OpenLLM-France/wikimedia huggingface dataset:
# PlanetPhysics/Category of Riemannian Manifolds 2
### Introduction

The very important roles played by Riemannian metric and Riemannian manifolds in Albert Einstein's General Relativity (GR) is well known. The following definition provides the proper mathematical framework for studying different Riemannian manifolds and all possible relationships between different Riemannian metrics defined on different Riemannian manifolds; it also provides one with the more general framework for comparing abstract spacetimes defined `without any Riemann metric, or metric, in general'. The mappings of such Riemannian spacetimes provide the mathematical concept representing transformations of such spacetimes that are either expanding or `transforming' in higher dimensions (as perhaps suggested by some of the superstring `theories'). Other, possible, conformal theory developments based on Einstein's special relativity (SR) theory are also concisely discussed.

#### Category of pseudo-Riemannian manifolds

The category of pseudo-Riemannian manifolds ${\mathcal {\mathbb {R} }}_{p}$ has as objects `pseudo-Riemannian manifolds' $\mathbb {R} _{p}$ representing generalized Minkowski spaces; the latter have been claimed to have applications in general relativity, $GR$. The morphisms of ${\mathcal {\mathbb {R} }}_{p}$ are mappings between pseudo-Riemannian manifolds, $\tau :\mathbb {R} _{p}^{i}\to \mathbb {R} _{p}^{j}.$
For a selected pseudo-Riemannian manifold, the endomorphisms $\epsilon :\mathbb {R} _{p}\to \mathbb {R} _{p}$ represent dynamic transformations.
In quantized versions of $\mathbb {R} _{p}$, as in `quantum Riemannian geometry' (QRG), such dynamic transformations may be defined for example by functors between (quantum) spin networks, or quantum spin `foams'. In General Relativity space-time may also be modeled as a 4-pseudo Riemannian manifold with signature $(-,+,+,+)$; over such spacetimes one can then consider the boundary conditions for Einstein's field equations in order to find and study possible solutions that are physically meaningful; it can be shown however that such boundary conditions are however insufficient to obtain physical solutions.
# PlanetPhysics/Center of Abelian Category

Let ${\mathcal {A}}$ be an abelian category. Then one also has the identity morphism (or identity functor) $id_{\mathcal {A}}:{\mathcal {A}}\to {\mathcal {A}}$. One defines the center of the Abelian category 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 \mathcal{A } } by $Z({\mathcal {A}})=End(id_{\mathcal {A}}).$
One can show that the center is $Z(CohX)\cong {\mathcal {O}}((X)$ for any algebraic variety where ${\mathcal {O}}(X)$ is the ring of global regular functions on $X$ and ${\mathbf {C} oh}(X)$ is the Abelian category of coherent sheaves over $X$.
One can show also prove the following lemma. \begin{theorem} {\mathbf Associative Algebra Lemma}
If $A$ is a associative algebra then its center $Z(A-mod)=ZA.$ \end{theorem}
# PlanetPhysics/Centre of Mass

The center of mass (en: centre of mass ) of an object is a point in physical pace where, for computational purposes in theoretical mechanics, the mass of the object can be considered to be concentrated. This concept is most often used for rigid bodies, but applies to any macroscopic arrangement of matter. The centre of mass can be used as a geometrical concept that allows in several ways to simplify an apparently complicated system or problem by treating an entire rigid body as a "point particle". For example, a rigid body hung from a string in a uniform gravitational field will have its centre of mass straight below the string if it is at rest. More generally, as long as the only forces acting are gravity and the tension in the string, in order to compute the motion of the object in space (disregarding possible rotations) one can conceptually replace the solid object by a point particle located at the object's centre of mass.
The momentum of an object with total mass $M$ is $\mathbf {p} =M\mathbf {v} _{\mathrm {cm} },$ and if a total force $\mathbf {F}$ acts on the object, Newton's second law may be formulated as $\mathbf {F} =M\mathbf {a} _{\mathrm {cm} }.$ In these equations $\mathbf {v} _{\mathrm {cm} }$ and $\mathbf {a} _{\mathrm {cm} }$ are the velocity and the acceleration of its centre of mass, respectively; these are defined below.
The centre of mass of a solid object, rigid body, etc., occupying a region $V$ in space, is defined as the average position of all the points of $V$, each point $\mathbf {x}$ being weighted with the density of the object at that point, $\rho (\mathbf {x} )$. This average is a volume integral over the region $V$: $\mathbf {x} _{\mathrm {cm} }\equiv {\frac {1}{M}}\int _{V}\rho (\mathbf {x} )\mathbf {x} \,\mathrm {d} V.$ Here $M$ is the total mass of the object: $M\equiv \int _{V}\rho (\mathbf {x} )\,\mathrm {d} V.$
If the object consists of a number of point particles, these integrals become sums over the particles. The centre of mass of a collection of $N$ particles with masses $m_{1},m_{2},\ldots ,m_{N}$ located at the positions $\mathbf {x} _{1},\mathbf {x} _{2},\ldots ,\mathbf {x} _{N}$ is $\mathbf {x} _{\mathrm {cm} }\equiv {\frac {1}{M}}\sum _{i=1}^{N}m_{i}\mathbf {x} _{i},$ where $M$ is now the sum of the masses of the particles: $M\equiv \sum _{i=1}^{N}m_{i}.$
The velocity and acceleration of the centre of mass are now simply defined as the first and second time derivatives of $\mathbf {x} _{\mathrm {cm} }$: $\mathbf {v} _{\mathrm {cm} }\equiv \mathbf {\dot {x}} _{\mathrm {cm} },\qquad \mathbf {a} _{\mathrm {cm} }\equiv \mathbf {\ddot {x}} _{\mathrm {cm} }.$
# PlanetPhysics/Category of Riemannian Manifolds
### Introduction

The very important roles played by Riemannian metric and Riemannian manifolds in Albert Einstein's General Relativity (GR) is well known. The following definition provides the proper mathematical framework for studying different Riemannian manifolds and all possible relationships between different Riemannian metrics defined on different Riemannian manifolds; it also provides one with the more general framework for comparing abstract spacetimes defined `without any Riemann metric, or metric, in general'. The mappings of such Riemannian spacetimes provide the mathematical concept representing transformations of such spacetimes that are either expanding or `transforming' in higher dimensions (as perhaps suggested by some of the superstring `theories'). Other, possible, conformal theory developments based on Einstein's special relativity (SR) theory are also concisely discussed.

#### Category of pseudo-Riemannian manifolds

The category of pseudo-Riemannian manifolds that generalize Minkowski spaces is similarly defined by replacing "Riemanian manifolds" in the above definition with "pseudo-Riemannian manifolds"; the latter has been claimed to have applications in Einstein's theory of general relativity ($GR$).
In General Relativity space-time may also be modeled as a 4-pseudo Riemannian manifold with signature $(-,+,+,+)$; over such spacetimes one can then consider the boundary conditions for Einstein's field equations in order to find and study possible solutions that are physically meaningful.
A category ${\mathcal {R}}_{M}$ whose objects are all Riemannian manifolds and whose morphisms are mappings between Riemannian manifolds is defined as the category of Riemannian manifolds .
The subcategory ${\mathcal {R}}_{C}$ of ${\mathcal {R}}_{M}$, whose objects are Riemannian manifolds, and whose morphisms are conformal mappings of Riemannian manifolds, is an important category for mathematical physics, in conformal theories. It can be shown that, if $(R_{1},g)$ and $(R_{2},h)$ are Riemannian manifolds, then a map $f\colon R_{1}\to R_{2}$ is conformal iff $f^{*}h=s.g$ for some scalar field $s$ (on $R_{1}$), where $f^{*}$ is the complex conjugate of $f$.
# Progress and Prospects in Parkinson's Research/Symptoms/Dyskinesia

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## Dyskinesia

Abnormality of muscle tone or movement.
The following references are relevant:-
Chung et al(2010) Objective Measurement of Dyskinesia in Parkinson Disease using a Force Plate
Timbasco et al (2012) Clinical Aspects and Management of Levodopa-Induced Dyskinesia
Espay et al (2012) “On” state freezing of gait in Parkinson disease -A paradoxical levodopa-induced complication
# Progress and Prospects in Parkinson's Research/Symptoms/Delusion

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Delusion
A fixed false belief that is resistant to reason or confrontation with actuality
The following references are relevant:-
Goldman (2011) New Thoughts on Thought Disorders in Parkinson's Disease: Review of Current Research Strategies and Challenges
Fénelon et al (2012) Feeling of presence in Parkinson's disease
Mack et al (2012) Prevalence of Psychotic Symptoms in a Community-Based Parkinson’s Disease Sample
Further Research
# Progress and Prospects in Parkinson's Research/Symptoms/Dysphagia

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Dysphagia
Difficulty in swallowing.
See also Aphagia
Further Research
References
# Progress and Prospects in Parkinson's Research/Symptoms/Dementia

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Dementia
Abnormal progressive decline in cognitive function
See also Cognitive Impairment
The following references are relevant.
Leverenz et al, (2009) Cognitive Impairment and Dementia in Patients with Parkinson Disease
Johnson and Galvin (2011) Longitudinal Changes in Cognition in Parkinson's Disease with and without Dementia
Weintraub et al (2011) Neurodegeneration Across Stages of Cognitive Decline in Parkinson Disease
Further Research
# Progress and Prospects in Parkinson's Research/Symptoms/Contractures

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Contractures
Permanent contraction at joints.
The following references are relevant:-
Ebin (1951) Surgical Treatment of Parkinsonism: Indications and Results
Kyriakides and Hewer (1988) Hand contractures in Parkinson's disease.
Shah et al (2005) Flexion contracture after total knee arthroplasty in a patient with Parkinson's disease: successful treatment with botulinum toxin type A.
# Progress and Prospects in Parkinson's Research/Symptoms/Coprolalia

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Coprolalia
Exclamatory swearing and use of hostile or obscene epithets.
Daniele et al (1997) Obsessive-compulsive behaviour and cognitive impairment in a parkinsonian patient after left putaminal lesion.
Shale et al (2005) Tics in a patient with Parkinson's disease†
Dale et al (2007) Contemporary encephalitis lethargica presenting with agitated catatonia, stereotypy, and dystonia-parkinsonism.
Further Research
# Progress and Prospects in Parkinson's Research/Symptoms/Dysarthria

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Dysarthria
Speech difficulties due to impairment of the muscles associated with vocalization.
The following references are relevant:-
MacPherson et al (2011) The Intonation-Syntax Interface in the Speech of Individuals with Parkinson’s Disease
Skodda (2012) Effect of Deep Brain Stimulation on Speech Performance in Parkinson's Disease
Walsh and Smith (2011) Linguistic Complexity, Speech Production, and Comprehension in Parkinson’s Disease: Behavioral and Physiological Indices
Further Research
References
* ↑ MacPherson, Megan K.; Huber, Jessica E. and Snow, David P.(2011) Full TextJ. Speech Lang. Hear. Res. 54 (1) 10 – 32 The Intonation-Syntax Interface in the Speech of Individuals with Parkinson’s Disease http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3441058/
* ↑ Skodda, Sabine (2012) Full TextParkinsons Dis. 2012: 85059 Effect of Deep Brain Stimulation on Speech Performance in Parkinson's Disease http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3512320/
* ↑ Walsh, Bridget and Smith, Anne (date) Full TextJ. Speech Lang. Hear. Res. 54 (3) 787 – 802 Linguistic Complexity, Speech Production, and Comprehension in Parkinson’s Disease: Behavioral and Physiological Indices http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3418801/
# Progress and Prospects in Parkinson's Research/Symptoms/Constipation

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Constipation
Decreased ability of intestinal muscles to move stool through the bowels
Gao et al (2011) A Prospective Study of Bowel Movement Frequency and Risk of Parkinson’s Disease
Forsyth et al (2011) Increased Intestinal Permeability Correlates with Sigmoid Mucosa alpha-Synuclein Staining and Endotoxin Exposure Markers in Early Parkinson's Disease
Wang et al (2013) Early recognition of pelvic floor dyssynergia and colorectal assessment in Parkinson's disease associated with bowel dysfunction.
Further Research
# Noah Baumbach
## Overview

Noah Baumbach is an American filmmaker known best for writing and directing witty intellectual comedies that are typically set in New York. Growing up, he was inspired by Woody Allen's films. Additionally, he notes Steve Martin as a comedic inspiration.

## Filmography
#### Baumbach's Direction

Noah Baumbach has directed 12 feature narrative films which are:
* Kicking and Screaming (1995)
* Mr. Jealousy (1997)
* Highball (2002) *film was never fully finished
* The Squid and the Whale (2005)
* Margot and the Wedding (2007)
* Greenberg (2010)
* Frances Ha (2012)
* While We’re Young (2014)
* Mistress America (2015)
* The Meyerowitz Stories (2017)
* Marriage Story (2019)
* White Noise (2022)

#### Baumbach's Writing

Noah Baumbach writes all of his own films. Noah Baumbach collaborates frequently with Wes Anderson. He was a writer on the following Anderson's films: Fantastic Mr. Fox (2009) and The Life Aquatic with Steve Zissou (2004). He also works with his partner Greta Gerwig. He was a writer and producer on Gerwig's 2023 smash hit Barbie (2023).

## Filmmaker's Aesthetics
### Mumblecore

Noah Baumbach was an important icon in popularizing the sub-genre of Mumblecore. Mumblecore was inspired by films by Andrei Tarkovsky and the film Slacker (Linklater 1990). Common aesthetics of mumblecore include natural feeling and sounding dialogue, static camera movements, and natural lighting. Frances Ha, directed by Baumbach and written by himself and Greta Gerwig was one of the first mumblecore films to skyrocket the genre. Even in his more recent films like Marriage Story (2019) and White Noise (2022) there are still mumblecore-like aesthetics like lower budget filmmaking techniques about characters struggling through life and leaving their youth.

### Common Themes

Baumbach has been called an auteur. He has many reoccuring themes and motifs in his films.

#### Locations Set in NYC

Most, if not all of his films are set on the East Coast, specifically New York City. Thus, he has many scenes set on a train or subways.

#### Divorce and Step Families

He is inspired by his own personal experiences and uses it for his films. All of Baumbach's films contain broken families or step families.

#### Prestigious References

Noah Baumbach is known for having characters with artistic careers, and these characters having intelligent conversations about high art.

#### Moments in His Films

Drawing from his love of Steve Martin, Noah Baumbach is known for having moments of screwball comedy in his films; as well as, moments of deep wisdom between the comedy.

## Reception/Awards

Noah Baumbach was been nominated for multiple prestigious awards during his career. Some of the highlights include:
* 2020 Nominee Oscar - Best Motion Picture of the Year - Marriage Story
* 2020 Nominee Oscar - Best Original Screenplay - Marriage Story
* 2020 Nominee BAFTA Film Award - Best Screenplay (Original) - Marriage Story
* 2017 Nominee Palme d'Or - The Meyerowitz Stories
* 2006 Nominee Oscar - Best Writing, Original Screenplay - The Squid and the Whale
# Noam Chomsky

Noam Chomsky, 85 years old, is a linguist, philosopher, cognitive scientist, logician, political commentator and activist.
Noam Chomsky (born December 7, 1928, Philadelphia, Pennsylvania, U.S.) is an American theoretical linguist whose work from the 1950s revolutionized the field of linguistics by treating language as a uniquely human, biologically based cognitive capacity. Through his contributions to linguistics and related fields, including cognitive psychology and the philosophies of mind and language, Chomsky helped to initiate and sustain what came to be known as the “cognitive revolution.” Chomsky also gained a worldwide following as a political dissident for his analyses of the pernicious influence of economic elites on U.S. domestic politics, foreign policy, and intellectual culture.

### see also

* reading group
* wikipedia: Noam Chomsky
# Nobel Prize in Physiology or Medicine

Welcome to the Wikiversity learning project for the Nobel Prize in Physiology or Medicine.
Participants in this learning project explore the science and practical applications for each year's Nobel Prize in Physiology or Medicine.
The Wikipedia articles about topics related to each Nobel Prize in Physiology or Medicine tens to be very technical descriptions of the underlying science. The goal of this learning project is to complement the Wikipedia articles in two ways. The first goal is to provide a user-friendly introduction to the topic. This means creating learning resources for people who would normally be unable to understand a technical Wikipedia article on the topic. These user-friendly introductions might particularly focus on the practical medical implications behind Nobel Prize-winning scientific research. The second goal is to provide learning resources that allow interested university students to explore the science behind each awarded Nobel Prize in more detail than is possible with the related Wikipedia article.

## By year

* 2006 Awarded to Andrew Z. Fire and Craig C. Mello for their discovery of RNA interference. Learn about RNA interference.
# Nobel Prize in Chemistry

Welcome to the Wikiversity learning project for the Nobel Prize in Chemistry.
Participants in this learning project explore the science and practical applications for each year's Nobel Prize in Chemistry.
The Wikipedia articles about topics related to each Nobel Prize in Physiology or Medicine tens to be very technical descriptions of the underlying science. The goal of this learning project is to complement the Wikipedia articles in two ways. The first goal is to provide a user-friendly introduction to the topic. This means creating learning resources for people who would normally be unable to understand a technical Wikipedia article on the topic. These user-friendly introductions might particularly focus on the practical medical implications behind Nobel Prize-winning scientific research. The second goal is to provide learning resources that allow interested university students to explore the science behind each awarded Nobel Prize in more detail than is possible with the related Wikipedia article.

## By year

* 2006 Awarded to Roger D. Kornberg for his work on the molecular basis of eukaryotic transcription. Learn about the work on eukaryotic transcription from Kornberg's laboratory.
# QB/a07energy cart2

* Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
* At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
** Quizbank physics 1 (id 60675)
** Quizbank physics 2 (id 61712)
** Quizbank astronomy (id 63705)
The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.
* Latest essay: MyOpenMath/Pulling loose threads
* Latest lesson: Phasor algebra
See special:permalink/1863130 for a wikitext version of this quiz.
# QB/a08linearMomentumCollisions

* Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
* At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
** Quizbank physics 1 (id 60675)
** Quizbank physics 2 (id 61712)
** Quizbank astronomy (id 63705)
The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.
* Latest essay: MyOpenMath/Pulling loose threads
* Latest lesson: Phasor algebra
See special:permalink/1863132 for a wikitext version of this quiz.
# QB/a09staticsTorques torque

* Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
* At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
** Quizbank physics 1 (id 60675)
** Quizbank physics 2 (id 61712)
** Quizbank astronomy (id 63705)
The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.
* Latest essay: MyOpenMath/Pulling loose threads
* Latest lesson: Phasor algebra
See special:permalink/1863453 for a wikitext version of this quiz.
# Peak oil, energy, and society/Ian's page

Solar it growing more popular by the day. one place where an example of this can be seen is at Massachusetts Innovation Collaborative, LLC, in Fitchburg Ma. Here, thanks to a government grant, over 100 solar panels are used to power this structure. This old Mill was renovated into a school and housing structure with the idea of recycling, green living, and being off the grid in mind. Old metal panels, used lumber, etc. leftover from the mill days were used in renovation as walls, ceilings and used for decoration. Along with solar panels powering the structure, two geothermal systems heat and cool oil-free all year long. The M.I.C continues to be worked on to this day and it is not yet used for housing but should be within the next year or so. This structure is an excellent example of re-using old abandoned structures as apposed to tearing them down, and good, real life solutions to oil for the greater good of the community. They also have the largest commercial solar installation in New England.
# Pearson product-moment correlation coefficient

This statistics resource is a "stub". Learn how you can help Wikiversity to develop it.

## Formula

$r_{X,Y}={\mathrm {cov} (X,Y) \over S_{X}S_{Y}}$

## Assumptions
### Normality

The Pearson product-moment correlation is a parametric statistics and thus assume that the univariate distributions are approximately normal. Consider descriptive, inferential, and graphical indicators of normality - see Testing for normality.
Ultimately, if still in doubt, then conduct both parametric and non-parametric analyses of association between two variables and compare the results. If they indicate the same conclusion, then it really doesn't matter which technique is used. If the results are different, then the researcher should try to work out why and which is more appropriate. If still in doubt, then report both.
# Pediatrics

Pediatrics is the field within medicine concerned with the health and wellbeing of children and adolescents.
It is a widely diverse field that is related to several other medical fields.
This course will be designed for medical students, pediatric residents and other healthcare providers seeking knowledge about topics within pediatrics.

## Resources

* Pediatrics (LMCC)