ag.algebraic geometry – Description of determinantal varieties in $mathbb{P}^n$ that are linear sections of determinantal varieties in $mathbb{P}^{n+1}$

Fix an algebraically closed field $k$ of characteristic 0. Consider an $n$-tuple $(A_1,ldots, A_n)$ of
$ntimes n$ matrices over $k$ and assign to it the determinantal surface in $mathbb{P}_k^{n-1}$ cut out by the polynomial $det(x_1A_1+ldots x_nA_n).$ Now consider a fixed non-zero matrix $G$ of rank $r<n$.

Now let $x$ be the vector with components $x_i$ and $G_{ij}$ be the components of $G$. We may then consider the variety cut out by the polynomial $det(sumlimits_{j=1}^nx_jA_iG_{ij}).$ With $y=Gx$, this is then a plane section of the variety cut out by $det(y_1A_1+ldots y_nA_n)$ with the $mathbb{P}_k^{r-1}$ corresponding to the image of $G$, and also a determinantal hypersurface of degree $n$ itself in said $mathbb{P}_k^{r-1}$.

My question is then whether a generic determinantal hypersurface of degree $n$ in $mathbb{P}_k^{r-1}$ is a linear section of a determinantal hypersurface of degree $n$ in $mathbb{P}_k^{n-1}$. I recently heard that even some curves in $mathbb{P}^2_k$ are not of this kind, but I don’t know a reference for this fact.

computer networks – Tearing down the FSM description of congestion control

I was going through the text Computer Networking- A Top-Down Approach by Kurose and Ross, there I found subtleties with the TCP congestion control FSM which is shown below:

TCP Congestion Control FSM

Mainly I am having difficulty in understanding the action transmit new segment(s), as allowed and transition to the Fast Recovery state.

I have read the equivalent portions from the textbook Data Communications and Networking by Forouzan but there though the explanation is easy but there is no FSM or a programmatic approach.

Now let us consider the slow start phase as shown in the Kurose & Ross text:

TCP Slow start phase

The time diagram which they explain about the $cwnd$ doubling after each transmission round is easy and is just like what the Forouzan text says. But I find it difficult to understand the implementation based on the arc labeled with :
Arc

in the slow start phase.

  1. Suppose the sender starts with $cwnd = 1$ $MSS$ then sends this (1st) segment to the network layer and awaits the acknowledgment.
  2. The sender gets “new ACK” for the previous packet and increases $cwnd$ to $2$ $MSS$. Then in accordance to “transmit new segment(s), as allowed”, the sender sends $2$ segments (2nd and 3rd) to the network layer and awaits the acknowledgments.
  3. Now the sender receives “new ACK” corresponding to 2nd segment and increases $cwnd$ to $3$ $MSS$. Then in accordance to “transmit new segment(s), as allowed”, the sender sends $3$ segments to the network layer and awaits the acknowledgments.
  4. Now the sender receives “new ACK” corresponding to 3rd segment and increases $cwnd$ to $4$ $MSS$. Then in accordance to “transmit new segment(s), as allowed”, the sender sends $4$ segments to the network layer and awaits the acknowledgments.

From points 3 and 4, I find that the situation does not match with the slow start phase as shown in Fig 3.51. (i.e. the no. of segments sent are 1,2, 3,4 instead of 1,2,4)


I cannot understand the Fast recovery state’s action. Specifically the Forouzan text says :

Most TCP implementations have two reactions:

  1. If a time-out occurs, there is a stronger possibility of congestion; a segment has probably been dropped in the network, and there is no news about the sent segments. In this case TCP reacts strongly:
    a. It sets the value of the threshold to one-half of the current window size.
    b. It sets cwnd to the size of one segment.
    c. It starts the slow-start phase again.

  2. If three ACKs are received, there is a weaker possibility of congestion; a segment may have been dropped, but some segments after that may have arrived safely since three ACKs are received. This is called fast transmission and fast recovery. In this case, TCP has a weaker reaction:
    a. It sets the value of the threshold to one-half of the current window size.
    b. It sets cwnd to the value of the threshold (some implementations add three segment sizes to the threshold).
    c. It starts the congestion avoidance phase.

In the Forouzan text, there is no such transition to the Fast Recovery state. But here in Kurose there is such a state and there is an arc labeled :

label

whose working I do not quite understand in detail.

What extra work is the version in Kurose doing as compared to the one given in the Forouzan text? Can anyone explain me the subtleties with a comprehensive example covering all the cases of the FSM, so that I can understand the thing better.

8 – Overwrite field description in an image widget

I have an image field (multiple).

In the node form, the ImageWiget has a process method that adds previews and form fields for images that have already been uploaded.

The description for the title tag is hard-coded on line 278: '#description' => t('The title is used as a tool tip when the user hovers the mouse over the image.'). We are actually showing the title as a caption and not a tooltip.

How can I override the description?

Youtube Video still showing old title and description

a specific you tube video keeps showing old title and description after clicking Save button although it shows the correct data in the editing mode…All other videos are updated successfully….what shall i do?

seo – Google results for my site are showing the title of a hidden modal element instead of my meta description

I have a site that features a listing of companies. Every company has its own page. Every page has its own meta description. There is no nofollow or noindex tag or anything like that.

Yet, instead of the meta description, Google chooses to show the title of an insignificant modal element on the page. This is true for most results from the site. Maybe 10% of results show the meta description correctly.

This behavior is so seemingly random that I have no idea how to help the situation. There is a big H1 title on the page, so if Google is ignoring the meta description, I would expect it to pick that.

The modal is hidden and it’s not even the first modal when you look at the HTML source of the page.

Any suggestions?

microsoft outlook – We can’t save your rule yet because a value is missing. To set it, click the underlined text in the rule description area

In Outlook 2016 (version is in the context menu of the task bar button), trying to get notified of emails i made a rule to move to my GitLab folder, it refuses to save due to this vague error:

We can’t save your rule yet because a value is missing. To set it,
click the underlined text in the rule description area.

Vague error message with the text above.

There are multiple underlined items. Which is it?

Drupal 9: How to add custom attributes to description meta tag?

I need to add ‘class’ and ‘data-type’ attributes to meta tag containing description attribute. I was able to locate the core Metatag module, however I’m unable to find any documentation on how to customize output without altering the core.

magento2 – Add description to Related Products

I try to add product Short Description in the Related Products section in Magento 2.4 version.

I overwrite this file:/app/design/frontend/Theme/MyTheme/Magento_Catalog/templates/product/list/items.phtml in my custom theme and I add the following code:

<?=/* @noEscape */ $_helper->productAttribute($item, $item->getShortDescription(), 'short_description')?>

The code work only for Simple Products if there in the related products are some configurable products the code is not return anything.

Is there any way to have the short description for both types of products?

Thank you

php – How do i change a website description on Google?

I’d like to change the description of a website on google search and put a short text that explains what the website is about.

I looked for a meta description and the one in landing.blade.php is

<meta name="description" content="{{AppMeta::where('type','main')->first() ? AppMeta::where('type','main')->first()->description : ""}}"> 

when you search the name of the website on google it shows .home_text_6. CONTATTI. GENGLE .about .faqs .blog.
here’s what you see

How can i change this?