OpenLLM-France/wikimedia huggingface dataset:
# Harmonic series/Finite/Exceeding/Exercise

Let
    $x_{n}:=\sum _{k=1}^{n}{\frac {1}{k}}\,.$
* Find the smallest $n$ such that
    $x_{n}\geq 2\,.$
* Find the smallest $n$ such that
    $x_{n}\geq 2{,}5\,.$
# Fundamentals of Neuroscience/Hearing
## Goals

* To learn how auditory information becomes encoded into neural signals
* To learn how those signals are processed and interpreted

## The Ear

The ultimate task of the ear is to translate the vibration of the air, which is all sound is, into nerve impulses. This imposing task requires three distinct intermediate steps: first, the vibration of air has to be converted into the vibration of fluid, second the mechanical vibration of that fluid has to be detected by nerve cells, and lastly, the results of that detection process have to be sent for processing deeper in the brain.
For the first step, vibrating air is funneled through the ear canal down to eardrum (also known as the tymphatic membrane). That air causes the eardrum to vibrate in turn. The eardrum is connected to a series of bones called ossicles, which due to their attachment to the eardrum, move at rate proportional to original air vibrations. The opposite end of the ossicles is attached to another membrane belonging to a spiraled structure called the cochlea, which is the fluid-filled portion of the ear. Hence the motion of the ossicles started by eardrum vibrations driven by outside air becomes fluid vibrations in the cochlea, completing the first stage.
Nestled within the cochlea are sensory hair cells, which hold the key to the next two stages of the process. The pressure waves in the cochlear fluid cause the hair cells to have their protruding hairs deflected. Hair cells are mechanoreceptors, meaning they can interpret tactile stimulus into nerve impulses. The movement of these hairs essentially acts like a tactile stimulus, so the hair cells can turn the motion of cochlear fluid into electrical signals. These signals then leave the ear via the auditory nerve.

## Auditory Processing

Before the signals from the ears reach any cortical areas, they first pass through lower level brain areas for basic processing. Areas in the brainstem determine the location of a sound by comparing the slightly different inputs each ear receives, and other rough data interpretation similar to that visual signals go through before reaching their respective cortical regions.
The primary auditory cortex is located along the inner portion of the temporal lobes of the brain, and along with the adjacent secondary cortex, has the task of extracting meaning from the sound signals. One important quality of a sound is its frequency, or pitch. The primary method the brain uses to determine this is to see what region of the cochlea the signal mainly originated from. Sounds corresponding to the stiff base of the cochlea correspond to very high pitches, while the more floppy cochlear apex corresponds to low pitches.
While the auditory cortices are adept at deciphering much of the perceptual qualities of sound, for more sophisticated functions like identification and attributing meaning, other brain areas are needed. For example, certain regions like Wernicke's area is vital for comprehending spoken language, while others have been implicated in the myriad of attributes that give rise to the experience of music.
# English-Chinese/Webpage

A webpage (or web page) is a document from the internet which can be seen with a web browser. Web pages each have a URL or address, which is how a page is found, and is different for every page. When a webpage is part of a larger group of pages managed by a company, person, or organization, it is part of a website.
网页 是 来自 Internet的 文档，可以 通过 网络浏览器 查看。每个 网页 都有 一个 URL 或 地址，这是 页面的 查找 方式，每个 页面 都 有所不同。当 网页 是 由 公司，个人 或 组织 管理的 更大 页面组的 一部分 时，它是 网站的 一部分。
# English-Chinese/Well you could stay in bed all day on Friday

Well you could stay in bed all day on Friday. And I could take the kids to school.
那么你星期五可以整天待在床上。我可以带小孩去上学。
# English-Chinese/We sleep as the world turns in darkness

We sleep as the world turns in darkness.
我们天黑就睡觉。
# English-Chinese/Weight loss

Weight loss is when a person weighs less than before. A person can lose weight by running, swimming or doing any other activity. Also, a person might eat a healthier diet to lose weight. There are many diet and exercises programs available to lose weight. Many people lose weight when they eat less sugar and more vegetables, fruits and lean meat.
体重减轻 是指 体重 比 以前 减轻。我们 可以 通过 跑步，游泳 或 做 任何 其他 活动 来 减肥。我们 也 可以 吃 更健康的 饮食 来 减肥。有 许多 节食 和 锻炼 计划 可 用于 减肥。许多 人 少吃 糖，多吃 蔬果 和 瘦肉 减肥。
# English-Chinese/Web server

Web server refers to server software, or hardware dedicated to running said software, that can serve contents to the World Wide Web. A web server processes incoming network requests over HTTP and several other related protocols.
Web服务器 是指 服务器软件 或 专用于 运行 所述软件的 硬件，其 可以 向 万维网 提供 内容。 Web服务器 通过 HTTP 和 其他 一些 相关 协议 处理 传入的 网络 请求。
# English-Chinese/Weight loss reasons

Weight loss can happen for different reasons
* Health related - losing weight because of sickness like flu and fever, or even more serious like cancer and HIV.
* Exercise related - when weight loss is caused by using more energy than you provide to your body - this will end up in burning your reserves - fat.
* Diet related - by lowering the energy intake or some part of diet causing fat to be burned.
In many countries weight loss is caused by sociological pressure mostly on woman to have slim and fit figure.
体重减少 可能会 因 不同的 原因 而 发生
* 健康 相关 - 由于 流感 和 发烧 等 疾病 而 减轻体重，或者 更加 严重，如 癌症 和 HIV。
* 运动 相关 - 当 体重减轻 是 由于 使用 比 您 提供 给 您的 身体 更多的 能量 而 导致的 - 这 将 最终 导致 您的 储备 燃烧 - 脂肪。
* 饮食 相关 - 通过 降低 能量 摄入 或 某些 部分 饮食 导致 脂肪 燃烧。
在 很多 国家，减肥 是 由 社会 压力 造成的，主要 是 女性 身材 苗条。
# English-Chinese/Weight loss surgery in those with obesity is sometimes an effective measure in those with type 2 DM

Weight loss surgery in those with obesity is sometimes an effective measure in those with type 2 DM.
肥胖患者的减肥手术有时是2型糖尿病患者的有效措施。
# English-Chinese/Were you at the party?

Were you at the party?
你 有 参加 party 吗？
# English-Chinese/We left the hotel and soon got on the boat

We left the hotel and soon got on the boat.
我们离开了酒店，很快就上了船。
# English-Chinese/Western world

Western world has meant various things at various times.
During the Roman Empire, it meant Italy and the countries west of there. At other times, it has meant Western Europe or Europe or Christendom. During the Cold War, it sometimes meant the democratic countries or those allied with the various NATO powers. Today, it often means the places where most people speak European languages.
西方世界 在 不同时期 意味着 不同的 意思。
在 Roma帝国 时期，它 意味着 Italy 及其 西面的 国家。在 其他 时候，它 意味着 西欧 或 欧洲 或 基督教世界。在 冷战期间，它 有时 意味着 民主国家 或 与 北约 各种 力量 结盟的 国家。今天，它 通常 意味着 大多数人 讲 欧洲语言 的 地方。
# Instructional design/Learning objectives/Conditions Self Test

Click Next to continue.
| Instructional Design | ID Learning Objectives | < Back | Next > |
Self-Test
Self-test
See how much you have learned. Take the short self-test below choosing the best answer.
1
In an objective, the condition can best be defined as?
Condition tells the learner how they will be measured.
Condition tells the learner what they will perform.
Condition tells the learner what they will or will not be allowed to use.
2
What are the three primary categories of materials used in conditions?
Tools, references, and aids
Tools, resources, and aids
Books, elements, and lists
3
A good question to ask yourself before writing a condition is______.
Is the performance a main intent of the instruction?
What tools, resources, and job aids will the learner be allowed to use?
How will we know if the objective has been achieved?
4
Adding an example of what the learner will perform to the objective is called?
Using a sample test plan
Using an example test item
Using a a sample test item
5
In the following objective, Given a list of twenty-five states, be able to recall (write) the state capitals of at least twenty. which is the condition?
Given a list of twenty-five states,
be able to recall (write) the state capitals
of at least twenty. :
Click Next to continue. Phonebein 17:37, 30 March 2008 (UTC) There is no next button. Provide one, or fix the navigation instruction.
Good stuff thus far. This lesson is coming together nicely. I like the navigation, the length of the pages, and the writing style.
| Instructional Design | ID Learning Objectives | < Back | Next > |
# Instructional design/Learning objectives/Cognitive Domain Verb Usage, Part 2/Explanation of Answers

1. Which of the following is a performance verb for analysis?
2. Which of the following is a performance verb for synthesis?
3. Which of the following is a performance verb for evaluation?
* < Back
# Instructional design/Learning objectives/Criterion Self-Test/Answers

1. Criteria in objectives can best be defined as?
2. Criteria can best be defined by _____________?
3. The areas criteria come from are_______.
4. Which is an example of pointing criteria?
5. A good question to ask yourself before writing criteria is______.
* < Back
# Instructional design/Learning objectives/Conditions

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## Introduction

The second component of a well-formed objective is the condition. Simply identifying the performance required from the learner is not enough. We also have to describe the conditions that affect that performance. In this lesson you will learn the definition of conditions and how to clarify the intended performance. Examples and information about what constitutes conditions will help the learner to correctly identify well-written conditions. A self-test will help the learner to remember some of the key concepts from this lesson. Topics include:
   * Defining Conditions
   * Where Conditions Come From
   * Examples and Non-Examples of Condition Phrases
   * Conditions Self-Test

## Defining Conditions

Once the performance phrase is written for the learning objective, the learner understands what action, or behavior, is required. By including conditions to the objective, instructions are provided to the learner concerning "how" the performance is done. It provides the circumstances, resources, and supervision that the learner is given (or not given) to initiate the behavior. According to Robert Mager, the inclusion of the condition is to prevent misunderstanding. The condition helps clarify the objective so the learner knows what is expected of him/her. In a well-formed objective the condition provides the following:
* It identifies what the learner will be able to use to meet the desired performance.
** Given a periodic table of the elements, the participant will state the atomic number of hydrogen......
* It identifies what the learner will not be able to use to meet the desired performance.
** Without reference to the periodic table of the elements, the participant will be able to state the number of protons in titanium.....
* It identifies the context or environment the performance is accomplished in.
** During a simulation where the laboratory catches on fire, the participant will be able to implement emergency procedures .....
# Instructional design/Learning objectives/Criterion

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## Introduction

One of the three components of an effective well-formed objective is the criteria. No matter how well the objective has been written, without a clear and specific way to measure whether the student has achieved an appropriate level of performance, the objective is flawed. In this lesson you will learn the definition of well-formed criteria and some of the advantages it gives to instructors and learners. Examples and information about where criteria comes from will help the learner to correctly answer the quizzes and gives their own explanations that are offered throughout. A self-test will help the learner to remember some of the key concepts from this lesson. Topics include:
   * Defining Criterion
   * Examples and Non-Examples of Criterion Phrases
   * Where Criteria Comes From
   * Criterion Self-Test

## Defining Criterion

Criteria or sometimes called degree or standard is a statement that tells the learner to what degree of accuracy or quantity they must achieve in order to demonstrate an acceptable level of performance. In other words, criteria provides the measurable portion of a well formed objective. It specifically tells the learner what they must do to reach an acceptable level of performance. Criteria can be defined in several ways; speed, accuracy, quality and quantity.
         * Speed- gives a time limit in which the acceptable performance must be completed. For example:
               * within 45 seconds
               * under 60 minutes
         * Accuracy- gives a range of acceptable performance. For example:
               * with no more than 3 incorrect answers
               * within 1/16 of accuracy
         * Quality- gives a degree or grade of excellence which can be measured by subjective evaluation or matching.
               * correctly scoring 90% from an expert panel
               * exceeding 8 out of 10 standards
         * Quantity- gives an amount or count.
               * producing at least 12 dozen widgets
               * writing at least 100 words
Robert Mager tells us that by using the “yardstick” of criteria in our objectives we strengthen their usefulness and give learners and educators several advantages including:
         * A standard to test the success of the instruction.
         * A gage for students to know whether they have achieved or exceed expectations.
         * Provides information that the instructor can use to prove that students can do what has been given to them to accomplish (1997).
# Instructional design/Learning objectives/Criterion Self-Test

| Instructional Design | ID Learning Objectives | < Back | Page 4 of 4 | Next > |
See how much you have learned. Take the short self-test below choosing the best answer.
1
Criteria in objectives can best be defined as?
Criteria is the outcome of a well formed objective.
Criteria provides the "how to" of a well formed objective
Criteria provides the measurable portion of a well formed objective.
2
Criteria can best be defined by _____________?
Speed, weight and measurement
Accuracy, speed, quality and quantity
Speed, measurement, experts and opinions
3
The areas criteria come from are_______.
Job, improvement,academic and personal experience
Business and education.
Experience and documentation.
4
Which is an example of pointing criteria?
answers must be accurate to the nearest whole number.
saw a 2" X 4" board in half within 60 seconds
according to criteria described on pg.5 of manual.
5
A good question to ask yourself before writing criteria is______.
How much time will this take?
How will we know if the object has been achieved?
What does it take to be correct? :

## Navigation

Congratulations, you have finished the three component lessons. Click Next to continue to the final lesson.
| Instructional Design | ID Learning Objectives | < Back | Page 4 of 4 | Next > |
# Instructional design/Learning objectives/Examples and Non-Examples of Conditions Phrases

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## Helpful Questions when writing Conditions

The intent of adding conditions to a learning objective is to provide clarification about what the learner must do and how they will accomplish the performance.
When deciding how to word the condition phrase answer the following questions:
   * What tools, resources, and job aids will the learner be allowed to use?
   * What will the learner not be allowed to use?
   * Under what conditions will the desired performance occur?

## Non-Examples of False Conditions

One common error when writing learning objectives is to include instructional activities, teaching strategies, or classroom events that precede the performance of the learner. But a learning objective is concentrated on what the "learner" must do and how they will do it. It is not focused on an instructor's performance.
For example:
* After listening to the instructor's presentation, the learner will be able to describe Ohm's Law.....
* After reading the chapter on electrical currents, the student will be able to explain Ohm's Law.....
* Given adequate practice, the student will be able to solve Ohm's Law
The conditional phrases "After listening to this presentation.." ,"After reading the chapter on electrical currents...", and "Given adequate practice" do not describe the resources or environment that will be provided to the learner in the performance of the actual behavior. The phrases describe what leads up to the behavior which is the teacher's performance or an instructional activity.
A better example to the previous objectives would be:
* Given a worksheet with a list of electrical laws, the learner will be able to circle Ohm's Law....
* Given the voltage and resistance of an electrical circuit, the student will be able to solve for the current (using Ohm's Law)....

## Non-Examples of Unclear Conditions

Another common error in writing learning objectives is a lack of specifics and clear guidance when creating the conditions phrase. Remember, one of the key points in adding conditions is to clarify any misunderstanding concerning the performance.
For example:
* Given a book, the student will be able to diagnose a problem in a Volkswagen air conditioning system.
* Given a dictionary, the student will conjugate 10 verbs in French.
A better example provides more description about the condition.
* Given the Volkswagen-issued technical manual, the student will be able to diagnose a problem in a Volkswagen air conditioning system.....
* Given an English-French dictionary, the student will conjugate 10 verbs in French.....

## Practice and Feedback

With reference to the helpful questions section, choose the best answer for the following two questions?
# Instructional design/Learning objectives/Conditions Self-Test

| Instructional Design | ID Learning Objectives | < Back | Page 4 of 4 | Next > |
See how much you have learned. Take the short self-test below choosing the best answer.
1
In an objective, the condition can best be defined as?
Condition tells the learner how they will be measured.
Condition tells the learner what they will perform.
Condition tells the learner what they will or will not be allowed to use.
2
What are the four primary categories of resources used in conditions?
Tools, references, aids, and context
Tools, books, aids, and context
Tools, checklists, references, and instructors
3
A good question to ask yourself before writing a condition is______.
Is the performance a main intent of the instruction?
What tools, resources, and job aids will the learner be allowed to use?
How will we know if the objective has been achieved?
4
Which one is not a good example of a condition statement?
With reference to the Experience Economy textbook,
After conclusion of the Goal-Based Scenario lecture,
Given the recall roster and emergency procedures checklist,
5
In the following objective, Given a list of twenty-five states, be able to recall (write) the state capitals of at least twenty states. which is the condition?
Given a list of twenty-five states,
be able to recall (write) the state capitals
of at least twenty states. :

## Navigation

Good job! You have finished the second lesson. Click Next to continue to Criterion for Learning Objectives.
| Instructional Design | ID Learning Objectives | < Back | Page 4 of 4 | Next > |
# Harmonic series/Computation/Termination/Exercise

Karl wants to compute approximately with his programmable pocket calculator the value of the series $\sum _{n=1}^{\infty }{\frac {1}{n}}$. The display of the calculator shows $8$ positions after the decimal point. The calculator performs one addition (meaning a member of the series is added to the previous sum) per second and shows the result. Karl has programmed correctly and considers the following strategy: "If the display does not change for a complete hour, then we are probably close to the true result and we accept this as a good approximation. Then the calculator shall stop“.
* What is roughly the last member to be added?
* What do you think about this strategy?
# Harder-Narasimhan filtration/Strong version/Tight closure/Section

In general, there exists an exact criterion for the affineness of the torsor $T(c)$ depending on $c$ and the strong Harder-Narasimhan filtration of ${\mathcal {S}}$. For this we give the definition of the Harder-Narasimhan filtration.

## Definition

Let ${\mathcal {S}}$ be a vector bundle on a smooth projective curve $C$ over an algebraically closed field $K$. Then the (uniquely determined) filtration
    $0={\mathcal {S}}_{0}\subset {\mathcal {S}}_{1}\subset \ldots \subset {\mathcal {S}}_{t-1}\subset {\mathcal {S}}_{t}={\mathcal {S}}\,$
of subbundles such that all quotient bundles ${\mathcal {S}}_{k}/{\mathcal {S}}_{k-1}$ are semistable with decreasing slopes $\mu _{k}=\mu ({\mathcal {S}}_{k}/{\mathcal {S}}_{k-1})$,
${\mathcal {S}}$
The Harder-Narasimhan filtration exists uniquely (by a Theorem of Harder and Narasimhan). A Harder-Narasimhan filtration is called strong if all the quotients ${\mathcal {S}}_{i}/{\mathcal {S}}_{i-1}$ are strongly semistable. A Harder-Narasimhan filtration is not strong in general, however, by a Theorem of A. Langer, there exists some Frobenius pull-back $F^{e*}({\mathcal {S}})$ such that its Harder-Narasimhan filtration is strong.

## Theorem

Let $C$ denote a smooth projective curve over an algebraically closed field $K$ and let ${\mathcal {S}}$ be a vector bundle over $C$ together with a cohomology class $c\in H^{1}(C,{\mathcal {S}})$. Let
    ${\mathcal {S}}_{1}\subset {\mathcal {S}}_{2}\subset \ldots \subset {\mathcal {S}}_{t-1}\subset {\mathcal {S}}_{t}=F^{e*}({\mathcal {S}})\,$
be a strong Harder-Narasimhan filtration. We choose $i$ such that ${\mathcal {S}}_{i}/{\mathcal {S}}_{i-1}$ has degree $\geq 0$ and that ${\mathcal {S}}_{i+1}/{\mathcal {S}}_{i}$ has degree $<0$. We set
${\mathcal {Q}}=F^{e*}({\mathcal {S}})/{\mathcal {S}}_{i}$
* The torsor $T(c)$ is not an affine scheme.
* Some Frobenius power of the image of $F^{e*}(c)$ inside $H^{1}(X,{\mathcal {Q}})$ is $0$.
# Harmonic analysis and conformal field theory

The operator product expansion of conformal field theory is analogous to the product of functions over a manifold in harmonic analysis. In particular, crossing symmetry is analogous to the associativity of the product of functions over the manifold. The bootstrap method from CFT can be used for studying a manifold's geometry, or conversely the calculation of integrals over some manifolds can help determine correlation functions in certain CFTs.

## Bootstrap approach to spectral geometry

Assuming unitarity of a CFT and discreteness of the spectrum, numerical bootstrap methods can derive bounds on quantities such as conformal dimensions, using semidefinite programming. The same method can be applied to problems of spectral geometry that obey analogous assumptions.

### Closed Einstein manifolds

Bounds on geometric data of closed Einstein manifolds can be derived.

### Closed hyperbolic surfaces

Bounds on the eigenvalues of the Laplace-Beltrami operator can similarly be derived. In particular, a bound on the spectral gap of surfaces of genus 2 is nearly saturated by the Bolza surface.

## Harmonic analysis in limits of two-dimensional CFTs

In certain limits of two-dimensional CFTs, correlation functions reduce to integrals over finite-dimensional manifolds.

### Liouville theory

In the light asymptotic limit where the central charge is large and the conformal dimensions are constant, correlation functions of Liouville theory reduce to integrals of products of Laplacian eigenvectors over $SL_{2}(\mathbb {C} )$, or equivalently over $H_{3}^{+}=SL_{2}(\mathbb {C} )/SU_{2}$.

### WZW models

In the large level limit, correlation functions of the $G$-WZW model reduce to integrals of products of Laplacian eigenvectors over the group $G$. In the case $G=SL_{2}(\mathbb {R} )$, this can be used for determining the three-point structure constant in that limit.