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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, […]

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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 \begin{equation} \langle x, y \rangle = \sum_{t \in G} x(t) \overline{y(t)} \end{equation} For $x,y \in \ell^2(G)$. […]

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Ask Mathematics

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 \begin{equation} \langle x, y \rangle = \sum_{t \in G} x(t) \overline{y(t)} \end{equation} For $x,y \in \ell^2(G)$. […]

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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!

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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 […]

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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 […]

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Development Linux

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 […]

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Development

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 […]

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C++ Development

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, […]