Algebraic Geometry · Mathematics 2016-07-05 Marcos Jardim , Daniela M. Prata

We study moduli spaces of vector bundles on a two-dimensional neighbourhood $Z_k$ of an irreducible curve $\ell = CP^1$ with $\ell^2 = -k$ and give an explicit construction of these moduli as stratified spaces. We give sharp bounds for the…

Algebraic Geometry · Mathematics 2009-09-04 Edoardo Ballico , Elizabeth Gasparim , Thomas Köppe