Managing spaces with Latex is not simple, in this tutorial, we will see how to manage horizontal spaces. How to write horizontal space: qquad, hspace, thinspace , enspace, \, , ! , !! , !!! , : , \; Latex horizontal spaces Very important No blank space before and after ...
In this set theory formulation of probability, the sample space for a problem corresponds to an important set. Since the sample space contains every outcome that is possible, it forms a set of everything that we can consider. So the sample space becomes the universal set in use for a parti...
In particular, cone structuresC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal ...
The PCA already follows this approach by default through the method definition [43]. We believe that by implementing this approach for our AEs, e.g. by making use of denoising AEs or regularization of latent space [44], we can create even better AE latent spaces for motor learning. This ...
Wireless communication systems employing multiple antennas at both ends of the link, commonly known as multiple-input multiple-output (MIMO) systems, are being considered as one of the key technologies to be deployed in current and upcoming wireless communication standards [1]. In this context, the...
14a, two slices were excluded due to the lack of L6b cells, which prevented the definition of ground truth. The experiments were not randomized. The Investigators were not blinded to allocation during experiments and outcome assessment. Reporting summary...
a, Definition of border cells in 3D arenas. We considered only neurons for which a 2D firing field was detected in each of the cell’s 2D planes (see Methods). 2D firing-rate maps were plotted in the three principal 2D views of the room geometry: the top view xy, and the two side...
By definition, the universe is everything in existence, so nothing can exist outside it. That said, modern theories such aschaotic inflation,brane theoryandparallel realitieshave blurred that definition. We'll address those ambiguities later. For the time being, when we think about shape, we're...
According to this definition, 𝑄̂ turns out to be the rotational component of the polar decomposition of 𝑌𝑇𝐺𝑋. When 𝛼=0, we obtain the rotational component of 𝑌𝑇𝑋, the classical Ordinary Procrustes Analysis (OPA). When 𝛼=1, then 𝑌𝑇𝐺𝑋=𝐴𝑋. In ...
Ordinarily, when you call a static member, you provide the type name along with the member name. Repeatedly entering the same type name to invoke members of the type can result in verbose, obscure code. For example, the following definition of aCircleclass references many members of theMathcl...