STAR WARS EPISODE I: THE PHANTOM MENACE by DeWyNGaLe (John Sylva) Rating: A+
http://members.aol.com/DeWyNGaLe
There is only one word in the English language that can describe my feelings right now. That word is "Woah!" Star Wars Episode 1: The Phantom Menace, which is the most anticipated movie of the century, was released into theaters this week. Many early reviews have trashed The Phantom Menace, accusing it of not developing characters, and stating many other negative aspects of the film. How could you dare trash this amazing masterpiece? Many reviewers have reviewed the film in comparison to the other three Star Wars films that were released from 1977-1983, but not the actual film itself. Well, here's a review of the film itself, and I hope it's what you are looking for.
The Phantom Menace takes place a few decades before the events in Star Wars Episode IV: A New Hope occurred. In The Phantom Menace, we are introduced to two Jedi, Qui-Gon Jinn (Liam Neeson), who is a newcomer to the Star Wars series, and Ben Obi-Wan Kenobi (Ewan McGregor), who is depicted in Episodes IV, V, and VI by Sir Alec Guinness. The two Jedi are off to save the innocent planet of Naboo from the evil forces of the Trade Federation, which is threatening to take over the planet. Upon their arrival at Naboo, they come across a creature of the species "Gungan", named Jar Jar Binks (Ahmed Best), who they have tag along for their adventures to serve as a guide to them. The two came to Naboo to hopefully rescue the 14-year old Queen Amidala (Natalie Portman) from the planet before it is too late to save her life. Knowing that the Trade Federation isn't in existence on the remote planet of Tatooine (sound familiar from Episode IV?), they take her there to hide her, and on their journey, discover a young child named Anakin Skywalker (Jake Lloyd) who they believe has the force strong inside of him. Also discovered at Tatooine is a new Sith, Darth Maul, played by Ray Park. Qui-Gon and Obi-Wan realize that he has Jedi training and could be a huge threat to themselves, as well as the worried Queen Amidala.
Above is a basic plot outline of The Phantom Menace, but there are many more details to each one of the plot, which all tie into Episodes IV, V, and VI. One of these major plots is the fact that Anakin Skywalker is actually a young Darth Vader, and if you have seen Episode VI: Return of the Jedi, you know so. The Phantom Menace ties in with Episodes IV, V, and VI in every way. It was amazing how George Lucas enabled everything to fit together so nicely, making it seem as if this film was released before the other three Episodes.
The acting in The Phantom Menace isn't what I would call the best acting in a movie ever, but it certainly added much content to the film. Liam Neeson and Natalie Portman in particular stood out from the cast, making every line that came out of their mouths believable and realistic. Ewan McGregor, who I think should have been used more in the film, turned out the best performance of his career in the time that he was present on screen. Many reviewers are also trashing Jake Lloyd's simple but effective performance as the young Anakin Skywalker. Remember folks, he is supposed to be nine years old, so most likely his acting performance will be very immature and childish. Considering Jake Lloyd was supposed to be playing a nine year old, he did a great job. Ahmed Best, who brilliantly voices the cute, realistic, and hysterical Jar Jar Binks, was sometimes hard to understand, but added much comic relief to the film.
Although I have stated some characters were underused, I am not saying it took away from the film at all. The point of Episode 1 was to build a bridge to the next two Episodes, and that it did. Sure, I would have loved to have seen Darth Maul for more than ten minutes, or some more of Samuel L. Jackson's character of Mace Windu, but nothing was taken away from the overall effect of the film.
Where do I even start about the marvelous special effects? I guess I will just put it plain and simple- The Phantom Menace contains the best special effects you will ever see in a film. The armies of battle droids, the ships flying through the air, and the amazing podrace sequence soar above any special effect that I have ever seen used in a film. Those who were wondering if The Phantom Menace would have better special effects than The Matrix have now had their questions answered. The special effects in the lightsaber battle scenes are extraordinary. The choreography during these sequences is much better and are much more exciting than the lightsaber battles in Episodes IV, V, and VI.
The use of sound in The Phantom Menace is overwhelming. I can certainly award The Phantom Menace with the loudest movie I have ever seen. Don't get me wrong, the sound is not loud and obnoxious, and it is loud when it should be loud, and quiet when it should be quiet. The sound of podracers and ships speeding through space were the most effective of the many different sound effects in the film.
Costume design and makeup both added quite a bit to the film as well. As you can probably tell, Queen Amidala makes up the majority of each one of these categories. Her outfits are so original, creative, and fun, it is amazing. Others, such as the eerie Darth Maul, or Senator Palpatine (later to become the dreaded Emperor Palpatine seen in Return of the Jedi), all of the outfits for each and every character are stunningly original.
What George Lucas has done with The Phantom Menace is simply genius. How many filmmakers would be willing to do a prequel to the biggest movie saga of all time with little known actors, sixteen years after the last one has been released? I can only think of one, and that would be George Lucas. The Phantom Menace is done with style, and I mean George Lucas style. It follows pretty much the same feel, despite what others say, that Episodes IV, V, and VI followed. Although comparing the film to others is not any part of my rating, The Phantom Menace soars above all three of the other Star Wars films. In almost every way, The Phantom Menace stood out. I would say it is most like 1983's Return of the Jedi, which used to be my favorite of the Star Wars bunch, but has now been replaced with this brilliant piece of work, Star Wars Episode I: The Phantom Menace.
The Bottom Line- Argue with me all you want to, but I think I just found the best movie of all time.
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# Presenter by Yuri Khan (Press `←`/`→` to change slides) ---- ## What is Presenter? * A simple web-based presentation tool * using Markdown as source format * released under the [MIT license][mit] [mit]: http://opensource.org/licenses/MIT ---- ## How is Presenter different from others? * It is very compact. The main script is less than 200 SLOC. * Based on Markdown. Less markup, more content. * Almost no visual design decisions made for you. Roll your own design without having to strip down the defaults. ---- ## How do I control Presenter? * There is not much to control, just switch slides * To advance to the next slide, press any of the following keys: `Space`, `→`, `↓`, `Page Down`, `n`, `f`, `k`, `l` * To go back: `Backspace`, `Shift`+`Space`, `←`, `↑`, `Page Up`, `p`, `b`, `h`, `j` * To jump to the first slide: `Home`, `a`, `^`, `g` * To the last slide: `End`, `e`, `$`, `G` (that’s `Shift`+`g`) * Also, use your browser controls to go fullscreen (`F11` in most of them) ---- ## How do I create a presentation? ```html
Your presentation title
Write your slides here </textarea> ``` ---- ## What is Markdown? * A simple [text-based syntax][md] for authoring HTML, devised by John Gruber * Markdown descends from a family of Wiki syntaxes, pioneered by the [WikiWikiWeb][c2]. [md]: http://daringfireball.net/projects/markdown/syntax [c2]: http://c2.com/cgi/wiki ### Which dialect does Presenter use? * Markdown is parsed by the [markdown-it][] JS library. * It accepts [CommonMark] (which includes fenced code blocks) and has a number of extensions, of which only a few are on by default: * Tables * Strikethrough [markdown-it]: https://github.com/markdown-it/markdown-it [CommonMark]: http://spec.commonmark.org/ ---- ## How do I delimit slides? * With anything that produces a top-level horizontal rule in Markdown: a sequence of three or more hyphens, underscores or asterisks. ```markdown ---- ``` ### But how do I then produce a horizontal rule? * It is expected that you won’t need one. * But if you *really* want, you can wrap it in another element: ```html
```
---- ## How do I do headings? ```markdown # Heading 1 ## Heading 2 ### Heading 3 #### Heading 4 ##### Heading 5 ###### Heading 6 ``` ---- # Heading 1 ## Heading 2 ### Heading 3 #### Heading 4 ##### Heading 5 ###### Heading 6 (But please refrain from using headings 5 and 6!) ---- Alternatively: ```markdown Heading 1 ========= Heading 2 --------- ``` Heading 1 ========= Heading 2 --------- ---- ## How do I do paragraphs? Any run of consecutive lines becomes a paragraph. Paragraphs are separated with empty lines. ```markdown Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. ``` ---- Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. (Note that lines don’t break automatically where you wrap.) ---- ## How do I do a line break? End a line with two or more spaces. ```markdown This·line·is·· broken. ``` This line is broken. * You don’t often need line breaks. Except for poetry and mailing addresses, paragraphs or lists are almost always a better idea. ---- ## How do I do a line break? * Sometimes you will want to line-break a header. In that case, use a `
`. ```html ## Some long header
that breaks wrong by default ``` ## Some long header
that breaks wrong by default ---- ## How do I do a blockquote?  Observe that blockquotes can nest. ---- ## How do I do lists? Bulleted lists can be marked with `*`, `+` or `-`: ```markdown * One * Two * Three ``` * One * Two * Three ---- ## How do I do lists? Bulleted lists can be marked with `*`, `+` or `-`: ```markdown + One + Two + Three ``` + One + Two + Three ---- ## How do I do lists? Bulleted lists can be marked with `*`, `+` or `-`: ```markdown - One - Two - Three ``` - One - Two - Three It doesn’t matter which. ---- ## How do I do lists? Numbered lists are just numbered. ```markdown 1. Alpha 2. Beta 3. Gamma ``` 1. Alpha 2. Beta 3. Gamma ---- ## How do I do lists? It’s not necessary to preserve continuity. ```markdown 1. Alpha 1. Beta 1. Gamma ``` 1. Alpha 1. Beta 1. Gamma ---- ## How do I do lists? Lists can be nested: ```markdown * One 1. Alpha 2. Beta * Two ``` * One 1. Alpha 2. Beta * Two ---- ## How do I do lists? Lists can contain paragraphs: ```markdown * Lorem ipsum dolor sit amet. Consectetur adipiscing elit. * Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. ``` * Lorem ipsum dolor sit amet. Consectetur adipiscing elit. * Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. ---- ## How do I do lists? Or blockquotes: ```markdown * Lorem ipsum dolor sit amet. > Consectetur adipiscing elit. * Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. ``` * Lorem ipsum dolor sit amet. > Consectetur adipiscing elit. * Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. ---- ## How do I do code blocks? Indent them with four spaces: ```markdown int main(int argv, char** argc) { } ``` int main(int argv, char** argc) { } ---- ## How do I do code blocks? Or fence them with three or more backticks ` ``` `, optionally specifying a language. ````markdown ```c int main(int argv, char** argc) { } ``` ```` ```c int main(int argv, char** argc) { } ``` (Note: The above example uses four backticks to produce a Markdown code block with a nested C code block.) ---- ## How do I enable syntax highlighting? * In fact it’s always on, for fenced blocks with language specified. It’s just that Presenter does not supply a default stylesheet for code. * Choose one of [Highlight.js styles][styles] (warning: slow page) * Find the corresponding [file name][files] * Include it like this (mind the `.min` suffix!): ```html
``` * Or if none of the existing styles please you, use the [class reference][classes] to design your own. [styles]: http://highlightjs.org/static/test.html [files]: https://github.com/isagalaev/highlight.js/tree/master/src/styles [classes]: http://highlightjs.readthedocs.org/en/latest/css-classes-reference.html ---- ## What if I’m talking about HTML? * It just works. * One thing that you can’t say is `</textarea>`. You have to escape `<` as `<`. ````markdown ```html </textarea> ``` ```` ```html </textarea> ``` * Of course when you want to say `<` you have to write `<`. Always double-check your presentation if it includes `&`! ---- ## How do I emphasize text? You can use single asterisks or underscores for normal emphasis, and double them for strong emphasis. Strike text out with double tildes. Use backticks for inline code. ```markdown *Normal emphasis* _Normal emphasis_ **Strong emphasis** __Strong emphasis__ ~~Strikeout~~ underscores_in_identifiers `code` ``` *Normal emphasis* _Normal emphasis_ **Strong emphasis** __Strong emphasis__ ~~Strikeout~~ underscores_in_identifiers `code` Observe that underscores in identifiers don’t cause emphasis, despite what that Markdown syntax highlighter says. ---- ## How do I do links? Links are automatically hyperlinked *if* they are in full URL format with schema. Otherwise there would be false positives on file names: ```markdown * http://github.com/ * www.google.com * command.com (shell in an ancient OS) * script.pl (Perl or Poland?) ``` * http://github.com/ * www.google.com * command.com (shell in an ancient OS) * script.pl (Perl or Poland?) ---- ## How do I do links? Mark a link explicitly, inline: ```markdown Fork this on [GitHub](http://github.com/) ``` Fork this on [GitHub](http://github.com/) ---- ## How do I do links? Mark a link explicitly, reference-style: ```markdown Fork this on [GitHub][1] [1]: http://github.com/ ``` Fork this on [GitHub][1] [1]: http://github.com/ **Note** that reference IDs have to be unique throughout your presentation. You can’t reuse `[1]` in each slide. ---- ## How do I do links? Omit the reference: ```markdown Fork this on [GitHub][] [GitHub]: http://github.com/ ``` Fork this on [GitHub][] [GitHub]: http://github.com/ ---- ![images](about:blank) ## How do I do images? Inline style: ```markdown ![Alt text](test/screenshot.png "Optional tooltip") ``` ![Alt text](test/screenshot.png "Optional tooltip") ---- ![images](about:blank) ## How do I do images? Reference style: ```markdown ![Alt text][sshot] [sshot]: test/screenshot.png "Optional tooltip" ``` ![Alt text][sshot] [sshot]: test/screenshot.png "Optional tooltip" ---- ![icons](about:blank) ## How do I do images? Images do not have to be the only thing in a paragraph: ```markdown Fork this on ![](https://assets-cdn.github.com/favicon.ico)GitHub ``` Fork this on ![](https://assets-cdn.github.com/favicon.ico)GitHub (Purely decorative icons do not need alt text.) ---- ![icons](about:blank) ## How do I do images? Images can be wrapped in links: ```markdown Fork this on [![][gh-icon]GitHub][gh] [gh-icon]: https://assets-cdn.github.com/favicon.ico [gh]: http://github.com/ ``` Fork this on [![][gh-icon]GitHub][gh] [gh-icon]: https://assets-cdn.github.com/favicon.ico [gh]: http://github.com/ ---- ![](test/screenshot.png) ## How do I do images? If an image is the first thing on a slide, it becomes the background. ---- ![special](test/screenshot.png) ## How do I do images? When a background image is used, the words in brackets become classes of the slide, to help you style your image slides separately. ```markdown ---- ![special](test/screenshot.png) ``` ```css .special h2 { color: white; text-shadow: -1.5px -1.5px 0 black, 0px -2px 0 black, 1.5px -1.5px 0 black, -2px 0px 0 black, 2px 0px 0 black, -1.5px 1.5px 0 black, 0px 2px 0 black, 1.5px 1.5px 0 black; } ``` ---- ## How do I do images? When a background image is used, the words in brackets become classes of the slide, to help you style your image slides separately. In fact, this feature can be (ab)used with a fake background. That’s how GitHub icons were sized a few slides above: ```markdown ---- ![icons](about:blank) ``` ```css .icons img { width: 0.75em; height: 0.75em; } ``` ---- ## How do I do tables? Draw colums with vertical bars. Separate the head with hyphens. Specify alignment with colons. ```markdown |Left|Center|Right| |----|:----:|----:| |1 | 2 | 3| ``` |Left|Center|Right| |----|:----:|----:| |1 | 2 | 3| ---- ## How do I do tables? You don’t have to maintain the columns. ```markdown |Left|Center|Right| |-|:-:|-:| |1|2|3| ``` |Left|Center|Right| |-|:-:|-:| |1|2|3| ---- ![index](about:blank) ## Index * [What is Presenter?](#s2) * [How is Presenter different?](#s3) * [How do I control Presenter?](#s4) * [How do I create a presentation?](#s5) * [What is Markdown?](#s6) * [How do I delimit slides?](#s7) * [How do I do headings?](#s8) * [How do I do paragraphs?](#s11) * [How do I do a line break?](#s13) * [How do I do a blockquote?](#s14) * [How do I do lists?](#s16) * [How do I do code blocks?](#s24) * [How do I enable syntax highlighting?](#s27) * [What if I’m talking about HTML?](#s28) * [How do I emphasize text?](#s29) * [How do I do links?](#s30) * [How do I do images?](#s34) * [How do I do tables?](#s40) * [Questions? Suggestions?](#s43) ---- ## Questions? Suggestions? * GitHub project: https://github.com/yurikhan/presenter/ * File [issues](https://github.com/yurikhan/presenter/issues) * Fork and send [pull requests](https://github.com/yurikhan/presenter/pulls)


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@* * Copyright 2023 HM Revenue & Customs * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. *@ @import models.ApplicationRoute._ @import controllers.ApplicationRouteState @(form: Form[_root_.forms.SignUpForm.Data], appRouteConfigMap: Map[ApplicationRoute, ApplicationRouteState], validAfterDeadlineSubmissionCode: Boolean)(implicit messages: Messages) @import models.ApplicationRoute @import views.html.widgets.{radioBoxVerticalMultiToggle, yesNoQuestion, yesNoRadioWithTogglePanel} @faststreamOpen = @{ appRouteConfigMap.get(Faststream).forall(_.newAccountsEnabled) || validAfterDeadlineSubmissionCode } @edipOpen = @{ (appRouteConfigMap.get(Edip).forall(_.newAccountsStarted) && appRouteConfigMap.get(Edip).forall(_.newAccountsEnabled)) || validAfterDeadlineSubmissionCode } @sdipOpen = @{ (appRouteConfigMap.get(Sdip).forall(_.newAccountsStarted) && appRouteConfigMap.get(Sdip).forall(_.newAccountsEnabled)) || validAfterDeadlineSubmissionCode } @edipUrl = @{ "https://www.faststream.gov.uk/edip-am-i-eligible/index.html" } @sdipUrl = @{ "https://www.faststream.gov.uk/sip-am-i-eligible/index.html" } @sdipDiversityHintText = @{ Some("To be considered for the Diversity SIP, confirm one or more of the following statements are true:" + "
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Event Location:
CIDA
"Sausiripaya" 123 Wijerama Mawatha
Colombo, Western, Sri Lanka
Abstract:
You can probably do a good job in configuring and maintaining transactional replication in your environment. You can get these things done with reasonable quality without knowing how SQL Server does things under the covers. However if you want to take your skills to the next level and troubleshoot complex replication issues, it's crucial to know how transactional replication works internally. This session will answers questions like; How does the log reader know where to start the scan? How does it add the commands to the Distribution database? How many threads are involved in a replication process? How does distribution agent look for pending transactions to distribute to its subscribers? Knowing all these will help you to manage and troubleshoot the replication very effectively. Come lets learn together!
Speaker(s): Prabhakaran Bhaskaran,
Abstract:
Data and Database are very important aspects of application development for businesses. Developers often come across situations where they face a slow server response, even though their hardware specifications are above par. This session is for all the Developers who want their server to perform at blazing fast speed, but want to invest very little time to make it happen. We will go over various database tricks which require absolutely no time to master and require practically no SQL coding at all. After attending this session, Developers will only need 60 seconds to improve performance of their database server in their implementation. We will have a quiz during the session to keep the conversation alive. Developers will walk out with scripts and knowledge that can be applied to their servers, immediately post the session.
Speaker(s): Pinal Dave,
Abstract:
Have you already incorporated “Big Data” into your analytical solution, but still feel you are going nowhere with it? Or are you planning to bring “Big Data” into your analytical solution, but not sure which way to go? Do you wonder about how to get it done, and what tools and methods that you need to use? Let us talk about it; let us understand the “Big Data” requirement; how to and the best way of bringing it into analytical stack using the Microsoft way, of course.
Speaker(s): Dinesh Priyankara,
Abstract:
Slow Running Queries are the most common problem that developers face while working with SQL Server. While it is easy to blame the SQL Server for unsatisfactory performance, however the issue often persists with the way queries have been written, and how Indexes has been set up. The session will focus on the ways of identifying problems that slow down SQL Server, and Indexing tricks to fix them. Developers will walk out with scripts and knowledge that can be applied to their servers, immediately post the session.
Speaker(s): Pinal Dave,
Abstract:
Data is all around us; it is in bits and pieces; it is in shapeless chunks. These data can tell us stories. Organizations have loads of these data lying around, but seldom make use of it. Modern data analytics methods however, give us a plethora of methods to access this data, mash them up and tell stories using them. Stories, that can help make effective decisions. This session looks at how you could collect data from the various sources in your organization, combine them, process them and tell stories using the wealth of tools given to us by Microsoft. Words you would hear are business intelligence, self-service data analytics and big data.
Speaker(s): Gogula Aryalingam,
Abstract:
Overview of the in-memory technologies which are included in SQL Server 2014. We will cover In-Memory OLTP (AKA "Hekaton"), In-Memory Data Warehousing (AKA "Apollo") as well as SSD Buffer Pool Extensions. This session will give understanding of the broad in-memory strategy as well as a basic understanding of the technologies involved.
Speaker(s): Nilabja Ball,
Abstract:
Join Pinal and Nilabja as they take questions from the audience that is anything SQL Server, business intelligence and data on the cloud! This is a great opportunity to pick the minds of a couple of great SQL minds. We would also the other speakers ready to go as well...
Speaker(s): Pinal Dave,
Abstract:
Have you ever wondered why we need a data warehouse when we have the good old stringent relational database scheme. Do you want to get to know the concepts of data warehousing and business intelligence? Then this is the session you have been looking for: A tour from OLTP to OLAP with Microsoft technologies. Gear up for the excitement!
Speaker(s): Vijayakumar Thurupathan,
Abstract:
Virtusa is a rapidly evolving company with diverse business intelligence needs spanning all level of the organization; from CxOs to Engineers (numbering around 8000 employees); from mobile devices to public area dashboards. In this session, I will share with you the challenges faced and how we have over come them so far, and plans for beyond future.
Speaker(s): Indika Ariyasinghe,
Abstract:
Microsoft Azure SQL Database (formerly SQL Azure) is another Microsoft Azure service that offers relational database-as-a-service with proven performance, scalability, data security and near-zero administration. This discussion will give you an understanding about Azure SQL Database; what this service is and what it offers. It will also help you understand what sort of requirements will benefit from Azure SQL Database, and what factors you need to know in order to choose this service, along with pros and cons of choosing Azure SQL Database
Speaker(s): Sammani Palansuriya,
Abstract:
NoSQL data stores have gone mainstream. In this session, we will survey the expanding NoSQL landscape on Azure, providing a big-picture view of these technologies. Also spend a bit more time on DocumentDB, Microsoft’s document database-as-a-service, and Azure Search. This session is aimed at anybody who’s new to NoSQL or is curious about the NoSQL options that Azure provides today.
Speaker(s): Nilabja Ball,
This is a list of speakers from the XML Guidebook records. The details and URLs were valid at the time of the event.
Contact: http://www.pythian.com/blog/author/Bhaskaran/
Prabhakaran is SQL Server consultant at Pythian, a company based in Ottawa, Canada, specializing in Remote database services. He is former SQL Server Support Engineer at Microsoft. He always loves to learn and share his knowledge.
Nilabja is a Premier Field Engineer for Microsoft Global Business Support (GBS), India. He has more than 8 years of SQL Server and BI experience. He is engaged with the customer either for proactive activities including health check, assessment and support or for reactive tasks to troubleshoot and fix complex and critical issues. He has an engineering degree from Visvesvaraya technological university and keen to learn new technologies.
I am working as a Associate Architect - Technology for Virtusa. My tenure at Virtusa is more than 11 years. I am holding a Software Engineering Degree from University of Peradeniya, Faculty of Engineering
LinkedIn: http://www.linkedin.com/in/pinaldave
Contact: https://blog.sqlauthority.com
Pinal Dave is a SQL Server Performance Tuning Expert and an independent consultant. He has authored 12 SQL Server database books, 30 Pluralsight courses and has written over 5000 articles on the database technology on his blog at a https://blog.sqlauthority.com. Along with 16+ years of hands-on experience, he holds a Masters of Science degree and a number of database certifications.
LinkedIn: http://lk.linkedin.com/in/thuru/
Contact: http://www.thuru.net
Thuru is a versatile technical person who has diversified experience in many areas of Information Technology for 6 years. Cloud computing, security, software development, business intelligence and databases are his most preferred technology areas. He is a frequent speaker in Sri Lanka .NET forum and Sri Lanka SQL Server Universe user groups. Thuru is the founder of Colombo Cloud Meet Up where he often talks about various cloud computing topics. Also he is a Microsoft MVP for Microsoft Azure.
LinkedIn: http://www.linkedin.com/in/pinaldave
Contact: https://blog.sqlauthority.com
Pinal Dave is a SQL Server Performance Tuning Expert and an independent consultant. He has authored 12 SQL Server database books, 30 Pluralsight courses and has written over 5000 articles on the database technology on his blog at a https://blog.sqlauthority.com. Along with 16+ years of hands-on experience, he holds a Masters of Science degree and a number of database certifications.
Nilabja is a Premier Field Engineer for Microsoft Global Business Support (GBS), India. He has more than 8 years of SQL Server and BI experience. He is engaged with the customer either for proactive activities including health check, assessment and support or for reactive tasks to troubleshoot and fix complex and critical issues. He has an engineering degree from Visvesvaraya technological university and keen to learn new technologies.
LinkedIn: https://lk.linkedin.com/in/sammanipalansuriya
Contact: http://sammanipalansuriya.blogspot.com/
Sammani Palansuriya is a Visual C#.net MVP in Sri Lanka with more than 5 years#39; experience in various aspects of .net technologies. Currently she is stationed as a Senior Software Engineer at Exilesoft and working on projects based on asp.net and azure technologies.
LinkedIn: http://lk.linkedin.com/in/dineshpriyankara/
Contact: http://dinesql.blogspot.com/
Dinesh is an experienced professional and database enthusiast with skills in database management systems and business intelligence. Possessing over 18 years of experience on data related technologies, he does training, consulting, and is a top contributor to the local SQL Server community. In recognition of his contributions and expertise he has demonstrated, he was awarded the Microsoft Most Valuable Professional (MVP) award for SQL Server for 13 consecutive years since 2006. He is a Subject Matter Expert on SQL Server exams and has contributed for SQL Server 2012, 2016, 2017 and Azure Data Engineering exam development and Job Task Analysis (JTA). Dinesh is the Founder/Principal Architect of dinesQL (Pvt) Ltd (http://dinesql.com). In his
LinkedIn: http://www.linkedin.com/in/gogula
Contact: http://datamaul.wordpress.com
Gogula is a data analytics professional from Sri Lanka, with 14+ years on the Microsoft data platform. He has worked with many aspects of data analytics and BI solutions from architecting, designing, developing and consulting across various industries and verticals. He is Regional Mentor for PASS South Asia, Data Platform MVP, MCSE, former MCT, and MSc in IT. Gogula's passion revolves data analytics and BI; hence enjoys writing, teaching and speaking about the things he works with. He was also involved as an SME for Microsoft certification development. He currently juggles his full time job as Lead Architect while speaking at local and foreign events, along with regular stints at the Sri Lankan Data Community which he co-founded.
LinkedIn: http://www.linkedin.com/in/pinaldave
Contact: https://blog.sqlauthority.com
Pinal Dave is a SQL Server Performance Tuning Expert and an independent consultant. He has authored 12 SQL Server database books, 30 Pluralsight courses and has written over 5000 articles on the database technology on his blog at a https://blog.sqlauthority.com. Along with 16+ years of hands-on experience, he holds a Masters of Science degree and a number of database certifications.
The following is a list of sponsors that helped fund the event.


We are collecting your donations in a PayPal donation pool every week. We make sure to record your name. So you'll be able to track your donation!
Learn MoreWe are managing your donations in our non-profit organization and distrubute roles to our volunteers in different locations! Contact us for opportunities!
Learn MoreServing food to homeless people are the most fun part of this project! We have many volunteers every week from different backgrounds!
Learn More


{% extends "layout.html" %} {% block pageTitle %} GOV.UK prototyping kit {% endblock %} {% block content %} {% import "release2-2/elements.html" as elements %} {% for page in data %} {% for question in page.validationPage %} {{ elements.backButton(page,question) }} {{ elements.header(page,question) }} Helper Details Validation Is someone helping you fill in this application? Checkbox must be selected The name of the person helping you No validation How you know them No validation Personal Details Validation Your name Title Option must be selected First name Mandatory field Middle name No validation Last name Must be completed National Insurance Number Mandatory field Must follow traditional NINO format Date of birth Age must fall within valid age range for claiming PIP Date must be a valid date Date of birth, Day Mandatory field Date of birth, Month Mandatory field Date of birth, Year Mandatory field Contact Details Validation Your address 1 Must be completed Your address 2 No validation Your address 3 No validation You need to have letters sent to a different address Optional checkbox Your phone number No validation You have hearing loss and need to be contacted by textphone Optional checkbox Alternative phone number No validation {{ elements.helpline(page) }} {{ elements.validation(page,question) }} {% endfor %} {% endfor %} {% endblock %}
Checkbox must be selected
No validation
Option must be selected
Mandatory field
Must be completed
Must follow traditional NINO format
Age must fall within valid age range for claiming PIP
Date must be a valid date
Optional checkbox


We need to use angular expressions to display the data now. Get rid of what you did before iterating through the array manually. Use a new expression like this {{list.name}}.
{{list.name}}


--- layout: post title: WebDrawer custom search results page categories: [] tags: webdrawer status: publish type: post published: true meta: {} ---
If you create one of more Search Form objects in RM these will be incorporated into the WebDrawer search page, as a drop down list of custom search pages. It is possible to customise the properties that are displayed in the search results for these pages, the trick is that different versions of WebDrawer require different customisations. This video details customising in 82 and earlier and also in 83 and later.


public class Trade
extends java.lang.Object
| Constructor and Description |
|---|
Trade()
Class constructor for a trade.
|
Trade(java.lang.String owner,
Item ownerItem,
Inventory borrowerItems)
Class constructor for a trade.
|
Trade(java.lang.String owner,
java.lang.String borrower,
Item ownerItem,
Inventory borrowerItems)
Class constructor for a trade.
|
Trade(Trade trade)
Class constructor for a trade.
|
| Modifier and Type | Method and Description |
|---|---|
java.lang.String |
getBorrower()
Gets the borrower name for the trade.
|
Inventory |
getBorrowerItems()
Gets the borrower items to be used in the trade.
|
int |
getId()
Gets the id for the trade.
|
java.lang.String |
getOwner()
Gets the owner name for the trade.
|
Item |
getOwnerItem()
Gets the owner's item to be used in the trade.
|
java.lang.String |
getStatus()
Gets the status of the trade.
|
void |
setBorrower(java.lang.String borrower)
Changes the borrower name for the trade.
|
void |
setBorrowerItems(Inventory borrowerItems)
Changes the borrower's items to be traded.
|
void |
setId(int id)
Changes the id for the trade.
|
void |
setOwner(java.lang.String owner)
Changes the owner name for the trade.
|
void |
setStatus(java.lang.String status)
Changes the status of the trade.
|
java.lang.String |
toString()
Returns the printing format for the trade statuses.
|
public Trade()
public Trade(Trade trade)
trade
- existing tradepublic Trade(java.lang.String owner, Item ownerItem, Inventory borrowerItems)
owner
- owner of the item in the tradeownerItem
- item from the ownerborrowerItems
- item from the borrowerpublic Trade(java.lang.String owner, java.lang.String borrower, Item ownerItem, Inventory borrowerItems)
owner
- owner of the item in the tradeborrower
- borrower of the item in the tradeownerItem
- item from the ownerborrowerItems
- item from the borrowerpublic int getId()
public void setId(int id)
id
- id of the tradepublic java.lang.String getOwner()
public void setOwner(java.lang.String owner)
owner
- name of the owner in the tradepublic java.lang.String getBorrower()
public void setBorrower(java.lang.String borrower)
borrower
- name of the borrower in the tradepublic Item getOwnerItem()
public Inventory getBorrowerItems()
public void setBorrowerItems(Inventory borrowerItems)
borrowerItems
- borrower's items to be tradedpublic java.lang.String getStatus()
public void setStatus(java.lang.String status)
status
- status of the tradepublic java.lang.String toString()
The format of the trade records are:
Offered: [borrower] offered a trade for [owner's item]
Completed: Trade for [owner's item] is completed.
Accepted: [owner] accepted your trade for [owner's item]
Pending: Trade for [owner's item] is pending.
Declined: [owner] declined your trade for [owner's item]
toString
in class java.lang.Object


--- title: Kap subtitle: Record your screen description: Kap is an open source macOS app I'm working on with my friends. It lets you quickly record your screen and then export to various formats and services. It supports plugins, trimming, window recording, and much more. type: macOS date: 2018-02-01 repo_url: https://github.com/wulkano/kap ---


|
BitMagic-C++
|
Modules | |
| Binary-distance metrics | |
Data Structures | |
| class | bm::rank_compressor< BV > |
| Algorithms for rank compression of bit-vector. More... | |
| class | bm::aggregator< BV > |
| Algorithms for fast aggregation of a group of bit-vectors. More... | |
| class | bm::random_subset< BV > |
| class | bm::sparse_vector_scanner< SV > |
| algorithms for sparse_vector scan/seach More... | |
| class | bm::set2set_11_transform< SV > |
| Integer set to set transformation (functional image in groups theory) https://en.wikipedia.org/wiki/Image_(mathematics) More... | |
Functions | |
| template<class BV , class Func > | |
| void | bm::for_each_bit (const BV &bv, Func &bit_functor) |
| bit-vector visitor scanner to traverse each 1 bit using C++ visitor More... | |
| template<class BV > | |
| void | bm::visit_each_bit (const BV &bv, void *handle_ptr, bit_visitor_callback_type callback_ptr) |
| bit-vector visitor scanner to traverse each 1 bit using C callback More... | |
| template<class BV , class It > | |
| void | bm::combine_or (BV &bv, It first, It last) |
| OR Combine bitvector and the iterable sequence. More... | |
| template<class BV , class It > | |
| void | bm::combine_xor (BV &bv, It first, It last) |
| XOR Combine bitvector and the iterable sequence. More... | |
| template<class BV , class It > | |
| void | bm::combine_sub (BV &bv, It first, It last) |
| SUB Combine bitvector and the iterable sequence. More... | |
| template<class BV , class It > | |
| void | bm::combine_and_sorted (BV &bv, It first, It last) |
| AND Combine bitvector and the iterable sequence. More... | |
| template<class BV , class It > | |
| void | bm::combine_and (BV &bv, It first, It last) |
| AND Combine bitvector and the iterable sequence. More... | |
| template<class BV > | |
| bm::id_t | bm::count_intervals (const BV &bv) |
| Compute number of bit intervals (GAPs) in the bitvector. More... | |
| template<typename BV , class It > | |
| void | bm::export_array (BV &bv, It first, It last) |
| Export bitset from an array of binary data representing the bit vector. More... | |
| template<typename Agg , typename It > | |
| void | bm::aggregator_pipeline_execute (It first, It last) |
| Experimental method ro run multiple aggregators in sync. More... | |
Set algebra algorithms using bit-vectors, arrays. Binary metrics and distances. Random sub-sets.
| void bm::aggregator_pipeline_execute | ( | It | first, |
| It | last | ||
| ) |
Experimental method ro run multiple aggregators in sync.
Pipeleine algorithm walts the sequence of iterators (pointers on aggregators) and run them all via aggregator<>::run_step() method
| first | - iterator (pointer on aggregator) |
| last | - iterator (pointer on aggregator) |
Definition at line 464 of file bmaggregator.h.
References bm::set_array_size.
Referenced by DNA_FingerprintScanner::FindCollection().
| void bm::combine_and | ( | BV & | bv, |
| It | first, | ||
| It | last | ||
| ) |
AND Combine bitvector and the iterable sequence.
Algorithm combines bvector with sequence of integers (represents another set). When the agrument set is sorted this method can give serious increase in performance.
| bv | - destination bitvector |
| first | - first element of the iterated sequence |
| last | - last element of the iterated sequence |
Definition at line 1420 of file bmalgo_impl.h.
References bm::combine_or().
Referenced by bm::aggregator< bvector_type >::combine_and(), DemoAND(), and main().
| void bm::combine_and_sorted | ( | BV & | bv, |
| It | first, | ||
| It | last | ||
| ) |
AND Combine bitvector and the iterable sequence.
Algorithm combines bvector with sorted sequence of integers (represents another set).
| bv | - destination bitvector |
| first | - first element of the iterated sequence |
| last | - last element of the iterated sequence |
Definition at line 1388 of file bmalgo_impl.h.
References BM_ASSERT.
Referenced by main().
| void bm::combine_or | ( | BV & | bv, |
| It | first, | ||
| It | last | ||
| ) |
OR Combine bitvector and the iterable sequence.
Algorithm combines bvector with sequence of integers (represents another set). When the agrument set is sorted this method can give serious increase in performance.
| bv | - destination bitvector |
| first | - first element of the iterated sequence |
| last | - last element of the iterated sequence |
Definition at line 1134 of file bmalgo_impl.h.
References bm::block_range_scan(), BM_ASSERT, BMGAP_PTR, bm::gap_limit(), bm::gap_set_value(), bm::id_max, bm::set_block_mask, bm::set_block_shift, bm::set_word_mask, and bm::set_word_shift.
Referenced by bm::combine_and(), bm::aggregator< bvector_type >::combine_or(), combine_or_test(), bm::rank_compressor< bvector_type >::compress(), bm::rank_compressor< bvector_type >::decompress(), DemoOR(), bm::operation_deserializer< BV >::deserialize(), main(), speed_test_sv_index(), and speed_test_vect_index().
| void bm::combine_sub | ( | BV & | bv, |
| It | first, | ||
| It | last | ||
| ) |
SUB Combine bitvector and the iterable sequence.
Algorithm combines bvector with sequence of integers (represents another set). When the agrument set is sorted this method can give serious increase in performance.
| bv | - destination bitvector |
| first | - first element of the iterated sequence |
| last | - last element of the iterated sequence |
Definition at line 1303 of file bmalgo_impl.h.
References bm::block_range_scan(), BM_ASSERT, BMGAP_PTR, bm::gap_limit(), bm::gap_set_value(), bm::gap_test_unr(), bm::id_max, bm::set_block_mask, bm::set_block_shift, bm::set_word_mask, and bm::set_word_shift.
Referenced by DemoSUB(), bm::operation_deserializer< BV >::deserialize(), and main().
| void bm::combine_xor | ( | BV & | bv, |
| It | first, | ||
| It | last | ||
| ) |
XOR Combine bitvector and the iterable sequence.
Algorithm combines bvector with sequence of integers (represents another set). When the agrument set is sorted this method can give serious increase in performance.
| bv | - destination bitvector |
| first | - first element of the iterated sequence |
| last | - last element of the iterated sequence |
Definition at line 1216 of file bmalgo_impl.h.
References bm::block_range_scan(), BM_ASSERT, BMGAP_PTR, bm::gap_limit(), bm::gap_set_value(), bm::gap_test_unr(), bm::id_max, bm::set_block_mask, bm::set_block_shift, bm::set_word_mask, and bm::set_word_shift.
Referenced by DemoXOR().
| bm::id_t bm::count_intervals | ( | const BV & | bv | ) |
Compute number of bit intervals (GAPs) in the bitvector.
Algorithm traverses bit vector and count number of uninterrupted intervals of 1s and 0s.
For example: empty vector - 1 interval<PHONE_NUMBER>0000 - gives us 3 intervals<PHONE_NUMBER>0000 - 4 intervals<PHONE_NUMBER>0000 - 1 interval<PHONE_NUMBER>1111 - 1 interval
Definition at line 1444 of file bmalgo_impl.h.
References bm::for_each_block().
| void bm::export_array | ( | BV & | bv, |
| It | first, | ||
| It | last | ||
| ) |
Export bitset from an array of binary data representing the bit vector.
Input array can be array of ints, chars or other native C types. Method works with iterators, which makes it compatible with STL containers and C arrays
| bv | - destination bitvector |
| first | - first element of the iterated sequence |
| last | - last element of the iterated sequence |
Definition at line 1473 of file bmalgo_impl.h.
References BM_ASSERT, bm::BM_BIT, bm::set_block_size, and bm::set_total_blocks.
| void bm::for_each_bit | ( | const BV & | bv, |
| Func & | bit_functor | ||
| ) |
bit-vector visitor scanner to traverse each 1 bit using C++ visitor
| bv | - bit vector to scan |
| bit_functor | (should support add_bits() and add_range() methods |
Definition at line 61 of file bmalgo.h.
References BM_SCANNER_OP, bm::set_array_size, and bm::sse42_test_all_zero_wave().
Referenced by bm::rank_compressor< bvector_type >::compress_by_source(), bm::sparse_vector< unsigned, bm::bvector<> >::extract(), and bm::visit_each_bit().
| void bm::visit_each_bit | ( | const BV & | bv, |
| void * | handle_ptr, | ||
| bit_visitor_callback_type | callback_ptr | ||
| ) |
bit-vector visitor scanner to traverse each 1 bit using C callback
| bv | - bit vector to scan |
| handle_ptr | - handle to private memory used by callback |
| callback_ptr | - callback function |
Definition at line 123 of file bmalgo.h.
References bm::for_each_bit().


Maintaining the style guide is a manual process. Any time the Sass is updated, the changes should be reflected here.
Handlebars Introduction
In order to lower maintenance overhead, the style guide is built using Handlebars, which allows you to create reusable template files and then specify the content for that page using a JSON object. You can learn more about this by following the Beginner's Guide to Handlebars.
Updating Page Content
With the exception of the index pages and this page, all pages in the style guide utilize Handlebars. To edit a particular page's content, you will need to modify the JSON object, which can be found in a script tag in the HTML file for that page. The JSON object should be setup as such:
var context = {
'category' : 'Section of the Style Guide',
'title' : 'Title of the Page',
'description' : 'Brief description about the use and function of the pattern.',
'sections' : [
{
'sectionName' : 'Base',
'sectionIdentifier' : 'base',
'sectionStatus' : 'Ready',
'sectionBadge' : '',
'snippets' : [
{
'snippetDescription' : 'Description for the base.',
'snippetLanguage' : '',
'snippetCode' : '

'
}
]
},
{
'sectionName' : 'Modifier',
'sectionIdentifier' : 'modifier',
'sectionStatus' : 'Ready',
'sectionBadge' : '',
'snippets' : [
{
'snippetDescription' : 'Description for the modifier.',
'snippetLanguage' : '',
'snippetCode' : '

'
},
{
'snippetDescription' : 'Description for the modifier\'s second snippet.',
'snippetLanguage' : 'JavaScript',
'snippetCode' : '$(\'.base.modifier\').on(\'click\', function() {\n ...\n});'
}
]
}
]
};
The page is then generated from the values you define in this JSON object. Here's what each variable means:
- category: The category the pattern falls under. Options are "Style Guide", "Design", "Structure", or "Patterns". This will appear at the top of the page above the page title.
- title: The page title for the pattern. This is what will appear at the top of the page.
- description: A brief description about the use and function of the pattern. This will appear below the title. You will need to escape any single quotation marks, like so
\'
. This variable also supports HTML. - sections: This variable contains an array of all of the sections on the page. You must have at least one section, but you can have as many as necessary. If you find yourself adding a lot of sections, you may want to consider breaking some of them out into their own pages. Each section is wrapped in
{}
and contains the following variables:- sectionName: The headline that will appear on the page for that section.
- sectionIdentifier: The ID that is used to link directly to that section. Do not include
#
, just the text. - sectionStatus: The current status of this part of the pattern. Options are "Ready", "Testing", or "In Development". This is what will appear in the badge next to the section headline.
- sectionBadge: The class modifier to change the color of the badge next to the section headline. Options are "style-badge-red" or "style-badge-yellow". The default is green and does not need a class.
- snippets: Like sections, this variable contains an array of all of the code snippets and their accompanying descriptions for this section. This allows a single section to have multiple code snippets, which is useful if switching between languages or making large code chunks more digestible.
- snippetDescription: A description for how this snippet's code works and any special considerations. You will need to escape any single quotation marks like so:
\'
. This variable also supports HTML. - snippetLanguage: The language that the code block will be in. Options are "JavaScript", "SCSS", "PHP", or "Bash". If left blank, this will default to standard markup (HTML).
- snippetCode: The code that will be displayed for this snippet. Everything must be on one line, so you will need to use
\n
for line breaks, and enter four spaces for each indentation level. You do not need to escape any HTML, but


Challenge 11
Create a tip calculator in javascript (Lesson 9 - Programming Concepts)
Your "Eat Out to Help Out" bill comes to £49.56,
if you would like to add a gratuity press the button below:
The final coded used to calculate the gratuity (tip) is listed below you can review chg11-tipCalculator.js for all the code iterations.
function calculateTip() { var billAmount = 49.56; var tipPercent = 17; var tipAmount = (billAmount * tipPercent / 100); document.getElementById('totalBillMessage').innerHTML = `Your total bill, including a gratuity of £${tipAmount.toFixed(2)}, comes to £${(billAmount + tipAmount).toFixed(2)}`; };


Range Slider
Range Slider let the user select a range of values by moving the slider thumb. The smallest value is to the left, the largest to the right.
We have used noUISlider plugin as a reference which we have then customized based on our Propeller theme.
For more options and documentation, visit : noUISlider
Single Handle Horizontal Slider
A handle snaps to a clicked location. It can immediatly be moved, without a mouseup + mousedown. There are many different types of single handler slider such as default slider, slider with steps, slider with visible tooltip, slider with bottom visible tooltip, slider which can be disabled and slider with input value.
Single Handle slider : It allows user to select a value along a subjective range. It does not require a specific value to make adjustments, although it may, in some instances, offer an editable numeric value.
Single Handle Slider with steps
Single Handle slider with visible tooltip : Add .pmd-range-tooltip
to make the slider tooltip visible by default.
Single Handle slider with visible tooltip (bottom direction) : Add .pmd-range-tooltip-bottom
to make the slider tooltip visible in bottom direction by
default.
Single Handle Slider which can be disabled.
Single Handle Slider which can be controlled by inputting values also.
Range Slider
Range slider are the ones with two handler. We can have range sliders of various types such as default range slider, range slider with visible tooltip, range slider whose both handlers can be disabled and range slider with input value.
Default range slider. Use .pmd-range-slider
to create the slider.
Range slider with visible tooltip. In order to make the tooltip visible, add .pmd-range-tooltip
to the slider.
Range slider with visible tooltip at the bottom. You can show tooltip at the bottom using .pmd-range-tooltip-bottom
.
Range slider with lower tooltip at the bottom. You can show tooltip at the bottom using .pmd-range-tooltip-left-bottom
.
Range slider with upper tooltip at the bottom. You can show tooltip at the bottom using .pmd-range-tooltip-right-bottom
.
Ranger slider each of which's handler can be disabled.
Range Slider with value
Verticle Slider
Instead of horizontal slider we can also show the slider vertically. For vertical sliders also we can have slider with steps, slider with tooltip towards left or right.
Single Handle Vertical Slider.
Single Handle Vertical Slider with steps
Single Handle Vertical Slider with visible tooltip. Use .pmd-range-tooltip
for slider with visible tooltip.
Single Handle Vertical Slider with visible tooltip at right. Add right tooltip using .pmd-range-tooltip-right
Verticle Range Slider
Vertical range slider is a slider with two handlers. We can have default slider or slider with visible tooltip. We can also have a slider with both tooltips in opposite direction to each other.
Default Vertical Range Slider
Vertical range slider with visible tooltip on left
Vertical range slider with lower handler tooltip towards right and upper handler tooltip towards left. Use .pmd-range-tooltip-bottom-right
to achieve this.
Vertical range slider with lower handler tooltip towards left and upper handler tooltip towards right. Use .pmd-range-tooltip-top-right
for this.
Configuration Options
The Propeller CSS classes apply various predefined visual enhancements to the slider. The table lists the available classes and their effects.
| Propeller Class | Effect | Remark |
|---|---|---|
.pmd-range-slider |
Used to create the slider. | Required |
.pmd-range-tooltip |
Used to make the tooltip visible. | Optional |
.pmd-range-tooltip-bottom |
Used to make the tooltip visible at the bottom. | Optional |
.pmd-range-tooltip-right |
Use to make the tooltip visible at the right of the vertical slider. | Optional |
.pmd-range-tooltip-bottom-right |
Use to make the lower tooltip visible at the right of the vertical slider. | Optional |
.pmd-range-tooltip-top-right |
Use to make the upper tooltip visible at the right of the vertical slider. | Optional |
.pmd-range-tooltip-left-bottom |
Use to make the lower tooltip visible at the bottom of the horizontal slider. | Optional |
.pmd-range-tooltip-right-bottom |
Use to make the upper tooltip visible at the bottom of the horizontal slider. | Optional |


A statement released by the police command says on October 2nd, the police received a report that Dumebi, aged 25, from Ubarunisionye village, Nando in Anambra East LGA, was kidnapped by unknown persons and taken away along with his tricycle (Keke) while operating it for commercial purpose.
Following the report, Police operatives attached to the Command State intelligence Bureau (SIB) swung into action. Its investigation led to the arrest of Chizoba who confessed that himself and one Ezennia Nweke alias Abada, allegedly conspired and killed the victim, buried the corpse inside the bush along Achalla-agu Nando road and made away with his keke.
He thereafter, led a team of Police detectives to the scene where the victim was buried in a shallow grave and his decomposing body was exhumed, certified by a medical doctor in the presence of the deceased’s parents who equally identified the clothes he wore. Thereafter, the body was photographed and released to the deceased’s father for proper burial.
Meanwhile, the snatched keke was recovered from one 27year old Anthony Charles alias ‘Walter’ from Ebonyi State.
The police has declared wanted the principal accomplice, Eziennia who allegedly conspired with Chizoba to perpetrate the dastardly act as is he said to be on the run.


Beta This is a test version of the layout of this page. Take the survey to help us improve it
Form
Application forms and assessment criteria for groups interested in opening a special free school.
Groups who wish to apply to open a special free school should use the forms on this page.
The ‘Free school applications: criteria for assessment’ document gives guidance on the application process, including the deadline for submitting applications.
If you are applying to open a special free school, you should also fill in the financial template (section G of the application). The template will help you plan your budget.
More information on opening a free school is available.
Special free schools are free schools for children with special educational needs or disabilities.


Scratch is a visual, block-based programming language that is the perfect tool for introducing children to coding and the design process. Scratch helps young people learn to think creatively and reason systematically. In Scratch classes, students will explore programming fundamentals like sequencing, loops, boolean logic, and variables while creating games and animations. Scratch classes are great for students who are new to programming and for experienced Scratchers who want to take their creations to the next level!
Group classes availible, recommended for students ages 7-9
Private classes availible, recommended for students ages 6 and up
Does your child love playing games on Roblox? Do they aspire to create a game of their own? Good news: they can use their creativity to build their own Roblox games while learning valuable computer science skills. In this class, students will learn the basics of Roblox Studio to create their very own games and will learn to code with Lua along the way to bring their games to life.
Group classes availible, recommended for students ages 9-12
Private classes availible, recommended for students ages 7 and up
What do YouTube, Google, Instagram, Spotify, DropBox, and Reddit all have in common? Aside from being tech giants, they all use the Python programming language! Python is a great language for any student interested in computer science to learn and is highly useful whether your goal is to enhance abstract thinking skills through learning a programming language or to build a large-scale project. In this class, students will learn the basics of programming with Python and while recreating classic games.
Group classes availible, recommended for students ages 13-17
Private classes availible, recommended for students ages 10 and up
Learn the core technologies of the World Wide Web. While learning the fundamentals of programming through JavaScript, HTML, and CSS, students in this class will create web pages, websites, web-applications, and games. We will also explore how the internet works and compare server-side and client-side development.
Private classes availible, recommended for students ages 10 and up
Private classes availible, recommended for students ages 13 and up
Students taking the AP Computer Science A or AP Computer Science Principles exam can drop in for tutoring sessions on specific tricky topics or schedule regular sessions for enrichment classes to help boost their knowledge in the subject matter, get more coding practice, and amp up their AP score.
Private classes availible.
Recommended for high school students taking an AP Computer Science Class (A or Principles).
**If your school does not offer an AP Computer Science Class, but you would like to take an AP Computer Computer Science exam, you can still do so. Private tutoring sessions combined with self-directed learning can be a great approach to learning an AP course.


Please paste your geocoding data below. Each line should be in the format "prefix|description". Lines without a "|" symbol will be ignored.


| GRFT alone or with mannose |
1.3 and 0.94 |
A domain-swapped dimer, a Jacalin-related lectin with a β-prism motif, and three identical mannose-binding sites on each monomer |
[
19]
|
| GRFT with glucose or
N-acetylglucosamine
|
30–1.50 and 30–1.56 |
All six monosaccharide binding sites of GRFT are occupied by both glucose and
N-acetylglucosamine with a mode of binding similar to that of mannose
|
[
23]
|
| GRFT with 1-6α-mannobiose or maltose |
2.0 and 1.5 |
The binding of 1-6α-mannobiose is similar to that of mannose and the binding of maltose is weaker than that of mannose |
[
22]
|
| Monomeric GRFT |
30–0.97 |
Reduced activity against HIV-1 due to a loss of multivalent interaction and the binding of a monomeric GRFT to two different nona-mannosides |
[
20]
|
| GRFT with a disrupted carbohydrate-binding site |
NMR study |
Reduced binding to mannose and a weaker correlation between anti-HIV-1 activity and gp120 binding |
[
21]
|


three approaches:
they focus on a third way, the interactionist, in which they develop on patterns of relation between people and objects
We suggest that aesthetic experience is a function of the perceiver’s processing dynamics: The more fluently the perceiver can process an object, the more positive is his or her aesthetic response.
Features that facilitate fluent processing include all the core features identified in the objectivist tradition, like goodness of form, symmetry, figure-ground contrast, as well as variables that have not received attention in traditional theories of aesthetic pleasure, like perceptual and conceptual priming procedures.
They focus on perceptual fluency, but applies just as well to conceptual fluency.
Objectively simpler stimuli are not always easier on the cognitive system (higher redundancy, for instance)
This study is then updated by Processing Fluency and Aesthetic Pleasure: Is Beauty in the Perceiver’s Processing Experience?, corrborating the theory of rebert et. al. by engaging into the relationship between beauty and truth, and with processing fluency being a cornerstone of both aesthetic and and epistemic judgments.


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GameOn!
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COUNT BAYESIE: PROBABLY A PROBABILITY BLOG
Review of Probability Theory (Stanford)
A First Course in Probability (Book: Sheldon Ross)
Statistics 110: Harvard
Lecture Series on Probability (following DL-book)
Probability Quora FAQs
Math review for Stat 110
Deep Learning Probability
Probability as Extended Logic
CS188 Probability Lecture (very intuitive)
Combinatorics (Notes)
Digital textbook on probability and statistics (!)
Motivation
- Uncertainty in General Systems and the need for a Probabilistic Framework:
- Inherent stochasticity in the system being modeled:
Take Quantum Mechanics, most interpretations of quantum mechanics describe the dynamics of sub-atomic particles as being probabilistic. - Incomplete observability:
Deterministic systems can appear stochastic when we cannot observe all the variables that drive the behavior of the system.i.e. Point-of-View determinism (Monty-Hall)
- Incomplete modeling:
Building a system that makes strong assumptions about the problem and discards (observed) information result in uncertainty in the predictions.
- Inherent stochasticity in the system being modeled:
-
Bayesian Probabilities and Frequentist Probabilities:
Frequentist Probabilities describe the predicted number of times that a repeatable process will result in a given output in an absolute scale.Bayesian Probabilities describe the degree of belief that a certain non-repeatable event is going to result in a given output, in an absolute scale.
We assume that Bayesian Probabilities behaves in exactly the same way as Frequentist Probabilities.
This assumption is derived from a set of “common sense” arguments that end in the logical conclusion that both approaches to probabilities must behave the same way - Truth and probability (Ramsey 1926). - Probability as an extension of Logic:
“Probability can be seen as the extension of logic to deal with uncertainty. Logic provides a set of formal rules for determining what propositions are implied to be true or false given the assumption that some other set of propositions is true or false. Probability theory provides a set of formal rules for determining the likelihood of a proposition being true given the likelihood of other propositions.” - deeplearningbook p.54
Basics
- Elements of Probability:
- Sample Space \(\Omega\): The set of all the outcomes of a stochastic experiment; where each outcome is a complete description of the state of the real world at the end of the experiment.
- Event Space \({\mathcal {F}}\): A set of events; where each event \(A \in \mathcal{F}\) is a subset of the sample space \(\Omega\) - it is a collection of possible outcomes of an experiment.
- Probability Measure \(\operatorname {P}\): A function \(\operatorname {P}: \mathcal{F} \rightarrow \mathbb{R}\) that satisfies the following properties:
- \(\operatorname {P}(A) \geq 0, \: \forall A \in \mathcal{f}\),
- \(\operatorname {P}(\Omega) = 1\), \(\operatorname {P}(\emptyset) = 0\)1
- \({\displaystyle \operatorname {P}(\bigcup_i A_i) = \sum_i \operatorname {P}(A_i) }\), where \(A_1, A_2, ...\) are disjoint events
Properties:
- \({\text { If } A \subseteq B \Longrightarrow P(A) \leq P(B)}\),
- \({P(A \cap B) \leq \min (P(A), P(B))}\),
- Union Bound: \({P(A \cup B) \leq P(A)+P(B)}\)
- \({P(\Omega \backslash A)=1-P(A)}\).
- Law of Total Probability (LOTB): \(\text { If } A_{1}, \ldots, A_{k} \text { are a set of disjoint events such that } \cup_{i=1}^{k} A_{i}=\Omega, \text { then } \sum_{i=1}^{k} P\left(A_{k}\right)=1\)
- Inclusion-Exclusion Principle:
$$\mathbb{P}\left(\bigcup_{i=1}^{n} A_{i}\right)=\sum_{i=1}^{n} \mathbb{P}\left(A_{i}\right)-\sum_{i< j} \mathbb{P}\left(A_{i} \cap A_{j}\right)+\sum_{i< j < k} \mathbb{P}\left(A_{i} \cap A_{j} \cap A_{k}\right)-\cdots+(-1)^{n-1} \sum_{i< \ldots< n} \mathbb{P}\left(\bigcap_{i=1}^{n} A_{i}\right)$$
- Properties and Proofs 110
- Random Variables:
A Random Variable is a variable that can take on different values randomly.
Formally, a random variable \(X\) is a function that maps outcomes to numerical quantities (labels), typically real numbers:$${\displaystyle X\colon \Omega \to \mathbb{R}}$$
Think of a R.V.: as a numerical “summary” of an aspect of the experiment.
Types:
- Discrete: is a variable that has a finite or countably infinite number of states
- Continuous: is a variable that is a real value
Examples:
- Bernoulli: A r.v. \(X\) is said to have a Bernoulli distribution if \(X\) has only \(2\) possible values, \(0\) and \(1\), and \(P(X=1) = p, P(X=0) = 1-p\); denoted \(\text{Bern}(p)\).
- Binomial: The distr. of #successes in \(n\) independent \(\text{Bern}(p)\) trials and its distribution is \(P(X=k) = \left(\begin{array}{l}{n} \\ {k}\end{array}\right) p^k (1-p)^{n-k}\); denoted \(\text{Bin}(n, p)\).
- Probability Distributions:
A Probability Distribution is a function that describes the likelihood that a random variable (or a set of r.v.) will take on each of its possible states.
Probability Distributions are defined in terms of the Sample Space.- Classes:
- Discrete Probability Distribution: is encoded by a discrete list of the probabilities of the outcomes, known as a Probability Mass Function (PMF).
- Continuous Probability Distribution: is described by a Probability Density Function (PDF).
- Types:
- Univariate Distributions: are those whose sample space is \(\mathbb{R}\).
They give the probabilities of a single random variable taking on various alternative values - Multivariate Distributions (also known as Joint Probability distributions): are those whose sample space is a vector space.
They give the probabilities of a random vector taking on various combinations of values.
- Univariate Distributions: are those whose sample space is \(\mathbb{R}\).
A Cumulative Distribution Function (CDF): is a general functional form to describe a probability distribution:
$${\displaystyle F(x)=\operatorname {P} [X\leq x]\qquad {\text{ for all }}x\in \mathbb {R} .}$$
Because a probability distribution P on the real line is determined by the probability of a scalar random variable X being in a half-open interval \((−\infty, x]\), the probability distribution is completely characterized by its cumulative distribution function (i.e. one can calculate the probability of any event in the event space)
- Classes:
- Probability Mass Function:
A Probability Mass Function (PMF) is a function (probability distribution) that gives the probability that a discrete random variable is exactly equal to some value.
Mathematical Definition:
Suppose that \(X: S \rightarrow A, \:\:\: (A {\displaystyle \subseteq } \mathbb{R})\) is a discrete random variable defined on a sample space \(S\). Then the probability mass function \(f_X: A \rightarrow [0, 1]\) for \(X\) is defined as:$$p_{X}(x)=P(X=x)=P(\{s\in S:X(s)=x\})$$
The total probability for all hypothetical outcomes \(x\) is always conserved:
$$\sum _{x\in A}p_{X}(x)=1$$
Joint Probability Distribution is a PMF over many variables, denoted \(P(\mathrm{x} = x, \mathrm{y} = y)\) or \(P(x, y)\).
A PMF must satisfy these properties:
- The domain of \(P\) must be the set of all possible states of \(\mathrm{x}\).
- \(\forall x \in \mathrm{x}, \: 0 \leq P(x) \leq 1\). Impossible events has probability \(0\). Guaranteed events have probability \(1\).
- \({\displaystyle \sum_{x \in \mathrm{x}} P(x) = 1}\), i.e. the PMF must be normalized.
- Probability Density Function:
A Probability Density Function (PDF) is a function (probability distribution) whose value at any given sample (or point) in the sample space can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
The PDF is defined as the derivative of the CDF:$$f_{X}(x) = \dfrac{dF_{X}(x)}{dx}$$
A Probability Density Function \(p(x)\) does not give the probability of a specific state directly; instead the probability of landing inside an infinitesimal region with volume \(\delta x\) is given by \(p(x)\delta x\).
We can integrate the density function to find the actual probability mass of a set of points. Specifically, the probability that \(x\) lies in some set \(S\) is given by the integral of \(p(x)\) over that set.In the Univariate example, the probability that \(x\) lies in the interval \([a, b]\) is given by \(\int_{[a, b]} p(x)dx\)
A PDF must satisfy these properties:
- The domain of \(P\) must be the set of all possible states of \(x\).
- \(\forall x \in \mathrm{x}, \: 0 \leq P(x) \leq 1\). Impossible events has probability \(0\). Guaranteed events have probability \(1\).
- \(\int p(x)dx = 1\), i.e. the integral of the PDF must be normalized.
- Cumulative Distribution Function:
A Cumulative Distribution Function (CDF) is a function (probability distribution) of a real-valued random variable \(X\), or just distribution function of \(X\), evaluated at \(x\), is the probability that \(X\) will take a value less than or equal to \(x\).$$F_{X}(x)=\operatorname {P} (X\leq x)$$
The probability that \(X\) lies in the semi-closed interval \((a, b]\), where \(a < b\), is therefore
$${\displaystyle \operatorname {P} (a<X\leq b)=F_{X}(b)-F_{X}(a).}$$
Properties:
- \(0 \leq F(x) \leq 1\),
- \(\lim_{x \rightarrow -\infty} F(x) = 0\),
- \(\lim_{x \rightarrow \infty} F(x) = 1\),
- \(x \leq y \implies F(x) \leq F(y)\).
- Marginal Probability:
The Marginal Distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset.
Two-variable Case:
Given two random variables \(X\) and \(Y\) whose joint distribution is known, the marginal distribution of \(X\) is simply the probability distribution of \(X\) averaging over information about \(Y\).- Discrete:
$${\displaystyle \Pr(X=x)=\sum_ {y}\Pr(X=x,Y=y)=\sum_ {y}\Pr(X=x\mid Y=y)\Pr(Y=y)}$$
- Continuous:
$${\displaystyle p_{X}(x)=\int _{y}p_{X,Y}(x,y)\,\mathrm {d} y=\int _{y}p_{X\mid Y}(x\mid y)\,p_{Y}(y)\,\mathrm {d} y}$$
- Marginal Probability as Expectation:
$${\displaystyle p_{X}(x)=\int _{y}p_{X\mid Y}(x\mid y)\,p_{Y}(y)\,\mathrm {d} y=\mathbb {E} _{Y}[p_{X\mid Y}(x\mid y)]}$$
Marginalization: the process of forming the marginal distribution with respect to one variable by summing out the other variable
Notes:
- Marginal Distribution of a variable: is just the prior distr of the variable
- Marginal Likelihood: also known as the evidence, or model evidence, is the denominator of the Bayes equation. Its only role is to guarantee that the posterior is a valid probability by making its area sum to 1.
- both terms above are the same
- Marginal Distr VS Prior:
- Discussion
- Summary:
Basically, it’s a conceptual difference.
The prior, denoted \(p(\theta)\), denotes the probability of some event 𝜔 even before any data has been taken.
A marginal distribution is rather different. You hold a variable value and integrate over the unknown values.
But, in some contexts they are the same.
- Discrete:
- Conditional Probability:
Conditional Probability is a measure of the probability of an event given that another event has occurred.
Conditional Probability is only defined when \(P(x) > 0\) - We cannot compute the conditional probability conditioned on an event that never happens.
Definition:$$P(A|B)={\frac {P(A\cap B)}{P(B)}} = {\frac {P(A, B)}{P(B)}}$$
Intuitively, it is a way of updating your beliefs/probabilities given new evidence. It’s inherently a sequential process.
- The Chain Rule of Conditional Probability:
Any joint probability distribution over many random variables may be decomposed into conditional distributions over only one variable.
The chain rule permits the calculation of any member of the joint distribution of a set of random variables using only conditional probabilities:$$\mathrm {P} \left(\bigcap _{k=1}^{n}A_{k}\right)=\prod _{k=1}^{n}\mathrm {P} \left(A_{k}\,{\Bigg |}\,\bigcap _{j=1}^{k-1}A_{j}\right)$$
- Independence and Conditional Independence:
Two random variables \(x\) and \(y\) (or events ) are independent if their probability distribution can be expressed as a product of two factors, one involving only \(x\) and one involving only \(y\):$$\mathrm{P}(A \cap B) = \mathrm{P}(A)\mathrm{P}(B)$$
Two random variables \(A\) and \(B\) are conditionally independent given a random variable \(Y\) if the conditional probability distribution over \(A\) and \(B\) factorizes in this way for every value of \(Y\):
$$\Pr(A\cap B\mid Y)=\Pr(A\mid Y)\Pr(B\mid Y)$$
or equivalently,
$$\Pr(A\mid B\cap Y)=\Pr(A\mid Y)$$
In other words, \(A\) and \(B\) are conditionally independent given \(Y\) if and only if, given knowledge that \(Y\) occurs, knowledge of whether \(A\) occurs provides no information on the likelihood of \(B\) occurring, and knowledge of whether \(B\) occurs provides no information on the likelihood of \(A\) occurring.
Pairwise VS Mutual Independence:
- Pairwise:
$$\mathrm{P}\left(A_{m} \cap A_{k}\right)=\mathrm{P}\left(A_{m}\right) \mathrm{P}\left(A_{k}\right)$$
- Mutual Independence:
$$\mathrm{P}\left(\bigcap_{i=1}^{k} B_{i}\right)=\prod_{i=1}^{k} \mathrm{P}\left(B_{i}\right)$$
for all subsets of size \(k \leq n\)
Pairwise independence does not imply mutual independence, but the other way around is TRUE (by definition).
Notation:
- \(A\) is Independent from \(B\): \(A{\perp}B\)
- \(A\) and \(B\) are conditionally Independent given \(Y\): \(A{\perp}B \:\vert Y\)
Notes:
- Unconditional Independence is very rare (there is usually some hidden factor influencing the interaction between the two events/variables)
- Conditional Independence is the most basic and robust form of knowledge about uncertain environments
- Pairwise:
- Expectation:
The expectation, or expected value, of some function \(f(x)\) with respect to a probability distribution \(P(x)\) is the “theoretical” average, or mean value, that \(f\) takes on when \(x\) is drawn from \(P\).The Expectation of a R.V. is a weighted average of the values \(x\) that the R.V. can take – \(\operatorname {E}[X] = \sum_{x \in X} x \cdot p(x)\)
- Discrete case:
$${\displaystyle \operatorname {E}_{x \sim P} [f(X)]=f(x_{1})p(x_{1})+f(x_{2})p(x_{2})+\cdots +f(x_{k})p(x_{k})} = \sum_x P(x)f(x)$$
- Continuous case:
$${\displaystyle \operatorname {E}_ {x \sim P} [f(X)] = \int p(x)f(x)dx}$$
Linearity of Expectation:
$${\displaystyle {\begin{aligned}\operatorname {E} [X+Y]&=\operatorname {E} [X]+\operatorname {E} [Y],\\[6pt]\operatorname {E} [aX]&=a\operatorname {E} [X],\end{aligned}}}$$
Independence:
If \(X\) and \(Y\) are independent \(\implies \operatorname {E} [XY] = \operatorname {E} [X] \operatorname {E} [Y]\)
- Discrete case:
- Variance:
Variance is the expectation of the squared deviation of a random variable from its mean.
It gives a measure of how much the values of a function of a random variable \(x\) vary as we sample different values of \(x\) from its probability distribution:$$\operatorname {Var} (f(x))=\operatorname {E} \left[(f(x)-\mu )^{2}\right] = \sum_{x \in X} (x - \mu)^2 \cdot p(x)$$
Variance expanded:
$${\displaystyle {\begin{aligned}\operatorname {Var} (X)&=\operatorname {E} \left[(X-\operatorname {E} [X])^{2}\right]\\ &=\operatorname {E} \left[X^{2}-2X\operatorname {E} [X]+\operatorname {E} [X]^{2}\right]\\ &=\operatorname {E} \left[X^{2}\right]-2\operatorname {E} [X]\operatorname {E} [X]+\operatorname {E} [X]^{2}\\ &=\operatorname {E} \left[X^{2}\right]-\operatorname {E} [X]^{2}\end{aligned}}}$$
Variance as Covariance: Variance can be expressed as the covariance of a random variable with itself:
$$\operatorname {Var} (X)=\operatorname {Cov} (X,X)$$
Properties:
- \(\operatorname {Var} [a] = 0, \forall a \in \mathbb{R}\) (constant \(a\))
- \(\operatorname {Var} [af(X)] = a^2 \operatorname {Var} [f(X)]\) (constant \(a\))
- \(\operatorname {Var} [X + Y] = a^2 \operatorname {Var} [X] + \operatorname {Var} [Y] + 2 \operatorname {Cov} [X, Y]\).
Notes:
- When comparing Variances, ALWAYS NORMALIZE FIRST: Variance depends on Scale
- Standard Deviation:
The Standard Deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values.
It is defined as the square root of the variance:$${\displaystyle {\begin{aligned}\sigma &={\sqrt {\operatorname {E} [(X-\mu )^{2}]}}\\&={\sqrt {\operatorname {E} [X^{2}]+\operatorname {E} [-2\mu X]+\operatorname {E} [\mu ^{2}]}}\\&={\sqrt {\operatorname {E} [X^{2}]-2\mu \operatorname {E} [X]+\mu ^{2}}}\\&={\sqrt {\operatorname {E} [X^{2}]-2\mu ^{2}+\mu ^{2}}}\\&={\sqrt {\operatorname {E} [X^{2}]-\mu ^{2}}}\\&={\sqrt {\operatorname {E} [X^{2}]-(\operatorname {E} [X])^{2}}}\end{aligned}}}$$
Properties:
- 68% of the data-points lie within \(1 \cdot \sigma\)s from the mean
- 95% of the data-points lie within \(2 \cdot \sigma\)s from the mean
- 99% of the data-points lie within \(3 \cdot \sigma\)s from the mean
- Covariance:
Covariance is a measure of the joint variability of two random variables.
It gives some sense of how much two values are linearly related to each other, as well as the scale of these variables:$$\operatorname {cov} (X,Y)=\operatorname {E} { {\big[ }(X-\operatorname {E} [X])(Y-\operatorname {E} [Y]){ \big] } }$$
Covariance expanded:
$${\displaystyle {\begin{aligned}\operatorname {cov} (X,Y)&=\operatorname {E} \left[\left(X-\operatorname {E} \left[X\right]\right)\left(Y-\operatorname {E} \left[Y\right]\right)\right]\\&=\operatorname {E} \left[XY-X\operatorname {E} \left[Y\right]-\operatorname {E} \left[X\right]Y+\operatorname {E} \left[X\right]\operatorname {E} \left[Y\right]\right]\\&=\operatorname {E} \left[XY\right]-\operatorname {E} \left[X\right]\operatorname {E} \left[Y\right]-\operatorname {E} \left[X\right]\operatorname {E} \left[Y\right]+\operatorname {E} \left[X\right]\operatorname {E} \left[Y\right]\\&=\operatorname {E} \left[XY\right]-\operatorname {E} \left[X\right]\operatorname {E} \left[Y\right].\end{aligned}}}$$
when \({\displaystyle \operatorname {E} [XY]\approx \operatorname {E} [X]\operatorname {E} [Y]}\), this last equation is prone to catastrophic cancellation when computed with floating point arithmetic and thus should be avoided in computer programs when the data has not been centered before.
Covariance of Random Vectors:
$${\begin{aligned}\operatorname {cov} (\mathbf {X} ,\mathbf {Y} )&=\operatorname {E} \left[(\mathbf {X} -\operatorname {E} [\mathbf {X} ])(\mathbf {Y} -\operatorname {E} [\mathbf {Y} ])^{\mathrm {T} }\right]\\&=\operatorname {E} \left[\mathbf {X} \mathbf {Y} ^{\mathrm {T} }\right]-\operatorname {E} [\mathbf {X} ]\operatorname {E} [\mathbf {Y} ]^{\mathrm {T} },\end{aligned}}$$
The Covariance Matrix of a random vector \(x \in \mathbb{R}^n\) is an \(n \times n\) matrix, such that:
$$ \operatorname {cov} (X)_ {i,j} = \operatorname {cov}(x_i, x_j) \\ \operatorname {cov}(x_i, x_j) = \operatorname {Var} (x_i)$$
Interpretations:
- High absolute values of the covariance mean that the values change very much and are both far from their respective means at the same time.
- The sign of the covariance:
The sign of the covariance shows the tendency in the linear relationship between the variables:- Positive:
the variables tend to show similar behavior - Negative:
the variables tend to show opposite behavior - Reason:
If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values, (i.e., the variables tend to show similar behavior), the covariance is positive. In the opposite case, when the greater values of one variable mainly correspond to the lesser values of the other, (i.e., the variables tend to show opposite behavior), the covariance is negative.
- Positive:
Covariance and Variance:
$$\operatorname{Var}[X+Y]=\operatorname{Var}[X]+\operatorname{Var}[Y]+2 \operatorname{Cov}[X, Y]$$
Covariance and Independence:
If \(X\) and \(Y\) are independent \(\implies \operatorname{cov}[X, Y]=\mathrm{E}[X Y]-\mathrm{E}[X] \mathrm{E}[Y] = 0\).- Independence \(\Rightarrow\) Zero Covariance
- Zero Covariance \(\nRightarrow\) Independence
Covariance and Correlation:
If \(\operatorname{Cov}[X, Y]=0 \implies\) \(X\) and \(Y\) are Uncorrelated.- Covariance/Correlation Intuition
- Covariance and Correlation (Harvard Lecture)
- Covariance as slope of the Regression Line
- Mixtures of Distributions:
It is also common to define probability distributions by combining other simpler probability distributions. One common way of combining distributions is to construct a mixture distribution.
A Mixture Distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized.
On each trial, the choice of which component distribution should generate the sample is determined by sampling a component identity from a multinoulli distribution:$$P(x) = \sum_i P(x=i)P(x \vert c=i)$$
where \(P(c)\) is the multinoulli distribution over component identities.
- Bayes’ Rule:
Bayes’ Rule describes the probability of an event, based on prior knowledge of conditions that might be related to the event.$${\displaystyle P(A\mid B)={\frac {P(B\mid A)\,P(A)}{P(B)}}}$$
where,
$$P(B) =\sum_A P(B \vert A) P(A)$$
- Common Random Variables:
Discrete RVs:- Bernoulli:
- Binomial:
- Geometric:
- Poisson:
Continuous RVs:
- Uniform:
- Exponential:
- Normal/Gaussian:
- Bernoulli:
-
Summary of Distributions:
- Formulas:
- \(\overline{X} = \hat{\mu}\),
- \(\operatorname {E}[\overline{X}]=\operatorname {E}\left[\frac{X_{1}+\cdots+X_{n}}{n}\right] = \mu\),
- \(\operatorname{Var}[\overline{X}]=\operatorname{Var}\left[\frac{X_{1}+\cdots+X_{n}}{n}\right] = \dfrac{\sigma^2}{n}\),
- \(\operatorname {E}\left[X_{i}^{2}\right]=\operatorname {Var} [X]+\operatorname {E} [X]^{2} = \sigma^{2}+\mu^{2}\),
- \(\operatorname {E}\left[\overline{X}^{2}\right]=\operatorname {E}\left[\hat{\mu}^{2}\right]=\frac{\sigma^{2}}{n}+\mu^{2}\:\), 2
-
Correlation:
In the broadest sense correlation is any statistical association, though it commonly refers to the degree to which a pair of variables are linearly related.There are several correlation coefficients, often denoted \({\displaystyle \rho }\) or \(r\), measuring the degree of correlation:
Pearson Correlation Coefficient [wiki]:
It is a measure of the linear correlation between two variables \(X\) and \(Y\).$$\rho_{X, Y}=\frac{\operatorname{cov}(X, Y)}{\sigma_{X} \sigma_{Y}}$$
where, \({\displaystyle \sigma_{X}}\) is the standard deviation of \({\displaystyle X}\) and \({\displaystyle \sigma_{Y}}\) is the standard deviation of \({\displaystyle Y}\), and \(\rho \in [-1, 1]\).
Correlation and Independence:
- Uncorrelated \(\nRightarrow\) Independent
- Independent \(\implies\) Uncorrelated
Zero correlation will indicate no linear dependency, however won’t capture non-linearity. Typical example is uniform random variable \(x\), and \(x^2\) over \([-1,1]\) with zero mean. Correlation is zero but clearly not independent.
-
Probabilistic Inference:
Probabilistic Inference: compute a desired probability from other known probabilities (e.g. conditional from joint).We generally compute Conditional Probabilities:
- \[p(\text{sun} \vert T=\text{12 pm}) = 0.99\]
- These represent the agents beliefs given the evidence
Probabilities change with new evidence:
- \(p(\text{sun} \vert T=\text{12 pm}, C=\text{Stockholm}) = 0.85\)
\(\longrightarrow\) - \[p(\text{sun} \vert T=\text{12 pm}, C=\text{Stockholm}, M=\text{Jan}) = 0.40\]
- Observing new evidence causes beliefs to be updated
Inference by Enumeration:
Problems:
- Worst-case time complexity \(\mathrm{O}\left(\mathrm{d}^{n}\right)\)
- Space complexity \(\mathrm{O}\left(\mathrm{d}^{n}\right)\) to store the joint distribution
Inference with Bayes Theorem:
- Diagnostic Probability from Causal Probability:
$$P(\text { cause } | \text { effect })=\frac{P(\text { effect } | \text { cause }) P(\text { cause })}{P(\text { effect })}$$
Discrete Distributions
-
- Bernoulli Distribution:
- A distribution over a single binary random variable.
It is controlled by a single parameter \(\phi \in [0, 1]\), which fives the probability of the r.v. being equal to \(1\).It models the probability of a single experiment with a boolean outcome (e.g. coin flip \(\rightarrow\) {heads: 1, tails: 0})
- PMF:
- \[{\displaystyle P(x)={\begin{cases}p&{\text{if }}p=1,\\q=1-p&{\text{if }}p=0.\end{cases}}}\]
- Properties:
$$P(X=1) = \phi$$
$$P(X=0) = 1 - \phi$$
$$P(X=x) = \phi^x (1 - \phi)^{1-x}$$
$$\operatorname {E}[X] = \phi$$
$$\operatorname {Var}(X) = \phi (1 - \phi)$$
- Binomial Distribution:
\({\binom {n}{k}}={\frac {n!}{k!(n-k)!}}\) is the number of possible ways of getting \(x\) successes and \(n-x\) failures
110
- Problems:
- deMortmonts/Matching problem
Sol: Inclusion-Exclusion
- Newton-Pepys: most likely event of rolling 6’s in dice
- deMortmonts/Matching problem
Notes, Tips and Tricks
-
It is more practical to use a simple but uncertain rule rather than a complex but certain one, even if the true rule is deterministic and our modeling system has the fidelity to accommodate a complex rule.
For example, the simple rule “Most birds fly” is cheap to develop and is broadly useful, while a rule of the form, “Birds fly, except for very young birds that have not yet learned to fly, sick or injured birds that have lost the ability to fly, flightless species of birds including the cassowary, ostrich and kiwi. . .” is expensive to develop, maintain and communicate and, after all this effort, is still brittle and prone to failure. - Disjoint Events (Mutually Exclusive): are events that cannot occur together at the same time
Mathematically:
- \(A_i \cap A_j = \varnothing\) whenever \(i \neq j\)
- \(p(A_i, A_j) = 0\),
-
Complexity of Describing a Probability Distribution:
A description of a probability distribution is exponential in the number of variables it models.
The number of possibilities is exponential in the number of variables. -
Probability VS Likelihood:
Probabilities are the areas under a fixed distribution
\(pr(\)data\(|\)distribution\()\)
i.e. probability of some data (left hand side) given a distribution (described by the right hand side)
Likelihoods are the y-axis values for fixed data points with distributions that can be moved..
\(L(\)distribution\(|\)observation/data\()\)Likelihood is, basically, a specific probability that can only be calculated after the fact (of observing some outcomes). It is not normalized to \(1\) (it is not a probability). It is just a way to quantify how likely a set of observation is to occur given some distribution with some parameters; then you can manipulate the parameters to make the realization of the data more “likely” (it is precisely meant for that purpose of estimating the parameters); it is a function of the parameters.
Probability, on the other hand, is absolute for all possible outcomes. It is a function of the Data. -
Maximum Likelihood Estimation:
A method that tries to find the optimal value for the mean and/or stdev for a distribution given some observed measurements/data-points. -
Variance:
When \(\text{Var}(X) = 0 \implies X = E[X] = \mu\). (not interesting) - Reason we sometimes prefer Biased Estimators:


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LiteSQL
0.3.17
|
Files | |
| file | backend.hpp [code] |
| Classes Backend, Backend::Cursor and Backend::Result. | |
| file | cursor.hpp [code] |
| Contains class Cursor. | |
| file | database.hpp [code] |
| Database-class. | |
| file | datasource.hpp [code] |
| selectObjectQuery<T> and DataSource<T> | |
| file | datetime.hpp [code] |
| constains Date, Time and DateTime - classes | |
| file | except.hpp [code] |
| contains litesql's exception classes | |
| file | expr.hpp [code] |
| Contains Expr-class hierarchy and operator overloadings for them. | |
| file | field.hpp [code] |
| contains FieldType- and Field-classes | |
| file | operations.hpp [code] |
| select<T>, intersect<T>, union_<T>, except<T> | |
| file | persistent.hpp [code] |
| Persistent. | |
| file | relation.hpp [code] |
| See Using Relations. | |
| file | selectquery.hpp [code] |
| contains SelectQuery-class. | |
| file | split.hpp [code] |
| contains class Split | |
| file | string.hpp [code] |
| helpful string utils | |
| file | types.hpp [code] |
| contains class Record and typedef Records | |
| file | updatequery.hpp [code] |
| contains UpdateQuery-class. | |
| file | utils.hpp [code] |
| includes string.hpp and split.hpp | |