Zobrazeno 1 - 10
of 667
pro vyhledávání: '"11K38"'
The mean squared error and regularized versions of it are standard loss functions in supervised machine learning. However, calculating these losses for large data sets can be computationally demanding. Modifying an approach of J. Dick and M. Feischl
Externí odkaz:
http://arxiv.org/abs/2409.13453
We study the integration problem over the $s$-dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions whose Haar wavelet coefficients exhibit a certain decay behavior measured
Externí odkaz:
http://arxiv.org/abs/2409.12879
Autor:
Robertson, Steven
The discrepancy of a sequence measures how quickly it approaches a uniform distribution. Given a natural number $d$, any collection of one-dimensional so-called low discrepancy sequences $\left\{S_i:1\le i \le d\right\}$ can be concatenated to create
Externí odkaz:
http://arxiv.org/abs/2409.05469
Autor:
Grepstad, Sigrid
We show that given a lattice $\Gamma \subset \mathbb{R}^m \times \mathbb{R}^n$, and projections $p_1$ and $p_2$ onto $\mathbb{R}^m$ and $\mathbb{R}^n$ respectively, cut-and-project sets obtained using Jordan measurable windows $W$ and $W'$ in $\mathb
Externí odkaz:
http://arxiv.org/abs/2409.05450
Autor:
Beretti, Thomas
This work investigates the relation between the Fourier transform of a planar convex body and its geometric properties. The second matter of study is the quadratic discrepancy of planar convex bodies, and we present sharp results on its asymptotic be
Externí odkaz:
http://arxiv.org/abs/2408.15412
Autor:
Das, Mithun Kumar
We estimate the number of zeros of a polynomial in $\mathbb{C}[z]$ within any small circular disc centered on the unit circle, which improves and comprehensively extends a result established by Borwein, Erd{\'e}lyi, and Littmann~\cite{BE1} in 2008. F
Externí odkaz:
http://arxiv.org/abs/2407.15306
The most versatile version of the classical divergence Borel-Cantelli lemma shows that for any divergent sequence of events $E_n$ in a probability space satisfying a quasi-independence condition, its corresponding limsup set $E_\infty$ has positive p
Externí odkaz:
http://arxiv.org/abs/2406.19198
We prove an Erd\H{o}s--Tur\'an type inequality for compact Lie groups, from which we deduce an effective version of Deligne's equidistribution theorem.
Comment: Improve the estimates in the previous version
Comment: Improve the estimates in the previous version
Externí odkaz:
http://arxiv.org/abs/2406.09633
In this note we study estimates from below of the single radius spherical discrepancy in the setting of compact two-point homogeneous spaces. Namely, given a $d$-dimensional manifold $\mathcal M$ endowed with a distance $\rho$ so that $(\mathcal M, \
Externí odkaz:
http://arxiv.org/abs/2406.03830
We study tractability properties of the weighted $L_p$-discrepancy. The concept of {\it weighted} discrepancy was introduced by Sloan and Wo\'{z}\-nia\-kowski in 1998 in order to prove a weighted version of the Koksma-Hlawka inequality for the error
Externí odkaz:
http://arxiv.org/abs/2405.12729