OpenLLM-France/wikimedia huggingface dataset:
# Past LSAT Explained/The Official LSAT PrepTest With Explanations and the LSAT Itemwise

October 2001 Form 1LSS51

## Section II Analytical Reasoning
### Question 01
### Question 14

As with all games, the key to understanding this game is to understand the rules behind it. Because the explanation of the rules can be confusing I will lay them out in an easier format.
1. "A train makes 5 stops around a loop through 5 stations P Q R S T, in that order - stopping at exactly three of the stations on each trip." Because the game does not state which states are stopped at first, any 3 of the 5 options can be picked as the first stations. Even though this is a 'loop' do not bother yourself with drawing a circle describing the stops. Simply write five vertical lines of the stations that are stopped at during each trip.
2. "The train stops at any given station on exactly 3 trips, but not on three consecutive trips." This is says the train will hit every station exactly 3 times in the course of 5 stops, but will not stop at that stations 3 times in a row.
3. "The train stops at any given station at least once in any two consecutive trips." This says that the train must stop at least once, could be more than once, at a station within two trips.
The inferences on this game are tricky, but try to map it out on paper. If you try to move more than one station per trip, you end up over lapping too many stations by the 5th trip and you are left with stations that have 3 consecutive trips. You can only move one station per trip to keep the rules in line.
# Past LSAT Explained/The Official LSAT SuperPrep

October 2001 Form 1LSS51

## Section IV Logical Reasoning
### Question 01
### Question 26

* Sandy Fritz, "Membrane Refrigerators." Copyright 1993 by Popular Science.
* Edward Hallet Carr, What is History? Copyright by Edward Hallet Carr.
* Feng-hsiung Hsu et al., "A Grandmaster Chess Machine." Copyright by Scientific American, Inc.
* Octavio Paz, Convergences: Essays on Art and Literature, tr. Helen Lane. 1987 by Harcourt Brace Jovanovich, Inc.
* David Roberts, "The Old Ones of the Southwest." Copyright 1996 by the National Geographic Society.
* Jonathan Rose, "The Invisible Sources of Nineteen Eight-Four." 1992 by the Journal of Popular Culture.
* William Raspberry, "Maturity Ends Delinquency" 1983 by Greenhaven Press, Inc.
# Past LSAT Explained/PrepTest 64
## Section I Logical Reasoning
### Question 01

Simple main conclusions question. Often when there is a but it is the counter-argument which everything else revolves around or is the main point so to speak.
Looking at the question we can look for something that states what is followed.
Done perfectly by answer C.
If we look at the other answers they are either premises or not stated in the conclusion this is an easy question without need to elaborate.

### Question 02

Must be true question- It tells us that in order for panthers to be self sustaining population it must reach 250 but, the habitat is not large enough to accommodate this. Hence we can infer that they will not be self sustaining.
Answers

### Question 03

This is a method of reasoning a little tricky. Think go the way the argument is set up it begins by telling us a criticism, then it states that this is wrong due to the fact that it fails to consider another outcome of implementing equality. . Looking at the answers we can look for something like that but, the way that they are stated often is confusing so POE is helpful
A- it says that the argument discredits the view by showing a slippery slope. It does not do this b- Yes, this is the answer the argument assumes that implementing will result in a certain outcome while the scents claims otherwise. c-it does not resort in ad hominem attack D- it does not do that e. Uses no universal claim

### Question 04

This is a correlation vs Causation type argument, it assumes that because something has happened it is a result of that.we must counter this. the argument assumes that the magentas resulted in a decrease in pain.
# Online OsiriX Documentation/SourceForge BugReporter

One of the better ways to file a bug report is via the SourceForge Bug Reporter. SourceForge is the World's largest OpenSource software repository and contains the source code for OsiriX.
You can access it via http://sourceforge.net/projects/osirix/ which should take you to a screen looking similar to this:
Clicking on the Bugs label will take you to a summary of all currently open bugs that have been filed via this system.
Click on the Submit New label to create a new bug.
Add a description.
Optionally upload a file, such as a CrashReporter log.
Click the Submit label and your newly reported bug will be added to the list.
One of the developers will pick up responsibility for this bug in due course. Once resolved the bug will be closed, perhaps with a message detailing the fix.
Please add {{alphabetical}} only to book title pages.
# Online OsiriX Documentation/Storage

If my requirement of storage is for a few weeks of studies:
# Online OsiriX Documentation/Using OsiriX Plugins

Before you can use plug-ins, you will either need to download a plug-in or write it yourself.

## Downloading Plug-ins

A number of plug-ins (plus their source code) can be downloaded off the main OsiriX website at:
Plug-ins currently available at this location include:
* Image Filters
** Invert & Web browser
** Duplicate
** Fill Gaps
** T2 Fit Map
* ROI Tools
** ROI Enhancement
** ROI Creation
** Ejection Fraction Calculation
** Pixel Normalization
* Fusion Filters
** CT Angio Subtraction
** Ratio T2 Map
* Other Filters
** OpenGL
Additionally, some plug-ins are only available as source from the main OsiriX SVN repository over at SourceForge.
* Image Filters
** Align Tools for the construction of EM image mosaics by manual registration
* ROI Tools
** Spine Counter Label dentritic spines by type and export to text files

## Developing Your Own Plug-ins

If you are interested in developing your own plug-ins, you may download Osirix source code which includes sample plug-ins as well as the OsiriX Plug-ins Developer Toolkit manual.
As Antoine says:
Writing a plug-in for OsiriX is a really easy process, and it's totally free! The development environment (XCode) is available with any Macs, you just need to install the Developer CD-ROM. You will have to use Objective-C language to write a plug-in. Objective-C is really a great object-oriented and dynamic language (like Java, but much faster!). (note: Xcode can also be downloaded for free by becoming a free ADC member at) http://developer.apple.com/membership/
For further details on writing plug-ins, please refer to the step-by-step manual that comes with the Plugin Developer Toolkit, or contact the OsiriX Developers Discussion Group.

## Installing Plug-ins

Once you have a plug-in, the next step is to put your plug-in in an appropriate place where OsiriX can find it.
OsiriX looks in 3 places:
* /Library/Application Support/OsiriX/plugins
* homeDirectory/Library/Application Support/OsiriX/plugins
* OsiriX/Contents/Plugins (This is the application package)
The first location (/Library/Application Support/OsiriX/plugins) is recommended, as this will allow all of the users on your system to use that plug-in.

## Uninstalling Plug-ins

Select the plugin you want to uninstall from installed plugin list. Hit delete on keyboard.
OsiriX
# Online OsiriX Documentation/Using OsiriX as a PACS workstation

Yes, you can use OsiriX as a PACS workstation! You don’t have to to buy multi-thousand $$ PACS workstation licenses! Save your bucks and buy Macintosh computers instead!
You only have to configure your modalities to automatically send exams to your OsiriX computer: configure the AETitle and Port number in OsiriX (see Importing DICOM images into OsiriX and Viewing DICOM headers).
Note: OsiriX website defines it self as a DICOM Client and explains how to get a free PACS system. It does not make it clear, however, what limitations OsiriX has over a PACS system.
OsiriX
# Online OsiriX Documentation/OsiriX System Requirements

For best performance:
OsiriX
# Online OsiriX Documentation/Using 2-D thick slabs

OsiriX supports a 2D thick slab mode in the 2D viewer. This mode is particularly interesting if you are working with multi-slice CT. It will allow you to navigate more efficiently through a huge series.
Thick slab mode is controlled in the tool bar:
There are actually 3 modes:
* Mean: all slices are added and the mean is computed.
* Maximum Intensity: maximum intensities of all pixels are extracted and displayed.
* Minimum Intensity: minimum intensities of all pixels are extracted and displayed.
You control the number of slices with the slider. You can view the thick slab information in the lower left hand corner of the window:
For more information about thick slab, read the following articles:
* Gruden JF, Ouanounou S, Tigges S, Norris SD, Klausner TS. Incremental benefit of maximum-intensity-projection images on observer detection of small pulmonary nodules revealed by multidetector CT. AJR Am J Roentgenol 2002 Jul;179(1):149-57.
* Coakley FV, Cohen MD, Johnson MS, Gonin R, Hanna MP. Maximum intensity projection images in the detection of simulated pulmonary nodules by spiral CT. Br J Radiol. 1998 Feb;71(842):135-40.
* Remy-Jardin M, Remy J, Giraud F, Marquette C-H. Pulmonary nodules: detection with thick-section spiral CT versus conventional CT. Radiology 1993;187:513–520.
OsiriX
# Online OsiriX Documentation/Using OsiriX Plugins/Align

WARNING! This plugin overrides a lot of fundamental OsiriX rendering routines. Many bugs are to be expected if this plugin is installed while doing anything other than creating mosaics of 8-bit images.
This plugin will make OsiriX tile images internally to increase the speed of texture uploads to the video card. This plugin has been tested using 8-bit black-on-white EM images. Some work has gone into making this plugin work with other images types. Your milage may vary. The faster texture upload speed may make this plugin useful for viewing very large images. Report bugs to Joël Spaltenstein.

# Tools for the construction of EM image mosaics by manual registration
## Using the Align plugin

Open two image viewers. One will be the tile being added to the mosaic, the other is the mosaic being constructed. It may be useful to have a small white 8-bit tiff with a single pixel set to 0x00 (in order to define the dynamic range of the image) to use as the first image of the mosaic. Define the viewers as as the tile and mosaic by using the Make Align Tile and Make Align Mosaic menu items. Now drag the file icon in the tile 's menu-bar to the mosaic, exactly as if making an image fusion. The tile should appear over the image in the mosaic window. In order to position the image correctly you will move control points on the images. Select the number of control points you wish to use with the appropriate menu items. Drag the control points in the tile to define their position. Drag the control points in the mosaic to define where the control points should map to. Once the alignment is satisfactory, make sure the mosaic viewer is the active window, and use the Merge Images menu item to paste the tile onto the mosaic. To save the mosaic, export it to a tiff, making sure of course that Set to original image size is selected in the OsiriX export preferences.

## Make Align Background

When creating a new mosaic, you may wish to take into account a mosaic created from EM images of a nearby slice. In order to do this, open up a viewer onto the said mosaic, Make Align Background and drag the newly created background onto the mosaic. In order to save memory, the mosaic viewer copies the image data from the background, making it safe to close the background viewer without the background disappearing from the mosaic. Of course this also means that no live link is kept between the mosaic and the background. The background can be positioned by selecting the Pan tool and panning while pressing the command (open-apple) key.

## Tips

Define three new CLUTs before using the plugin. One that goes from white to mostly Red and Blue, another that goes from white to mostly Red and Green, and yet another that goes from white to mostly Green and Blue. By using these newly created CLUTs, it will be very easy to see it the alignment of the new tile is good. For example, if the Red and Blue CLUT is used for the mosaic and the Green and Blue CLUT is used for the tile, the intersection of the images will appear as a sharp blue image.
# Online OsiriX Documentation/Printing

D1-Are there any more solutions than aycan printing system.
D2-Do I need a third workstation just for printing?
# Online OsiriX Documentation/Using getosirixCVS.pl

I have written (or more accurately pinched from the bibdesk website) a perl script to get the osirix source code called getosirixCVS.pl. Download this onto your machine. it is probably easiest to save it in your development directory. Mine is /Users/jefferis/dev. Go to the Terminal and run as follows:
gjg5:~/dev jefferis$ perl getosirixCVS.pl
Answer the questions and you will get a response that looks like this if you are using anonymous cvs
or like this if you are using Developer access:
And voila!
Here is the perl script. Save as getosirixCVS.pl. If you have the choice, make sure that you use Unix line terminations otherwise perl will complain.:
--Jefferis 02:17, 15 Jan 2005 (UTC)
# Micronations/List of already existing micronations/Grand Duchy of Westarctica

Westarctica (officially the Grand Duchy of Westarctica, formerly known as the Protectorate of Westarctica) is a micronation founded in 2001 by Travis McHenry. It claims the territory known as Marie Byrd Land, located between the New Zealand Antarctic Territory and the Chilean one, specifically the portion of Antarctica located between 90 degrees and 150 degrees west longitude and south of the 60th parallel. It includes 620,000 square miles of land, but though it claims over 2,000 citizens, none of them reside within the claimed territory.
In 2018 the government of Westarctica established an honorary consul in Nerja, Spain.

## References

* ↑ Bahareth, Mohammad (December 2011). Micronations: For Those Who Are Tired of Existing Incompetent Governments and Are Longing for Something New and Refreshing. iUniverse. ISBN 9781462069262.
* ↑ Milan Aleck (2 February 2018). "Molossia, Westarctica und Co.: Kennen Sie diese Mikronationen?". Web.de (in German).
* ↑ Justin Streight (11 April 2015). "Micronations Summit In California: Biggest Names From Tiniest Nations". Inquisitr. https://www.inquisitr.com/2001850/micronations-summit-in-california-biggest-names-from-tiniest-nations/.
* ↑ Eugenio Cabezas (1 November 2018). "Westarctica abre una embajada en Nerja". Sur (in Spanish).
# Micronations/List of already existing micronations/Autonomous Kingdom of Neoptolemia

The Autonomous Kingdom of Neoptolemia is located in an apartment in central Athens, the capital of Greece. It has 3 legal citizens.The King's name is Georgios and national motto is " Our Kingdom, our Home". The national currency is the Neoptolemian Drachma and it’s formal religion is Christianity. National colours are dark blue, blue and white (as the flag's colours) and national animal is the bird. The nation was founded in 22/02/2016 at a notary office in Ampelokipi city in Athens by Georgios, Nektarios and Despina.
Long live the Kingdom of Neoptolemia!
# Micronations/List of already existing micronations/Kingdom of Elleore

The Kingdom of Elleore is a micronation located on the island of Elleore in the Roskilde Fjord, north of Roskilde on the Danish island of Zealand.

## History

The island was purchased by a group of Copenhagen schoolteachers in 1944 for use as a summer camp. They proclaimed the island's tongue-in-cheek "independence" as a Kingdom as a gentle parody of the government structure and royal traditions of Denmark. It's been stated that the kingdom's ancestry has been traced to a "monastic society of Irish monks who arrived in the middle of the 10th century."
Prior to 1944, the island was known mainly as the location at which the controversial film Løvejagten was shot in 1907.
Numerous traditions peculiar to the kingdom have evolved over the subsequent decades, including a ban on the novel Robinson Crusoe, and the use of "Elleore Standard Time", which is 12 minutes behind Danish time. Many of the place names on the island, the kingdom's "government" and the titles assumed by its "nobility" are parodies of Danish equivalents.
The kingdom has issued several stamps and coins.

## Geography and demographics

The island has been estimated to be approximately 1500 square metres in size. Elleore is unoccupied save for a week-long annual gathering attended by dozens of its "citizens" and known as the "Elleuge" (meaning "Elle week"). The ceremonial enthronement of the reigning monarch takes place at this time. The purported capital is the tented town of Maglelille, erected only during the week of habitation.

## Kings and queens of Elleore

Elleore has had six monarchs since its inception.
* Erik I (1945–1949)
* Leo I den Lille (1949–1960)
* Erik II den Storartede (1961–1972)
* Leo II den Folkekære (1972–1983)
* Leodora den Dydige (1983–2003)
* Leo III (2003– )

## References

* 1 2 Vaccari, Andres (September 23, 2006). "Micronations (Book review)". The Australian. http://www.theaustralian.com.au/news/micronations/story-e6frg8no-1111112236240. Retrieved January 5, 2012.
* 1 2 3 4 5 6 Jardine Nick (December 26, 2011). "Check Out 10 Of Europe's Oddest Micronations". Business Insider. Retrieved January 1, 2012.
* 1 2 3 John Ryan, Simon Sellars and George Dunford. Micro Nations – The Lonely Planet Guide to Home-Made Nations. Lonely Planet. 2006. ISBN 1-74104-730-7
* ↑ Sellars, Simon "Kingdom of Elleore" Simonsellars.com. Accessed January 2012.

## External links

* Official website
* Kingdom of Elleore Coinage
* Catalogue of coins minted by the Kingdom of Elleore
# Micronations/List of already existing micronations/Aynvaul

Aynvaul, officially the Micronational Government of High Aynvaul, is a micronation on Long Island, New York in the United States of America and was among several micronations listed as attending Microcon 2017. Its identity is based on the local Irish diaspora and Irish-American community also located on the island, to which the two could be synonymous according to 'the Aynvaul Community' Facebook page. In this case, the Aynvauls would be an subethnicity of Irish America located on Long Island. It is the oldest continuous micronation located on Long Island, having been founded some time in 2006.
The Micronational Government serves as a ceremonial entity inside a larger open community with members using the identity to express a more revivalistic connection to their Irish-American roots. Its Flag is also used as a show of support for the local revival of the Irish language and culture.
* ↑ Bennett, Gary (July 12, 2024). "Garden City News". Garden City News. Litmor Publishing Corp. Retrieved July 27, 2024.
* ↑ Arnold, B.B. (2023). Pseudo-States and Sovereign Citizens. In: Gray, K.W. (eds) Global Encyclopedia of Territorial Rights. Springer, Cham. https://doi.org/10.1007/978-3-319-68846-6_735-1>
* ↑ http://www.rcimun.org/uploads/2/4/1/3/24139345/political_1_shared_.pdf
* ↑ "MicroCon 2017 Attendees". MicroCon. June 22, 2017. Retrieved June 13, 2024.
* ↑ https://www.facebook.com/AynvaulCommunity
* ↑ Bennett, Gary (July 12, 2024). "Garden City News". Garden City News. Litmor Publishing Corp. Retrieved July 27, 2024.
# Micronations/List of already existing micronations/Cordoba Empire

Cordoba Empire
Cordoba EMPIRE Flag.png
Flag Royal Family seal .jpg
Coat of arms
Motto “Magna EST Veritas et Praevalet, Nose defendat nostra.”
Anthem For Glory by Two Steps from Hell
Utah, USA
Largest city Mitchell Grove
Official language(s) English
Official religion(s) Christian
Demonym Cordobian
Government Absolute Monarchy
Emperor HIM Emperor Arturo Cordova I
Established 21 September 2018
Area claimed N/A
Population 6
Currency Cordoba Dollar
Time zone Mountain
National drink Tea
National animal Cats/Wolves
Contents
Government and symbolism
The Cordoba Empire's form of government is an absolute monarchy with a few advisers to the Emperor, hence why the monarchy uses both an emblem and a royal coat of arms
History The Cordoba Empire was established due to an corrupt government. On the 21st of September 2018 The Empire is Highly esteemed member of the League of Christian Micronations.
# LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Minimizing Norm by Scaling
## Minimizing Norm by Scaling

There are many cases in which a norm should be minimized, such as in applications of the $H_{2}$ or $H_{\infty }$ norm optimal control.

## The System

$M$ is a matrix $M\in \mathbb {C} ^{nxn}$. $D$ is some diagonal, nonsingular $D$.

## The Data

The optimal diagonally scaled norm of a matrix $M\in \mathbb {C} ^{nxn}$ is defined as $\nu (M){\overset {\underset {\mathrm {def} }}{=}}inf\left\lbrace \lVert DMD^{-1}\rVert \quad |D\in \mathbb {C} ^{n\times n}\right\rbrace$ , where $D$ is diagonal and nonsingular.

## The LMI:Minimizing Norm by Scaling

Therefore, $\nu (M)$ is the optimal value of the generalized eigenvalue problem
minimize $\quad \gamma$
subject to $\quad P>0$ and diagonal, $\quad M^{T}PM-\gamma ^{2}P<0$

## Conclusion:

This result can be extended in many ways, such as in applications of $H_{2}$ or $H_{\infty }$ optimal control.

## Implementation

This implementation requires Yalmip and Sedumi.
Minimizing Norm by Scaling

## External Links

* 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 Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & amp; Francis Group, 2013.

## Return to Main Page:

LMIs in Control: https://en.wikibooks.org/wiki/LMIs_in_Control
# LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Non Strict Projection Lemma
## Introduction

Projection Lemma is also known as Matrix Elimination Lemma. Strict Projection Lemma is one of the characteristics of the Projection Lemma.

## Non Strict Projection Lemma

Consider $\Psi \in \mathbb {S} ^{n}$, $G\in \mathbb {R} ^{n\times m}$, $\Lambda \in \mathbb {R} ^{m\times p}$, and $H\in \mathbb {R} ^{n\times p}$. There exists $\Lambda$ such that:
${\begin{aligned}\ \Psi +G\Lambda H^{T}+H\Lambda ^{T}G^{T}\leq 0,\end{aligned}}$
if and only if
${\begin{aligned}\ N_{G}^{T}\Psi N_{G}\leq 0\end{aligned}}$,
${\begin{aligned}\ N_{H}^{T}\Psi N_{H}\leq 0\end{aligned}}$,
and
${\begin{aligned}\ \ker G\cap \ker H\cap \{\xi \in \mathbb {R} ^{n}\mid \xi ^{T}\Psi \xi =0\}\subset \ker \Psi .\end{aligned}}$

## External Links

A list of references documenting and validating the LMI.
# LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Projection Lemma (Matrix Elimination Lemma)

WIP, Description in progress
A condition for eliminating a variable in an LMI using orthogonal complements is presented.

## Definition 1: Orthogonal Complements

Let $A\in \mathbb {R} ^{m\times n}$, Then, $M_{a}$ is called a left orthogonal complement of $A$ if it satisfies
$M_{a}A=0,\quad {\text{rank}}(M_{a})=m-{\text{rank}}(A)$;
and $N_{a}$ is called a right orthogonal complement of $A$ if it satisfies
$AN_{a}=0,\quad {\text{rank}}(N_{a})=n-{\text{rank}}(A)$.
Using the definition of orthogonal complements, we have the following projection lemma:

## Projection Lemma

Let $P$, $Q$ and $H=H^{T}$ be given matrices of appropriate dimensions, $N_{p}$ and $N_{q}$ be the right orthogonal complement of $P$ and $Q$, respectively. Then, there exists $X$ such that
$H+P^{T}X^{T}Q+Q^{T}XP<0$
if and only if
$N_{p}^{T}P^{T}=0,\quad N_{q}^{T}Q^{T}=0$.
WIP, additional references to be added

## External Links

A list of references documenting and validating the LMI.