Convolution theoremAsymptotic efficiencyInformation boundSemiparametric modelLocal asymptotic normalityDifferentiabilityRegular estimatorA useful approach to asymptotic efficiency for estimators in semiparametri
The extension of this functional to molecular (complex) fluids is now made possible by uncovering the relation between the convolution decomposition for spheres and the Gauss-Bonnet theorem for the geometry of convex bodies (Rosenfeld, Y., 1994, Phys. Rev. E, 50, R3318). This provides (i)...
where * denotes convolution, and hL(t) corresponds in this case to a boxcar window, i.e. hL(t) = 1/L for |t| ≤ M and zero otherwise. According to the convolution theorem $$\hat{z}(f)=(1-{\hat{h}}_{L}(f))\hat{y}(f)$$ (11) and the fluctuation reads $$...
We show that, if the arithmetic functions \\(f, g\\colon\\mathcal{O}_Kightarrow \\mathbb{C}\\) both have level of distribution \\(\\vartheta\\) for some \\(0<\\vartheta\\leq 1/2\\) then the Dirichlet convolution \\(f*g\\) also has level of distribution \\(\\vartheta\...
Hence, estimates (1.3) in Theorem 1.1 show that, if we subtract the term e−t/2Wα,β(x,t), which may have the singularities coming from the initial data, then the solution φ to (1.2) is an asymptotic profile of the solution V to (1.1). However, if the initial data V0 and ...
As introduced in [77], we use a separable Gaussian convolution operator to reduce the time complexity of a Sinkhorn iteration from O(Npixels2) to O(Npixels3/2) in dimension d=2 and O(Npixels4/3) in dimension d=3. 2. As detailed in [19, 33, 34], we use the KeOps library to ...
The basic idea is to apply the convolutions to the image and the set of filters and consider this new image as input to the next layer. Depending on the filer you use, the output image will smooth the edges, capture them, or sharpen the key patterns. You will build highly relevant fea...
Reference [8] used a smaller convolution kernel and designed the model to be deeper, so that it could better learn the high-level semantics of intelligently translated content. Reference [9] deepens the depth of the model and improves the overall performance. Generally speaking, if the ...
Finally, in Section 4 we prove Theorem 1.2 as well as an asymptotic stability result for train of peakons to the DP equation. Note that we postponed to the Appendix the proof of an almost monotonicity result for the DP equation that leads to the uniform exponential decay result for Y-...
After computing the convolution, the result is multiplied elementwise with f. Therefore, every element of this new array indicates how many connections the corresponding material voxel has, including itself. Thus, an element with a value of 5 represents a voxel connected to 4 neighbors and a val...