Zobrazeno 1 - 10
of 86
pro vyhledávání: '"Pausinger, Florian"'
Autor:
Pausinger, Florian, Petrecca, David
We study the symmetry groups and winding numbers of planar curves obtained as images of weighted sums of exponentials. More generally, we study the image of the complex unit circle under a finite or infinite Laurent series using a particular parametr
Externí odkaz:
http://arxiv.org/abs/2407.09217
This paper addresses the challenge of extending general finite sequences of real numbers within a subinterval of the real line, maintaining their inherent statistical properties by employing machine learning. Our focus lies on preserving the gap dist
Externí odkaz:
http://arxiv.org/abs/2312.01507
Autor:
Pausinger, Florian
We study the expected $\mathcal{L}_2$-discrepancy of stratified samples generated from special equi-volume partitions of the unit square. The partitions are defined via parallel lines that are all orthogonal to the diagonal of the square. It is shown
Externí odkaz:
http://arxiv.org/abs/2310.13927
In this note we extend our study of the rich geometry of the graph of a curve defined as the weighted sum of two exponentials. Let $\gamma_{a,b}^{s}: [0,1] \rightarrow \mathbb{C}$ be defined as $$\gamma_{a,b}^s(t) = (1-s) \exp(2 \pi i a t) + (1+s) \e
Externí odkaz:
http://arxiv.org/abs/2303.01128
Autor:
Kirk, Nathan, Pausinger, Florian
For $m, d \in \mathbb{N}$, a jittered sample of $N=m^d$ points can be constructed by partitioning $[0,1]^d$ into $m^d$ axis-aligned equivolume boxes and placing one point independently and uniformly at random inside each box. We utilise a formula for
Externí odkaz:
http://arxiv.org/abs/2208.08924
Classical jittered sampling partitions $[0,1]^d$ into $m^d$ cubes for a positive integer $m$ and randomly places a point inside each of them, providing a point set of size $N=m^d$ with small discrepancy. The aim of this note is to provide a construct
Externí odkaz:
http://arxiv.org/abs/2204.09340
Autor:
Kiderlen, Markus, Pausinger, Florian
We prove that classical jittered sampling of the $d$-dimensional unit cube does not yield the smallest expected $\mathcal{L}_2$-discrepancy among all stratified samples with $N=m^d$ points. Our counterexample can be given explicitly and consists of c
Externí odkaz:
http://arxiv.org/abs/2106.01937
Autor:
Kiderlen, Markus, Pausinger, Florian
We extend the notion of jittered sampling to arbitrary partitions and study the discrepancy of the related point sets. Let $\mathbf{\Omega}=(\Omega_1,\ldots,\Omega_N)$ be a partition of $[0,1]^d$ and let the $i$th point in $\mathcal{P}$ be chosen uni
Externí odkaz:
http://arxiv.org/abs/2008.12026
Autor:
Pausinger, Florian
For coprime integers $N,a,b,c$, with $0
Externí odkaz:
http://arxiv.org/abs/2006.00461
Autor:
Pausinger, Florian
This paper establishes a connection between a problem in Potential Theory and Mathematical Physics, arranging points so as to minimize an energy functional, and a problem in Combinatorics and Number Theory, constructing 'well-distributed' sequences o
Externí odkaz:
http://arxiv.org/abs/1905.09641