Fresh installed magento 2.3 with sample data showing blank front page

Running mode: developer I was getting blank frontend page. I checked system.log and debug.log in magento and found out there was some errors related to some broken reference.

main.INFO: Broken reference: the 'logger' element cannot be added as child to 'after.body.start', because the latter doesn't exist [] [] main.INFO: Broken reference: the '' element cannot be added as child to 'after.body.start', because the latter doesn't exist [] [] 

The frontend page was showing blank but it was actually loading some html. I check for solution and found an answer in this thread

This thread suggested to delete the global.php file located in generated/metadata, and following this solved my issue and front end of my website loaded properly.

But now whenever I run the command

php bin/magento setup:di:compile 

the global.php file is generated again and my website’s frontend shows blank page again and deleting global.php solves it. I got some information related to global.php file in this thread Purpose of magento\generated\metadata\global.php file and is it safe to delete this file?

According to above thread

“The code compiler creates generated/metadata/global.php, which is a PHP serialized map of all constructor definitions mixed with object linking configuration defined in di.xml. di.xml is the dependency injection configuration. There is a global app/etc/di.xml and there can one defined for every module .”

This also happens when I run my website in production mode, and deleting global.php solves it. Now my question is why magento is generating global.php file if it is neither using it in developer mode nor production mode as deleting this file does not give any error and the website works perfectly.

And also broken reference error in fresh install of magento, does it means that it is some bug related to magento and how can one debug this problem further. I am asking how to debug it because as we can see in the error there is no mention of any file just a reference ‘after.body.start’.

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Algorithm for selecting a sample that’s as spread out as possible?

I have a large database of data with dates. There are large gaps and large chunks of data without gaps. I want to get a sample of this data such that the dates are as spread out as possible (i.e. as close to evenly distributed as possible).

E.g. if the dates are [1, 2, 3, 4, 100] and I want to sample 3 elements, the ideal sample would be [1, 50.5, 100] and the closest available dates are [1, 4, 100].

Is this a known problem with an existing algorithm?

What is the large-n limit of a distribution of the following sample statistic:

What is the large-n limit of a distribution of the following sample statistic:$ $ \displaystyle\frac{\sum^{n}X_{i}}{\,\sqrt{\,\sum^{n}X_{i}^{2}\,}\,}$ $ when sampling the Cauchy(0,1) distribution? Monte Carlo simulation indicates that convergence to this limit is quite fast, and that the resulting (symmetric) PDF has very sharp cusps at -1 and +1, but of course does not yield an analytic expression for this PDF – would anyone be able to find it? The following image indicates how the positive half of the PDF looks like

Determining Sample Spaces for Sylvester’s Four Point Problem

I don’t have any background in geometric probability, so may I ask for forgiveness if the following is wrong or doesn’t make sense:


  • no three sampled points are collinear
  • the (naive) geometric probability in euclidean space is equal to the ratio of lengths or areas
  • the probabilites do not change under isometric transformations and/or uniform scaling
  • the probability of a set $ P4:=\lbrace p_1,\ p_2,\ p_3,\ p_4\rbrace$ of four points being in convex configuration in the euclidean plane is independent of the order in which the elements are drawn by the sampling process; that in turn means that we assume that
  • $ \lbrace p_1,\ p_2,\ p_3\rbrace$ resembles the corners of $ T_{max}$ , the triangle of largest area
  • $ \lbrace p_1,\ p_2,\ p_3\rbrace$ have been drawn uniformly from the boundary of their circumcircle, which has implications on the probability of encountering $ T_{max}$ with specific values for the pair of smallest central angles.
  • the smallest circle enclosing $ P4$ is the unit circle centered at the origin
  • the longest side of $ T_{max}$ is bisected by the non-negative part of the x-axis

Under the above assumptions the probability of encountering a convex quadrilateral equals the blue area divided by the blue plus red area in the images below:

probability of 4 four points in convex configuration if the largest triangle is acute

the sampling area in case of acute $ T_{max}$ equals the entire unit disk

probability of four points in convex configuration if the largest triangle is obtuse

the sampling area in case of acute $ T_{max}$ equals the unit disk with a notch

The notch in the case of obtuse $ T_{max}$ is owed to the assumption that the first three points resemble $ T_{max}$ which implies that points outside $ T_{max}$ that generate a deltoid configuration would contradict the maximality of the area of $ T_{max}$

If the above makes sense, then the probability of four points being in convex configuration could be calculated by integrating over the ratios of the blue areas over the entire sampling area as defined by the $ T_{max}$ multiplied with the probability of $ T_{max}$ as a consequence of uniform sampling on the boundary of the unit circle.


  • have similar ways of defining the sample spaces for Sylvester’s Four Point Problem already been described or investigated?
  • what are objections against the proposed against the proposed definition of the available sample space on basis of $ T_{max}$ ?


in case of obtuse $ T_{max}$ the area of the sample space can be calculated on basis of angles $ \alpha$ and $ \beta$ that are adjacent to the longest side of $ T_{max}$ as follows, keeping in mind that that longest edge is the diameter of the unit circle:

  • the area of the lower blue half-disk equals $ \ \frac{\pi}{2}\ $
  • the area $ \ A_{\alpha}\ $ of the union of $ \ T_{max}\ $ with the blue region opposite to angle $ \ \alpha$ equals $ \ \alpha+\sin(\alpha)cos(\alpha)\ $ and analogous $ \ A_{\beta}\ $ for angle $ \ \beta\ $
  • the area of $ \ A_{T_{max}}\ $ of $ \ T_{max}\ $ equals $ \ \frac{1}{\cot(\alpha)+\cot(\beta)}\ $

The area of the sampling area for obtuse $ \ T_{max}\ $ then equals $ \ \frac{\pi}{2}+A_{\alpha}+A_{\beta}-A_{T_{max}}$