OpenLLM-France/wikimedia huggingface dataset:
# Introduction to Philosophy/Philosophy of Mind

The philosophy of mind is about the form and content of our thoughts, and how and why we come to think them. Understanding the philosophy of mind gives us some fairly universally applicable rules to understand ourselves, other people, animals and even computers.
Philosophy of mind covers similar domains to psychology, artificial and non-artificial (synthetics) intelligence, developmental and non-developmental psychology, evolutionary and non-evolutionary psychology, evolutionary and non-evolutionary developmental psychology, forensics and non-forensics-based developmental psychology, developmental and non-developmental neuropsychology, epistemology, etymology, phenomenology, anthropology, ethnography, sociology and psychiatry, and helps us look at these disciplines within a specifically philosophical context. There is now growing evidence of a computational theory of mind.
You can either look at things in a hermetic (closed) or empirical (open) way.
Philosophy of mind is closely connected to cognitive psychology. It is connected also to neuroscience, which is still attempting to sort out (once and for all) whether our minds and our brains are separate.
Questions one may ask are: 'What is the difference between reality and illusion?', 'How is the mind related to the body, or to physical things in general?', 'How do I know that other minds exist?' In studying these questions one might start with Descartes' Meditations, then go on to study George Berkeley, Edmund Husserl and Gilbert Ryle, to mention just one or two.
Further questions include: 'What, if anything, is the "subconscious"?' If this cannot be put on a sound footing, how do we talk about 'self deception'? 'What, if anything, is "mental illness"?'
Another area of philosophy of mind that grew during the second half of the 20th Century is artificial intelligence. The Turing test challenges us to say whether we are talking to a human being or to a computer. People have been developing computers to the point where these tools could be said to have minds. Perhaps they will think autonomously.
Philosophy of mind can be expressed as 'thoughts about thoughts'.

## Reading List

Wikibook on Consciousness Studies : pursues the problem of mind from Aristotle to fMRI.
Descartes, R. Meditations on First Philosophy
Kim, Jaegwon. "Philosophy of Mind" Westview, 2006.
Ryle, G. The Concept of Mind 1949
Turing, A. 'Computing Machinery and Intelligence' Mind 1950, pp. 433-460
Searle, J. The Rediscovery of the Mind 1992
Sternberg, E. Are You a Machine? 2007
also see Thinking And Moral Problems
Further Inquiries into Philosophy of Mind involve questions of whether specific thoughts or activities of the mind such as perception of color or feeling pain can be identified, in a strict sense, with the physical brain event which corresponds to such mental activities, or whether there is a distinction between the two. See Saul Kripke's "Naming and Necessity".
# Introduction to Philosophy/Mystical Experience

Mystical experience as a proof for the existence of God has both a strong element in its favor and a strong weakness against it. Traditionally the mystical experience involves a realization of the One being all, and the All being one. This is a pantheistic view of 'God', i.e. that God is all and all is God. This believe is most common in Eastern religions, such as Hinduism and Taoism, is common among New Age spirituality, and has inconsistently been held by some who claim to be theists.
Mystical experience as evidence for the existence of God has as its strongest argument in its favor the effects upon the person who claims such things. However, according to atheist Andre Comte-Sponville, the mystical experience as defined above can be experienced without belief in God. Compt-Sponville gave account of his mystical experience of all being one and one being all, himself included i the oneness, while he and his friends were walking the woods one night. The conversation slowing came to end, his mind became empty, and the happy, peaceful experience overcame him for a short while until he began to think again (The Little Book of Atheist Spirituality,155-159).
There is another religious experience that is different from an ineffable mystical experience. The religious experience that is called conversion. Often more theistic, although not limited to theism, conversion stories are generally remarkable and undeniable. St. Paul's conversion from persecutor to Church proclamator as recorded in the New Testament book of Acts, chapter nine, can be seen as an archetype of other such conversion stories of individuals who have met "God" and had their lives forever changed by such a meeting.
The strongest element against such proof of God's existence is how extremely subjective this type of evidence is. Only Paul saw the vision he claimed he did; but even though the men with him saw no one, they, too, heard the voice (Acts 9:7). Was he delusional? Experiencing a psychotic break brought on by religious zeal? Or did he have an encounter with the Most Divine Being of the Universe?
For the believer, the answer is the former. For the non-convinced skeptic, the answer might be the latter. For both the question is still begged: is there a God, and is there some kind of objective substaniation beyond the mere anecdotal to support such a claim?
# Jeep Liberty/Authors

* unixxx
* JeepKJ02
* AdamIsAdam
* Kevin
* Tokyojoe
* Kugellager
# Jeep Liberty/Dana 30a

The 27 spline Dana 30a, also know by Chrysler as the 186FIA, has always been the only front axle available in the Jeep Liberty. It's an IFS axle with an aluminum housing as indicated by the 'FI' and 'A'/'a' respectively. Essentially, it's an aluminum version of the Dana 30 with a longer pinion shaft. Unfortunately, the light weight aluminum construction makes it weaker than the D30 and the longer pinion shaft means pinion related D30 parts won't fit it. The D30a requires a 1-1/8" socket to remove and install the pinion nut.
CRD Libertys have a different front cradle that lowers and leftward shifts the differential to provide more clearance for the diesel engine. The lowering results in better half-shaft constant velocity joint angles but too little clearance for a differential collar. The leftward shift requires different length half-shafts than those used in the gas Liberty. Due to the shorter left side half shaft CRD models cannot be lifted as high before the CV joints begin to bind.

## Traction Aiding Devices

The axle housing's aluminum construction is weak and installing a locker in the front differential could cause it to crack. It is recommended that an LSD be installed in place of a locker. It should be noted that installing any traction aiding device in the front will make steering slightly stiffer and cause the steering wheel to spring back to center more quickly than usual.

## Gear Lube

The gear lube in the Dana 30a should be changed every 12,000 miles. Off-roading and towing subjects the differential to increased torque, dirt, and water. If the Liberty isn't off-roaded, isn't used for towing, and follows the Schedule A maintenance plan, it may be possible to stretch this interval. The differential housing requires 2.6 pints (1.24 liters) of lube. 75W-140 synthetic lube should be used for either light duty applications or heavy duty off-roading.

## Gearing

Mopar is the only manufacturer of the longer pinion gears required by the Dana 30a. As a result, there are only three sources of 4.10 gears for the Liberty's front differential: wrecked I4 Libertys, online stores that sell discounted Mopar parts, and Jeep dealerships.

## External Links

* AMSOIL
* Chrysler Parts Direct - Dana 30a Ring & Pinion Gears
* World Parts Express - Cheap Dana 30a Ring & Pinion Gears
# Jeep Liberty/Dana 35C

The Dana 35C is a steel rear axle found in some 2002 Jeep Libertys. Strength wise, it's weaker than the more common Chrysler 8.25" rear axle. The Dana 35C is different from the Dana 35. The "C" in the model number refers to custom, not complete. It indicates that Dana Corporation ships their Dana 35 to DiamlerChrysler who then builds it.
# Jeep Liberty/Electrical

* Auxiliary Lights
* Batteries
* CB Radio
* ESP
* Head Units
* Firewall Penetration
* Overhead Consoles
* PCI Bus
* Satellite Radios

## External Links

* L.O.S.T KJ - Electronics...Stereo...GPS...CBs
* Jeep KJ Country - Electronics
* Basic Car Audio Electronics
# Jeep Liberty/Electrical/CB Radio
## Antenna

The most popular mobile CB antenna electrical lengths are 1/4 and 5/8 wave. The best practical mobile antenna is the 102" steel whip as it's electrically closest in length to 1/4 of the CB wavelength. According to FireStik, a popular mobile CB antenna manufacturer, the antenna cable between the atenna and the radio should be exactly 18' long for optimum performance. Using coax with a dense shield and twisted center ensures the least loss and least susceptibility to interference. The short length of mobile CB atennas makes a proper ground plane very important. For optimum radiation pattern and efficiency the antenna should be mounted in the center of the Liberty's roof. If the antenna can't be mounted on the Jeep's roof, at least 60% of it should clear the roof. Remember that when mounting the antenna near the edge of the Jeep like the front or the back that the radiation pattern will be most focused in the direction of the mass of the vehicle. If at all possible try using top loaded antennas followed by middle and then bottom loaded.

### Popular Mounting Locations

Most people mount a fiberglass antenna to either the rear spare tire mount or the front left hood lip. Other possible mounting locations include roof, the roof basket if equipped, the tail light seam, the factory AM/FM antenna bracket, and the front bull bar if equipped. As noted previously, the best locations are those closer to the center and top of the Liberty. If you don't want to permanently install a bracket on your Liberty you can use a temporary magnetic mount just when you're off-roading.
* Original CB Antenna Installation (replaces AM/FM antenna)
* Upgraded CB Antenna Installation (replaces AM/FM antenna)

## Radio
### Permanent

* Cobra 75 WX ST - a popular all-in-one handset radio that numerous people have installed in their Libertys

### Handheld

* Cobra 38 WX ST - Cobra's equivalent to the Midland 75-822, only it can't be snapped into a car harness, doesn't have channel memories, and supports VOX

### Hybrid

* Midland 75-822 - similar to the Cobra 75 WX ST in form, only it can be snapped off of the car harness and onto a battery pack to become a portable handheld CB radio

## External Links

* Cobra Electronics
* Midland
# Jeep Liberty/Electrical/Auxiliary Lights

There are many auxiliary light manufacturers with prices ranging from less than $100 up through $500. Shape, wattage, and size also varies from model to model.

## Hella

Hella fog lights and a Hella lightbar come standard on the 05 Jeep Liberty Renegade. Unfortunately, the lenses of the Hella fog lights are known to crack when used in cold weather. The difference in temperature between the hot air inside of the lamp when it's turned on the and the cold air outside the lamp when it's cold causes the glass to stress crack.

## PIAA

Warranty valid for as long as the original purchaser owns the light. Stress cracks are covered under the warranty.
# Jeep Liberty/Drivetrain/Limited Slip/Auburn ECTED

The Auburn ECTED is an electric locker for the Jeep Liberty's Chrysler 8.25" rear axle. The benefits of an electrically controlled locker such as the ECTED are the ability to turn it on and off and the simpler installation when compared to an air locker.
# Jeep Liberty/Electrical/Batteries

The Jeep Liberty Renegade comes stock with a 120CC and 600RC battery and upgraded 160 amp alternator (over the 136 amp in other models) which can power most accessories. A CRD comes with a red top Optima battery from the factory. However, adding an accessory with high current draw, such as a winch, warrants a battery upgrade. A battery with a reserve capacity of at least what the winch manufacturer recommends is a smart idea. Many people opt to install an Optima red top battery which are designed to handle engine cranking and the abuse of off-camber and uneven offroad driving. An Optima yellow top battery can be used instead as they have a greater reserve capacity, but you'll need to over specify the battery to be able to provide the same cold cranking amps that a red top, or any other starting battery for that matter, would otherwise provide.
# LMIs in Control/pages/Schur Complement

An important tool for proving many LMI theorems is the Schur Compliment. It is frequently used as a method of LMI linearization.

### The Schur Compliment

Consider the matricies $Q$, $M$, and $R$ where $Q$ and $M$ are self-adjoint. Then the following statements are equivalent:
      * $Q>0$ and $M-RQ^{-1}R^{*}>0$ both hold.
      * $M>0$ and $Q-R^{*}M^{-1}R>0$ both hold.
      * ${\begin{bmatrix}M&R\\R^{*}&Q\end{bmatrix}}>0$ is satisfied.
More concisely:
       ${\begin{bmatrix}M&R\\R^{*}&Q\end{bmatrix}}>0\iff {\begin{bmatrix}M&0\\0&Q-R^{*}M^{-1}R\end{bmatrix}}>0\iff {\begin{bmatrix}M-RQ^{-1}R^{*}&0\\0&Q\end{bmatrix}}>0$

## 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/pages/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 detecability 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/pages/Schur Stabilization

LMI for Schur Stabilization
Similar to the stability of continuous-time systems, one can analyze the stability of discrete-time systems. A discrete-time system is said to be stable if all roots of its characteristic equation lie in the open unit disk. This provides a condition for the stability of discrete-time linear systems and a linear time-invariant system with this property is called a Schur stable system.

## The System

We consider the following system:
${\begin{aligned}x(k+1)=Ax(k)+Bu(k)\end{aligned}}$
where the matrices $A\in \mathbb {R} ^{n\times n}$, $B\in \mathbb {R} ^{n\times r}$, $x\in \mathbb {R} ^{n}$, 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 $A$ and $B$ are given.
We define the scalar as $\gamma$ with the range of $0<\gamma \leq 1$.

## The Optimization Problem

The optimization problem is to find a matrix ${\begin{aligned}K\in \mathbb {R} ^{r\times n}\end{aligned}}$ such that:
${\begin{aligned}||A+BK||_{2}<\gamma \end{aligned}}$
According to the definition of the spectral norms of matrices, this condition becomes equivalent to:
${\begin{aligned}(A+BK)^{T}(A+BK)<\gamma ^{2}I\end{aligned}}$
Using the Lemma 1.2 in LMI in Control Systems Analysis, Design and Applications (page 14), the aforementioned inequality can be converted into:
${\begin{aligned}{\begin{bmatrix}-\gamma I&(A+BK)\\(A+BK)^{T}&-\gamma I\end{bmatrix}}<0\\\end{aligned}}$

## The LMI: LMI for Schur stabilization

The LMI for Schur stabilization can be written as minimization of the scalar, $\gamma$, in the following constraints:
${\begin{aligned}&{\text{min}}\quad \gamma \\&{\text{s.t.}}\quad {\begin{bmatrix}-\gamma I&(A+BK)\\(A+BK)^{T}&-\gamma I\end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

After solving the LMI problem, we obtain the controller gain $K$ and the minimized parameter $\gamma$. This problem is a special case of Intensive Disk Region Design (page 230 in [1]). This problem may not have a solution even when the system is stabilizable. In other words, once there exists a solution, the solution is robust in the sense that when there are parameter perturbations, the closed-loop system's eigenvalues are not easy to go outside of a circle region within the unit circle [1].

## Implementation

A link to Matlab codes for this problem in the Github repository:
https://github.com/asalimil/LMI-for-Schur-Stability

## Related LMIs

LMI for Hurwitz stability

## External Links

* - LMI in Control Systems Analysis, Design and Applications

## Return to Main Page

LMIs in Control/Tools
# LMIs in Control/pages/S Procedure

LMIs in Control/pages/S Procedure
S-Procedure

## The Optimization Problem

In general procedures, considering following quadratic function $F_{0}(x):\mathbb {R} ^{n}\to \mathbb {R}$, $F_{i}(x):\mathbb {R} ^{n}\to \mathbb {R}$ where $i=1,...,m$. The inequality $F_{0}(x)\leq 0$ is satisfied when all $F_{i}(x)\geq 0$.
       ${\begin{aligned}F_{0}(x)+\sum _{i=1}^{m}\tau _{i}F_{i}(x)\leq 0\end{aligned}}$
Where $x\in \mathbb {R} ^{n}$, and $\tau _{i}\in \mathbb {R} _{\geq 0}$
This type of procedure is used to help solve problems that were originally NP-hard problems. An example of this is the following inequality: $x^{T}Fx\geq 0:\forall x\geq 0$. By using the defined problem above, an LMI can be constructed using the S-Procedure:
       ${\begin{aligned}F-\tau G\succeq 0\end{aligned}}$
Where the scalar $\tau \geq 0$.

## The Data

The data is dependent on the type of problem being solved, and is used more as a tool to solve complex problems that were difficult to solve before.

## The LMI: S-Procedure

There exists a scalar $\tau \geq 0$ where:
       ${\begin{aligned}F-\tau G\succeq 0\end{aligned}}$

## Conclusion:

The results from this LMI will help construct quadratic stability as quadratic stability requires matrix positivity on a subset. Examples of this implementation include creating a controller based on parametric, norm-bounded uncertainties for robust problems.

## Implementation

* S-Procedure Example

## 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/pages/Stability of Quadratic Constrained Systems
## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+B_{p}p(t)+B_{u}u(t)+B_{w}w(t),\\q(t)&=C_{q}x(t)+D_{qp}p(t)+D_{qu}u(t)+D_{qw}w(t),\\z(t)&=C_{z}x(t)+D_{zp}p(t)+D_{zu}u(t)+D_{zw}w(t)\\\int _{0}^{t}&p^{\top }(\tau )p(\tau )\ d\tau \leq \int _{0}^{t}q^{\top }(\tau )q(\tau )\ d\tau .\end{aligned}}$

## The Data

The matrices $A,B_{p},B_{w},C_{q},C_{z},D_{qp},D_{zw}$.

## The LMI:

The following feasibility problem should be solved.
       ${\begin{aligned}{\text{Find}}\;&\{P\succ 0,\lambda \geq 0\}:\\&s.t.\quad {\begin{bmatrix}A^{\top }P+PA+\lambda C_{q}^{\top }C_{q}&PB_{p}+\lambda C_{q}^{\top }D_{qp}\\(PB_{p}+\lambda C_{q}^{\top }D_{qp})^{\top }&\lambda (I-D_{qp}^{\top }D_{qp})\end{bmatrix}}\prec 0.\end{aligned}}$

## Implementation

https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/38f3b55ca7060a1260384a96e9dc31142af07a9a

## Conclusion

The integral quadratic constrained system is stable if the provided LMI is feasible

## Remark

The key point of the proof is to satisfy ${\dot {V}}<0$ whenever $p^{\top }p\leq q^{\top }q$, using ${\mathcal {S}}$-procedure.

## 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.