OpenLLM-France/wikimedia huggingface dataset:
# Topology/Hilbert Spaces

A Hilbert space is a type of vector space that is complete and is of key use in functional analysis. It is a more specific kind of Banach space.

## Definition of Inner Product Space

An inner product space or IPS is a vector space V over a field F with a function $\langle \cdot ,\cdot \rangle :V\times V\to F$ called an inner product that adheres to three axioms.
1. Conjugate symmetry: $\langle x,y\rangle ={\overline {\langle y,x\rangle }}$ for all $x,y\in V$. Note that if the field $F$ is $\mathbb {R}$ then we just have symmetry.
2. Linearity of the first entry: $\langle ax,y\rangle =a\langle x,y\rangle$ and $\langle x+y,z\rangle =\langle x,z\rangle +\langle y,z\rangle$ for all $x,y,z\in V$ and $a\in F$.
3. Positive definateness: $\langle x,y\rangle \geq 0$ for all $x,y\in V$ and $\langle x,y\rangle =0$ iff $x=y$.

## Definition of a Hilbert Space

A Hilbert Space is an inner product space that is complete with respect to its inferred metric.

## Exercise

Prove that an inner product has a naturally associated metric and so all IPSs are metric spaces.

## Example

$\ell ^{2}$ is a Hilbert space where its points are infinite sequences $(a_{n})$ on I, the unit interval such that
    $\sum _{i=1}^{\infty }a_{i}^{2}$
converges and is a Hilbert space with the inner product $\langle (x_{n}),(y_{n})\rangle =\sum _{i=1}^{\infty }x_{i}{\overline {y_{i}}}$.

## Characterisation Theorem

There is one separable Hilbert space up to homeomorphism and it is $\ell ^{2}$.

## Exercises

(under construction)
# Transportation Economics/About

Transportation Economics is aimed at advanced undergraduate and graduate civil engineering, planning, business, and economics students, though the material may provide a useful review for practitioners. While incorporating theory, there is a very applied bent to the course, as all the ideas covered are intended to help inform the real decisions that are made (or should be made) in practice.
This book uses two core ideas:
* Individuals (firms, agencies, agents, actors) behave according to incentives provided by their environment.
* The environment is shaped by the collective behavior of individuals.
The material of each page can be covered in a ninety-minute lecture.

## Authors

Authors of this book include David Levinson, David Gillen, Michael Iacono, and others ...
# Transportation Economics/Agents/Solution2
## Problem Extension

3. What happens if there is a third price $300, for which demand is 375 passengers.
Reformulate the problem.

## Solution

| ' | ' | ' | American | ' |
| | | $200 | $300 | $400 |
| United | $200 | [0,0] | [50000,-50000] | [50000, -50000] |
| | $300 | [-50000, 50000] | [6250, 6250] | [62500, -50000] |
| | $400 | [-50000, 50000] | [-50000, 62500] | [0,0] |
At [300,300] Each airline gets 375/2 share = 187.5 pax * $300 = $56,250, cost remains $50,000
At [300, 400], 300 airline gets 375*300 = 112,500 - 50000
What is the equilibrium in a non-cooperative, 1 shot game? [$200,$200].
What is equilibrium in a repeated game?
Note: No longer zero sum.

## Return

Agents
# Transportation Economics
## Table of contents

| Introduction About Introduction Games | Organization Ownership Regulation Productivity Revenue Pricing Supply chains | Microeconomics Production Costs Negative externalities Utility Demand Positive externalities |

## Related Wikibooks

* Fundamentals of Transportation
** Planning
** Decision Making
** Modeling
** Data
** Land Use Forecasting
** Evaluation
* Transportation Geography and Network Science

## Other Resources

* Other Resources
# Transportation Economics/Goods
## Types of Goods

There are four types of goods that are determined by their technical characteristics concerning excludability and rivalry:
| ' | ' | Excludability | ' |
| | | Yes | No |
| Rivalry | Yes | Private | “Congesting” |
| | No | Club | Public |
Public goods are non-excludable and non-rivalrous,
Private goods are both excludable and rivalrous.
Club goods (for instance a country club membership) are excludable, but non-rivalrous (in the absence of crowding).
Congesting goods are rivalrous but not excludable, for instance a crowded street. While an individual cannot be excluded from a city street that person’s presence may cost you extra time and his occupation of space does prevent you from occupying the same space at a given time. (Note that limited access highways are potentially excludable, unlike city streets.)

### Excludability

Excludability implies that the good’s provider can prevent a user from obtaining it without charge
National defense for instance is non-excludable, America’s nuclear weapons protect anyone in the country, whether or not they want it. On the other hand the sale of anything in a store is excludable – the owner can prevent a customer from obtaining a good unless the customer pays (assuming enforceable property rights etc.).

### Rivalry

Rivalry implies that one person’s consumption of a particular good prevents another individual from consuming it.
National defense again is non-rivalrous – one person’s protection does not prevent another’s protection. Shoes are rivalrous, only one person can wear a pair at a time.
# Transportation Economics/Agents/Solution1
## Problem

Two airlines (United, American) each offer 1 flight from New York to Los Angeles.
Price = $/pax, Payoff = $/flight.
Each plane carries 500 passengers.
Fixed cost is $50000 per flight, total demand at $200 is 500 passengers.
At $400, total demand is 250 passengers.
Passengers choose cheapest flight.
Payoff = Revenue - Cost
Work in pairs (4 minutes):
Formulate the Payoff Matrix for the Game

## Solution

| ' | ' | American | ' |
| | | $200 | $400 |
| United | $200 | [0,0] | [50000, -50000] |
| | $400 | [-50000, 50000] | [0,0] |
Equilibrium is [$200,$200]
SOLUTION: Maximin criterion
For a two-person, zero sum game it is rational for each player to choose the strategy that maximizes the minimum payoff, and the pair of strategies and payoffs such that each player maximizes her minimum payoff is the “solution to the game."

## Return

Agents
# Quantum Field Theory

This book is about Quantum Field Theory, a theoretical framework for constructing quantum mechanical models of subatomic particles.

## Contents

* Classical Lagrangian field theory
* Transformational properties of fields
* Quantization of free fields
* Interacting quantum fields
* Introduction to The Standard Model
# Quantum Field Theory/Quantization of free fields
## Spin 0 field
### Real and complex scalar fields.

The equations of motion for a real scalar field $\phi$ can be obtained from the following lagrangian densities
${\begin{matrix}{\mathcal {L}}&=&{\frac {1}{2}}\partial _{\mu }\phi \partial ^{\mu }\phi -{\frac {1}{2}}M^{2}\phi ^{2}\\&=&-{\frac {1}{2}}\phi \left(\partial _{\mu }\partial ^{\mu }+M^{2}\right)\phi \end{matrix}}$
and the result is $\left(\Box +M^{2}\right)\phi (x)=0$.
The complex scalar field $\phi$ can be considered as a sum of two scalar fields: $\phi _{1}$ and $\phi _{2}$, $\phi =\left(\phi _{1}+i\phi _{2}\right)/{\sqrt {2}}$
The Langrangian density of a complex scalar field is
${\mathcal {L}}=(\partial _{\mu }\phi )^{+}\partial ^{\mu }\phi -M^{2}\phi ^{+}\phi$

### Klein-Gordon equation

Klein-Gordon equation is precisely the equation of motion for the spin-0 particle as derived above: $\left(\Box +M^{2}\right)\phi (x)=0$

## Spin 1/2 field
### Dirac equation

The Dirac equation is given by:
$\left(i\gamma ^{\mu }\partial _{\mu }-m\right)\psi \left(x\right)=0$
where $\psi$ is a four-dimensional Dirac spinor. The $\gamma$ matrices obey the following anticommutation relation (known as the Dirac algebra):
$\left\{\gamma ^{\mu },\gamma ^{\nu }\right\}\equiv \gamma ^{\mu }\gamma ^{\nu }+\gamma ^{\nu }\gamma ^{\mu }=2g^{\mu \nu }\times 1_{n\times n}$
Notice that the Dirac algebra does not define a priori how many dimensions the matrices should be. For a four-dimensional Minkowski space, however, it turns out that the matrices have to be at least $4\times 4$.
# Used Car Buyer's Guide
## Table of contents

* General tips

### Specific models

* Chevrolet Astro
* Chevrolet Aveo
# Used Car Buyer's Guide/Chevrolet Aveo

Launched in 2004 as a replacement for the Used Car Buyer's Guide/Chevrolet Metro, which was axed in 2000, this was Chevrolet's "supermini". Based on the Daewoo Kalos sold elsewhere in the world (in Europe it's a Daewoo and a Chevrolet!), it was European-styled, and Euro-designed too, but was built in South Korea.
Unlike its predecessor, it was a five-door hatchback only, but a four-door saloon was available as well.

## Trim levels

The Aveo came in base and + trim levels. The base trim level was plain, and rather spartan, so avoid this version.

## Engines

One engine was available, a 1.6-litre/103hp 4-cylinder. It's OK, and not as thrashy for a car this size.

## Other variants

* Suzuki Swift+
* Pontiac Wave
# Use the Source/What do you mean Open Source isn't Free Software

Let's get a few terms out of the way and define them:
    program : the finished product of programming a single independent ready to use file that serves a specific purpose.
    suite : a set of programs which work in conjunction to perform a set of tasks.
    product : the result of one's programming, can be a singular program, a suite or entire operating system.
    source code : the entire human usable collection of code put into a product.
    open source : used to describe any software where you are given the right to at least look at the source code necessary to generate the product.
    freeware : any type of product which can be obtained free of charge.
    Open Source : a label for a product approved by the OSI.
    Free Software : a label for a product approved by the FSF.
When someone says the word "open", what do you immediately think of? Do you think of something that is ajar? Of something which is obvious? Where anyone can see it? Unobstructed? Or maybe something that is available for immediate usage? When you're in the programming world those possibilities come close but fall short of what open means. And what of the word "free"? Do you think of something that you don't need to pay for? Or do you think something that is unrestricted? Once again, it's a little more complicated in the world of programmers.
To the layman Open Source and Free Software are the same thing; however, these two groups hold tense and sometimes hostile relations with one another. These programming sects believe in particular freedoms and work towards the betterment of these goals through the development of their software.
People often like to think of this intellectual property in the same way they would physical property. If the various open source models are looked at in this manner then the public domain is public property and no one can deny access to that code for any reason or use. GPL code is private property that is granted to the public under the condition that all released works generated from it remains in the same position. BSD is property anyone can use for any reason or use on the condition that they maintain due credit.
End this chapter with something along the lines of, "much like with a rented car, you've using licensed code or software, you've got responsibilities you must uphold." Which then leads into the next chapter.
# Use the Source/Sources

| Use the Source | Edit template |
1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 20
The sources of information that can be documented will be documented here. Some information however is within the head of the writer and the source is lost to time.
Websites:
   * Éric Lévénez's History of Unix page. - Used to track down websites and dates.
   * NetBSD's History page
   * Sun's History page
   * The GNU website
   * FreeBSD's BSD Family Tree
   * Bell Lab's Oral History of Unix
   * Lucent Technologies History of Unix
   * The Open Group's Unix History
   * Tom Van Vleck's Unix and Multics article
   * USL versus BSDi information page
   * an Archived e-mail - Caldera's release of old UNIX code.
   * The Open Source Initiative
   * Quasijarus' website - an excellent resource on the stance of the project and its goals.
   * the FreeBSD website
   * the DragonFlyBSD website
   * the NetBSD website
   * the OpenBSD website
   * The Register - home of a few choice quotes
   * How To Become A Hacker - by Eric Steven Raymond
Books:
   * Open Sources: Voices from the Open Source Revolution - Published by O'Reilly & Associates, Inc.
Contributors:
   * DouglasGreen - Proof reading and editing.
Special Thanks:
   * Michael Sokolov, the Developer of 4.3BSD-Quasijarus, who spoke with Nate via e-mail.
   * google.com, which was an excellent tool to help track some quotes and information sources.
License:
This wikibook in all that was contributed by Nate Montague, the base writer, is released as public domain for anyone to do as they wish with. Nate does not support the ideals nor the means of the GNU movement, he believes in true freedom, not forced cooperation and needless restrictions.
# Used Car Buyer's Guide/Chevrolet Astro

Launched in 1985 to rival Dodge Caravan/Plymouth Voyager twins and the Japanese Toyota Van.

## Engines

* 2.5L Tech IV 98 hp (73 kW) I4
* 4.3L 4300 165 hp (123 kW) V6
* 4.3L 4300 200 hp (150 kW) V6
* 4.3 L 190 hp (140 kW) V6

## Weak Spots

* The front end steering components.

## Other variants

* Dodge Caravan
* Plymouth Voyager
* Toyota Hiace
# Use the Source/Theft or Copying

Theft - The crime of taking someone else's property without consent, so as to deny the owner their property.
Copyright Infringement - The unauthorized use of copyrighted material in a manner that violates one of the copyright owner's exclusive rights.
Corporations and special interest groups working for corporations have for years been fighting the online duplication of digital media by calling it stealing, yet stealing requires the deprivation of property, while duplication is only violation of a copyright holder's rights.
Get into the Betamax case a little, mention the levy on recordable media in Canada - harddrives, flash, CDs and DVDs, compare the situation in Canada to the United States of America, discuss the content providers push in Canada to change the system to one more similar to the United States of America and talk about how code lines up in all this.
# Simulation with AnyLogic/Pedestrian Simulation/Step 8. Adding ticket windows
## Step 8. Adding Ticket Windows

Now we will expand our model by adding ticket windows.
Modify the model animation
* Draw lines representing ticket windows as shown in the figure below.
* Add these lines to a new group. Name the group windowsGroup.
* Draw polylines representing queues to ticket windows as shown in the figure below.
* The starting point of the polyline is important since it stands for the head of the queue. Place the first point of each polyline near the corresponding service line.
* Add these polylines to a new group. Name the group windowsQueuesGroup.
* Move lineBeforeGates a little bit down:
Now we will modify the model flowchart.
Modify the flowchart
* Add new objects and connect them as shown below:
* Configure PedServices object. This object will define parameters of a service representing ticket windows. Services defined by this object can be referenced by flowchart objects PedServices. Set the following object properties:
** Name this object windows.
** Specify the group containing lines representing services. Type windowsGroup in the Services (group of lines) field.
** Specify the group containing polylines representing queues to services. Type windowsQueuesGroup in the Queues (group of lines, polylines) field.
** Specify the service time. Type triangular(15*second, 25*second, 35*second) in the Delay field (you can use code assist). We assume that service time is triangularly distributed with minimum value of 15 seconds, average value of 25, and maximum value of 35 seconds.
** Change the Service type to Delay. Delay service is defined by a line, which pedestrians should step on for service delay time.
* Configure PedSelectOutput object. We need it to route non-ticketed passengers to ticket windows while other ones – straight to the ticket control gates. PedSelectOutput object is a decision making block of Pedestrian Library. The pedestrian arrived at the PedSelectOutput object is forwarded along one of five output ports depending on ratios specified for these ports. Set up the following object properties:
** Specify ratios for flows going to ticket control gates (Chance 1) and to ticket windows (Chance 2) correspondingly. In this flowchart we assume that the number of passengers that have already bought their tickets is actually significantly higher.
* Configure just added PedService object. This flowchart object references to PedServices object defining a service representing subway ticket windows. Set the following object properties:
** Specify the PedServices object defining the service pedestrians will pass through. Type windows (the name of our PedServices object) in the Service (PedServices) field.
Run the model. Note that now some passengers first go to the ticket windows to buy a ticket and only then pass through ticket control gates.
# Simulation with AnyLogic/System Dynamics/Step 10. Adding charts

Step 10. Adding Charts
You can also observe how the values of variables change during the simulation using charts. Namely, we want to examine the adopter and potential adopters populations dynamics. We will also use the same chart to show how the adoption rate changes in our model.
Create a data set for the PotentialAdopters variable
* In the graphical editor, right-click the PotentialAdopters variable and choose Create Data Set from the popup menu. The data set PotentialAdoptersDS will be created. It will store the history of the variable that can be displayed on the chart. Move the data set icon aside like shown on the figure below.
* Go to the General page of the Properties view.
* Specify the data set title in the Title edit box: # of potential adopters. It will be displayed in the legend displayed for this data item in the chart.
* Clear the Show at Runtime check box to prevent showing the data set icon in the presentation window at model runtime.
Create one more data set for Adopters
Draw a time plot displaying adopter and potential adopter population pools
* Drag the Time Plot element from the Analysis page of the Palette view into the graphical editor (right to the place where you want to locate this chart).
* Resize it as shown on the figure.
* Go to the General page of the Properties view.
* Set up the chart’s time diapason. In the Time Window edit box, type: 8 (so the chart will display all the simulation run).
* Specify data sets to be displayed on the time plot.
* Add PotentialAdoptersDS data set to be visualized on this plot by clicking the Add Data Set button and defining settings for the data set in the property section above. Choose PotentialAdoptersDS data set from the Data Set drop-down list. Choose the first option from the Point Style drop-down list to turn off indicating data set values with a marker.
* Add AdoptersDS data set in the same way.
* Define how the plot will be updated with new data set values. At the botom of the properties page, choose Update automatically option and specify the update rate in the Recurrence (in time units) edit box to the right: 0.1.
Now you can run the model and examine the trend of potential adopter and adopter populations over time. You will see classic S-shaped diffusion curves.
# Simulation with AnyLogic/Pedestrian Simulation/Step 5. Running the model
## Step 5. Running the Model

We have finished creating a simple model using AnyLogic Pedestrian Library. Now you can run the model.
Build your model by clicking the Build Model toolbar button. If there are some errors in your model, the building fails and the Problems view appears listing all the errors found in your model. Double-click an error in the list to open the location of the error and fix it.
After the model is successfully built, you can start it. Running the simulation, you automatically bring the current model up to date.
Start the model
* Click the Run toolbar button and choose the experiment you want to run from the drop-down list. Your simulation experiment is called Subway Entrance/Simulation. In the case this model is the only one opened in the workspace at the moment you will be prompted to run this particular experiment. Later on this button will start the previously run experiment. To run any other experiment, right-click the experiment in the Project view and choose Run from the context menu.
Having started the model, you will see the presentation window. It displays the presentation designed for your simulation experiment.
Click the button to Run the model and switch to Main view and observe the process you have modeled. You can see that the model behaves correct: passengers enter the subway entrance and pass through the corridor leading to the subway trains.
You can adjust the execution speed to your needs using Slow down and Speed up toolbar buttons. You can also switch to virtual time mode to view simulation run at its maximum speed and simulate a long period of time. To enable virtual time mode click the Toggle real/virtual time mode toolbar button.
# Simulation with AnyLogic/Pedestrian Simulation/Step 7. Changing passenger arrival rate interactively
## Step 7. Changing Passenger Arrival Rate Interactively

In the current model the passenger arrival rate is fixed. However, AnyLogic provides a set of controls enabling changing the model parameters at the model runtime.
Now we will introduce how you can vary parameters of Pedestrian Library objects dynamically. We want to interactively change the passenger arrival rate to assure acceptable performance of service points with hypothetic load. We will introduce the corresponding control element in the presentation to change the rate interactively.
Add a slider to vary passenger arrival rate
* Open the Controls stencil of the Palette and drag the Slider element from there into the graphical editor, e.g. to the right of the entrance layout:
* Set the properties of the slider. We want to vary the passenger arrival rate from 0 to 5000 pedestrians per hour. Therefore, specify 5000/hour as slider’s Maximum value. We type 5000/hour here since the default model time unit in pedestrian models is day. And since we want to define our rate in peds per hour, we divide the value by the constant defining time value equal to one hour according to the current time unit setting.
* Type 1000/hour as the slider's Default value.
* Specify pedSource.set_rate(value); as the slider's Action. This code will modify the rate of our PedSource object each time the user will move the slider. value here is the local variable that stores the current value of the slider.
Add text labels for the slider
* Add a title for the slider. Drag the Text element from the Presentation palette onto the diagram (above the slider).
* Define the text to be displayed by this label in the Text property:
* In the same way add two text labels displaying slider's minimum (0) and maximum (5000) values. Place them below the slider as shown in the figure below:
Run the model. Now you can change the passenger rate interactively with the slider. Therefore, you can find the maximal passenger arrival rate that can be served.