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Development : Naro Dev

Garphics : Graphéin

Imazone.dz – Decoration & Equipments

https://imazone.dz

In web applications, you try to decide when to use either JSON Web Tokens (JWTs) or sessions (cookies) for authentication. When you browse the web you use HTTP, which is a stateless protocol. So, the only way to remember the states of your application is using either sessions or tokens.

Medicocare.dz – Medical Equipments

https://medicocare.dz/

A Narodev Creation :
– Amine G –
– Ilyes A –
– Mohammed .N.B –

Saiko Sushi – Japaneese Food .

Facebook Image Sizes

With 1.18 billion monthly active users, Facebook is the world’s largest social network. One bad image choice could spell the difference in attracting and engaging with this huge user base and being completely ignored.

One thing to remember when choosing your photos is that there is a difference between how things will display on your personal timeline and how things will display in a user’s news feed. Make sure that you are choosing dimensions based on where you want the majority of viewers to see your image.

Profile Picture: 180 x 180 (Displays 170 x 170 on Desktop)

Say cheese: this is going to be the photo representing you or your brand on Facebook. This is the square photo that appears on your timeline layered over your cover photo. Your profile picture will also appear when you post to other walls, comment on posts or when your profile is searched.

Image Guidelines

• Must be at least 180 x 180 pixels.
• Photo will appear on page as 170 x 170 pixels on desktop and 128 x 128 on smartphones.
• Profile pictures are located 16 pixels from the left and 176 pixels from the top of your cover photo on desktop.
• Profile pictures are located 24 pixels from the left, 24 pixels from the bottom and 196 pixels from the top of your cover photo on smartphones.
• Photo thumbnail will appear throughout Facebook at 32 x 32 pixels.

Business Page Profile Picture: 180 x 180 (Displays 170 x 170 on Desktop)

Facebook recently changed its Profile image for Business Pages to appear to the left side of the screen. The new look helps Facebook Business Pages stand out among personal accounts. However, the dimensions are the same, but the photo appears on the page slightly different.

Image Guidelines

• Must be at least 180 x 180 pixels.
• Photo will appear on page as 170 x 170 pixels on desktop, 128 x 128 on smartphones, and 36 x 36 on most feature phones.
• Photo thumbnail will appear throughout Facebook at 32 x 32 pixels.
• Business Page images will be cropped to fit a square.

Cover Photo: 820 x 312

Your Facebook cover photo will only appear on your Facebook timeline, but it is a lot bigger than the profile picture, which gives you more freedom to choose something creative. Where your profile picture might be a good choice for a picture of you, or a brand logo, use this space to post something that speaks more toward you as an individual or as a brand.

Image Guidelines

• Appear on page at 820 x 312 pixels. Anything less will be stretched.
• Minimum size of 400 x 150 pixels.
• Displays at 820 x 312 pixels on desktop and 640 x 360 pixels on smartphones.
• For best results, upload an sRGB JPG file less than 100 KB.
• Images with a logo or text may be best as a PNG file.
• Business Page dimensions are exactly the same as personal accounts.

Shared Image: 1,200 x 630

A shared image is one of the most common forms of sharing on Facebook. These images will always appear on your timeline, and ideally they will show up in most of your followers’ News Feeds — though with the decrease in organic reach, it’s unlikely that everyone will see your post. The more people engage with your post, the more likely it is that the rest of your followers and their followers will see that activity.

Image Guidelines

• Recommended upload size of 1,200 x 630 pixels.
• Will appear in feed at a max width of 470 pixels (will scale to a max of 1:1).
• Will appear on page at a max width of 504 pixels (will scale to a max of 1:1).

Shared Link: 1200 x 628

Another great tool in your Facebook belt is the ability to share a link. It’s very similar to posting a shared image, but it gives you even more fields to work with. You can choose to create a shared link with a small square image to the left and text on the right, or with a larger rectangular image on top with text underneath.

Image Guidelines

• Recommended upload size of 1,200 x 628 pixels.
• Square Photo: Minimum 154 x 154px in feed.
• Square Photo: Minimum 116 x 116 on page.
• Rectangular Photo: Minimum 470 x 246 pixels in feed.
• Rectangular Photo: Minimum 484 x 252 on page.
• Facebook will scale photos under the minimum dimensions. For better results, increase image resolution at the same scale as the minimum size.

Event Image: 1920 x 1005 (Recommended)

Facebook Events help capture the attention of users and cut through the noise on Facebook. Reminders are sent to your audience and having a good space with an even better image is important. Make sure you have the right dimensions down for a Facebook Event cover photo.

Image Guidelines

• Facebook will scale down to minimum dimensions: 470 × 174.
• Shows in feed: 470 × 174.

Fundraiser image: 800 x 300 (recommended)

Facebook has added the ability to create a fundraiser for charitable organizations or personal causes. The cover photo for these fundraisers slightly varies from a typical Facebook cover photo, with a minimum size of 400 x 150. The best experience across many display types will come from a higher resolution image, though.

Looking for Facebook ad sizes?

Facebook ad formatting can be even more complex than organic posts, so for more guidelines, check out our complete guide to every Facebook ad size!

Find more information on the image sizes for Facebook, visit the Facebook Help Center.

Twitter Image Sizes

Don’t let its logo fool you–Twitter is not just for the birds. In fact, with 313 million monthly active users, Twitter is one of the social media networks that your customers will most often use to discuss your brand. And recently, Twitter made some big changes to its overall layout.

Profile Photo: 400 x 400 (Displays 200 x 200)

Your Twitter profile photo is the main image that represents you or your brand across the network. It’s going to be seen across the site in a number of places by a number of people so make sure it’s of the highest quality. Here’s the places your profile photo will be visible on the site.

• On Your Page: The largest display of your profile picture is on your homepage and can be viewed by your followers as well as individuals who stumble upon your page.
• In-Stream: A smaller version of your profile picture appears in a follower’s Twitter stream every time you Tweet. It also appears in the stream of your followers’ followers every time you’re Retweeted.
• Who to Follow: Your profile picture is also going to appear next to a link to your page in the “Who to follow” box. This is located directly to the right of your twitter stream. Choose a recognizable image here.

Image Guidelines

• Square Image recommended 400 x 400 pixels.
• Maximum file size 5 MB.
• Image types include: JPG, GIF or PNG.

Header Photo: 1,500 x 500

Your header photo is the image that spans the top of your Twitter profile page. It’s quite a bit larger than your profile photo so make sure to save it at the highest resolution possible. Because you have more room to be creative with this picture and it will likely be the first thing your visitors see, make it something captivating.

Image Guidelines

• Recommended 1,500 x 500 pixels.
• Maximum file size of 5 MB.
• Image types include: JPG, GIF or PNG.

In-Stream Photos and Shared Links

Twitter users can attach photos to any of their Tweets. Depending on whether you’re attaching one photo, multiple, or sharing a link, the way photos crop and display in stream will vary slightly.

Fortunately, in 2021, Twitter made waves with #Twittercropisgone, eliminating the sometimes-unfavorable automated cropping for vertical images that had often become the subject of memes and in-jokes among users of the platform. Extremely wide or tall images with unusual dimensions may still get cropped, but for most images in standard 4:3 or 16:9 dimensions (or close to them), you won’t have to worry as much about centering subjects around automated cropping. https://platform.twitter.com/embed/Tweet.html?dnt=true&embedId=twitter-widget-0&features=eyJ0ZndfZXhwZXJpbWVudHNfY29va2llX2V4cGlyYXRpb24iOnsiYnVja2V0IjoxMjA5NjAwLCJ2ZXJzaW9uIjpudWxsfSwidGZ3X2hvcml6b25fdHdlZXRfZW1iZWRfOTU1NSI6eyJidWNrZXQiOiJodGUiLCJ2ZXJzaW9uIjpudWxsfSwidGZ3X3NwYWNlX2NhcmQiOnsiYnVja2V0Ijoib2ZmIiwidmVyc2lvbiI6bnVsbH19&frame=false&hideCard=false&hideThread=false&id=1390026628957417473&lang=en&origin=https%3A%2F%2Fsproutsocial.com%2Finsights%2Fsocial-media-image-sizes-guide%2F&sessionId=71b283bf197c3b452a96a741b52e9d0453471d13&theme=light&widgetsVersion=9fd78d5%3A1638479056965&width=550px

The following are some best practices to get an optimal result, and you can also preview the end result in Sprout’s Compose window before you publish.

Recommended sizes for images by types of Tweets:

• Image from a Tweet with shared link: 1200 x 628 pixels
• Tweet sharing a single image: 1200 x 675 pixels (recommended, but most images with standard aspect ratios will not be cropped)
• Tweet sharing two images: 700 x 800 pixels (both images)
• Tweet sharing three images:
  • Left image: 700 x 800 pixels
  • Right images: 1200 x 686 pixels
• Tweet sharing four images: 1200 x 600 pixels (per image)
  • Four is the maximum number of images available on one Tweet
• Recommended aspect ratio is 16:9.
• Can edit images if tweeting from Twitter iOS or Android app.
• Maximum file size of 5 MB for photos, and 5 MB for animated GIFs on mobile and 15 MB on web.

Find more information on in-stream photos at the Twitter Help Center.

Instagram Image Sizes

Instagram is one of the most popular photo-sharing social networks. It’s the best place to showcase your visual creativity, even down to making a compelling grid out of the way your photos’ thumbnails display in sequence.

Profile Picture: 110 x 110

Instagram is based on visuals, which should be an indication of how important it is to follow these image size guidelines. Ensure your profile image is recognizable so users can find you even easier through search or explore.

Image Guidelines

• Appear on your profile at 110 x 110 pixels.
• Square photo: make sure to maintain an aspect ratio of 1:1.

Photo Thumbnails: 161 x 161

When someone goes to your page, they’ll be presented with all of your content arranged in rows of thumbnails. These smaller renditions of your images and videos will expand when clicked and include a place for people to comment.

Image Guidelines

• The thumbnails will appear on the page at 161 x 161 pixels.
• Square photo: make sure to maintain an aspect ratio of 1:1 ratio.

Photo Size: 1080 x 1080

Instagram is all about the images and videos presented in your followers’ feed. In fact, Instagram higher resolution photos when taken from the native application. If you decided to upload a photo or video from any other device, the resolution will be much lower.

Image Guidelines

• The size of Instagram images has been increased to 1080 x 1080 pixels.
• Instagram still scales these photos down to 612 x 612 pixels.
• Appear in feed at 510 x 510 pixels.
• Square or rectangle photos: make sure to maintain an aspect ratio between 1:1 or 1.91:1.
• For portrait (4:5) photos, recommended dimensions are 1080 x 1350 pixels.

Instagram Stories: 1080 x 1920

With more than 300 million daily users, Instagram Stories are a popular source of visuals on the app. There are both video and image options available to publish. And while this feature is meant to be ephemeral, it’s possible to upload your own content.

Image Guidelines

• Recommended resolution is 1080 x 1920.
• Minimum resolution is 600 x 1067.
• Aspect ratio is 9:16.

For those looking for more info on Instagram ad sizes, including video specs, check out this guide!

LinkedIn Image Sizes

With 467 million registered users, LinkedIn is the world’s largest professional network. Where other social networks may be good drivers of traffic and customers, LinkedIn is a great place for you to source great employees and to connect with other industry leaders.

Personal Profile Image: 300 x 300 (Recommended)

LinkedIn started using a new layout for personal profiles and kept the box logo with company pages (more on that below). However, the personal profile dimensions for LinkedIn is very straightforward. This is the main image that represents you on your personal profile. So anytime someone takes a look at your profile for some quick info, this is the prominent image that represents you. It’s important to get the size right.

Image Guidelines

• Minimum 300 x 300 pixels
• Maximum file size 10MB.
• Image types includeL JPG, GIF or PNG.

Personal Background Image: 1584 x 396

LinkedIn’s background image is a newer feature for your personal profile. It’s a little bit trickier to find something that really fits that space well, but if you get it right, your profile will look great.

Image Guidelines

• Recommended 1584 x 396 pixels.
• Maximum size of 4MB.
• Image types include: JPG, PNG or GIF.

Company Logo Image: 300 x 300

One of the two brand logos that you should be uploading to LinkedIn is the standard company logo. This is the bigger of the two and is going to show up right next to your brand name on your LinkedIn homepage. This image also appears in the “Companies you may want to follow” section. The more enticing the photo, the more likely you’ll gain followers.

• Recommended 300 x 300 pixels.
• Minimum 300 x 300 pixels.
• Maximum 4MB (Square layout).
• Image types include: PNG, JPG or GIF.

Company Cover Image: 1128 x 191 (recommended)

Unlike the personal background image, the company or standard business background image covers the entire top of the page. The image appears much larger than the personal dimensions, giving businesses a bit more space.

Image Guidelines

• Recommended size 1128 x 191.
• Maximum file size of 4MB.
• Image types include: PNG, JPG or GIF.

Shared Image or Link: 1200 x 627 (Recommended)

This size works for LinkedIn posts that share a photo or a link with image to a blog post or article to your company page’s feed.

Image Guidelines

• Recommended size for images or links: 1200 x 627 pixels based on mobile scaling
• Image types include: JPNG, JPG or GIF.

Life Tab – Main Image & Company Photos

The life tab on LinkedIn company pages lets you provide a more in-depth look at the day to day experience of your company’s employees. Currently, the two types of images you can upload here are the main image, which serves as a hero and highlight to your page, and the horizontal scrolling gallery of other company photos beneath.

Image Guidelines

• Recommended size for main image: 1128 x 376
• Recommended size for company photos: 900 x 600
• Image types include: JPNG, JPG or GIF.
• The life tab only appears on the mobile app, and not the mobile web version of LinkedIn, so exact display sizes will vary by device. Upload the recommended size for the best experience.

Find more information in the Linkedin Help Center.

Pinterest Image Sizes

Pinterest can be an amazing social tool for driving referral traffic to your site. This is mostly due to the fact that 90% of Pinterest pages are external links.

So it’s very important for you to make sure you’re optimizing your Pinterest page regularly and using proper image sizes for your boards and pins.

Profile Picture: 165 x 165

When setting up your Pinterest account you have the option to do so using Facebook, Twitter or email. If you choose Facebook or Twitter, Pinterest will pull in the profile image that you have set there.

If you’re using email, or would prefer to use a different photo, you can do that too: just upload a square photograph (the larger the better) and Pinterest will resize it to fit. Like other social sites your profile picture on Pinterest should be something closely tied to you or your brand.

Image Guidelines

• Recommended size: 165 x 165 pixels
• Maximum 10 MB.
• Image types include: JPG and PNG for profile pictures.

Pin Sizes

When adding a pin to your board, it’s important to remember that Pinterest puts a limit on the width of the image but not the length. This gives you the opportunity to add a photo that’s square or one that will scale to be even taller. Just remember to make sure you’re creating large images because they add more value, not just because you can.

Image Guidelines

• It’s recommended to use an image aspect ratio of 2:3 to 1:3.5
• Expanded pins have a minimum width 600 pixels, so to maintain aspect ratio, 900 px is the recommended height.

Board Display

Creating boards is one of the most important things that you can do on Pinterest. It’s important to make sure you’re using an image that fits the size criteria perfectly. Not only is it important to choose a photo that is enticing to your audience, it’s important to choose one that’s relevant to that particular board.

Image Guidelines

• 222 x 150 pixels (large thumbnail)
• 55 x 55 (smaller thumbnail)

Find more information in the Pinterest Help Center.

YouTube Image Sizes

YouTube has more than 1 billion unique users every month and is available on hundreds of millions of devices. More than 1 million brands have already realized that YouTube is a great opportunity to reach their fan-base.

Channel Profile Image: 800 x 800

YouTube allows you to select different profile image borders, but the dimensions stay the same. Ensure your YouTube has a profile image set up before you select your border.

Image Guidelines:

• Recommended 800 x 800 pixels.
• Image types: JPG, GIF, BMP or PNG.

Channel Cover Photo: 2,048 x 1,152

Spice up your YouTube channel with some “channel art.” When users click through your YouTube videos to your channel, some appealing images could entice them to stay on your page longer and watch more of your videos.

Image Guidelines:

• Recommended 2560 x 1440 pixels.
• Safe area for mobile and web (without text and logo cropping) 1546 x 423 pixels.
• Maximum file size: 4MB.
• Image types: JPG, GIF, BMP or PNG.

Across Different Devices

There are a lot of different platforms and devices that users can stream YouTube on so it’s important that you review your creative across devices and confirm that the most important parts of your image, such as text or logos, are displaying legibly in the ‘safe zone’ noted above.

Find more information in the YouTube Help Center.

Video Uploads: 1280 x 720 (Minimum HD)

Uploading your content to YouTube is the one of the most important parts of establishing your presence on the site. Videos can tell viewers something about you as a person, or it could show off something that your business might offer.

Video Guidelines

• Videos must maintain a 16:9 aspect ratio. Smaller videos such as 4:3 will be pillarboxed to fit.

For more on the specifics of YouTube video optimization, or to size video on any other social network, check out our complete guide to social media video specs.

Google My Business Image Sizes

Google My Business has become an essential platform for businesses with local, brick-and-mortar presences to gain visibility and conduct their review management strategy.

Types of Images for Google My Business:

• Logo: Your recognizable logo image. May not be available for all types of businesses–see Google guidelines for more detail.
• Cover photo: A photo of your business that will typically be the first one shown. Choose a photo that gives the best overall representation of your place of business for this photo.
• Business photo: You can use your other business photos to highlight different elements of your business or offices and help show off what local visiting customers should look for when they stop by.

For all three types of images, Google’s official guidelines recommend the below specs for the best appearance on the platform.

Image Guidelines:

• Recommended resolution: 720 x 720 pixels
• Minimum resolution:250 x 250 pixels
• File size maximum: 5 MB
• Format: JPG or PNG.

Membership & Main Features Fees (HT)

• Member ship fees : 50000 DZD
• Integration slot openning fee : 10000 DZD / Day
• SATIM Testing resources access fees :
  • 5000 DZD / Day
  • 6000 DZD / Hour (when opened on non business hours)

• Yearly Subscription fee (based on transactions amount) :
  • 0 to 1000 operations : 0 DZD
  • 1001 to 10000 operations : 10000 DZD
  • 10 001 to 50 000 operations : 50 000 DZD
  • 50 001 to 100 000 operations : 100 000 DZD
  • More then 100 001 operations : 150 000 DZD

• Other Fees (optional) :
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• Transacyions Based Fees :

• Miminum Operation Amount : 100 DZD (the minimum allowed amount per trasaction)

This video is mainly about different techniques about how to use SSH tunneling serving and maintaining access when not possible .

i am actually adding this video particularly because of the graphic approach followed explaining how communication in the internet work , more precisely , IP PORTS .

Types of Port Forwarding

SSH’s port forwarding feature can smuggle various types of Internet traffic into or out of a network. This can be used to avoid network monitoring or sniffers, or bypass badly configured routers on the Internet. Note: You might also need to change the settings in other programs (like your web browser) in order to circumvent these filters.

There are three types of port forwarding with SSH:

• Local port forwarding: connections from the SSH client are forwarded via the SSH server, then to a destination server
• Remote port forwarding: connections from the SSH server are forwarded via the SSH client, then to a destination server
• Dynamic port forwarding: connections from various programs are forwarded via the SSH client, then via the SSH server, and finally to several destination servers

Local port forwarding is the most common type. For example, local port forwarding lets you bypass a company firewall that blocks Wikipedia.

Remote port forwarding is less common. For example, remote port forwarding lets you connect from your SSH server to a computer on your company’s intranet.

Dynamic port forwarding is rarely used. For example, dynamic port forwarding lets you bypass a company firewall that blocks web access altogether. Although this is very powerful, it takes a lot of work to set up, and it’s usually easier to use local port forwarding for the specific sites you want to access.

Port-forwarding is a widely supported technique and a feature found in all major SSH clients and servers, although not all clients do it the same way. For help on using a specific client, consult the client’s documentation. For example, the PuTTY manual has a section on port forwarding in PuTTY.

To use port forwarding, you need to make sure port forwarding is enabled in your server. You also need to tell your client the source and destination port numbers to use. If you’re using local or remote forwarding, you need to tell your client the destination server. If you’re using dynamic port forwarding, you need to configure your programs to use a SOCKS proxy server. Again, exactly how to do this depends on which SSH client you use, so you may need to consult your documentation.

Local Port Forwarding

Local port forwarding lets you connect from your local computer to another server. To use local port forwarding, you need to know your destination server, and two port numbers. You should already know your destination server, and for basic uses of port forwarding, you can usually use the port numbers in Wikipedia’s list of TCP and UDP port numbers.

For example, say you wanted to connect from your laptop to http://www.ubuntuforums.org using an SSH tunnel. You would use source port number 8080 (the alternate http port), destination port 80 (the http port), and destination server www.ubuntuforums.org. :

ssh -L 8080:www.ubuntuforums.org:80 <host>

Where <host> should be replaced by the name of your laptop. The -L option specifies local port forwarding. For the duration of the SSH session, pointing your browser at http://localhost:8080/ would send you to http://www.ubuntuforums.org/.

In the above example, we used port 8080 for the source port. Ports numbers less than 1024 or greater than 49151 are reserved for the system, and some programs will only work with specific source ports, but otherwise you can use any source port number. For example, you could do:

ssh -L 8080:www.ubuntuforums.org:80 -L 12345:ubuntu.com:80 <host>

This would forward two connections, one to www.ubuntuforums.org, the other to www.ubuntu.com. Pointing your browser at http://localhost:8080/ would download pages from www.ubuntuforums.org, and pointing your browser to http://localhost:12345/ would download pages from www.ubuntu.com.

The destination server can even be the same as the SSH server. For example, you could do:

ssh -L 5900:localhost:5900 <host>

This would forward connections to the shared desktop on your SSH server (if one had been set up). Connecting an SSH client to localhost port 5900 would show the desktop for that computer. The word “localhost” is the computer equivalent of the word “yourself”, so the SSH server on your laptop will understand what you mean, whatever the computer’s actual name.

Remote Port Forwarding

Remote port forwarding lets you connect from the remote SSH server to another server. To use remote port forwarding, you need to know your destination server, and two port numbers. You should already know your destination server, and for basic uses of port forwarding, you can usually use the port numbers in Wikipedia’s list of TCP and UDP port numbers.

For example, say you wanted to let a friend access your remote desktop, using the command-line SSH client. You would use port number 5900 (the first VNC port), and destination server localhost:

ssh -R 5900:localhost:5900 guest@joes-pc

The -R option specifies remote port forwarding. For the duration of the SSH session, Joe would be able to access your desktop by connecting a VNC client to port 5900 on his computer (if you had set up a shared desktop).

Dynamic Port Forwarding

Dynamic port forwarding turns your SSH client into a SOCKS proxy server. SOCKS is a little-known but widely-implemented protocol for programs to request any Internet connection through a proxy server. Each program that uses the proxy server needs to be configured specifically, and reconfigured when you stop using the proxy server.

For example, say you wanted Firefox to connect to every web page through your SSH server. First you would use dynamic port forwarding with the default SOCKS port:

ssh -C -D 1080 laptop

The -D option specifies dynamic port forwarding. 1080 is the standard SOCKS port. Although you can use any port number, some programs will only work if you use 1080. -C enables compression, which speeds the tunnel up when proxying mainly text-based information (like web browsing), but can slow it down when proxying binary information (like downloading files).

Next you would tell Firefox to use your proxy:

• go to Edit -> Preferences -> Advanced -> Network -> Connection -> Settings…
• check “Manual proxy configuration”
• make sure “Use this proxy server for all protocols” is cleared
• clear “HTTP Proxy”, “SSL Proxy”, “FTP Proxy”, and “Gopher Proxy” fields
• enter “127.0.0.1” for “SOCKS Host”
• enter “1080” (or whatever port you chose) for Port.

You can also set Firefox to use the DNS through that proxy, so even your DNS lookups are secure:

• Type in about:config in the Firefox address bar
• Find the key called “network.proxy.socks_remote_dns” and set it to true

The SOCKS proxy will stop working when you close your SSH session. You will need to change these settings back to normal in order for Firefox to work again.

To make other programs use your SSH proxy server, you will need to configure each program in a similar way.

The Theory

Generated Columns is a feature released on MySQL 5.7. They can be used during CREATE TABLE or ALTER TABLE statements. It is a way of storing data without actually sending it through the INSERT or UPDATE clauses in SQL. The database resolves what the data will be.

There are two types of Generated Columns: Virtual and Stored. They work with:

• mathematical expressions (product_price * quantity)
• built-in functions (RIGHT(), CONCAT(), FROM_UNIXTIME(), JSON_EXTRACT())
• literals (“2”, “new”, 0)

Besides that, they can be indexed but they don’t allow subqueries in it.
A Generated Column works within the table domain. If you need subqueries on a particular column, you may have to look at Views.

The basic example

As an example I am going to use an e-commerce database as based on my past experience of what I have seen and worked. You will probably have at least these tables or something similar:

• users – stores user info
• products – stores product info like price and description
• orders – stores the user_id, date of order
• orders_items – stores product_id, order_id, quantity and price at the time of purchase

This is the whole DB: Gist.

Notice the order_items definition:

CREATE TABLE `orders_items` (
  `id` int(10) unsigned NOT NULL AUTO_INCREMENT,
  `order_id` int(10) unsigned NOT NULL,
  `product_id` int(10) unsigned NOT NULL,
  `product_price` decimal(10,2) unsigned NOT NULL DEFAULT '0.00',
  `quantity` int(10) unsigned NOT NULL DEFAULT 1,
  `created_at` timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP,
  `updated_at` varchar(45) NOT NULL DEFAULT 'CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP',
  PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=1 DEFAULT CHARSET=utf8mb4;

The retrieval would bring:

SELECT
  `id`, `order_id`, `product_id`, `product_price`, `quantity`
FROM `orders_items`
LIMIT 5;

One example is to get the total of that order_item row, something like total_item_price that would store the value of product_price * quantity to show how much the summed amount of an item would be. Some databases have the MONEY type to store price, as with MySQL it is recommended to work with DECIMAL.

People solve this problem in different ways:

• store the calculated price on a new column to make it easier to retrieve;
• create a view;
• or they calculate in the application itself, which in this case might cause problems due to how the language handles floats. There are libraries to deal with money values in a lot of languages and frameworks, however, the overhead of converting each row into a money object could be costly depending on the amount of data being transferred.

Another way I’ve seen is: people calculate in the query the total amount for the orders_items row as product_price * quantity:

SELECT
  `id`, 
  `order_id`, 
  `product_id`, 
  `product_price`, 
  `quantity`,
  `product_price` * `quantity` AS total_item_price
FROM `orders_items`
LIMIT 5;

Virtual Columns

• They take no disk space, except when using a Virtual Column as in a Secondary Index.
• They are an INPLACE operation: it means the table definition is changed without having to recopy all the data again. More info.
• The values are calculated on the fly during read operations and BEFORE triggers.

Consider using virtual columns for data where changes happens in a significant number of times. The cost of a Virtual Column comes from reading a table constantly and the server has to compute every time what that column value will be.

Stored Columns

• They do use disk space.
• It has the same cost of adding a new column, so it is a COPY operation
• Values are updated in every INSERT and UPDATE statement.

You should consider using Stored Columns for when the data doesn’t change significantly or at all after creation, like for instance, the example above with the orders_items table. Once a purchase is made, the price of the product is stored, not being changed, neither the quantity. Considering this information we could create total_item_price as a Stored Column.

The code

Creating a table

Virtual Column :

CREATE TABLE `orders_items` (
`id` int(10) unsigned NOT NULL AUTO_INCREMENT,
`order_id` int(10) unsigned NOT NULL,
`product_id` int(10) unsigned NOT NULL,
`product_price` decimal(10,2) unsigned NOT NULL DEFAULT '0.00',
`quantity` int(10) unsigned NOT NULL DEFAULT 1,
`total_item_price` decimal(10,2) AS (`quantity` * `product_price`),
`created_at` timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP,
`updated_at` varchar(45) NOT NULL DEFAULT 'CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP',
PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=1 DEFAULT CHARSET=utf8mb4;

Stored Column :

CREATE TABLE `orders_items` (
`id` int(10) unsigned NOT NULL AUTO_INCREMENT,
`order_id` int(10) unsigned NOT NULL,
`product_id` int(10) unsigned NOT NULL,
`product_price` decimal(10,2) unsigned NOT NULL DEFAULT '0.00',
`quantity` int(10) unsigned NOT NULL DEFAULT 1,
`total_item_price` decimal(10,2) AS (`quantity` * `product_price`) STORED,
`created_at` timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP,
`updated_at` varchar(45) NOT NULL DEFAULT 'CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP',
PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=1 DEFAULT CHARSET=utf8mb4;

Notice how the definition changes on line 9 and 23: you have another keyword, AS, then an expression and specifically on line 23 you see a STORED keyword. In both lines they are generated columns, if nothing is specified will be a VIRTUAL column.

Altering a table

It uses the same syntax as adding a column, just adding the “AS (expression)” after the data type:

full_name as VIRTUAL COLUMN

ALTER TABLE users
ADD COLUMN `full_name` VARCHAR(500)
AS (CONCAT_WS(" ", `first_name`, `last_name`));

total_item_price as STORED COLUMN

ALTER TABLE orders_items
ADD COLUMN `total_item_price` DECIMAL(10, 2)
AS (`quantity` * `product_price`) STORED;

Final considerations

When the type is STORED, it must be specified after the expression otherwise the default behaviour will be to be VIRTUAL.

Generated columns can have indexes created as the following, no matter if stored, virtual or extracted from a JSON field:

ALTER TABLE users
ADD INDEX `ix_full_name` (`full_name`);

Which is the same syntax for normal columns.

What you will learn

By following through the material in this primer, you will learn:

• How quantum physics gives us a new way to compute
• The similarities and differences between quantum computing and classical computing
• How the fundamental units of quantum computing (qubits) are manipulated to solve hard problems
• Why Quantum Computing is well suited to AI and machine learning applications, and how quantum computers may be used as ‘AI co-processors’

SECTION 1

1.1 – Conventional computing

To understand quantum computing, it is useful to first think about conventional computing. We take modern digital computers and their ability to perform a multitude of different applications for granted. Our desktop PCs, laptops and smart phones can run spreadsheets, stream live video, allow us to chat with people on the other side of the world, and immerse us in realistic 3D environments. But at their core, all digital computers have something in common. They all perform simple arithmetic operations. Their power comes from the immense speed at which they are able to do this. Computers perform billions of operations per second. These operations are performed so quickly that they allow us to run very complex high level applications. Conventional digital computing can be summed up by the diagram shown in figure 1.

Figure 1. Dataflow in a conventional computer

Although there are many tasks that conventional computers are very good at, there are still some areas where calculations seem to be exceedingly difficult. Examples of these areas are: Image recognition, natural language (getting a computer to understand what we mean if we speak to it using our own language rather than a programming language), and tasks where a computer must learn from experience to become better at a particular task. Even though there has been much effort and research poured into this field over the past few decades, our progress in this area has been slow and the prototypes that we do have working usually require very large supercomputers to run them, consuming a vast quantities of space and power.

We can ask the question: Is there a different way of designing computing systems, from the ground up? If we could start again from scratch and do something completely different, to be better at these tasks that conventional computers find hard, how would we go about building a new type of computer?

1.2 – A new kind of computing

Quantum computing is radically different from the conventional approach of transforming bits strings from one set of 0’s and 1’s to another. With quantum computing, everything changes. The physics that we use to understand bits of information and the devices that manipulate them are totally different. The way in which we build such devices is different, requiring new materials, new design rules and new processor architectures. Finally, the way we program these systems is entirely different. This document will explore the first of these issues, how replacing the conventional bit (0 or 1) with a new type of information – the qubit – can change the way we think about computing.

1.3 – The light switch game

To begin learning about quantum computing, it is important to understand why we can’t use conventional digital computers to solve certain problems. Let’s consider a mathematical problem, which we’ll call the light switch game, that illustrates this point.

The light switch game involves trying to find the best settings for a bunch of switches. Here’s a graphical example introducing this problem:

Figure 2. The light switch game

Let’s imagine that each light switch has a number associated with it, which is chosen for you (you don’t get to change this). We call this a ‘bias value’. You get to choose whether to turn each light switch ON or OFF. In our game, ON = +1 and OFF = -1. We then add up all the switches’ bias values multiplied by their ON/OFF values. This gives us a number. The objective of the game is to set the switches to get the lowest number. Mathematically, we call the bias values of each switch hi and the switch settings are called si

.

Figure 3. Playing the light switch game – add up the bias values of each switch multiplied by their settings (which you have to choose)

So depending upon which switches we set to +1 and which we set to -1, we will get a different score overall. You can try this game. Hopefully you’ll find it easy because there’s a simple rule to winning:

Figure 4. Working out the answer for a particular “guess” at the switch settings

We find that if we set all the switches with positive biases to OFF and all the switches with negative biases to ON and add up the result then we get the lowest overall value. Easy, right? I can give you as many switches as I want with many different bias values and you just look at each one in turn and flip it either ON or OFF accordingly.

OK, let’s make it harder. So now imagine that many of the pairs of switches have an additional rule, one which involves considering PAIRS of switches in addition to just individual switches… we add a new bias value (called J) which we multiply by BOTH the switch settings that connect to it, and we add the resulting value we get from each pair of switches to our overall number too. Still, all we have to do is decide whether each switch should be ON or OFF subject to this new rule.

Figure 5. Making the game harder by adding additional terms that depend on the settings of pairs of switches.

But now it is much, much harder to decide whether a switch should be ON or OFF, because its neighbors affect it. Even with the simple example shown with 2 switches in the figure above, you can’t just follow the rule of setting them to be the opposite sign to their bias value anymore (try it!). With a complex web of switches having many neighbors, it quickly becomes very frustrating to try and find the right combination to give you the lowest value overall.

Figure 6. The light switch game with connecting terms added, generating an ‘interacting’ web of light switches

1.4 – How does quantum mechanics help?

With a couple of switches you can just try every combination of ON’s and OFF’s, there are only four possibilities: [ON ON], [ON OFF], [OFF ON] or [OFF OFF]. But as you add more and more switches, the number of possible ways that the switches can be set grows exponentially:

​

Figure 7. The exponential problem with the light switch game.

You can start to see why the game isn’t much fun anymore. In fact it is even difficult for our most powerful supercomputers. Being able to store all those possible configurations in memory, and moving them around inside conventional processors to calculate if our guess is right takes a very, very long time. With only 500 switches, there isn’t enough time in the universe to check all the configurations.

Quantum mechanics can give us a helping hand with this problem. The fundamental power of a quantum computer comes from the idea that you can put bits of information into a superposition of states. You can think of this as being a situation where the qubit has not yet decided which state it wants to be in. Some people like to refer to the qubit in superposition as ‘being in both states at the same time’. You can alternatively think of the qubit’s state as being undecided as to whether it is +1 or -1. Which means that using a quantum computer, our light switches can be ON and OFF at the same time:

Figure 8: A quantum mechanical bit of information (qubit) can reside in what is known as a superposition state, where it has not yet decided whether to be in the +1 or the -1 state (alternatively, you can think of it as being ‘in both states’).

Now lets consider the same bunch of switches as before, but now held in a quantum computer’s memory (notice that the bias values haven’t been added yet):

Figure 9. A network of connected quantum bits in superposition. The answer is in there somewhere!

Because all the light switches are on and off at the same time, we know that the correct answer (correct ON/OFF settings for each switch) is represented in there somewhere – it is just currently hidden from us. But that is OK, because quantum mechanics is going to find it for us. The D-Wave quantum computer allows you to take a ‘quantum representation’ like this, and extract the configuration of ONs and OFFs with the lowest value. Here’s is how it works:

Figure 10. The computer begins with the bits in superposition, ends with them behaving as regular classical bits, and finds the answer along the way.

You start with the system in its quantum superposition as described above, and you slowly adjust the quantum computer to turn off the quantum superposition effect. At the same time, you slowly turn up all those bias values (the h and J’s from earlier). As this operation is performed, the switches slowly drop out of their superposition state and choose a classical state, either ON or OFF. At the end, each switch MUST have chosen to be either ON or OFF. The quantum mechanics working inside the computer helps the light switches settle into the right states to give the lowest overall value when you add them all up at the end. Even though with N switches there are 2N

possible configurations it could have ended up in, it finds the lowest one, winning the light switch game. So we see that the quantum computer allows us to minimize expressions such as the one considered here:

E(s)=∑ihisi+Jijsisj

which can be difficult (if not impossible) for classical computers.

SECTION 2

2.1 – It’s a math expression – who cares?

We didn’t build a machine to play a strange masochistic light switch game. The concept of finding a good configuration of binary variables (switches) in this way lies at the heart of many problems that are encountered in everyday applications. A few are shown in figure below. Even the concept of scientific discovery itself is an optimization problem (you are trying to find the best ‘configuration’ of terms contributing to a scientific equation which match real world observations).

Figure 11. Examples of applications which under the hood all involve finding good ‘switch settings’ and can be tackled more efficiently with quantum computers.

2.2 – The energy program

To understand how these problems might be cast as finding settings of switches, let’s consider how the quantum computer is programmed. Recall Figure 1, where bit strings in were transformed into other bits strings via the application of a logic program. Instead of that, we now have a resource where bits can be undecided, so the computation is performed in a fundamentally different way, as shown in Figure 12. In this case, a group of qubits are initialized into their superposition states, and this time an ENERGY PROGRAM (instead of a logic program) is applied to the group. The qubits go from being undecided at the beginning of the computation, to all having chosen either -1 or +1 states at the end of the computation. What is an Energy Program? It is just those h and J numbers – the bias settings – that we introduced earlier. In the light switch game, we said that the H and J’s were given to you. Well, now we see where they come from – they are the definition of the problem you are trying to solve.

Figure 12. The basic operation of a quantum computer is to supply an energy program (a series of h and J numbers) and let the computer find the switch settings (+1 and -1).

Crafting an energy program as a series of h and J values – to encode a real world problem that you care about – is exceedingly hard and time-consuming. It would be the equivalent of programming your desktop PC by sending in machine code to the microprocessors inside! Luckily, there is a better way to program quantum computers by using a quantum compiler. This process is explained in more detail in the Programming with D-Wave white paper.

2.3 – Quantum computers can LEARN

The discipline of teaching computers to reason about the world and learn from experience is known as machine learning. It is a sub-branch of the field of artificial intelligence. Most of the code we write is fairly static – that is, given new data it will perform the same computation over and over again and make the same errors. Using machine learning we can design programs which modify their own code and therefore learn new ways to handle pieces of data that they have never seen before.

The type of applications that run very well on D-Wave quantum computers are applications where learning and decision making under uncertain conditions are required. For example, imagine if a computer was asked to classify an object based on several images of similar objects you had shown it in the past. This task is very difficult for conventional computing architectures, which are designed to follow very strict logical reasoning. If the system is shown a new image, it is hard to get it to make a general statement about the image, such as ‘it looks similar to an apple’. D-Wave’s processors are designed to support applications that require high level reasoning and decision making.

How can we use a quantum computer to implement learning, for example, if we want the system to recognize objects? Writing an energy program for this task would be very difficult, even using a quantum compiler, as we do not know in detail how to capture the essence of objects that the system must recognize. Luckily there is a way around this problem, as there is a mode in which the quantum computer can tweak its own energy program in response to new pieces of incoming data. This allows the machine to make a good guess at what an object might be, even if it has never seen a particular instance of it before. The following section gives an overview of this process.

2.4 – A computer that programs itself

In order to get the system to tweak its own energy program, you start by showing the system lots and lots of instances of the concept that you want it to learn about. An example in shown in Figure 13. Here the idea is to try to get the computer to learn the difference between images of different types of fruit. In order to do this, we present images (or rather, a numeric representation of those images) to the system illustrating many different examples of apples, raspberries and melons. We also give the system the ‘right’ answer each time by telling it what switch settings (labels) it should be ending up selecting in each case. The system must find an energy program (shown as a question mark as we do not know it at the beginning) so that when an image is shown to the system, it gets the labels correct each time. If it gets many examples wrong, the algorithm knows that it must change its energy program.

Figure 13. Teaching the quantum chip by allowing it to write its own energy program. The system tweaks the energy program until it labels all the examples that you show it correctly. This is also known as the ‘training’ or ‘learning’ phase.

At first the system chooses an energy program (remember that it is just a bunch of H and J values) at random. It will get many of the labellings wrong, but that doesn’t matter, as we can keep showing it the examples and each time allow it to tweak the energy program so that it gets more and more labels (switch settings) correct. Once it can’t do any better on the data that it has been given, we then keep the final energy program and use that as our ‘learned’ program to classify a new, unseen example (figure 14).

In machine learning terminology this is known as a supervised learning algorithm because we are showing the computer examples of images and telling it what the correct labels should be in order to help it learn. There are other types of learning algorithms supported by the system, even ones that can be used if labeled data is not available.

Figure 14. After the system has found a good energy program during the training phase, it can now label unseen examples to solve a real world problem. This is known as the ‘testing’ phase.

2.5 – Uncertainty is a feature

Another interesting point to note about the quantum computer is that it is probabilistic, meaning that it returns multiple answers. Some of these might be the answer that you are looking for, and some might not. At first this sounds like a bad thing, as a computer that returns a different answer when you ask it the same question sounds like a bug! However, in the quantum computer, this returning of multiple answers can give us important information about the confidence level of the computer. Using the fruit example above, if we showed the computer an image and asked it to label the same image 100 times, and it gave the answer ‘apple’ 100 times, then the computer is pretty confident that the image is an apple. However, if it returns the answer apple 50 times and raspberry 50 times, what this means is that the computer is uncertain about the image you are showing it. And if you had shown it an image with apples AND raspberries in, it would be perfectly correct! This uncertainty can be very powerful when you are designing systems which are able to make complex decisions and learn about the world.