Covariance Functions for Gaussian Laplacian Fields in Higher Dimension

2020 ◽  
pp. 19-29
Author(s):  
Gyorgy H. Terdik
Keyword(s):  
Higher Dimension ◽  
Covariance Functions

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

scholarly journals Vibrational mechanics in higher dimension: Tuning potential landscapes

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
David Cubero ◽  
Ferruccio Renzoni
Keyword(s):  
Higher Dimension ◽  
Vibrational Mechanics

scholarly journals A note on moduli spaces of conformal classes for flat tori of higher dimension and on their conformal multiplication

2021 ◽  
Author(s):  
Anna Gori ◽  
Alberto Verjovsky ◽  
Fabio Vlacci
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Abelian Varieties ◽  
Complex Multiplication ◽  
Higher Dimension ◽  
Geometric Constructions ◽  
Flat Torus ◽  
Flat Tori

AbstractMotivated by the theory of complex multiplication of abelian varieties, in this paper we study the conformality classes of flat tori in $${\mathbb {R}}^{n}$$ R n and investigate criteria to determine whether a n-dimensional flat torus has non trivial (i.e. bigger than $${\mathbb {Z}}^{*}={\mathbb {Z}}{\setminus }\{0\}$$ Z ∗ = Z \ { 0 } ) semigroup of conformal endomorphisms (the analogs of isogenies for abelian varieties). We then exhibit several geometric constructions of tori with this property and study the class of conformally equivalent lattices in order to describe the moduli space of the corresponding tori.

scholarly journals LOOP VARIABLES AND GAUGE-INVARIANT INTERACTIONS — II

2001 ◽  
Vol 16 (10) ◽  
pp. 1679-1701 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Gauge Transformation ◽  
Dimensional Reduction ◽  
Mass Shell ◽  
Bosonic String ◽  
Higher Dimension ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Variable Approach

We continue the discussion of our previous paper on writing down gauge-invariant interacting equations for a bosonic string using the loop variable approach. In the earlier paper the equations were written down in one higher dimension where the fields are massless. In this paper we describe a procedure for dimensional reduction that gives interacting equations for fields with the same spectrum as in bosonic string theory. We also argue that the on-shell scattering amplitudes implied by these equations for the physical modes are the same as for the bosonic string. We check this explicitly for some of the simpler equations. The gauge transformation of space–time fields induced by gauge transformations of the loop variables are discussed in some detail. The unintegrated (i.e. before the Koba–Nielsen integration), regularized version of the equations, are gauge invariant off-shell (i.e. off the free mass shell).

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

Matérn Cross-Covariance Functions for Multivariate Random Fields

2010 ◽  
Vol 105 (491) ◽  
pp. 1167-1177 ◽  
Author(s):  
Tilmann Gneiting ◽  
William Kleiber ◽  
Martin Schlather
Keyword(s):  
Random Fields ◽  
Covariance Functions ◽  
Cross Covariance

scholarly journals Regularity of the m-symphonic map

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Masashi Misawa ◽  
Nobumitsu Nakauchi
Keyword(s):  
Critical Points ◽  
Conformal Invariance ◽  
Hölder Continuity ◽  
Energy Functional ◽  
Higher Dimension ◽  
Holder Continuity ◽  
New Energy ◽  
Symphonic Map

AbstractWe introduce a new energy functional of conformal invariance and consider its critical points, named the m-symphonic map. We study a Hölder continuity of m-symphonic maps from domains of $$\mathbb {R}^m$$ R m into the spheres in the higher dimension $$m \ge 4$$ m ≥ 4 .

scholarly journals Rényi holographic dark energy in higher dimension Cosmology

2021 ◽  
Vol 426 ◽  
pp. 168403
Author(s):  
A. Saha ◽  
S. Ghose ◽  
A. Chanda ◽  
B.C. Paul
Keyword(s):  
Dark Energy ◽  
Holographic Dark Energy ◽  
Higher Dimension

Investigating Local Dependence with Conditional Covariance Functions

1998 ◽  
Vol 23 (2) ◽  
pp. 129 ◽  
Author(s):  
Jeff Douglas ◽  
Hae Rim Kim ◽  
Brian Habing ◽  
Furong Gao
Keyword(s):  
Local Dependence ◽  
Conditional Covariance ◽  
Covariance Functions
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