First moment

Population: $ \Omega = \{ x_1, \dots, x_N \} $
Collection of $n$-samples: $\mathcal{S} = \{ s \in \Omega^n \mid \forall i,j \in s, i \ne j \} $
Collection of $n$-samples containing $x$: $ \mathcal{S}_x = \{ s \in \mathcal{S} \mid x \in s \} $
Observe that $ |\mathcal{S}_x| = \binom{N-1}{n-1} $.
Let population mean be zero. $\mu = 0$, i.e. $ \sum_{i = 1}^N x_i = 0 $
Fix an order for $\mathcal{S}$: $ \mathcal{S} = \{ s_1, s_2, \dots, s_{|\mathcal{S}|} \} $.
$j$-th $n$-sample mean $ m_j = \frac1n \sum_{x \in \mathcal{S}_j} x $
Remark: I don’t use $ \sum s_j $ as in $ \cup \mathcal{T} $ in topology to avoid misreading the $n$-sample $ s_j $ as an element.
mean of $n$-sample mean $ m = \frac{1}{|\mathcal{S}|} \sum_{s_j \in \mathcal{S}} m_j $

Problem

Since the recent Hugo upgrade to v0.55.3, the following messages popped up after each local site regeneration with hugo server.

WARN 2019/04/24 18:07:00 Page's .URL is deprecated and will be removed in a futu
re release. Use .Permalink or .RelPermalink. If what you want is the front matte
r URL value, use .Params.url.
WARN 2019/04/24 18:07:00 Page's .Hugo is deprecated and will be removed in a fut
ure release. Use the global hugo function.
WARN 2019/04/24 18:07:00 Page's .RSSLink is deprecated and will be removed in a 
future release. Use the Output Format's link, e.g. something like: 
    {{ with .OutputFormats.Get "RSS" }}{{ .RelPermalink }}{{ end }}.
Total in 136 ms

GitLab’s online runner also gave the same type of warnings. This was reported in Beautiful Hugo issue #261.

Problem

During the installation of RCall.jl, the package wasn’t successfully built due to a missing variable $R_HOME.

$ julia -q
julia> Pkg.add("RCall")
 Resolving package versions...
 Installed WinReg ─ v0.3.1
 Installed RCall ── v0.13.2
  Updating `~/.julia/environments/v1.0/Project.toml`
  [6f49c342] + RCall v0.13.2
  Updating `~/.julia/environments/v1.0/Manifest.toml`
  [6f49c342] + RCall v0.13.2
  [1b915085] + WinReg v0.3.1
  Building RCall → `~/.julia/packages/RCall/ffM0W/deps/build.log`
┌ Error: Error building `RCall`:
│ ERROR: LoadError: R_HOME is not a directory.
│ Stacktrace:
│  [1] error(::String) at ./error.jl:33
│  [2] top-level scope at logging.jl:322
│  [3] top-level scope at /home/vin100/.julia/packages/RCall/ffM0W/deps/build.jl
:19
│  [4] include at ./boot.jl:317 [inlined]
│  [5] include_relative(::Module, ::String) at ./loading.jl:1041
│  [6] include(::Module, ::String) at ./sysimg.jl:29
│  [7] include(::String) at ./client.jl:388
│  [8] top-level scope at none:0
│ in expression starting at /home/vin100/.julia/packages/RCall/ffM0W/deps/build.
jl:10
└ @ Pkg.Operations /buildworkjr/worker/package_linux64/build/usr/share/julia/std
lib/v1.0/pkg/src/operations.jl:1069

Discussion

It took me a few minutes to realise that the cause of this error is the absence of R. I referred to CRAN’s installation instructions for Ubuntu and added

Tonight, the screen of Xubuntu suddenly enlarged and blurred. Typing “xubuntu screen display enlarged” on Google, I’ve learnt that the <Alt> key and the mouse scroll wheel can enlarge/minify screen display from Ubuntu Forums.

This is a linklog to Christopher Rackauckas’s article about Julia, Cython & Numba. Unluckily, I don’t have time to read this now. Hope I can return to this later.

This is a linkblog to a post on Discuss HK which claims how Mandarin (普通話) messes up the flat and oblique tones (平仄) of the regulate verse (近體詩) below.

《山行》　杜牧
遠上寒山石徑斜，白雲生處有人家。
停車坐愛楓林晚，霜葉紅於二月花。

However, Kimery has checked the Mandarin pinyin (拼音) and (s)he doesn’t found such problem except for some characters with entering tone (入聲). Luckily, such characters are located at the odd numbered position of a verse. Eventually, (after considering other factors,) that won’t harm the variation of tones in principle.

Pour simuler les trajectoires d’une équation différentielle, le schéma le plus facile est l’un découvert par Euler.

Cependant, en espérant mettre ce que j’ai vu au cours de ma licence en pratique, j’ai cherché un peu sur des méthodes numériques pour les EDS sur Google, et je suis tombé sur un article écrit par Brian D. Ewald.

Les différences entre les schémas « forts » et « faibles » seraient-ils pertinents pour mon stage ? On va voir.

I intend to post this for a Borel-Cantelli lemma exercise on Math.SE.

The target event is ${\exists i_0 \in \Bbb{N} : \forall i \ge i_0, X_i = 1}$, whose complement is

$$ {\forall i_0 \in \Bbb{N} : \exists i \ge i_0, X_i > = 0} = \limsup_i {X_i = 0}. $$

To apply Borel-Cantelli, one has to determine whether $\sum_i P(X_i = 0)<+\infty$.

Contexte

J’ai publié mon template de lettre en Xe$\LaTeX$ sur mon ancien blog (hébergé sur GitHub Pages) il y a trois ans.

Problème et solution

Après le changement de l’ordi portable, il me faut l’installation du pacquetage “texlive-lang-french” sur la nouvelle version d’Ubuntu. Sinon, une erreur du pacquetage Babel se surviendra.

! Package babel Error: Unknown option `frenchb'. Either you misspelled it
(babel)                or the language definition file frenchb.ldf was not foun
d.

See the babel package documentation for explanation.
Type  H <return>  for immediate help.


l.445 \ProcessOptions*

?

A ce stade, Xe$\LaTeX$ parviendra à compiler le fichier $\TeX$ avec une remarque à propos de l’obsolescence de l’option frenchb pour le pacquetage Babel.

After reading Hugo Comments with Staticman on Kostas Tsalikis’ web site, I tried to leave the following comment.

As far as I know, Staticman can be used only with GitHub, since it works as a GitHub bot. Obviously, not all static sites are saved in GitHub, and this may be a showstopper for someone using another service. Thanks to eduardoboucas/staticman#219, Staticman now supports GitLab. You may view my demo Hugo site on Framagit at https://staticman-gitlab-pages.frama.io/bhdemo/posts/my-second-post/ Source) as a working example.

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