OpenLLM-France/wikimedia huggingface dataset:
# How To Search/PubMed

PubMed
* Purpose: "to provide access to citations from biomedical literature."
* Audience: PubMed is run by National Center for Biotechnology Information (NCBI) which is part of the National Library of Medicine (NLM) in the United States. NCBI was established in 1988 as a national resource for molecular biology information, NCBI creates public databases, conducts research in computational biology, develops software tools for analyzing genome data, and disseminates biomedical information - all for the better understanding of molecular processes affecting human health and disease.
* Scope: Biomedical literature. Pubmed "allows users to access a superset of NLM's MEDLINE database containing MEDLINE, in-process citations, and citations to articles from selectively indexed journals that normally would not be selected for MEDLINE indexing."
* Refresh Rate: ?

#### Boolean Operators

| Boolean Operator | Syntax | Example |
| AND | {Default} | skunk tomato |
| OR | OR | skunk OR tomato |
| NOT | NOT | skunk NOT tomato |

#### Other Operators

| Syntax | Example | Description |
| "" | "kidney allograft" | phrase search |

#### Search Fields

"PubMed uses an Automatic Term Mapping feature to search for unqualified terms. When you click Go, PubMed will look for a match in up to four lists. It looks first for a match in the MeSH Translation Table. If it doesn't find a match, it looks in the Journals Translation Table and finally in the Author Index. As soon as PubMed finds a match, the mapping stops. That is, if a term matches in the MeSH Translation Table, PubMed does not continue looking in the next table." When there are no matches found during the automatic term mapping process, individual words are searched in all fields.
| Syntax | Example | Description |
| {Default} | | MeSH (Medical Subject Headings) |
| {Default} | | Journal Title |
| [au] or {Default} | Washington G | Author |
| | *cardiogra* | Truncation |
| YYYY/MM/DD | 1999/04/19 | Date of Publication |
| YYYY/MM/DD | 1999/04/19 | Entrez Date - Date publication was entered into Pubmed |
| YYYY/MM/DD | 1999/04/19 | Date publication was given MeSH terms |

#### Alternative Search Interface

* iPubMed An interface allowing interactive and fuzzy search

#### Other Features

An excellent PubMed tutorial can be found at http://www.nlm.nih.gov/bsd/pubmed_tutorial/m1001.html.

## External links

* PubMed Reader -- PubMed Reader is a free web-based research program for displaying PubMed / Medline search results on an individual, custom tailored basis.
* iPubMed An interface allowing interactive and fuzzy search
* Customizable PubMed Alerts
# How To Search/Stanford Encyclopedia of Philosophy

Stanford Encyclopedia of Philosophy
* Purpose: To provide a dynamic and up to date reference work in the subject area of philosophy.
* Audience: General philosophy researchers.
* Scope: Philosophy
* Refresh Rate:

## Boolean Operators

| Boolean Operator | Syntax | Example |
| AND | AND | skunk AND tomato |
| OR | OR | skunk OR tomato |
| NOT | NOT | skunk NOT tomato |

## Other Operators

| Syntax | Example | Description |
| | "skunk#" | wildcard for one or more characters |

## Other Features

There is a directory available for those who just want to browse by title of encyclopedic article or by date of article creation.
# How To Tie A Tie

How To Tie A Tie
A tie or necktie is a garment, conventionally worn around a man's neck with a collared shirt. There are several ways that the knot can be tied. A common and easy knot is the Four-In-Hand. However this is not the simplest knot.

## Contents

* The Knots
* Tying the Knots
* General Tips

## Reference

* Main methods easily explained (with pictures) - How to Tie a Tie
* Easy Steps - How to Tie a Tie
* How to Tie a Tie: How to tie a tie
* Easy way to learn how to tie a necktie, 9 famous knots: How to tie a tie
* For some pictures: How to tie a tie
* For a method shown on video: https://www.youtube.com/watch?v=-9u1VK1eTTc
* And: Theory of Tie Knots
* And: Tie-a-Tie.net
* For the mathematical basis of tie knots: Tie knots and random walks
* The history of the necktie: Necktie Down the Ages
* With slideshow and instructions: How to Tie a Tie
* Animated slideshow with clear pictures: - How to tie a tie
# How To Search/OhioLINK

OhioLINK
* Purpose: To "provide easy access to information and rapid delivery of library materials throughout the state."
* Audience: Students and employees of institutions which are part of the OhioLINK consortium.
* Scope: All cataloged material from OhioLINK member institutions.
* Refresh Rate: Item records are made available as items are purchased and catalogued by librarians.
* Further Information: OhioLINK uses the Millennium library system. Further searching information can be found at Millennium-III. Most of the items found in the OhioLINK catalog are available via Inter Library Loan from your local library if you live in the United States.

## Boolean Operators

See Millennium-III

## Other Operators

See Millennium-III

## Search Fields

See Millennium-III
# How To Search/Other search type list

The following list contains search mechanisms that have yet to be categorized but are described in this book.
* Directory of Open Access Journals
* grep
* Millennium-III
* MS Windows file search
* Stanford Encyclopedia of Philosophy
* Wikibooks
# How To Search/Yahoo

Yahoo! Search
* Purpose: "Our mission is to be the most essential global Internet service for consumers and businesses."
* Audience: All Internet users.
* Scope: The Internet. All documents that Yahoo's web crawling software can process.
* Refresh Rate: Constant
* Other Information: It is important to differentiate between Yahoo! Search, which this page is about, and the Yahoo web site directory. Yahoo! Search is a fully automated Internet search engine. (Although it seems to incorporate a few "Yahoo! Shortcuts," listed below, that may be human indexed.) On the other hand each web page in the web site directory is categorized by humans, it is not automated.

## Boolean Operators

| Boolean Operator | Syntax | Example |
| AND | {Default} | skunk tomato |
| OR | OR | skunk OR tomato |
| NOT | - | skunk -tomato |

## Other Operators

| Syntax | Example | Description |
| "" | "skunk smell removal" | phrase search |
| + | skunk +and tomato | include a common word that Google usually does not search |

## Search Fields

Yahoo! refers to the following as "Search Meta Words."
| Syntax | Example | Description |
| site: | site:wikibooks.org "how to search" | searches web pages that have the specified domain |
| hostname: | hostname:en.wikibooks.org "how to search" | searches web pages that have the specified hostname |
| link: | link:wikibooks.org | searches web pages that link to the specified URL |
| url: | url:http://www.wikibooks.org | searches the Yahoo index for the specified URL; this should return either 0 or 1 results |
| inurl: | inurl:wikibooks | searches web pages that contain the specified text (wikibooks) somewhere in the URL |
| intitle: | intitle:wikibooks | searches web pages that have the specified word in the title |

## Search Shortcuts

Yahoo refers to the following as Yahoo! Shortcuts. Some have yet to be listed in this wikibook.
When typing a shortcut it looks just like a normal word search. The difference shows up when the search results appear. Below advertisements and above the numbered search results there will be an entry with a red Yahoo Y next to it. This shortcut entry may provide an answer, if using the calculator or dictionary, or it may link to further pages with the answer.
| Shortcut | Description | Example | Further Information |
| Calculator | Allows calculations to be done from the search box. | 45*12 | 45*12 |
| Definitions | Defines words | define numeral | define numeral |

## Other Features

Yahoo! Search also allows a number of searches which can only be done using templates on their web pages. These can be found in the advanced search. These include file format (doc, html, pdf, ppt, rss, txt, xls), search language, safesearch filter, and country.
Other features not directly impacting search results include number of results listed per page.
# How To Tie A Tie/The Knots

Four basic knots exist for tying a tie: the Four-In-Hand, the Half-Windsor, the Windsor, and the Pratt knot.
The Windsor or Half-Windsor knots are more commonly used for interviews or other formal occasions. Their heftiness and symmetry will convey an air of confidence.
The Four-In-Hand are usually used in more casual scenarios.

### Oriental or Small Knot

The most basic knot. It forms an asymmetric knot with a wider base than the Four-in-Hand. It is not worn very often, possibly because it is not self-releasing.

### Four-In-Hand

The Four-In-Hand is a basic knot worn frequently in the West. It is also the easiest and fastest knot to tie. The knot produced by this method is on the narrow side, slightly asymmetric, and appropriate for all occasions.

### Half Windsor

The Half Windsor is for situations of moderate formality. It is luxury without pretense. It requires a little bit more time and practice than the Four, but the results are worth it. It is considered a simpler version of the Windsor knot, and gives a neat, triangular knot. The size of this knot falls in between the four-in-hand and the Windsor knots. It works particularly well with lighter fabrics.

### Windsor

The Windsor knot is generally perceived as the most formal and "upper-class" of the necktie realm. It is sometimes referred to as a full Windsor, to distinguish it from the half-Windsor. It produces a wide triangular knot. The knot is named after the Duke of Windsor (Edward VIII after abdication), who preferred a wide knot and had his ties specially made with thicker cloth in order to produce a wider knot when tied with the conventional four in hand knot. In Ian Fleming's James Bond series, the British spy remarked that the Windsor knot was "the mark of a cad." Its broad loop and wide knot are unmistakable. However, wearers of the Windsor knot may be marked as arrogant, especially as the current fashion is for smaller knots.

### Pratt / Shelby / Shelby-Pratt

The Pratt offers a good balance between simplicity and class. Once learned, it's quite easy to tie. For the Pratt knot, the starting position is 'reverse side out'. It uses less length than the Half Windsor or Windsor knots, and so is well suited to shorter ties. Unlike the Four in Hand knot, the Pratt method produces a symmetrical knot. It is of medium thickness. Its one disadvantage is that the tie occasionally comes a little loose around the neck with extended wear, but a simple tug is all that's needed to refresh it. It shapes itself naturally, requires almost no adjustment, forms its own dimples, and is very easy to learn.

## Reference

* Learn by video: Windsor Knot, Half Windsor Knot, Four in Hand Knot, Pratt Knot
* Learn step-by-step how to tie these knots: Four in Hand Knot, Half Windsor Knot, Windsor Knot, Pratt Knot, Bow Tie Knot
* And: Theory of Tie Knot
* Video: Necktie Instructional Video
# LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Continuous Time/Structured Singular Value

LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Continuous Time/Structured Singular Value
The LMI can be used to find a $\Theta$ that belongs to the set of scalings $P\Theta$. Minimizing $\gamma$ allows to minimize the squared norm of $\Theta M\Theta ^{-}1$.

## The System

    ${\begin{aligned}M{\text{ with transfer function }}{\hat {M}}(s)=C(sI-A)^{-1}B+D,&&{\hat {M}}\in H_{\infty }\end{aligned}}$

## The Data

The matrices $A\in R^{n\times n},B\in R^{n\times m},C\in R^{o\times n},D\in R^{o\times m}$.

## The Optimization Problem

${\begin{aligned}{\text{There exists }}\Theta \in \Theta {\text{ such that }}||\Theta M\Theta ^{-1}||^{2}<\gamma .\end{aligned}}$

## The LMI:

       ${\begin{aligned}{\text{Find}}\;&X>0:\\{\begin{bmatrix}A^{T}X+XA&XB\\B^{T}X&-\Theta \end{bmatrix}}+\gamma ^{-2}{\begin{bmatrix}C^{T}\\D^{T}\end{bmatrix}}\Theta {\begin{bmatrix}C&D\end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

${\text{The optimization problem and the LMI are equivalent. }}\gamma {\text{ must be optimized using bisection.}}$

## Implementation

https://github.com/mcavorsi/LMI

## Related LMIs

Eigenvalue Problem

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
# LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/D-stability Rise Poles

LMI for Rise Time Poles
The following LMI allows for the verification that poles of a system will fall within a rise time constraint. This can also be used to place poles for rise time when the system matrix includes a controller, such as in the form A+BK.

## The System

We consider the following system:
${\begin{aligned}{\dot {x}}(t)&=Ax\end{aligned}}$
or the matrix $A\in \mathbb {R} ^{n\times n}$, which is the state matrix.

## The Data

The data required is the matrix A and the rise time $t_{r}$ you wish to verify.

## The Optimization Problem

To begin, the constraint of the pole locations is as follows: $z^{*}z-{1.8^{2} \over {t_{r}}^{2}}{\leq }0$, where z is a complex pole of A. We define $r^{2}{\geq }z^{*}z$. The goal of the optimization is to find a valid P > 0 such that the following LMI is satisfied.

## The LMI: LMI for Rise Time Poles

The LMI problem is to find a matrix P> 0 satisfying:
${\begin{aligned}{\begin{bmatrix}-rP&AP\\(AP)^{T}&-rP\end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

If the LMI is found to be feasible, then the pole locations of A, represented as z, will meet the rise time specification of $z^{*}z-{1.8^{2} \over {t_{r}}^{2}}{\leq }0$, and the poles of A satisfy the previously defined constraint.

## Implementation

A link to Matlab codes for this problem in the Github repository:
https://github.com/maxwellpeterson99/MAE509Code

## Related LMIs

- D-stabilization
- D-stability Controller
- D-stability Observer

## External Links

- LMI in Control Systems Analysis, Design and Applications
- A course on LMIs in Control by Matthew Peet

## Return to Main Page

-Matrix and LMI Properties and Tools
# LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Concatenation of LMIs
## Introduction

Matrix concatenation is the process of joining one or more matrices to make a new matrix. This process is similar for concatenating the LMIs as well.

## Concatenation of LMIs

A useful property of LMIs is that multiple LMIs can be concatenated together to form a single LMI. For example, satisfying the LMIs
is equivalent to satisfying the concatenated LMI:
${\begin{bmatrix}A&&0\\0&&B\end{bmatrix}}$ ${\begin{aligned}<0\end{aligned}}$,
More generally, satisfying the LMIs $A_{i}<0$, where $i=1,...,n$ is equivalent to satisfying the concatenated LMI:
${\begin{bmatrix}A_{1}&&0&&0&&.&&.&&0\\0&&A_{2}&&0&&.&&.&&0\\0&&0&&A_{3}&&.&&.&&0\\.&&.&&.&&.&&.&&0\\.&&.&&.&&.&&.&&0\\0&&0&&0&&0&&0&&A_{n}\\\end{bmatrix}}$ ${\begin{aligned}<0\end{aligned}}$,

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
* LMI Properties and Applications in Systems, Stability, and Control Theory - A downloadable book on LMIs by Ryan James Caverly and James Richard Forbes.
# LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Congruence Transformation

LMIs in Control/Matrix and LMI Properties and Tools/Congruence Transformation
This methods uses change of variable and some matrix properties to transform Bilinear Matrix Inequalities to Linear Matrix Inequalities. This method preserves the definiteness of the matrices that undergo the transformation.

## Theorem

Consider $Q\in \mathbb {S} ^{n},W\in \mathbb {R} ^{n\times n}$, where $\operatorname {rank} (W)=n$. The matrix inequality $Q<0$ is satisfied if and only if $WQW^{T}<0$ or equivalently, $W^{T}QW<0$.

## Example

Consider $A\in \mathbb {R} ^{n\times n},B\in \mathbb {R} ^{n\times m},K\in \mathbb {R} ^{m\times p},C^{T}\in \mathbb {R} ^{n\times p},P\in \mathbb {S} ^{n}$ and $V\in \mathbb {S} ^{p}$, where $P>0$ and $V>0$. The matrix inequality given by
${\begin{aligned}\ Q&={\begin{bmatrix}\ A^{T}P+PA&-PBK+C^{T}V\\\ *&-2V\\\end{bmatrix}}\ <0,\end{aligned}}$
is linear in variable $V$ and bilinear in the variable pair $(P.K)$. Choose the matrix $\operatorname {diag} (P^{-1},V^{-1})$ to obtain the equivalent BMI given by
${\begin{aligned}\ WQW^{T}&={\begin{bmatrix}\ P^{-1}A^{T}+AP^{-1}&-BKV^{-1}+P^{-1}C^{T}\\\ *&-2V^{-1}\\\end{bmatrix}}\ <0,\end{aligned}}$
Using a change of variable $X=P^{-1},U=V^{-1}$ and $F=KV^{-1}$, the above equation becomes
${\begin{aligned}\ WQW^{T}&={\begin{bmatrix}\ XA^{T}+AX&-BF+XC^{T}\\\ *&-2U\\\end{bmatrix}}\ <0,\end{aligned}}$
which is an LMI of variables $X,U$ and $F$. The original variable $K$ is recovered by doing a reverse change of variable $K=FU^{-1}$.

## Conclusion

A congruence transformation preserves the definiteness of a matrix by ensuring that $Q<0$ and $W^{T}QW<0$ are equivalent. A congruence transformation is related, but not equivalent to a similarity transformation $TQT^{-1}$, which preserves not only the definiteness, but also the eigenvalues of a matrix. A congruence transformation is equivalent to a similarity transformation in the special case when $W^{T}=W^{-1}$.

## 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.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
* LMI Properties and Applications in Systems, Stability, and Control Theory - A downloadable book on LMIs by Ryan James Caverly and James Richard Forbes.
# LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Continuous Time/Eigenvalue Problem

LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Continuous Time/Eigenvalue Problem
The maximum eigenvalue of a matrix is going to have the most impact on system performance. This LMI allows for minimization of the maximum eigenvalue by minimizing $\gamma$.

## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+Bu(t),\\y(t)&=Cx(t)\end{aligned}}$

## The Data

The matrices $A\in R^{n\times n},B\in R^{n\times m},C\in R^{o\times n}$.

## The Optimization Problem

${\text{ Minimize }}\gamma {\text{ subject to the LMI below.}}$

## The LMI:

       ${\begin{aligned}{\text{Find}}\;&P>0:\\{\begin{bmatrix}-A^{T}P-PA-C^{T}C&PB\\B^{T}P&\gamma I\end{bmatrix}}>0\\\end{aligned}}$

## Conclusion:

The eigenvalue problem can be utilized to minimize the maximum eigenvalue of a matrix that depends affinely on a variable.

## Implementation

https://github.com/mcavorsi/LMI

## Related LMIs

Structured Singular Value

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
# LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/D-stability Max Percent Overshoot Poles

LMI for Max Percent Overshoot Poles
The following LMI allows for the verification that poles of a system will within a maximum percent overshoot constraint. This can also be used to place poles for max percent overshoot when the system matrix includes a controller, such as in the form A+BK.

## The System

We consider the following system:
${\begin{aligned}{\dot {x}}(t)&=Ax\end{aligned}}$
or the matrix $A\in \mathbb {R} ^{n\times n}$, which is the state matrix.

## The Data

The data required is the matrix A and the max percent overshoot $M_{p}$ you wish to verify.

## The Optimization Problem

To begin, the constraint of the pole locations is as follows: $z-z^{*}+{{\pi } \over ln({M_{p}})}|z+z^{*}|{\leq }0$, where z is a complex pole of A. The goal of the optimization is to find a valid P > 0 such that the following LMI is satisfied.

## The LMI: LMI for Max Percent Overshoot Poles

The LMI problem is to find a matrix P satisfying:
${\begin{aligned}{\begin{bmatrix}\pi (AP+(AP)^{T})&lnM_{p}(AP-(AP)^{T})\\lnM_{p}(AP-(AP)^{T})^{T}&\pi (AP+(AP)^{T})\end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

If the LMI is found to be feasible, then the pole locations of A, represented as z, will meet the max percent overshoot specification of $z-z^{*}+{{\pi } \over ln({M_{p}})}|z+z^{*}|{\leq }0$, and the poles of A satisfy the previously defined constraint.

## Implementation

A link to Matlab codes for this problem in the Github repository:
https://github.com/maxwellpeterson99/MAE509Code

## Related LMIs

- D-stabilization
- D-stability Controller
- D-stability Observer

## External Links

- LMI in Control Systems Analysis, Design and Applications
- A course on LMIs in Control by Matthew Peet

## Return to Main Page

-Matrix and LMI Properties and Tools
# LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Change of Subject

LMIs in Control/Matrix and LMI Properties and Tools/Change of Subject
A Bilinear Matrix Inequality (BMI) can sometimes be converted into a Linear Matrix Inequality (LMI) using a change of variables. This is a basic mathematical technique of changing the position of variables with respect to equal signs and the inequality operators. The change of subject will be demonstrated by the example below.

## Example

Consider $A\in \mathbb {R} ^{n\times n},B\in \mathbb {R} ^{n\times m},K\in \mathbb {R} ^{m\times n}$, and $Q\in \mathbb {S} ^{n}$, where $Q>0$.
The matrix inequality given by:
$QA^{T}+AQ-QK^{T}B{T}-BKQ<0$ is bilinear in the variables $Q$ and $K$.
Defining a change of variable as $F=KQ$ to obtain
$QA^{T}+AQ+-F^{T}B^{T}-BF<0$,
which is an LMI in the variables $Q$ and $F$.
Once this LMI is solved, the original variable can be recovered by $K=FQ^{-1}$.

## Conclusion

It is important that a change of variables is chosen to be a one-to-one mapping in order for the new matrix inequality to be equivalent to the original matrix inequality. The change of variable $F=KQ$ from the above example is a one-to-one mapping since $Q^{-1}$ is invertible, which gives a unique solution for the reverse change of variable $K=FQ^{-1}$.

## 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.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
* LMI Properties and Applications in Systems, Stability, and Control Theory - A downloadable book on LMIs by Ryan James Caverly and James Richard Forbes.