An advanced method for the generation of two-dimensions parametric models in computer-aided design system is presented. The method is based on designer's idea from conceptual models to geometry models. Through dimension-driven, the system partly modifies and evalutes the model shapes, and auto-...
computing dimensions of coinvariant rings, characters of finite-dimensional representations, coefficients of Kazhdan-Lusztig polynomials, web bases etc. This is closely related to understanding what optimality we could expect and in particular the computational complexity aspects of those problems. Their com...
The 3D line chart will give you a line graph in three dimensions. Select the data range. Go to the Insert tab and select the 3D Line chart as shown in the following image. A 3D Line Graph with multiple lines is returned as shown in the following image. How to Customize Line Graph in...
bosons and Abelian anyons—this principle guarantees that the braiding of identical particles leaves the system unchanged2,3. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes
{ij}\)is the degree matrix of\(\tilde{A}\). HereG1isN × h1and is a new embedding of nodes inh1dimensions that incorporates the graph structure viaf(A). In the two-layer NeuLay-2, we apply another GCN with outputG2 = σ(f(A)G1W(2)) and dimensionsN × h2. ...
Therefore, u2ℓ1, as the local minimizer of problem PU for k=2, must be a two-valued signal. More generally, we can prove the following corollary. Corollary 5 If ⁎⁎x∈XU⁎⁎ and rank(U)=k−1, then x have at most k different components. Proof Suppose ϕ(x)=M∈RN×...
The singular value decomposition is widely used to project data into a space of reduced dimensions, often before applying other analysis techniques. For instance, data can be projected into a lower dimensional space in order to effectively apply nearest neighbor techniques, which tend to break down...
(output_shape)-2:# Add a newline between the last two dimensions, e.g. 3x3 \n 64output_shape_txt+="\n"# Add the name of the layer to the text, as a new lineoutput_shape_txt+=f"\n{layer.name}"# Return the text value and if it should be drawn above the layerreturnoutput_...
two autoencoders. We used two autoencoders to generate the initial embeddings for cells and genes, respectively. The cell autoencoder reduces gene dimensions for each cell from\({{{\rm{I}}}\)dimensions to 512 dimensions and eventually to 256 dimensions; a gene autoencoder reduces cell dimens...
For example, in poly(3-hexylthiophene) (P3HT) the crystallites are ~20 nm along the chain axis and if the disordered domains are of similar dimensions, then an extended chain of ~150 repeat units can span two domains as a tie chain. Using a description from polymer mechanics of the ...