OpenLLM-France/wikimedia huggingface dataset:
# Guide to The Lord of the Rings/Index

This is a listing of all the pages in this book

## Books

* The Hobbit
* The Fellowship of the Ring
* The Two Towers
* The Return of the King

## Characters

The list of Characters

## Items

This is a list of Items
# LMIs in Control/Click here to continue/Optimal control systems

Optimal control systems
* H2-optimal control
** H2-optimal Full-state Feedback control
** Discrete-time H2-Optimal Full-state Feedback control
** H2-optimal Dynamic output Feedback control
** Discrete-time H2-optimal Dynamic output Feedback control
** H2-optimal Control with Regional Pole Assignment via State Feedback
* Hinf -Optimal Control
** Hinf-optimal Full-state Feedback Control
** Discrete-time Hinf-Optimal Full State Feedback Control
** Hinf-optimal Dynamic output Feedback control
** Discrete-time Hinf-optimal Dynamic output Feedback control
* Mixed H2-Hinf Optimal Control
** Mixed H2-Hinf-optimal Full-state Feedback Control
** Discrete-time H2-Hinf-optimal Full state Feedback control
** Mixed H2-Hinf-optimal Dynamic output Feedback control
** Discrete-time H2-Hinf-optimal Dynamic output Feedback control
* H2-Optimal State Estimation
** H2-Optimal Observer
** Discrete-Time H2-Optimal observer
* Hinf-Optimal State Estimation
** Hinf-Optimal Observer
** Discrete-time Hinf-Optimal Observer
* Mixed H2-Hinf Optimal State Estimation
** Mixed H2-Hinf-Optimal Observer
** Discrete-Time Mixed H2-Hinf Optimal Observer
* Optimal Filtering
** H2-Optimal Filtering
** Hinf-Optimal Filtering
** Discrete time H2 optimal filter
** Discrete time Hinf optimal filter
# LMIs in Control/Click here to continue/Observer synthesis/Schur Detectability

Schur Detectability
Schur detectability is a dual concept of Schur stabilizability and is defined as follows, the matrix pair $(A,C),$ is said to be Schur detectable if there exists a real matrix $L$ such that $A+LC$ is Schur stable.

## The System

We consider the following system:
${\begin{aligned}x(k+1)=Ax(k)+Bu(k)\\y(k)=Cx(k)+Du(k)\\\end{aligned}}$
where the matrices $A\in \mathbb {R} ^{n\times n}$, $B\in \mathbb {R} ^{n\times r}$, $C\in \mathbb {R} ^{m\times n}$,$D\in \mathbb {R} ^{m\times r}$$x\in \mathbb {R} ^{n}$,$y\in \mathbb {R} ^{m}$ , and $u\in \mathbb {R} ^{r}$ are the state matrix, input matrix, state vector, and the input vector, respectively.
Moreover, $k$ represents time in the discrete-time system and $k+1$ is the next time step.
The state feedback control law is defined as follows:
${\begin{aligned}u(k)=Kx(k)\end{aligned}}$
where $K\in \mathbb {R} ^{n\times r}$ is the controller gain. Thus, the closed-loop system is given by:
${\begin{aligned}x(k+1)=(A+BK)x(k)\end{aligned}}$

## The Data

* The matrices $A,B,C,D$ are system matrices of appropriate dimensions and are known.

## The Optimization Problem

There exist a symmetric matrix $P$ and a matrix W satisfying
${\begin{aligned}{\begin{bmatrix}-P&A^{T}P+C^{T}W^{T}\\PA+WC&P\end{bmatrix}}<0\\\end{aligned}}$
There exists a symmetric matrix $P$ satisfying
${\begin{aligned}{\begin{bmatrix}-N_{c}^{T}PN_{c}&N_{c}^{T}A^{T}P\\PAN_{c}&-P\end{bmatrix}}<0\\\end{aligned}}$
with $N_{c}$ being the right orthogonal complement of $C$. There exists a symmetric matrix P such that ${\begin{aligned}{\begin{bmatrix}-P&PA\\A^{T}P&-P-\gamma C^{T}C\end{bmatrix}}<0\\\end{aligned}}$
$\gamma >1$

## The LMI:

The LMI for Schur detectability can be written as minimization of the scalar, $\gamma$, in the following constraints:
${\begin{aligned}&{\text{min}}\quad \gamma \\&{\text{s.t.}}\end{aligned}}$
${\begin{aligned}{\begin{bmatrix}-P&A^{T}P+C^{T}W^{T}\\PA+WC&P\end{bmatrix}}<0\\\end{aligned}}$
${\begin{aligned}{\begin{bmatrix}-N_{c}^{T}PN_{c}&N_{c}^{T}A^{T}P\\PAN_{c}&-P\end{bmatrix}}<0\\\end{aligned}}$
${\begin{aligned}{\begin{bmatrix}-P&PA\\A^{T}P&-P-\gamma C^{T}C\end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

Thus by proving the above conditions we prove that the matrix pair $(A,C)$ is Schur Detectable.

## Implementation

A link to Matlab codes for this problem in the Github repository: Schur Detectability

## Related LMIs

LMI for Hurwitz stability LMI for Schur stability Hurwitz Detectability

## External Links

* - LMI in Control Systems Analysis, Design and Applications

## Return to Main Page

LMIs in Control/Tools
# LMIs in Control/Click here to continue/Optimal control systems/Discrete-time H2-Hinf-optimal Full state Feedback control

Discrete-Time Mixed H2-H∞-Optimal Full-State Feedback Control
A discrete time system operates on a discrete time signal input and produces a discrete time signal output. They are used in digital signal processing, such as digital filters for images or sound. The class of discrete time systems that are both linear and time invariant, known as discrete time LTI systems.
A full-state feedback controller $K=K_{d}\in {R^{n_{u}*n_{x}}}$ (i.e., $uk=K_{d}x_{k}$) is to be designed to minimize the H2 norm of the closed loop transfer matrix $T11(z)$ from the exogenous input $w_{1,k}$ to the performance output $z_{1,k}$ while ensuring the H∞ norm of the closed-loop transfer matrix $T22(z)$ from the exogenous input $w_{2,k}$ to the performance output $z_{2,k}$ is less than $\gamma _{d}$.

## The System

Discrete-Time LTI System with state space realization
${\begin{aligned}x_{k+1}&=A_{d}x_{k}+B_{d1,1}w_{1,k}+B_{d1,2}w_{2,k}+B_{d2}u_{k},\\{\begin{bmatrix}Z_{1,k}\\Z_{2,k}\end{bmatrix}}&={\begin{bmatrix}C_{d1,1}\\C_{d1,2}\end{bmatrix}}x_{k}+{\begin{bmatrix}0&D_{d11,12}\\D_{d11,21}&D_{d11,22}\end{bmatrix}}{\begin{bmatrix}w_{1,k}\\w_{2,k}\end{bmatrix}}+{\begin{bmatrix}D_{d12,1}\\D_{d12,2}\end{bmatrix}}u_{k}\\y_{k}&=x_{k}\\\end{aligned}}$

## The Data

The matrices: System $(A_{d},B_{d1,1},B_{d1,2},B_{d2},C_{d1,1},C_{d1,2},D_{d11,12},D_{d11,21},D_{d11,22},,D_{d12,1},D_{d12,2}),P,F_{d}$.

## The Optimization Problem

The following feasibility problem should be optimized:
Minimize the H2 norm of the closed loop transfer matrix $T11(z)$, while ensuring the H∞ norm of the closed-loop transfer matrix $T22(z)$ is less than $\gamma _{d}$, while obeying the LMI constraints.

## The LMI:

Discrete-Time Mixed H2-H∞-Optimal Full-State Feedback Controller is synthesized by solving for $P\in S^{n_{x}},Z\in S^{n_{w}},F_{d}\in R^{n_{u}*n_{x}}$, and $\mu \in R_{>0}$ that minimize $\mu$ subject to $P>0,Z>0$
The LMI formulation
H∞ norm < $\gamma _{d}$
H2 norm < $\mu$
${\begin{aligned}{\begin{bmatrix}P&A_{d}P-B_{d2}F_{d}&B_{d1,1}\\*&P&0\\*&*&1\end{bmatrix}}&>0\\{\begin{bmatrix}P&A_{d}P-B_{d2}F_{d}&B_{d1,2}&0\\*&P&0&PC_{d1,2}^{T}-F_{d}^{T}D_{d12,2}^{T}\\*&*&\gamma _{d}I&D_{d11,22}^{T}\\*&*&*&\gamma _{d}I\end{bmatrix}}&>0\\{\begin{bmatrix}Z&C_{d1,1}P-D_{d12,1}\\*&P\end{bmatrix}}&>0\\trace(Z)&<\mu ^{2}\end{aligned}}$

## Conclusion:

The H2-optimal full-state feedback controller gain is recovered by $K_{d}=F_{d}P^{-1}$

## Implementation

A link to CodeOcean or other online implementation of the LMI MATLAB Code

## Related LMIs

- Continuous Time Mixed H2-H∞ Optimal Full State Feedback Control

## External Links

A list of references documenting and validating the LMI.
* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
* LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
# LMIs in Control/Click here to continue/Optimal control systems/Discrete-time H2-Optimal Full-state Feedback control

Discrete-Time H2-Optimal Full-State Feedback Control
A discrete time system operates on a discrete time signal input and produces a discrete time signal output. They are used in digital signal processing, such as digital filters for images or sound. The class of discrete time systems that are both linear and time invariant, known as discrete time LTI systems.
A full state feedback controller design for a Discrete Time system, to minimize the H2 norm of the closed loop system with exogenous input $w_{k}$ and performance output $z_{k}$.

## The System

Discrete-Time LTI System with state space realization $(A_{d},B_{d},C_{d},D_{d})$ ${\begin{aligned}x_{k+1}&=A_{d}x_{k}+B_{d1}w_{k}+B_{d2}u_{k}\\z_{k}&=C_{d1}x_{k}+D_{d12}u_{k}\\y_{k}&=x_{k}\\\end{aligned}}$

## The Data

The matrices: System $(A_{d},B_{d1},B_{d2},C_{d1},D_{d12}),P,Z,F_{d}$.

## The Optimization Problem

The following feasibility problem should be optimized:
$\mu$ is minimized while obeying the LMI constraints.

## The LMI:

Discrete-Time H2-Optimal Full-State Feedback Control
The LMI formulation
H2 norm < $\mu$
${\begin{aligned}P\in {S^{n_{x}}};Z\in {S^{n_{z}}};&F_{d}\in {R^{n_{u}*n_{x}}};\mu \in {R_{>0}}\;\\&P>0\\&Z>0\\{\begin{bmatrix}P&A_{d}P+B_{d2}F_{d}&B_{d1}\\*&P&0\\*&*&I\end{bmatrix}}&>0,\\{\begin{bmatrix}Z&C_{d1}P+D_{d12}F_{d}\\*&P\end{bmatrix}}&>0,\\&trZ<\mu ^{2}\end{aligned}}$

## Conclusion:

The H2-optimal full-state feedback gain is recovered by $K_{d}=F_{d}P^{-1}$

## Implementation

A link to CodeOcean or other online implementation of the LMI MATLAB Code

## Related LMIs

- Continuous Time H2 Optimal Full State Feedback Control

## External Links

A list of references documenting and validating the LMI.
* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
* LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
# Learn to Play Drums/Regular Contributors
## Li

Li's been drumming for about three years. His favourite bands are Muse, Franz Ferdinand and Maximo Park. His favourite Muse songs are Screenager, Citizen Erased, Ruled by Secrecy and Knights of Cydonia - just in case you'd like to know...

## Eugene

Eugene has only started drumming and has a Sonor Special Edition 505 Stage Set. His favourite bands are Muse, Iron Maiden, Cardiac Attack and Avenged Sevenfold. His favourite Avenged Sevenfold Songs are Critical Acclaim, Scream and Gunslinger - just in case you'd like to know...
Add your name if you make a contribution (not just spelling corrections, though - unless you scour the wikibook correcting them)
# Learning Arimaa
## Table of Contents

* Overview
* Playing The Game
* Glossary
# Learn to Play Drums/Starting Out/Reading Sheet Music

Drum tabs are great, but the more complicated the rhythms get, the harder they are to read. They can quickly get very confusing. Musical scores are great for reading music quickly and accurately. Although learning to read sheet music is more involved than learning to read tabs, there is a lot more you can do with sheet music once you are fluent in reading it. Reading sheet music is not strictly necessary for you to be a skilled drummer. However, sheet music is a powerful tool that is useful to learn and will probably benefit you in many situations, especially when collaborating with other musicians.

## Why learn to read sheet music?

Drum tabs are a very imprecise way of explaining how to play a passage of music. You can use tabs to find out a rhythm to play, but tabs will usually leave out such things as: time signature, accents, tempo, number of times to repeat a passage, and more. Sheet music has a higher learning curve for you to overcome than tabs because there are more symbols and pieces to understand. However, just like with playing drums, practice makes perfect.
One of the best uses of sheet music is aiding in communication. For example, say you are playing drums for a musical and the piano player is trying to tell you that you need to play an accent at a certain part of a song. The pianist could mention that you play the accent when a certain melody comes along, but what if that melody comes about several times? It sure would be handy to have a way to denote exactly the point in a song the pianist is talking about...
Sheet music to the rescue! With sheet music you can refer to a specific measure number to find out when a certain part of the song is supposed to be played. This makes things easier for you and the pianist. Rather than saying, "Play the accent when this melody comes in", now we can say "Play this accent at measure 23" which is much more precise. Also, this makes it easy to make a note on your sheet music at that measure.
And a final note before we get started. Reading sheet music fluently allows you to instantly know things about how to play some music you've never heard before. Rather than being stuck playing only what you've previously heard, now you will be able to play music just by mentally translating notes on paper into physical drum hits. If you become skilled at this, your range of opportunities for having fun with music will expand, which is always a good thing.

## Reading sheet music

(More lessons coming soon)

## More information

More general information regarding sheet music can be found at http://en.wikipedia.org/wiki/Sheet_music
And here are a few external tutorials you can make use of to get some more practice reading sheet music.
* http://www.drumlessons.net/reading-sheet-music/
* http://www.learnhowtoreadsheetmusic.com/how-to-read-drum-music/
# Learning Arimaa/Overview

Arimaa is a two-player board game invented by Omar Syed, a computer engineer trained in artificial intelligence. Inspired by Garry Kasparov's defeat at the hands of the chess computer Deep Blue, Syed wanted to design a new game which would be difficult for computers to play well, but would have rules simple enough for his four-year-old son Aamir to understand. In fact, "Arimaa" is "Aamir" spelled backwards plus an initial "a." In 2002 Syed published the rules to Arimaa and announced a $10,000 prize, available through 2020, for the first computer program able to defeat a top-ranked human player in a match six games or longer. The prize was won in 2015.

# Ways to Use This Book

If you're someone who likes to dive right in, you can read the rules and start playing right away.
TODO:link to PDF of gameboard. link to Arimaa gameroom.
# Learning C With Game Concepts
## Table of Contents

* Introduction
* Designing A Roleplaying Game
* Inventory System
# Java Web Application Development With Click Framework

Java Web Application Development With Click Framework
Click Framework is a modern Jakarta EE web application framework, providing a natural rich client style programming model. Click is designed to be very easy to learn and use, with developers getting up and running within a day.

### Highlights

* Very easy to learn
* Component and Page Oriented design
* Event base programming model
* Automatic form rendering and client/server side validation
* Page templating
* Velocity and JSP page rendering
* High performance
The design philosophy behind Click is best summarized in the Swedish word lagom which translates to not too little or too much, but optimal.
If you want to dive straight into some code examples see the Introduction.
Otherwise if you want to know why anyone would want to build another web application framework read Why Click?
The Click project has been lead by Malcolm Edgar, and has included contributing developers Phil Barnes, Ahmed Mohombe, Naoki Takezoe, Christian Essl, Stephen Haberman and Bob Schellink.
Click was hosted by SourceForge and later by Apache (ASF).

## Table of Contents

* Introduction
* Why Click
* Pages
* Controls
* Configuration
* Quick Start
* Best Practices
* Extras
* Building
* ClickIDE
* Velocity

### Appendices

* Appendix A: FAQ
* Appendix B: Examples
* Appendix C: Click DTD
* Appendix D: API
* Appendix E: Cheat Sheet
# Java Web Application Development With Click Framework/Appendix B: Examples

Click provides an Examples web application to demonstrate Click features and common design patterns. The examples application is an important learning resource, and will help you to get up and running with Click as soon as possible.
This application will allows you to view the Page source code, templates and config files online.
You can view this application online at http://www.avoka.com:8080/click-examples

## Deploying Examples

Pre built dist/click-examples.war file is provided in the Click distribution. Simply copy this file to your application servers deployment directory.
This WAR file will deploy to the contexts: /* murali */
    /click-examples

## Building Examples

To build the Examples application see the Building topic for details.
Please also see the examples/README.txt file for additional details.
# Java Web Application Development With Click Framework/Appendix C: Click DTD

Click application XML descriptor Documentation Type Definition (DTD):
# Java Web Application Development With Click Framework/ClickIDE

ClickIDE is an Eclipse plug-in for the developing Click web applications. The ClickIDE project has been lead by Naoki Takezoe.
The section discusses the ClickIDE and includes the following topics:
* Installing
* Features

## Installing

ClickIDE requires Eclipse 3.2.x and WTP 1.5.x. The easiest way to use ClickIDE is introducing WTP using Callisto.
After WTP installed, get ClickIDE from the SF.net download page. Unzip clickide-x.x.x.zip and put 2 folders (plugins/ and features/) into your ECLIPSE_HOME.

## Features

ClickIDE is based on Eclipse and the Eclipse Web Tools Project (WTP), and provides extended features for developing web applications using Click.
* Fast switching between Page classes and templates (Ctrl Alt S)
* Project creation wizard
* Click page creation wizard
* Visual editor for the Click configuration file
* Velocity template editor
* Integrated Click documentation

#### Create Dynamic Web Project

Create "Dynamic Web Project" in the J2EE perspective and select "Click" as Project Facet. The project creation wizard will add Click JARs, web.xml and template of click.xml into your project.

#### Configuration Editor

ClickIDE provides the visual editor for the Click configuration file (click.xml). It has some tabs. You can edit click.xml using this editor easily.
In the "Source" tab of the configuration file editor, you can edit click.xml directly and you can jump to the source code of the page class and the page template by CTRL CLICK. ClickIDE also provides the validation for click.xml. Error markers are displayed in the editor and "Problems" view.

#### Page Creation Wizard

You can create the page class and the page template file using the page creation wizard. In the wizard, you can choose template for the page class and the html file. These template can be configured at the preference dialog ("Window" > "Preferences" > "Click").

#### Velocity Template Editor

ClickIDE also provides the Velocity template editor. This editor provides code-completion, highlighting and validation as velocity syntax. You can also configure highlighting colors in the preference dialog.

#### Fast switch between Page classes and templates

In the JDT's Java editor and the Velocity template editor, you can switch between the page class and the html file by CTRL ALT S.

#### Online Help

Click documentation is integrated with the Eclipse help system.

#### Cayenne Integration (since ClickIDE 2.0.0)

ClickIDE also support Apache Cayenne since ClickIDE 2.0.0.
You can create new Cayenne mapping project using the New Cayenne Mapping Project wizard.
# Java Web Application Development With Click Framework/Appendix E: Cheat Sheet

PDF version of the Cheat Sheet
# Learning anatomy/Large bowel

Small bowel - Rectum and anus
Template:Toc

## Anatomy

The large bowel or large intestine is made up of the vermiform appendix, the cecum, and the colon. The colon is made up of the ascending colon, transverse colon, descending colon, and sigmoid colon. The large intestine connects the small intestine to the rectum.

## Function

The cecum absorbs fluids and salts. The vermiform appendix is a storage for the gut bacteria that help with digestion. Gut bacteria is an example of a good bacteria. The colon absorbs water and electrolytes.
# Learning anatomy/Muscle
## Anatomy

There are 650 muscles in the body made by myocytes.

## Function

Skeletal muscles control movement so we can walk, run, and jump and even breathing and chewing needs muscles. Smooth muscle is what we can’t control. Cardiac muscle is found only in the heart.

## Illustrations

* Skeletal Muscle diagram
* Smooth Muscle diagram
* Smooth Muscle contraction diagram
* Cardiac Muscle diagram
# Learning anatomy/Ear
## Anatomy

The parts of the ear are:
* Pinna
* Ear canal
* Eardrum
* Ossicles
** Hammer
** Anvil
** Stirrup
* Cochlea

## Function

When sound waves are made the pinna (auricle) gathers them up and then the sound waves move into the ear canal (external auditory meatus, EAM). The sound waves then vibrate the eardrum (tympanic membrane) which strikes the hammer (malleus) bone which moves the anvil (incus) bone and the stirrup (stapes) bone. The stapes vibrates the liquid that fills the cochlea. The hair cells at the bottom detect the highest sounds. The hair cells in the middle detect lower sounds. The hair cells at the top control the lowest sounds. This gets going to the auditory nerve and then into the brain where you hear the sound.

## Illustrations

* the pinna of the ear
* ear canal highlighted
* tympanic membrane
* ossicles
* cochlea
# Learning anatomy/Esophagus

Learning anatomy - Stomach

## Anatomy

The esophagus is a tube connecting the throat to the stomach. The parts of the esophagus are the upper esophagus, middle esophagus, and lower esophagus. The esophagus also passes through a hole in the diaphragm called the esophageal hiatus.

## Function

The function of the esophagus is to move the swallowed food from the throat into the stomach. The lower esophageal sphincter or cardiac sphincter is between the lower esophagus and cardiac region of the stomach. Peristalsis happens throughout the gastrointestinal tract.
# Learning anatomy/Dermis
## Anatomy

The dermis is made up of the papillary dermis and the reticular dermis. It consists of collagen, elastin, blood capillaries, lymph vessels, sweat glands, sebaceous glands, nerve endings, and hair follicles.

## Function

The dermis makes sweat and regulates the body’s temperature, it produces oil, it makes hair grow, feels things and if it is too hot or too cold, your body tells you to get away from it and the dermis also protects the body from harmful pathogens, keeping the skin in shape, and distributing blood so that it can feed the skin, removes toxins, and supplies the epidermis with blood.
# Learning anatomy/Epidermis
## Anatomy

The parts of the epidermis are:
* Stratum basale
* Stratum spinosum
* Stratum granulosum
* Stratum lucidum
* Stratum corneum

## Function

The epidermis prevents microbes from entering the body. The epidermis is also waterproof, preventing the ingress of liquids which would otherwise wreck havoc on the chemistry body. After all, how would you wash your hands if they were not waterproof?
# Learning anatomy/Liver

Accessory organs
* Liver
* Biliary tract
* Pancreas exocrine
* Pancreas endocrine
* Kidney
_______________________________________________________________________
Rectum and anus - Biliary tract

## Anatomy

The liver is made up of the left lobe, right lobe, caudate lobe, and quadrate lobe. The ligaments are the falciform ligament and the coronary ligament. They are not real ligaments. Instead, they are a piece of peritoneal membrane holding the liver. The lobes of the liver are divided into 8 segments.

## Function

The liver has many functions and is a critical part of the digestive system. Did you know that the liver has more than 500 functions and can do 200 functions at the same time!? The liver makes bile, stores nutrients and performs metabolism. Bile is made by hepatocytes which are also called liver cells.