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The growth of planar and spatial objects is often modelled using one-dimensional size parameters, e.g., volume, area or average width. We take a more detailed approach and model how the boundary of a growing object expands in time. We mainly consider star-shaped planar objects. The model can be regarded as a dynamic deformable template model.
Jónsdóttir, Kristjana Ýr +1 more
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Gaussian Processes and Gaussian Measures
The subject of this paper is the study of the correspondence between Gaussian processes with paths in linear function spaces and Gaussian measures on function spaces. For the function spaces $C(I), C^n\lbrack a, b\rbrack, AC\lbrack a, b\rbrack$ and $L_2(T, \mathscr{A}, \nu)$ it is shown that if a Gaussian process has paths in these spaces then it ...
Rajput, Balram S., Cambanis, Stamatis
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Gaussian Quantum Discord [PDF]
4 pages, 2 figures, new version, typos ...
P. Giorda, M. Paris
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2D affine transform parameters by Gaussian elimination with pivoting [PDF]
In many geomatics, computer vision, and computer-aided applications, coordinate transformations are needed to transform from one coordinate system to another, especially in geodesy and photogrammetry.
Tariq N. Ataiwe +2 more
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Gaussian and Non-Gaussian operations on non-Gaussian state: engineering non-Gaussianity
AbstractMultiple photon subtraction applied to a displaced phase-averaged coherent state, which is a non-Gaussian classical state, produces conditional states with a non trivial (positive) Glauber-Sudarshan Prepresentation. We theoretically and experimentally demonstrate that, despite its simplicity, this class of conditional states cannot be fully ...
S. Olivares, A. Allevi, M. Bondani
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Bimodal Fusion Network with Multi-Head Attention for Multimodal Sentiment Analysis
The enrichment of social media expression makes multimodal sentiment analysis a research hotspot. However, modality heterogeneity brings great difficulties to effective cross-modal fusion, especially the modality alignment problem and the uncontrolled ...
Rui Zhang +5 more
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Gaussian Intrinsic Entanglement [PDF]
6+17 pages, 2 figures.
Mišta Jr., Ladislav, Tatham, Richard
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Generalized Asymmetric Hermite–Gaussian and Laguerre–Gaussian Beams
We derive analytical formulae for the complex amplitudes of variants of generalized Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) beams. We reveal that, at particular values of parameters of the exact solution of the paraxial propagation equation ...
Eugeny G. Abramochkin +3 more
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Consider the functions \(\exp (-\zeta x^2)p_j(x)\) with \(p_j(x)= \sin [\pi/2 (x+1) (j+1/2)]\) and \(\text{Re} \zeta>0\). It is shown in this note that the family \(h_{j,k} (x)=h_j(x-2k)\), \(j=0,1, \dots, k\in Z\) is an unconditional basis for \(L^2(R)\). Also the dual basis for this is constructed. When \(\zeta>0\), this result is implicit in \textit{
Coifman, R.R., Meyer, Y.
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AbstractAs the standard method for solving systems of linear equations, Gaussian elimination (GE) is one of the most important and ubiquitous numerical algorithms. However, its successful use relies on understanding its numerical stability properties and how to organize its computations for efficient execution on modern computers.
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