Zobrazeno 1 - 10
of 18 735
pro vyhledávání: '"Betti, P."'
We prove a general result on the existence of irreducible symplectic compactifications of non-compact Lagrangian fibrations. As an application, we show that the relative Jacobian fibration of cubic fivefolds containing a fixed cubic fourfold can be c
Externí odkaz:
http://arxiv.org/abs/2410.01566
Autor:
Akhalwaya, Ismail Yunus, Bhayat, Ahmed, Connolly, Adam, Herbert, Steven, Horesh, Lior, Sorci, Julien, Ubaru, Shashanka
Several quantum and classical Monte Carlo algorithms for Betti Number Estimation (BNE) on clique complexes have recently been proposed, though it is unclear how their performances compare. We review these algorithms, emphasising their common Monte Ca
Externí odkaz:
http://arxiv.org/abs/2408.16934
We prove that for a finite set of points $X$ in the projective $n$-space over any field, the Betti number $\beta_{n,n+1}$ of the coordinate ring of $X$ is non-zero if and only if $X$ lies on the union of two planes whose sum of dimension is less than
Externí odkaz:
http://arxiv.org/abs/2408.14064
We determine the higher weight spectra of $q$-ary Reed-Muller codes $C_q=RM_q(2,2)$ for all prime powers $q$. This is equivalent to finding the usual weight distributions of all extension codes of $C_q$ over every field extension of $F_q$ of finite d
Externí odkaz:
http://arxiv.org/abs/2408.02548
Autor:
Dai, Pimeng, Yu, Li
We determine which simplicial complexes have the maximum or minimum sum of Betti numbers and sum of bigraded Betti numbers with a given number of vertices in each dimension.
Comment: 22 pages, 1 figure
Comment: 22 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2407.19423
This note proves that only a linear number of holes in a \v{C}ech complex of $n$ points in $\mathbb{R}^d$ can persist over an interval of constant length. The proof uses a packing argument supported by relating the \v{C}ech complexes with correspondi
Externí odkaz:
http://arxiv.org/abs/2409.05241
In this work, we propose an efficient algorithm for the calculation of the Betti matching, which can be used as a loss function to train topology aware segmentation networks. Betti matching loss builds on techniques from topological data analysis, sp
Externí odkaz:
http://arxiv.org/abs/2407.04683
This paper extends the possibility to examine the underlying curvature of data through the lens of topology by using the Betti curves, tools of Persistent Homology, as key topological descriptors, building on the clique topology approach. It was prev
Externí odkaz:
http://arxiv.org/abs/2406.15505
We prove that, on any closed manifold of dimension at least two with non-trivial first Betti number, a $C^\infty$ generic Riemannian metric has infinitely many closed geodesics, and indeed closed geodesics of arbitrarily large length. We derive this
Externí odkaz:
http://arxiv.org/abs/2407.02995
Let $I_{n,m} = (x_1\cdots x_{m},x_2 \cdots x_{m+1},\ldots,x_{n+1}x_{n+2}\cdots x_{n+m})$ be the $m$-path ideal of a path of length $n + m-1$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_{n+m}]$. We compute all the graded Betti numbers of all p
Externí odkaz:
http://arxiv.org/abs/2405.04747