Optimization: How to minimize a quadratic form with the restriction that the sum of vector elements is one?

I've been trying to solve the following optimization problem

$$
begin {array} {rl}
min limits _ { boldsymbol {w}} & boldsymbol {w} boldsymbol {C} boldsymbol {w} \
mbox {s.t.} & sum_ {j = 1} ^ K w_j = 1 \
end {array}
$$

Where $ boldsymbol {w} in mathbb {R} ^ K $ Y $ boldsymbol {C} in mathbb {R} ^ {K times K} $ Y $ boldsymbol {C} $ it is symmetrical, that is to say $ boldsymbol {C} = boldsymbol {C} ^ top $.

Enter lagrange multiplier $ lambda in mathbb {R} $ and build the Lagrangian using the vector $ boldsymbol {1} ​​= (1, ldots, 1) ^ top in mathbb {R} ^ K $
$$
mathcal {L} ( boldsymbol {w}, lambda) = boldsymbol {w} boldsymbol {C} boldsymbol {w} – lambda ( boldsymbol {1} ​​^ top boldsymbol {w} – one )
$$

Then take the derivative with respect to $ boldsymbol {w} $

$$
nabla _ { boldsymbol {w}} mathcal {L} ( boldsymbol {w}, lambda) = 2 boldsymbol {C} boldsymbol {w} – lambda boldsymbol {1}
$$

However, I'm not sure how to solve this now …

8 – Cancel entity form handler

I am trying to alter an entity form controller. The EntityType :: setHandlerClass () method allows the & # 39; form & # 39 ;, controller to be set, but this value is an array, and I just want to override a single array element.

The definition of entity handlers:

handlers = {
    "storage" = "DrupaluserUserStorage",
    "storage_schema" = "DrupaluserUserStorageSchema",
    "access" = "DrupaluserUserAccessControlHandler",
    "list_builder" = "DrupaluserUserListBuilder",
    "views_data" = "DrupaluserUserViewsData",
    "route_provider" = {
      "html" = "DrupaluserEntityUserRouteProvider",
    },
    "form" = {
      "default" = "DrupaluserProfileForm",
      "cancel" = "DrupaluserFormUserCancelForm",
      "register" = "DrupaluserRegisterForm"
    },
    "translation" = "DrupaluserProfileTranslationHandler"
  }

I'm trying to figure out how to override the form.register controller, but since the first argument to setEntityHandler () is a string, I can't understand how to set a nested value.

User behavior – Preload for search form

I have a tool (web application) that allows people to search my database. They can choose filters and sort their results, etc. I wanted to add to the experience so that the user knows that his search is loading, once he clicks on the Submit button.

Then the search form looks like this

*** SEARCH FIELD || SEND BUTTON ****

* FILTERS *

* RESULTS *

I am trying to decide between:

  • the send button becomes a graphic preloader. Therefore, it initially has a value of & # 39; SEARCH & # 39 ;, when clicked, it is replaced with a pre-loaded gif, to give the effect of a load. This is nice, tidy and simple.
  • or a preloader in the center of the screen. This should also be accompanied by a layer of transparency on the top of the current screen, so that the preload is more outstanding. This seems a bit exaggerated, and it's the same as everyone else.
  • Another thought would be to eliminate all current search results and replace them with a preload (results will be obtained when the page is reloaded, NOT ajax).

I don't think any of them have much effect on conversions. I was more worried about the real experience. I want people to know that when they have clicked on the search button, we have received their request and are loading their results, particularly if the search is taking a while.

I am open to other ideas.

custom taxonomy – Contact form 7 – Fill drop-down list with terms related to the publication

I found another post that had the code to dynamically fill a CF7 drop-down menu with the terms of a taxonomy, and I have it working, but I wanted the terms not only to be all within the taxonomy, but I wanted them to only be related to the publication in which it is

To give you a little more context, this is an application form in a work publication. The type of personalized publication are job listings. I have a taxonomy of locations. Those terms are assigned to a publication. I just want the selected terms to appear in this drop-down menu.

This is the code I have:

function dynamic_select_list( $tag ) {

    // Only run on select lists
    if( 'select' !== $tag('type') && ('select*' !== $tag('type')) ) {
        return $tag;
    } else if ( empty( $tag('options') ) ) {
        return $tag;
    }

    $term_args = array();

    // Loop thorugh options to look for our custom options
    foreach( $tag('options') as $option ) {

        $matches = explode( ':', $option );

        if( ! empty( $matches ) ) {

            switch( $matches(0) ) {

                case 'taxonomy':
                    $term_args('taxonomy') = $matches(1);
                    break;

                case 'parent':
                    $term_args('parent') = intval( $matches(1) );
                    break;

            }
        }

    }

    // Ensure we have a term arguments to work with
    if( empty( $term_args ) ) {
        return $tag;
    }

    // Merge dynamic arguments with static arguments
    $term_args = array_merge( $term_args, array(
        'hide_empty' => false,
    ) );

    $terms = get_terms( $term_args );

    // Add terms to values
    if( ! empty( $terms ) && ! is_wp_error( $term_args ) ) {

        foreach( $terms as $term ) {

            $tag('values')() = $term->name;

        }

    }

    return $tag;

}
add_filter( 'wpcf7_form_tag', 'dynamic_select_list', 10 );

dnd 5e – For spells of Conjure animals, are summoned fairy spirits "intelligent enough" to take a form that fits the place of invocation?

I'm currently running Conjure animals quite restrictive

The player says that he is casting the spell and designates the places where they will appear (then I label them, as they are designated). I roll which animals take the form of a table that was designed to fit the whole Bell.

However, this has now bitten me in the butt several times, since the animals evoked campaign table often do not fit rubber and road encounter. I've got War Horses on sloping and slippery houses, vultures in dark, damp basements, and a rhinoceros in a narrow hallway.

While this was often humorous, I wonder if I should re-roll animals that clearly do not fit the meeting place. Are fairy spirits summoned "smart" enough to take a form that fits the place of invocation?

dnd 5e – For spells of Conjure animals, how "intelligent" are the summoned spirits that take the form of animals?

I am currently running Conjure Animals quite restrictively. The player says that he is casting the spell and designates the places where they will appear (then I label them, as they are designated) and then I roll which animals take the form of a table designed to fit the set Bell. However, this has bitten me in the ass several times when the animals conjured campaign table often do not fit rubber and road encounter. I've got War Horses on sloping and slippery houses, vultures in dark, damp basements, and a rhinoceros in a narrow hallway. While this was often humorous, I wonder if I should re-roll animals that are clearly poorly adapted to the meeting place, due to the intelligence / pragmatism of a fairy spirit.

linear algebra: volume form expressed in local coordinates in Riemannian collector

I am beginning to study the Riemannian geometry, and in particular the shape of the volume in a Riemannian collector $ (M, g) $. I was first introduced as a differential $ n $-to form $ dV $ for which $ dV (e_1, cdots, e_n) = 1 $ for any choice (positive) of orthonormal basis $ e_1, cdots, e_n $ in a tangent space $ T_p M $. It's easy to see that in this local framework, with a dual base $ omega ^ 1, cdots, omega ^ n $, we have:

$$ dV = omega ^ 1 wedge cdots wedge omega ^ n $$

That is well defined, as a change of basis to another positive orthonormal framework, say, $ tilde {e} _1, cdots, tilde {e} _n $ with double base $ tilde { omega} ^ 1, cdots, tilde { omega} ^ n $ yields:

$$ dV = det (A) tilde { omega} ^ 1 wedge cdots wedge tilde { omega} ^ n $$

Where $ A $ is the change of base matrix, which must satisfy $ det (A) = 1 $ because both bases are orthonormal and positive. However, I have now seen that in local coordinates, the shape of the volume looks like this:

$$ dV = sqrt {g_ {ij}} dx ^ 1 wedge cdots wedge dx ^ n $$

And I'm not sure how to move from the previous representation to this one. I can see that we will have:

$$ dV = det (B) dx ^ 1 wedge cdots wedge dx ^ n $$

Where $ B $ is the change of base matrix with components $ omega ^ i ( frac { partial} { partial x ^ j}) $but i'm not sure how to relate $ B $ in a sensible way to metric. I guess we can also put $ g $ in local coordinates such as:

$$ g = omega ^ i otimes omega ^ i $$

But this does not seem manageable.

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sharepoint online: how can I delete the document library from form templates?

I recently created a hub site in SharePoint Online and associated 3 sites to the hub site. Everything is OK until now.
However, in the Site Content of each site there is a Document Library called & # 39; Form Templates & # 39 ;.

This is causing confusion because there is a folder in another Document Library that users should use called & # 39; Form templates & # 39; (similar but different)

So, my question is how can I remove the document library from the form template? There is no option to do so, but there are in the Document Libraries that I create.

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Or should I keep it, since it is an essential part of the configuration of the Hub site?

All help appreciated.

Dan

Organize the checkbox and the vertical to horizontal alignment option button on a new form in the SharePoint online list

We have several check boxes and columns of option buttons on our SharePoint online list form. We want to change the display of all check boxes and option buttons horizontally.

We try below the script, but all checkboxes and radio buttons are shown on a line (see screenshot below). We want horizontal alignments based on columns.

Any suggestions on how to do it?

Thank you

enter the description of the image here

Script tested: