Categories

## how do you estimate the mortality rate of the corona virus?

Disclaimer: I initially posted this question on math.stackexchange.com, but a user there suggested I should post it here instead. I’ve seen mortality rates for the coronavirus reported for different countries. For example, Worldometers gives the worldwide mortality rate as $3.4\%$. Under the estimate it says ‘Globally, about $3.4\%$ of reported COVID-19 cases have died[…]’ However, […]

Categories

## Dirac functions, inner products and $T \in \mathcal{L}(G)$

If G is a countable group with neutral element e (and with the composition written multiplicatively). $\ell^2(G)$ consist of functions $x: G \to \mathbb{C}$ such that $\sum_{t \in G} \vert x(t) \vert^2 < \infty$ and with inner product $$\langle x, y \rangle = \sum_{t \in G} x(t) \overline{y(t)}$$ For $x,y \in \ell^2(G)$. […]

Categories

## Dirac functions, inner products and $T \in \mathcal{L}(G)$

If G is a countable group with neutral element e (and with the composition written multiplicatively). $\ell^2(G)$ consist of functions $x: G \to \mathbb{C}$ such that $\sum_{t \in G} \vert x(t) \vert^2 < \infty$ and with inner product $$\langle x, y \rangle = \sum_{t \in G} x(t) \overline{y(t)}$$ For $x,y \in \ell^2(G)$. […]

Categories

## Find the radius of convergence for $\sum_{n=0}^{\infty}\frac{z^{n}}{\mathit{e}^{n}}$.

Find the radius of convergence for $\sum_{n=0}^{\infty}\frac{z^{n}}{\mathit{e}^{n}}$. Here is what I tried: $a_{n}=\frac{1}{\mathit{e}^{n}}$. Then $a_{n+1}=\frac{1}{\mathit{e}^{n+1}}$. Then $\frac{a_{n+1}}{a_{n}}=\frac{1}{\mathit{e}}$, right? Then $\sqrt[n]{\frac{1}{\mathit{e}}}\to 1$ as $n\to \infty$, since $\lim_{x\to \infty}\mathit{e}^{\frac{1}{x}}=1$. Then the radius of convergence is 1, right? However, I don’t think what I did was correct. Any tips are appreciated!

Categories

## Why is the Fisher information matrix both an expected outer product and a Hessian?

If $X$ is a random variable distributed as $X \sim p(x ; {\theta^*})$, the Fisher information matrix is defined as the expected outer product matrix: $$I(\theta) = E_{X \sim p(x ; {\theta^*})} \left[ \,\left(\nabla_ \log p(X\,; {\theta}) \right) \left(\nabla_ \log p(X\,; {\theta}) \right)^\top \,\right].$$ However, it is also defined as the expected Hessian […]

Categories

## Why is the Fisher information matrix both an expected outer product and a Hessian?

If $X$ is a random variable distributed as $X \sim p(x ; {\theta^*})$, the Fisher information matrix is defined as the expected outer product matrix: $$I(\theta) = E_{X \sim p(x ; {\theta^*})} \left[ \,\left(\nabla_ \log p(X\,; {\theta}) \right) \left(\nabla_ \log p(X\,; {\theta}) \right)^\top \,\right].$$ However, it is also defined as the Hessian matrix […]

Categories

## Nvidia Optimus with Nouveau drivers

I’m trying to get the optirun command to work with the FOSS Nouveau drivers on my computer that has an embeddded graphics unit and a discrete graphics processing unit. Here’s my setup provided by the lspci | egrep -i ‘vga|3d’command: 00:02.0 VGA compatible controller: Intel Corporation Skylake GT2 [HD Graphics 520] (rev 07) 01:00.0 3D […]

Categories

## Training NN to calculate atan2(y, x)

I’ve been working on a Q reinforcement learning implementation, where Q(π, a) is is approximated with a neural network. During trouble-shooting, I reduced the problem down to a very simple first step: train a NN to calculate atan2(y, x). I’m using FANN for this problem, but the library is largely irrelevant as this question is […]

Categories

## SLURM C++ sees more cores available than assigned

I am trying to run a single process multithreading job on a SLURM managed HPC cluster. I intend to use multi-cores for my thread. When I allocate the resources to HPC, I use the command: #SBATCH –nodes=1 #SBATCH –ntasks=1 #SBATCH –cpus-per-task=8 This should allocate 8 CPUs to one process on the same machine, right? However, […]