How machine-learning experts define vectors, how they are visualized, and how vector technology improves website search results and recommendations.
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature arevelocity, momentum, force,electromagnetic fieldsand weight. A quantity or phenomen...
from the standard Gaussian distribution expresses the acceptable uncertainty in measuring the statistical quantity ψ. We thus get that \(\hat{{{\Delta }}} \, < \, qs(\hat{\psi })\) at the q-confidence level (95%, 99% or similar) under the null hypothesis. To detect an EWS at th...
5f. Since we have only obtained the combined quantity \(A\lambda={({\sigma }^{2}/4{\gamma }^{2})}^{2}\), we still need to determine A and m in Eq. (1). We do that from the best linear fit to the mean level \(\mu=m+\sqrt{|\lambda|/A}\) observing that \(\mu=m...
The existence of multiple conserved charges in the non-Abelian theory has to be contrasted with the Abelian U(1) case of quantum electrodynamics (QED), where the electric charge is the only conserved quantity. In QED, the total electric charge coincides with the baryon number B of the system...
Let X be a d-dimensional random vector and be independent copies of X. For each and positive integer n, define [Math Processing Error] where denotes the convex hull of a set . We also define [Math Processing Error] as the reasonable number of observations we need. As and are only depen...
Toward this end, it discretizes each cell state into a binary vector of length , where denotes the number of samples in the discovery cohort. Collectively, these vectors comprise binary matrix , with same number of rows as cell states across cell types and columns (samples). Given sample ,...
For any matrix \mathbf{A}\in \mathbb{R}^{m\times n}, define the following quantity \lVert \mathbf{A}\lVert_\infty = \underset{x\in\mathbb{R}^n,x\neq 0}{\sup}\frac{\lVert \mathbf{A}x\lVert_\infty}{\lVert x \lVert_\infty}\\ (a) Prove that \lVert\mathbf{A}\lVert...
The scalar quantity of the spatially dependent far-UVC intensity, \(E_p(\varvec{r})\), that irradiates aerosolized (or airborne) virus was obtained by integrating over the angular dimensions of the intensity variable, $$\begin{aligned} E_p(\varvec{r}) = \int _{\varvec{\Omega }} ...
This quantity can be approximated under the assumption that there is a single spreader and the population is locally tree-like, where nodes have 〈k〉k neighbors. In this case, assuming that node i is a spreader, the shortest sequence of events that will drive the process to the absorbing ...