scholarly journals Almost Sure Convergence for the Maximum and Minimum of Normal Vector Sequences

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 618
Author(s):  
Zhicheng Chen ◽  
Hongyun Zhang ◽  
Xinsheng Liu
Keyword(s):  
Almost Sure Convergence ◽  
Normal Vector ◽  
Vector Sequences

In this paper, we prove the almost sure convergences for the maximum and minimum of nonstationary and stationary standardized normal vector sequences under some suitable conditions.

scholarly journals Almost sure convergence for the maxima of strongly dependent stationary Gaussian vector sequences

2010 ◽  
Vol 367 (1) ◽  
pp. 242-248 ◽  
Author(s):  
Zhichao Weng ◽  
Lunfeng Cao ◽  
Zuoxiang Peng
Keyword(s):  
Almost Sure Convergence ◽  
Gaussian Vector ◽  
Vector Sequences

On almost Sure Convergence for Negatively Superadditive Dependent Random Variables

2019 ◽  
Vol 19 (1) ◽  
pp. 95-102
Author(s):  
Liuyong Tao ◽  
Hyeyoung Seo ◽  
Jongil Baek
Keyword(s):  
Random Variables ◽  
Almost Sure Convergence ◽  
Dependent Random Variables

scholarly journals On the Markov Transition Kernels for First Passage Percolation on the Ladder

2011 ◽  
Vol 48 (02) ◽  
pp. 366-388 ◽  
Author(s):  
Eckhard Schlemm
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Asymptotic Variance ◽  
Almost Sure Convergence ◽  
First Passage Percolation ◽  
First Passage ◽  
Percolation Problem ◽  
Vertex Set ◽  
Step Transition

We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times l n between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of l n / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.

scholarly journals Clothoid fitting and geometric Hermite subdivision

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Ulrich Reif ◽  
Andreas Weinmann
Keyword(s):  
Building Block ◽  
Numerical Results ◽  
Normal Vector ◽  
Subdivision Schemes ◽  
Planar Curves ◽  
Nonlinear Subdivision ◽  
New Strategy ◽  
Vector Information ◽  
Hermite Subdivision

AbstractWe consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive a new strategy to approximate Hermite interpolating clothoids. We employ the proposed approach to define the geometric Hermite analogues of the well-known Lane-Riesenfeld and four-point schemes. We present numerical results produced by the proposed schemes and discuss their features.

scholarly journals Using Least-Squares Residuals to Assess the Stochasticity of Measurements—Example: Terrestrial Laser Scanner and Surface Modeling

2021 ◽  
Vol 5 (1) ◽  
pp. 59
Author(s):  
Gaël Kermarrec ◽  
Niklas Schild ◽  
Jan Hartmann
Keyword(s):  
Least Squares ◽  
Laser Scanner ◽  
Real Data ◽  
Point Clouds ◽  
Statistical Testing ◽  
Normal Vector ◽  
Engineering Structures ◽  
3D Point Clouds ◽  
Least Squares Adjustment ◽  
Correlation Parameters

Terrestrial laser scanners (TLS) capture a large number of 3D points rapidly, with high precision and spatial resolution. These scanners are used for applications as diverse as modeling architectural or engineering structures, but also high-resolution mapping of terrain. The noise of the observations cannot be assumed to be strictly corresponding to white noise: besides being heteroscedastic, correlations between observations are likely to appear due to the high scanning rate. Unfortunately, if the variance can sometimes be modeled based on physical or empirical considerations, the latter are more often neglected. Trustworthy knowledge is, however, mandatory to avoid the overestimation of the precision of the point cloud and, potentially, the non-detection of deformation between scans recorded at different epochs using statistical testing strategies. The TLS point clouds can be approximated with parametric surfaces, such as planes, using the Gauss–Helmert model, or the newly introduced T-splines surfaces. In both cases, the goal is to minimize the squared distance between the observations and the approximated surfaces in order to estimate parameters, such as normal vector or control points. In this contribution, we will show how the residuals of the surface approximation can be used to derive the correlation structure of the noise of the observations. We will estimate the correlation parameters using the Whittle maximum likelihood and use comparable simulations and real data to validate our methodology. Using the least-squares adjustment as a “filter of the geometry” paves the way for the determination of a correlation model for many sensors recording 3D point clouds.

scholarly journals On the almost sure convergence of sums

2021 ◽  
Vol 172 ◽  
pp. 109045
Author(s):  
Luca Pratelli ◽  
Pietro Rigo
Keyword(s):  
Almost Sure Convergence

Portraits of courage: Caught in the sovereign’s gaze

2021 ◽  
pp. 136754942098584
Author(s):  
Robin Wagner-Pacifici
Keyword(s):  
Normal Vector ◽  
Us Veterans ◽  
Commander In Chief ◽  
Ongoing Project

Reversing the normal vector of sovereign representation, former US President George W. Bush is engaged in an ongoing project of painting his former subjects, hundreds of portraits of wounded US veterans of the wars in Iraq and Afghanistan. This article explores what it means to have a sovereign observe and render in oil the very subjects he sent to war. It will track the politically vexed communicative exchanges of deference, recognition, power, and identity in such portrait making. Furthermore, assessing the meaning of the invitation to wounded veterans to be painted by one’s former Commander in Chief, the article raises complex issues of victimhood and responsibility. Asking the questions, ‘Who gets to look at whom?’ and ‘Who gets to render whom?’, the article takes as its model Foucault’s analysis of the troubled ‘reciprocal visibility’ in Velazquez’s painting, Las Meninas.

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