## BLP in terms of a Hilbert space

I am reading Stein’s 2013 monograph ‘Interpolation of Spatial Data’ where he characterizes the best linear predictor (BLP) in terms of a Hilbert space.

Let $$Q$$ be the set on which a random process $$Z$$ is observed. All linear predictors of $$h\in H_R$$, with $$R\subset\mathbb{R^d}$$, are of the form $$c+g$$, where $$c\in\mathbb{R}$$ is a scalar and $$g\in H_Q$$. Let $$g(h)$$ be the unique element in $$H_Q$$ that satisfies $$\mathrm{cov}[h-g(h),g^\prime]= 0$$ $$\forall g^\prime\in H_Q$$ and set $$c(h) = \mathbb{E}[h] – \mathbb{E}[g(h)]$$. From this it follows that $$c(h)+g(h)$$ is the BLP of $$h$$, which follows from $$\mathbb{E}[(h-c(h)-g(h))(c^\prime+g^\prime)]=0~\forall c^\prime\in\mathbb{R}$$.

I have three questions:

1. How do I see that $$h$$ is of the form $$c+g$$?
• Does the scalar take me from one Hilbert space to another?
2. Why is $$g(h)$$ unique for that covariance restriction? How can I interpret this covariance?
3. $$\mathbb{E}[(h-c(h)-g(h))(c^\prime+g^\prime)] = 0$$ should be obvious from these definitions but I don’t see it.
• The first parenthesis could be 0 since $$\mathbb{E}[h]-\mathbb{E}[g(h)]$$ is 0, but I’m really not sure.

Thanks for the help.

## Focusing and nonfocusing nonlinear terms

What is the mathematical and physical meaning of the terms focusing and nonfocusing when they refer to nonlinear terms in a dispersive equations?

## Migrate taxonomy terms with CSV

I would like to import some taxonomy terms with a taxonomy term in it. field_regio2 is a entityreference field to an existing taxonomy term Regio. But for some reason it is not working. Everything is working except the field_regio2.

$drush mmsg import_gemeentes gives:  the entity_lookup plugin requires a value_key, none located ? uuid: 7eef6b86-80db-40ab-8359-91d20675e0f2 langcode: en status: true dependencies: { } id: import_gemeentes class: null field_plugin_method: null cck_plugin_method: null migration_tags: null migration_group: migrated_terms label: 'Migrate gemeentes from the source CSV to taxonomy terms' source: plugin: csv path: 'public://gemeentes.csv' header_row_count: 1 keys: - id column_names: - id: id - vid: vid - name: name - field_stratenplan_luchtfoto_refe: field_stratenplan_luchtfoto_refe - rid: rid - rid22: rid2 process: vid: plugin: default_value default_value: gemeente name: name field_stratenplan_luchtfoto_refe: field_stratenplan_luchtfoto_refe field_regio: rid field_regio2: plugin: entity_generate source: rid22 destination: plugin: 'entity:taxonomy_term' migration_dependencies: null  ## What is the (number) showing in front of terms and vocabularies in Drupal? I am new to these staffs, so it is a little bit confusing for me. Can anyone please tell what does this number just telling us? ## Are the terms stable and reliable interchangeable? Is there a difference between stability and reliability (at least in software engineering context) or can they be used interchangeably? If not, what would be some examples of reliable but not necessarily stable systems, and vice versa? ## Hide Parent Terms in Taxonomy Term View Block in Twig Trying to hide the top two terms (or first two levels) in my org listing via twig. The listing itself is a view block using the term reference tree formatter. ## Magento 2 – build a unique id for the term’s checkbox for payment methods using vault For payment methods using vault, the id generated for term’s checkbox is duplicated as the payment method name is same. /** * build a unique id for the term checkbox * * @param {Object} context - the ko context * @param {Number} agreementId */ getCheckboxId: function (context, agreementId) { var paymentMethodName = '', paymentMethodRenderer = context.$  parents[1];              // corresponding payment method fetched from parent context             if (paymentMethodRenderer) {                 // item looks like this: {title: "Check / Money order", method: "checkmo"}                 paymentMethodName = paymentMethodRenderer.item ?                   paymentMethodRenderer.item.method : '';             }              return 'agreement_' + paymentMethodName + '_' + agreementId;         }, 

I see this code in checkout-agreements.js. However, in my case, cybersource vault method results in same paymentMethodName, leading it to duplication if there is more than one stored payment/ saved card.

I need help in coding the id attribute of term’s checkbox dynamically here:

<input type="checkbox" class="required-entry"                        data-bind="attr: {                                     'id': $parent.getCheckboxId($  parentContext, agreementId),                                     'name': 'agreement[' + agreementId + ']',                                     'value': agreementId                                     }"/> 

and its respective ‘for’ attribute of label.

## How to get the vocabulary terms for the current language

How do I programmatically get all the terms within a vocabulary for the current language?

This is a similar question to Get translated term name, but not for a single term, but for the entire tree.

## Recognizing Regular Languages in Layman terms

I understand that regular languages are languages which can be computed by Finite Automata however i am having some trouble understanding how one can identify a regular from non-regular.

I know that 0*1* is regular because the machine just needs to make sure the 0s and 1s are in order

I know that 0^n 1^nis non regular because the machine needs to keep count to make sure there is an equal number of 0s and 1s

But why is (01)^n considered regular? Doesn’t the machine have to keep track to make sure that there are n amount of 01?

How about {0^m 1^n | n>m}?

What is the general rule for quickly figuring out if something is regular or not in layman terms?

## Taxonomy terms not localized in view with enabled aggregation

On a view on content, I added a field “All taxonomy terms” (Display all taxonomy terms associated with a node from specified vocabularies) and enabled aggregation, see screenshot of view attached. This view is listing exclusively terms that are actually used in content. While the view is working for the standard language of the site, the terms are not translated into the other languages despite the vocabulary is translatable. Once I disable the aggregation, the translation of terms is working again.

So how can I make the translation of terms work?