# Tag Archives: metric

## Metric and Binary Variable in Cluster Analysis

we´re working on a seminar paper and have to conduct a cluster analysis (n = 130,000) with knn and k-means clustering. Our dataset consists mostly of binary variables such as gender. However, we have some metric variables tha…

## How to resolve a LuaLaTeX font error regarding missing or bad metric data?

I always get the following error when I want to compile my tex file with lualatex:

I have no clue what I …

## Conformal factor between Euclidean metric and metric on Poincaré Ball of arbitrary radius

Usually, a Poincaré Ball is given as the set
$\mathbb{D}^n = \{ x \in \mathbb{R}^n : \|x\|^2 < 1\}$

Let $g_{E,x}$ be the Euclidean Riemannian metric induced at $x \in \mathbb{R}^n$ — in that case, $g_{E,x} = I_n$ for …

## Open balls in Lawvere metric spaces

Let $V$ be the monoidal category $[0,\infty)$ (as a poset) with $+$ and $0$. Lawvere shows that $V$-enriched categories are a more natural generalisation of the notion of a metric space (note no symmetry). Where it turns out …

## Toroidal metric in a random geometric graph

I have some code I’ve been using to generate some random geometric graphs.

The boundary conditions on the rectangular domain I am using sometimes interferes with a clean measurement of some sensitive exponents.

Can I modify…

## Metric on unit circle

How do you define a Riemannian metric for the unit circle. Is it $ds^2=dx^2+d\theta^2$?

I want to also measure the length of the vector from the origin. This would be a standard euclidean metric given by $ds^2=dx^2+dy^2$?

## Is there to take the square root of this metric?

I have a metric which describes the space-time continuum in a universe I’ve constructed:
$$ds^2=-a_0^2dt^4+dx^2+dy^2+dz^2$$
I want to visualize what this looks like. Plotting just the x, y and t dimensions using this formula:…

## Finding a metric in $\Bbb R^2$ depending on $s$ such that $x^s+y^s=1$ is a geodesic wrt. the metric

Looking for a metric in $\Bbb R^2$ depending on $s$ such that $x^s+y^s=1$ is a geodesic wrt. the metric, $x,y\in(0,1), s\in \Bbb R(1, \infty).$

## What metric is appropriate for measuring hybrid electric planes for comparison with traditional turbofans?

Solar (electric) planes have been successful and there has been talk and startups to commercialize electric flight. That being said, solar planes are very light weight when compared to a Boeing airliner (1 million+ pounds).

## null geodesics and conformal rescalings of metric

Let $(\mathfrak{M},g)$ denote a Lorentzian metric and suppose that $\beta$ is a null geodesic in $\mathfrak{M}$. Consider $(\mathfrak{M},cg)$ where $c \in C^{\infty}(\mathbb{R})$ and $c >0$. We know that $\beta$ is also a …