OpenLLM-France/wikimedia huggingface dataset:
# Tri-BotHack
## Problem/Finish Description

* Get all 5 tribots running
* Begin programming tribots to go in a patterns like squares, circles
* Add remote emergency take over capability
* Add automous ability to travel the cooridors of first floor Clark Library Building
* Add features from the head
* Replace arduino with papilio
* Pull all existing documentation into one place in the below context

## Conceive

Project was inspired by this video that shows a robot balanced on top of a basketball. A completely powered Omni wheel connected to some accelerometer/gryo can create a powered unicycle that moves sideways. This is completely different than the one wheel motor cycle, the monocycle or the R.O.I.T wheel.
The goal is to duplicate the robot balanced on top of a basketball and ultimately duplicate the powered unicycle.

## Design

Reverse engineering a toy is similar to forward design. It starts with re-creating the implmentation/operation documentation that already exists.

## Implement

These are the steps to take apart a toy Tribot WowWee and add an arduino
Connecting cables to Arduino :
| Motor | Function | Color | Arduino Pin |
| 1 | yellow | on/off | 12 |
| 2 | teal | on/off | 11 |
| 3 | blue | on/off | 10 |
| 1 | white | direction | 9 |
| 2 | gray | direction | 8 |
| 3 | purple | direction | 7 |
| 1 | orange | encoder | 6 |
| 2 | red | encoder | 5 |
| 3 | brown | encoder | 4 |
| head switch | white | start | 3 |
Gyro-Accelerometer :
| IMU Pins | Arduino Pins |
| 3.3V | 3.3V |
| Ground | Ground |
| X-Acc | A0 |
| Y-Acc | A1 |
| Z-Acc | A2 |
| X-Rate (formerly Vref) | A3 |
| Y-Rate | A4 |
| EMPTY (formerly x-rate) | A5 |

## Operate

* Find screwdriver that works
* Put batteries in (8 AA batteries)
* Turn on
* Push head down
* Turn off
* Take batteries out
Creating Program to go in a Square :
* the path that Tribot follows to go in a square using the different commands
* The new commands inserted into the loop section of the Arduino code. The new commands allow Tribot to go in a square pattern.

## Demo

Presentation
Seminar Presentation 2014MAR20
A demonstration of a working tribot with the Motor test installed is shown on the following video: Tribot Demo Test

## Next Steps

* Explore possibilities of line-following tribot
* Apply power to the head and try to control it's features with arduion
* Start capturing wheel turning information from the encoder
* Test new base to see if tribot can work equally well on ground and ball
* Define working, test all 5 and document current status
* Add simple mechanism so that all 5 spill out of a door when is opened
* Add remote controller
* Add speakers
* add a camara
* Determine if accelerometer and gyro have to be calibrated, start testing with PID software
# Tricolour Voting Game

The Tricolour Voting Game is a game where participants use cards to vote for three colours.

## Summary

Players are given a selection of cards at the beginning. These cards have a value and a colour. At the end of the game the players can put the cards in the voting boxes of the different colours. A card put in a voting box of the same colour adds its value to the tally of that box. A card with a different colour detracts from the tally of that box. White cards are an only add to the tally. The game is designed to work in the background of other activity during which players can determine the level of engagement they wish to have with the game. Players can try and gain more cards, swap cards with other players or give their cards away. All participants are invited to predict the result. The votes for the different colours are calculated by the teller and the reult announced. Prizes may be awarded to the person with the rosette of the winning colour and the person with closest prediction of the result.

## Sample cards

These can be customised by incorporating other images

## Initial Hands

Each player is given a set of five cards, one blue card, one red card, one green card, one positive wild card (value 4) and one negative wild card (value -2). Each player will have one card of value 1, 3 and 5: Thus there are six starting possibilities:
* 5 Blue, 2 Wild+, 3 Red, -2 Wild-, Green 1
* 5 Blue, 2 Wild+, 3 Green, -2 Wild-, Red 1
* 5 Red, 2 Wild+, 3 Blue, -2 Wild-, Green 1
* 5 Red, 2 Wild+, 3 Green, -2 Wild-, Blue 1
* 5 Green, 2 Wild+, 3 Blue, -2 Wild-, Red 1
* 5 Green, 2 Wild+, 3 Red, -2 Wild-, Blue 1

## Rosettes

The game can be played with different ways of gaining Rosettes:
* Buying rosettes with a specified number of cards on a first come first served basis
* Auctioning the different rosettes

## Game, Simulation and Stimulation

This game has been designed as an open simulation - i.e. the actual game offers an overall structure. Players can then develop ways in which they can make it simulate something in which they are interested. The game may also simulate disinterest i.e. if run as the background to an event perhaps not everyone will maintain an interest in the game, which can be an interesting way of simulating disinterest. Also the game was originally designed for a conference, whereby the game could play the role of an ice-breaker stimulating social interaction particularly amongst people who don't know one another.
# Trifluoperazine versus placebo for schizophrenia

Summary :
Trifluoperazine is an effective first-generation antipsychotic that can be used to treat the positive symptoms of schizophrenia; however, it was shown to increase the risk of extrapyramidal adverse effects when compared to placebo. :
| Outcome | Findings in words | Findings in numbers | Quality of evidence |
| Global state ||||
| Clinical improvement Follow-up: average 19 weeks | Trifluoperazine increases the chance of being 'improved' when compared to placebo. Data are based on low quality evidence. | RR 4.61 (1.54 to 13.84) | Low |
| Relapse or worsening Follow-up: average 5 months | Trifluoperazine reduces the risk of relapse when compared with placebo. Data are based on low quality evidence. | RR 0.34 (0.23 to 0.49) | Low |
| Mental state ||||
| Experiencing 'intensified symptoms' Follow-up: average 16 weeks | At present it is not possible to be confident about the difference between trifluoperazine and placebo for this outcome and data supporting this finding are very limited. | RR 1.05 (0.54 to 2.05) | Very low |
| Leaving the study early ||||
| - Because of any reason Follow-up: average 5 months | Trifluoperazine may reduce loss to follow-up, but, at present it is not possible to be confident about the difference between the two treatments and data supporting this finding are very limited. | RR 0.67 (0.38 to 1.19) | Very low |
| - Because of severe adverse effects Follow-up: average 2 months | It is not possible to be confident about the difference between trifluoperazine and placebo. Data supporting this finding are very limited. | RR 1.31 (0.22 to 7.8) | Very low |
| Behavior ||||
| Any clinically significant agitation or distress Follow-up: 4 months | There was no clear differences between trifluoperazine and placebo for this outcome. Data supporting this finding are very limited. | RR 2.0 (0.19 to 20.72) | Very low |
| Economic outcomes ||||
| | No included randomized study reported on economic outcomes. | | |
# Trigonalizable mapping/Eigentheorie/No proof/Section
## Definition

Let $K$ denote a field, and let $V$ denote a finite-dimensional vector space. A linear mapping $\varphi \colon V\rightarrow V$
is called trigonalizable, if there exists a basis such that the describing matrix of $\varphi$ with respect to this basis is an
Diagonalizable linear mappings are in particular trigonalizable. The reverse statement is not true, as example shows.

## Theorem

Let $K$ denote a field, and let $V$ denote a finite-dimensional vector space. Let
    $\varphi \colon V\longrightarrow V$
denote a
* $\varphi$ is trigonalizable.
* The characteristic polynomial $\chi _{\varphi }$ has a factorization into linear factors.
$\varphi$
$M$
$B\in \operatorname {Mat} _{n\times n}(K)$ such that $BMB^{-1}$ is an

### Proof

$\Box$

## Theorem

Let $M\in \operatorname {Mat} _{n\times n}(\mathbb {C} )$ denote a square matrix with complex entries. Then $M$ is

### Proof

This follows from fact and the Fundamental theorem of algebra.
$\Box$
# Triangular matrix/Characteristic polynomial/Eigenvalues/Example

For an upper triangular matrix
    $M={\begin{pmatrix}d_{1}&\ast &\cdots &\cdots &\ast \\0&d_{2}&\ast &\cdots &\ast \\\vdots &\ddots &\ddots &\ddots &\vdots \\0&\cdots &0&d_{n-1}&\ast \\0&\cdots &\cdots &0&d_{n}\end{pmatrix}}\,,$
the characteristic polynomial is
    $\chi _{M}=(X-d_{1})(X-d_{2})\cdots (X-d_{n})\,,$
due to fact. In this case, we have directly a factorization of the characteristic polynomial into linear factors, so that we can see immediately the zeroes and the eigenvalues of $M$, namely just the diagonal elements $d_{1},d_{2},\ldots ,d_{n}$ (which might not be all different).
# Tribology

Tribology is the science of friction and wear. It is a sub-class of mechanical engineering, and is especially important for machine designing. There has been studies that indicate the influence of friction and wear in design. About 80% of all machine failures are associated with friction and wear.
Tribology usually looks that the reduction of friction and wear. It covers modes of surface failures (e.g. wear, pitting, galling). It talks about material selection, coatings, lubrications, and processes to increase efficiency.
Here is a "Cliff note" what I can remember from my college studies on this subject:
- increasing contact surface area (e.g. line contact of roller bearings instead of point contact of ball bearings) to reduce pitting
- hardening a surface will reduce its wear rate
- reducing friction will reduce wear
- softer materials flow better than harder ones, thus reducing friction
- a great combination of hard and soft would be to coat a hardened material with a softer one. For example, anodizing can put a hard thin shell onto an aluminum part. Dipping it into Teflon afterwards can embed Teflon molecules into the honeycomb matrix of the anodized surface. This leaves a soft Teflon surface (low friction) on a hard material (anodized shell).
- journal bearings only work when the shaft is spinning at a high enough speed to float it in the oil. This is why it is better to leave an engine idling for a few minutes than to stop and restart it. During startup, the shaft grinds against the inside of the journal bearing and create wear.
- some situations require making a profile to keep a part floating a moving fluid (e.g. the read/write head inside a hard drive floating on a very-thin stream of air above the spinning disc). It turns out that a step profile is actually better than a slanted or an airplane-wing one.
- on a macroscopic level, surface area has no significant effect on friction. Only the force pushing 2 surfaces together and their materials (listed as their coefficient of friction against each other) matter. For instance, a 100 lbs block of steel will slide with the same difficulty no matter how you change its surface area in contact with the ground. This is because decreasing the surface area decreases the area that covalent bonding between the block and the ground (decreases friction), but it increases the force-per-area that supports the weight (increases friction), and the two friction methods cancel each other out. This assumes that you don't decrease it so much that the block digs into the ground. This gets more into a mechanical method for stopping the movement instead of surface friction.
- decreasing surface roughness usually reduces "friction" and wear by decreasing the mechanical method for stopping the movement
- however, decreasing surface roughness also increases the contact surface area such that two too-smooth surfaces will experience molecular "sticktion" and can cause them to bind. Hard drive discs are very smooth. On the surface, there is a thin area near their center that have pits to reduce the smoothness. This allows the read/write head to dock there when the disc is not spinning.
# Trigeno/Q/Almost ordering/0 maximum/Exercise

On the recently discovered planet Trigeno there lives a species which has some ability to calculate. They use like us the rational numbers with "our“ addition and multiplication. They also use a kind of "ordering“ on the rational numbers, denoted by $\succeq$. This trigenometric ordering coincides with our ordering as long as both numbers are$\neq 0$. However, they put
    $0\succeq x\,$
for every rational number $x$. The well-known Ethnomathematician Dr. Eisenbeis thinks that this is related to the fact that they worship the number $0$.
Show that $\succeq$ fulfils the following properties.
* For any two elements $a,b\in \mathbb {Q}$ either $a\succ b$ or $a=b$ or $b\succ a$ holds.
* From $a\succeq b$ and $b\succeq c$ we get $a\succeq c$ (for arbitrary $a,b,c\in \mathbb {Q}$).
* From $a\succeq 0$ and $b\succeq 0$ we get $a+b\succeq 0$.
* From $a\succeq 0$ and $b\succeq 0$ we get $ab\succeq 0$.
Which property of an ordered field does $(\mathbb {Q} ,\succeq )$ not fulfil?
# PlanetPhysics/Rotational Inertia of a Solid Sphere

The Rotational Inertia or moment of inertia of a solid sphere rotating about a diameter is
   $I={\frac {2}{5}}MR^{2}$
This can be shown in many different ways, but here we have chosen integration in spherical coordinates to give the reader practice in this coordinate system. If we choose an axis such as the z axis, then we just have one moment of inertia given by
   $I=\int {z^{2}dm}$
It is important to understand this distinction and the more general case about an arbitrary axis is handled by the inertia tensor. Since we have chosen z as our axis of rotation, then z in formula (2) is the distance from dm (dV) to the z axis. In the figure below this is shown as the purple line.
\begin{figure} \includegraphics[scale=.6]{InertiaSphere.eps} \caption{Rotational inertia of a solid sphere rotating about a diameter, z} \end{figure}
Then from spherical coordiantes we obtain z through
$z=r\sin \theta$
leaving us with the integral
$I=\int {r^{2}\sin ^{2}\theta dm}$
Assuming a constant density throughout the sphere converts the infinitesimal mass dm to
$dm=\rho dV$
and in spherical coordinates the infinitesmal volume dV is given by
$dV=r^{2}\sin \theta d\theta d\phi$
giving the final function to integrate as
$I=\rho \int _{0}^{2\pi }\int _{0}^{\pi }\int _{0}^{R}{r^{4}\sin ^{3}\theta \,\,drd\theta d\phi }$
Integrating the r term is simply
$I={\frac {R^{5}\rho }{5}}\int _{0}^{2\pi }\int _{0}^{\pi }{\sin ^{3}\theta \,\,d\theta d\phi }$
The $\theta$ term is a little more involved and we substitude in the trigonometric relation $\sin ^{2}\theta =(1-\cos ^{2}\theta )$
and the integrand for the $\theta$ term becomes
$\int _{0}^{\pi }{(\sin \theta -\cos ^{2}\theta \sin \theta \,\,d\theta )}$
Using the technique of u substitution to solve this
$u=\cos \theta$ $du=-\sin \theta d\theta$ $d\theta ={\frac {-du}{\sin \theta }}$
so
$\int _{0}^{\pi }{\sin \theta \,d\theta +u^{2}\,du}$
completing the integration yields
$I={\frac {4R^{5}\rho }{15}}\int _{0}^{2\pi }{d\phi }$
Finally, the $\phi$ term integrates to $2\pi$ so
   $I={\frac {8\pi R^{5}\rho }{15}}$
Using the simple formula for density
$\rho =M/V$
and we know that the volume of a sphere is
$V={\frac {4}{3}}\pi R^{3}$
plugging these into (3) gives us our original equation in (1)
$I={\frac {2}{5}}MR^{2}$
# PlanetPhysics/Scanning Force Microscopy SFM

Scanning force microscopy (SFM) or Atomic Force Microscopy (AFM) is a very high-resolution type of scanning probe microscopy that uses a very sharp scan tip probe of about 50 microns, with demonstrated resolution in the AFM images of fractions of a nanometer, or at least 1000 times better than the optical diffraction limit. The precursor to the AFM, the scanning tunneling microscope, was developed by Gerd Binnig and Heinrich Rohrer in the early 1980s at IBM Research - Zurich, a development that earned them the Nobel Prize for Physics in 1986.
# PlanetPhysics/Section Functor
## Essential data

Let us consider an abelian category ${\mathcal {C}}$ which is locally small and a dense subcategory ${\mathcal {A}}$ of ${\mathcal {C}}$, with $T:{\mathcal {C}}\to {\mathcal {C}}/{\mathcal {A}}$ being the canonical functor. Moreover, let us assume that $T$ has a right adjoint denoted by $S$ such that one has the following functorial isomorphism, or natural equivalence:
$Hom_{\mathcal {C}}(X,S(Y))\cong Hom_{{\mathcal {C}}/{\mathcal {A}}}$.
The right adjoint functor $S:{\mathcal {C}}/{\mathcal {A}}\to {\mathcal {C}}$ of $T$-- which is specified by the essential data above-- is called a section functor .
Note: the category ${\mathcal {A}}$ is defined as a localizing subcategory .
Reference cited.
# PlanetPhysics/Schwarz Christoffel Transformation

Let $w=f(z)=c\int {\frac {dz}{(z-a_{1})^{k_{1}}(z-a_{2})^{k_{2}}\ldots (z-a_{n})^{k_{n}}}}+C,$ where the $a_{j}$'s are real numbers satisfying\, $a_{1}<a_{2}<\ldots <a_{n}$, the $k_{j}$'s are real numbers satisfying\, $|k_{j}|\leqq 1$;\, the integral expression means a complex antiderivative, $c$ and $C$ are complex constants.
The transformation\, $z\mapsto w$\, maps the real axis and the upper half-plane conformally onto the closed area bounded by a broken line.\, Some vertices of this line may be in the infinity (the corresponding angles are = 0).\, When $z$ moves on the real axis from $-\infty$ to $\infty$, $w$ moves along the broken line so that the direction turns the amount $k_{j}\pi$ anticlockwise every time $z$ passes a point $a_{j}$.\, If the broken line closes to a polygon, then\, $k_{1}\!+\!k_{2}\!+\!\ldots \!+\!k_{n}=2$.
This transformation is used in solving two-dimensional potential problems.\, The parameters $a_{j}$ and $k_{j}$ are chosen such that the given polygonal domain in the complex $w$-plane can be obtained.
A half-trivial example of the transformation is $w={\frac {1}{2}}\int {\frac {dz}{(z-0)^{\frac {1}{2}}}}={\sqrt {z}},$ which maps the upper half-plane onto the first quadrant of the complex plane.
# PlanetPhysics/Sigma Finite Borel and Radon Measures
### Introduction

Let us recall the following data related to Borel space and measure theory:
* sigma-algebra, or $\sigma$-algebra;
* the Borel algebra which is defined as the smallest $\sigma$-algebra on the field of real numbers
$\mathbb {R}$ generated by the open intervals of $\mathbb {R}$;
* Borel space
* Consider a locally compact Hausdorff space $X$; a Borel measure is then defined as any measure $\mu$ on the sigma-algebra of Borel sets, that is, the Borel $\sigma$-algebra ${\mathcal {B}}(X)$ defined on a locally compact Hausdorff space $X$;
* When the Borel measure $\mu$ is both inner and outer regular on all Borel sets, it is called a Borel measure;
* Recall that a topological space $X$ is $\sigma$-compact if there exists a sequence
$\left\{K_{n}\right\}_{n}$ of compact subsets $K_{n}$ of $X$ such that:
       $X=\bigcup _{n=1}^{\infty }K_{n}.$

## Definition: Borel Space

Let $(X;{\mathcal {B}}(X))$ be a Borel space (with the $\sigma$-algebra ${\mathcal {B}}(X)$ of Borel sets of a topological space $X$), and let $\mu$ be a measure on the space $X$. Then, such a measure is called a $\sigma$--finite (Borel) measure if there exists a sequence $\left\{A_{n}\right\}_{n}$ with $A_{n}\in {\mathcal {B}}(X)$ for all $n$, such that $\bigcup _{n=1}^{\infty }A_{n}=X,$ and also $\mu (A_{n})<\infty$ for all $n$, (ref.).

## Definition: Radon Measure

If $\mu$ is an inner regular and locally finite measure, then $\mu$ is said to be a Radon measure .

## Note

Any Borel measure on $X$ which is finite on such compact subsets is also (Borel) $\sigma$-finite in the above defined sense (Definition 0.1).
# PlanetPhysics/SI Unit Prefixes

The SI unit prefixes are given in the table below.
| prefix | symbol | factor |
| yocto | $\mathrm {y}$ | $10^{-24}$ |
| zepto | $\mathrm {z}$ | $10^{-21}$ |
| atto | $\mathrm {a}$ | $10^{-18}$ |
| femto | $\mathrm {f}$ | $10^{-15}$ |
| pico | $\mathrm {p}$ | $10^{-12}$ |
| nano | $\mathrm {n}$ | $10^{-9}$ |
| micro | $\mathrm {\mu }$ | $10^{-6}$ |
| milli | $\mathrm {m}$ | $10^{-3}$ |
| centi | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \mathrm} | $10^{-2}$ |
| deci | $\mathrm {d}$ | $10^{-1}$ |
| deka | $\mathrm {da}$ | $10^{1}$ |
| hecto | $\mathrm {h}$ | $10^{2}$ |
| kilo | $\mathrm {k}$ | $10^{3}$ |
| mega | $\mathrm {M}$ | $10^{6}$ |
| giga | $\mathrm {G}$ | $10^{9}$ |
| tera | $\mathrm {T}$ | $10^{12}$ |
| peta | $\mathrm {P}$ | $10^{15}$ |
| exa | $\mathrm {E}$ | $10^{18}$ |
| zetta | $\mathrm {Z}$ | $10^{21}$ |
| yotta | $\mathrm {Y}$ | $10^{24}$ |
Here is an example of using the SI unit prefixes: A centimeter is 1 meter * $10^{-2}$ or in scientific notation, $1\times 10^{-2}$ meters. \vspace{4ex}
\noindent Reference: National Institute of Standards and Technology, http://physics.nist.gov/cuu/Units/
# Public health strategies for HIV

Safe sex remains the primary method of preventing the spread of HIV/AIDS. Test and treat (in addition to safe sex) has also been proposed as a method for stemming the spread of HIV/AIDS.

## Online resources

* United Kingdom HIV - highly centered on UK issues
* Canada- Global component
* WHO Tuberculosis
* UNAIDS
* USAID - HIV/AIDS main page
* USA State Department - page on Emergency Plan for AIDS Relief
* Gates Foundation - HIV/AIDS main page
* "The Global HIV/AIDS pandemic, 2006" by Centers for Disease Control and Prevention in Morbidity and Mortality Weekly Report (2006) Volume 55, pages 841-844. Full text online via: Entrez PubMed 16902393
* "Health Development versus Medical Relief: The Illusion versus the Irrelevance of Sustainability" by Gorik Ooms in PLoS Med. (2006) Online publication: e345. PMC 1539094
* AIDSPortal - knowledge sharing network