OpenLLM-France/wikimedia huggingface dataset:
# Greek Mythology/Titans

The Titans, often called as the Elder Gods, are the children of Uranus (Ορανος) . Their role/function was to oppose the gods run by Zeus and the other Olympians. They are not simply big gods. That role is for the Gigantes who came out of a god's blood. The Titans were involved in epic wars, many of which have been written about. Some sons of Titans include important gods like Prometheus and Atlas.
# Greek Mythology/Stories/The Minotaur

The Minotaur was a half-man, half-bull imprisoned in the labyrinth on the island of Crete. King Minos was very fond of bulls (most likely due to the fact that his mother Europa was courted by Zeus in the form of a white bull). Minos came to own an extensive collection of bulls and one of the finest was a white prize bull. His wife, Queen Pasiphae was a beautiful woman who loved Minos very much and was fond of the compliments he offered her concerning her beauty. She boasted once that she was even lovelier than Aphrodite, the goddess of love and thus incurred the wrath of Aphrodite. Aphrodite cursed Pasiphae by sending her son, Eros, to make her fall in love with King Minos' prized white bull with one of his magical arrows. Pasiphae was struck and fell violently and passionately in love with the bull. She resisted her urges all she could, but eventually she could resist no more. She requested the aide of Daedalus who was currently a servant of Minos to help her. Daedalus built Pasiphae a wooden cow which looked remarkably realistic. It was hollow on the inside so that Pasiphae may fit inside it and it had wheels under the hooves so she could roll toward the object of her affection. At nights Pasiphae would approach the bull to quench her passion and all went well until she became pregnant and gave birth to a monstrosity. The infant was covered in short dense fur with beastial features. Its eyes were beady, its nostrils smushed and flared, it had hooves for feet and atop its head were two protruding knobs which would soon turn into great horns. Rumor spread throughout the kingdom of this beast and it became known as the Minotaur, which means Minos' bull. King Minos, enraged but rational, had Daedalus construct the labyrinth and promptly imprisoned Pasiphae, the Minotaur and even Daedalus within, for he could not forgive Daedalus for building Pasiphae the wooden cow. There the Minotaur grew and grew, more ferocious and powerful each day. Minos forever jaded by the shame became cruel and sadistic. After defeating King Aegeus in war Minos compromised that the city of Athens would not be conquered so long as Athens sent seven of the best young men and seven of the loveliest young women as sacrifices to Knossos at the hands of the Minotaur. Henceforth, the Minotaur devoured the sacrifices that were forced into the labyrinth annually from Athens. That is, until Theseus came and slew the Minotaur
# Examples and counterexamples in mathematics

          The originator of this book is now retired. Any competent enthusiast is welcome to further this project.

## Introduction

"Any blockhead can cite generalities, but the mind-master discerns the particular cases they represent." (George Eliot in "Daniel Deronda", Chapter 52)
Examples are inevitable for every student of mathematics. It often happens that a student sees only a series of similar simple examples and therefore cannot appreciate the volume and depth of a new notion, which leads to numerous misconceptions. As a result, the student misses the difference between general and special case, true and false statement, correct and incorrect proof.
"Counterexample is an example with a negative connotation. Whereas an example may be used to support or illustrate a claim, a counterexample is used to refute an assertion. How an example is being used often depends on the purpose or the formulation. For example, the word "nth" is an example of an English word without a vowel. It is a counterexample to the claim that every English word contains a vowel. ... In the opinion of B. R. Gelbaum and J. M. H. Olmsted - the authors of two popular books on counterexamples - much of mathematical development consists in finding (and proving) theorems and counterexamples." (Quoted from cut-the-knot)
* Counterexample at Wikipedia.
Several books of counterexamples are pointed in "cut-the-knot" and Wikipedia:
* Lynn Arthur Steen, J. Arthur Seebach, Jr.: Counterexamples in Topology, Springer, New York 1978, ISBN 0-486-68735-X.
* Joseph P. Romano, Andrew F. Siegel: Counterexamples in Probability and Statistics, Chapman & Hall, New *York, London 1986, ISBN 0-412-98901-8.
* Gary L. Wise, Eric B. Hall: Counterexamples in Probability and Real Analysis, Oxford University Press, New York 1993. ISBN 0-19-507068-2.
* Bernard R. Gelbaum, John M. H. Olmsted: Theorems and Counterexamples in Mathematics, Springer-Verlag 1990, ISBN 978-0-387-97342-5.
* Bernard R. Gelbaum, John M. H. Olmsted: Counterexamples in Analysis, Corrected reprint of the second (1965) edition, Dover Publications, Mineola, NY 2003, ISBN 0-486-42875-3.
* Jordan M. Stoyanov: Counterexamples in Probability, Second edition, Wiley, Chichester 1997, ISBN 0-471-96538-3.
* Michael Copobianco, John Mulluzzo: Examples and Counterexamples in Graph Theory, Elsevier North-Holland 1978, ISBN 0-444-00255-3.

## Table of contents

* Sets
* Infinite sequences
* Real-valued functions of one real variable
# Exercise Physiology/Fundamentals of Exercise Physiology
## Overload Principle

If you habitually overload a system, it will respond accordingly by adapting to the demands of the stressor. Continuing to subject a system to progressively higher demands not only triggers adaptive responses but also fosters enhanced resilience, as the system undergoes continuous refinement to meet and even surpass the challenges imposed by the stressors. This iterative process of overloading and adaptation contributes to the system's ongoing development and capacity for handling increased loads.

## Individuality Principle

While the physiological response to a particular stimulus are predictable, the precise responses to varying stimuli will vary among individuals and subpopulations.

## Specificity Principle

Only the system or body part stressed will adapt. For example, someone will not build muscle in the arm from walking because that body part is not being stressed in that activity.

## Reversibility Principle

There reversibility principle, also aptly referred to as the "use it or lose it" principle states: whereas overloading will result in training adaptations, inactivity (also referred to as "detraining") will result in a return to baseline (pre-training levels) of adaptation. Training adaptations are gradually lost with inactivity over time.
# Evolutionary Biology/Thomas Malthus

In 1798, he published the Principle of Population where he made the observations that the human race would be likely to overproduce if the population size was not kept under control.
Malthus then focused his studies on the human race. His calculations and theories produced an idea that the human population would increase geometrically while the food supply and natural resources would only increase arithmetically. This is a potential explanation for the predicted poverty and famine. He concluded that as more offspring are born, a more competitive nature would arise. As more offspring come into the population, fewer resources will be available for the population. This has the potential for competition between organisms for survival due to lack of resources. This competitive nature would be necessary for survival of individuals within a large population size unable to be supported by the environment. He believed that this uncontrollable population size would eventually be the cause of famine and poverty among humans. His reasoning behind this idea was divine intervention. He believed that this would be the punishment for man if he became too lazy.
Malthus’ Principle of Population caused Darwin to rethink many issues while coming up with his theory of natural selection. Malthus’ work made Darwin realize the importance of overpopulation and how it was necessary to have variability in different populations. Darwin also used Malthus’ ideas to use competition as well as the survival in numbers idea to come up with his full idea of natural selection.

## References

Campbell, Reece. Biology, Sixth edition. Benjamin Cummings. 2001. http://www.ucmp.berkeley.edu/history/malthus.html http://www.blupete.com/Literature/Biographies/Philosophy/Malthus.htm http://geography.about.com/library/weekly/aa033001a.htm
# Examples and counterexamples in mathematics/Sets
## Set without members

* Empty set at Wikipedia.
The empty set, denoted by $\emptyset$ (or sometimes $\{\}$) contains no members. If you find it strange and disturbing, think about the number zero (denoted 0); it was a strange and disturbing idea, but now is generally accepted. The number of members in $\emptyset$ is 0.
The empty set is a set, not "absence of set". Likewise, an empty box is a box, not "absence of box"; and 0 is a number, not "absence of number". Substituting 0 into a function f we get another number f(0), generally not 0. For example, $\cos 0=1$. Also, $2^{0}=1.$ The latter fact has a set-theoretic counterpart, see the next item.

## The powerset of the empty set is not empty

* Power set at Wikipedia.
The power set (or "powerset") of any set S is the set of all subsets of S, including the empty set and S itself. If $S=\emptyset ,$ then its power set contains $\emptyset$ and nothing else; it is $\{\emptyset \},$ that is, $\{\{\}\}.$ Likewise a box that contains only an empty box is a non-empty box. The number of elements in this power set is 1. Generally, if S contains n elements, then its power set contains $2^{n}$ elements. In particular, $2^{0}=1.$
# Example

| bad | good |
| Introduction | Organic Chemistry/Introduction |
| Overview of Functional Groups | Organic Chemistry/Overview of Functional Groups |
| Authors | Organic Chemistry/Authors |
# Exercise Physiology

Exercise Physiology is the study of how the body responds and adapts to physical activity and exercise. It delves into the physiological processes that occur within our bodies when we engage in various forms of exercise, from a leisurely walk to ultramarathoner training, and everything in between. This WikiBook aims to give you a deeper scientific understanding of how the body reacts to exercise and functions in general. By understanding these mechanisms, we can optimize training programs, improve athletic performance, and enhance the overall health and well-being of individuals.

## Table of contents

Here's the planned outline, which is unfinal:
* Introduction to Exercise Physiology
** 1.1 Fundamentals of Exercise Physiology
** 1.2 History and Milestones
** 1.3 Physiological Systems in Action
* Cardiovascular Physiology
** 2.1 Cardiovascular Adaptations to Exercise
** 2.2 Heart Function and Exercise
** 2.3 Blood Pressure Regulation
** 2.4 Oxygen Transport and Utilization
* Muscle Physiology
** 3.1 Skeletal Muscle Structure and Function
** 3.2 Muscle Contraction and Energy Metabolism
** 3.3 Muscular Adaptations to Training
* Respiratory Physiology
** 4.1 The Respiratory System and Exercise
** 4.2 Ventilation and Gas Exchange
** 4.3 Oxygen Transport in the Blood
* Nutrition and Exercise
** 5.1 Macronutrients and Micronutrients
** 5.2 Dietary Strategies for Performance
** 5.3 Hydration and Exercise
* Training Principles and Program Design
** 6.1 Principles of Training
** 6.2 Program Design and Periodization
** 6.3 Monitoring and Assessment
* Special Topics
** 7.1 Endurance Training
** 7.2 Strength and Power Training
** 7.3 Aging and Exercise
** 7.4 Environmental Factors in Exercise
* Applied Exercise Physiology
** 8.1 Exercise for Health and Disease Prevention
** 8.2 Sports Performance Enhancement
** 8.3 Rehabilitation and Injury Prevention
* Current Research and Trends
** 9.1 Emerging Concepts and Technologies
** 9.2 Recent Studies and Breakthroughs
** 9.3 Future Directions in Exercise Physiology
* References and Further Reading
** 10.1 Books and Textbooks
** 10.2 Scientific Journals and Articles
** 10.3 Online Resources and Organizations
# Houdini 101/Background
## What is procedural dataflow modelling

Procedural dataflow modelling is a procedural approach to creating parametric models. It allows designers to to efficiently explore alternative forms without having to manually build each different version of the design model for each scenario. Such systems are used by architects and engineers to automate the design processes and accelerate design iterations.
The dataflow approach may be familiar if you have used programs like Bentley's Microstation Generative Components and McNeel's Rhino Grasshopper. In these cases, plugins have been created for standard CAD packages in order to enable users to work with the dataflow modelling approach. In the case of Houdini, the dataflow approach has always been at the core of the whole software, and everything that you do is controlled by dataflow networks

## What is Houdini

Houdini is a high-end 3D CAD and animation software. Historically, Houdini's main strength has been its particle animation system. Houdini chief distinction from other packages is its use of the procedural dataflow approach not just for modelling, but for for all tasks including animation, rendering, and compositing. Houdini's approach to dataflow modelling is more sophisticated than either Grasshopper or GenerativeComponents. This means that Houdini is a little harder to learn at first, bit it scales better as more complex tasks are undertaken.
# House Construction

* /Planning/
* /Setting the Stage/
* /Structural building/
* /Commodities infrastructure/
* /Exterior details/
* /Interior details/
* /Landscaping/

# See also

* Do-It-Yourself

# Externalities

External links
* How Stuff Works: How House Construction Works
* Hvactrainingtools.com
Books
* Independent Builder: Designing & Building a House Your Own Way by Sam Clark, Real Goods Independent Living Books
* Do-It-Yourself Housebuilding: The Complete Handbook by George Nash
* IEE Wiring Regulations
* UK Building Regulations, NBS for Department for Communities and Local Government, Crown Copyright 2008
# Houdini 101/External links
## Websites

* The developers of Houdini.
* The Houdini forum.
# House Construction/Landscaping
### Landscape Hardscape

Walls, Terraces, Walks, Stairs, Curbs and Driveways

#### Landscape Structures

Gazebo, Cabana, Canvas Awnings and BBQ/Cooking Areas

### Landscape Watering

Sprinkler, Driblers

#### Landscape Pool/Spa

Swimming Pool, Spa, Fountains and Reflecting Pools

#### Landscape Plantings

Lawn, Trees, Shrubs, Flowers and Potted Plants

### Landscape Lighting

Path/Walk, Stair, Plant/Tree, Water Features and Security
# Houdini 101

Houdini 101 is a book to help you get started with using version 10 of Houdini digital modelling and animation package developed by SideEffects Software. It is assumed that the reader has very little prior experience in using Houdini or similar software. As a result, we have tried to introduce the fundamentals of Houdini in a way that is as simple and easy to understand as possible. Note that this is a very broad introduction that necessarily glosses over many of the details.
In particular, this book focuses on the concepts and assumes that you have a basic knowledge of Houdini user interface. This basic knowledge can best be learnt by watching the various videos online. (Note that Houdini changed its interface significantly when they released version 9, but version 10 remains very similar to version 9. So any videos for version 9 are still relevant.) A good place to start is the videos available here:
    Start here video tutorials

## Contents

    Noted contributors · External links
* Background
* How Houdini works
* Modelling
* Scripting
* Conclusions
# Exterior details
## Exterior Wall Surfaces

Materials as Stucco, Brick, Stone, Wood Clapboard and Shingle are all cladding products. Modern wood frame construction requires the installation of a weather-resistive-barrier (WRB) under the cladding. The WRB provides the primary function of protecting the structure from water.

## Exterior Cast Stone

Door/Window Surrounds, Eaves, Balconies, Columns/Pilasters and Steps/Coping

## Exterior Openings

Installation of Exterior Windows, Doors, Roof Hatch and Skylights requires weather proofing be at its best.

### Door & Window Hardware

Installation of Door Hinges, Knobs/Lever, Cremone/Lock, Thresholds and Window Locks/Cranks "Taqi". Although older houses may still contain single glazed wooden framed windows and doors; modern house usually have a steel or aluminum reinforced uPVC framed double glazed system. These window systems are fixed to the preformed concrete ope by use of usually a galvanized steel fixing bracket which clips to the frame of the window or door and is fix back to reveal.
The window will sit either on the upstand of a pre-cast concrete cill or onto a PVC of aluminum PPC cill. A silicone sealant or expandable foam can be used to weather the window or door once in place.
Doors may have to be sunk a few millimeters in order to achieve the correct height of threshold depending on building regulations governing the use of the door.
# Houdini 101/How Houdini works
## How Houdini works

Modelling in Houdini consists of creating dataflow procedures. So, for instance, if you want a line, you don't draw a line. Instead, you create a dataflow procedure to draw a line. Such procedures take the form of networks of nodes.
Networks consist of nodes organised into a hierarchy and linked up using wires. There are two types of nodes: operator nodes and container nodes. Operator nodes do stuff, while container nodes are limited to containing operator nodes. The hierarchy of nodes is created using container nodes. Inside each container node, there may be one or more operator nodes and also other container nodes, all wired up together to achieve some result.
Cooking is the process of driving information through the networks, from the outputs of operators to the inputs of operators to which they are wired, to create and animate the scene. By default, cooking is interactive, so every time you make a change, all affected nodes will be re-cooked.

## Node paths

The hierarchy of nodes is just like a folder system on the computer. You can navigate the hierarchy using paths, like this: /a/b/c. In this case the path starts at the root, indicated by the first /. There is a container called a, which contains another container called b, which contains a node (could be either an operator or container) called c. You can also use relative paths, using .. to mean go up one level, and ., meaning the location where I am now. For example, the container of c is b, so if you are at c, you can point to its container like this: ./...
A nodes container is called its parent. The nodes inside a container are called its children. All nodes have exactly one parent. Container nodes can have zero or more children, but operator nodes cannot have any children.
There are many different types of containers for gathering together operators that do many amazing things. The top-level containers (immediately after the first /) have fixed names that cannot be changed. The naming in Houdini is very distracting at first, but you get used to it. These are:
* /obj
** OBJ network
** contains geometry containers (called Surface Operator Networks or SOP Networks) which in turn contain the actual geometry in the scene, created using surface operators
/part Particle Operator Network, or POP network contains operators for creating particle systems.
/img Compositing Operators Network, or COP network contains operators for manipulating 2d pixel data.
/out Rendering Operators Network, or ROP network. contains operators for rendering
/dynamics Dynamics Operators Network, or DOP Network contains operators for creating dynamics systems
/shop : Shading Operator Network, or SHOP Network contains operators for shading and materials
/ch : contains operators for manipulating graphs /vex : contains some very advanced stuff
# Definition

Forward orbit of a critical point is called a critical orbit.

# Importance

Critical orbits are very important because every attracting periodic orbit attracts a critical point, so studying the critical orbits helps us understand the dynamics in the Fatou set.
$z_{0}=z_{cr}=0\,$
$z_{1}=f_{c}(z_{0})=c\,$
$z_{2}=f_{c}(z_{1})=c^{2}+c\,$
$z_{3}=f_{c}(z_{2})=(c^{2}+c)^{2}+c\,$
This orbit falls into an attracting periodic cycle.

## Shape

Relation between shape types and dynamics:
* n-th arm spiral: attracting or repelling n-periodic orbit ( cycle)
* closed curve: Siegel disc ( rotation)
* n-th arm star = period n parabolic root
The shape of critical orbit can show the type of dynamics and the period
* parabolic n-th arm star
* Siegel disc ( closed curve)
* weakly attracting fixed point = long spiral

## Level sets

Points of critical orbit ( including crirital point and fixed point = finite attractor) are on the level curves like notes on the musical staff ( dots on curves) .
How to compute attracting radius (AR) to get such effect ?
* period 1 parabolic
* period 1 attracting
* period 2 attracting

# images

* images of critical orbitsat commons
* by Mike Croucher
* Chris King
* Kerry Mitchel: cardioid-boundary-orbits
* Visualizing Escape Paths in the Mandelbrot Set by Anne M. Burns
* Stefan Zenker

# lists

* critical orbits
* Lori GardiThe Mandelbrot set and the fractal nature of light, the Universe, and everything by
* The Mandelbrot Set as a Quasi-Black Hole by Lori Gardi
* Mandelbrot Z Orbits by Stefan Bion
* Plot the orbits from the list by Stefan Bion
* images by Conan written in Rainbow
** intro
** examples
* Mandelbrot Sequences and Orbits by Stefan Forcey
* Moiré interferences in the map of orbits of the Mandelbrot Set by P. Alcover Published 2017

# programs

* Geogebra (interactive)
** Mandelbrot Iteration Orbits by Ben Sparks
** Mandelbrot kümesi by Hüseyin KAVAK
* Java Script by Stefan Forcey

# videos

* Mandelbrot Set as a Vortex Generator by Fractal Woman

# See also

* Spreading points on a disc

# References

* ↑ Wikipedia: orbit (dynamics)
* ↑ Wikipedia: Complex quadratic polynomial - Critical point
* ↑ MandelOrbits - A visual real-time trace of Mandelbrot iterations by Ivan Freyman
* ↑ Wikipedia: Periodic points of complex quadratic mappings
* ↑ M. Romera, G. Pastor, and F. Montoya: Multifurcations in nonhyperbolic fixed points of the Mandelbrot map. Fractalia 6, No. 21, 10-12 (1997)
* ↑ Burns A M: Plotting the Escape: An Animation of Parabolic Bifurcations in the Mandelbrot Set. Mathematics Magazine, Vol. 75, No. 2 (Apr., 2002), pp. 104-116
* ↑ Khan Academy: Mandelbrot Spirals 2
* ↑ Complex Power Towers (Or ‘mucking around with Mathematica’) by Mike Croucher
* ↑ /DarkHeart by Chris King
* ↑ Alexandre Devert blog
* ↑ codeproject: Fractals-in-theory-and-practice
# Fractals/Iterations in the complex plane/idifferent

Local dynamics near indifferent fixed point/cycle :
* rationally indifferent ( parabolic ) - Leau-Fatou flower theorem
* irrationally indifferent ( elliptic ) - Siegel disc

## Key words

* parabolic enrichment :
** geometric limits
** Lavaurs maps
** Ecalle maps
** horn maps
** Fatou coordinates

## References

* ↑ Does a Julia set depend continuously on the polynomial? Adrien Douady Jan 1995