OpenLLM-France/wikimedia huggingface dataset:
# PlanetPhysics/Quantized Riemann Spaces
## Quantized Riemannian Manifolds and Geometry

An interesting, but perhaps limiting approach to quantum gravity (QG), involves defining a quantum Riemannian geometry in place of the classical Riemannian manifold that is employed in the well-known, Einstein's classical approach to general relativity (GR). Whereas a classical Riemannian manifold has a metric defined by a special, Riemannian tensor, the quantum Riemannian geometry may be defined in different theoretical approaches to QG by either quantum loops (or perhaps 'strings'), or spin networks and spin foams (in locally covariant GR quantized space-times). The latter two concepts are related to the 'standard' quantum spin observables and thus have the advantage of precise mathematical definitions. As spin foams can be defined as functors of spin network categories, quantized space-times (QST SUSY2)s can be represented by, or defined in terms of, natural transformations Variable Category 2 of 'spin foam' functors. The latter definition is not however the usual one adopted for quantum Riemannian geometry, and other (for example, noncommutative geometry) approaches attempt to define a QST metric not by a Riemannian tensor --as in the classical GR case-- but in relation to a generalized, quantum 'Dirac' operator in a spectral triplet.
Remarks. Other approaches to Quantum Gravity include: loop quantum gravity (LQG), AQFT approaches, topological quantum field theory (TQFT)/ homotopy Quantum Field Theories (HQFT; Tureaev and Porter, 2005), quantum theories on a lattice (QTL), string theories and spin network models.
quantum geometry is defined as a field Cosmological Constant 2 of Mathematical or theoretical physics based on geometrical and algebraic topology approaches to Quantum Gravity - one such approach is based on Noncommutative Geometry and SUSY (the 'Standard' Model in current Physics).
A Result for quantum spin foam Triangulation Methods For Quantized Spacetimes 2 representations of quantum space-times (QST)s: There exists an $n$-connected CW model $(Z,QSF)$ for the pair $(QST,QSF)$ such that: $f_{*}:\pi _{i}(Z)\rightarrow \pi _{i}(QST)$, is an isomorphism for $i>n$, and it is a monomorphism for $i=n$. The $n$-connected CW model is unique up to homotopy equivalence. (The $CW$ complex, $Z$, considered here is a homotopic 'hybrid' between QSF and QST).
# PlanetPhysics/Quantum Algebraic Topology Topics

This is a new, contributed topic on Quantum Algebraic Topology.

## Quantum Algebraic Topology (QAT) Topics

Quantum algebraic topology can be described as the area of mathematical physics and physical mathematics concerned with the application of algebraic topology concepts, procedures and results to quantum theories such as quantum field theories (QFT, AQFT, locally covariant relativististic quantum theories and quantum gravity (QG)). QAT has close connections to several other fundamental fields of mathematics, such as: noncommutative geometry (NCG), the theory of categories, functors and natural transformations (TCFN), non-Abelian algebraic topology (NAAT), and higher dimensional algebra (HDA).
Related references are available at the websites and documents in the following topics list.

### QAT Topics : Online Resources

* QAT: Quantum Algebraic Topology-preprint.
* AT: Algebraic Topology papers
* NAAT: A first textbook on "Non-Abelian Algebraic Topology"
* QA: Quantum automata and quantum supercomputers
* NAQAT: Non-Abelian QAT
* NAAT-List: Category Theory, Homotopy Theory and AT Publications
* SPE: Stanford Plato: Category Theory and Applications
* Abc
# PlanetPhysics/Projective Object

Let us consider the category of Abelian groups ${\mathbf {A} b}_{G}$. An object $P$ of an abelian category ${\mathcal {A}}$ is called projective if the functor 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 Hom_A (P,âˆ’) : \mathcal{A} \to {\mathbf Ab}_G} is exact.
{\mathbf Remark.}
This is equivalent to the following statement: An object $P$ is projective if given a short exact sequence 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 0 \to Mâ€² \to M \to Mâ€²â€² \to 0} in an Abelian category ${\mathcal {A}}$, one has that: Failed to parse (syntax error): {\displaystyle 0 \to Hom_{\mathcal{A}}(Mâ€², P) \to Hom_{\mathcal{A}}(M, P) \to Hom_{\mathcal{A}}(Mâ€²â€², P) \to 0}
is exact in ${\mathbf {A} b}_{G}$.
# PlanetPhysics/Quantum 6J Symbols and TQFT State on the Tetrahedron

\newcommand{\sqdiagram}[9]{Failed to parse (unknown function "\diagram"): {\displaystyle \diagram #1 \rto^{#2} \dto_{#4}& \eqno{\mbox{#9}}} }

## Topological Quantum Field (TQFT) State on the Tetrahedron

Let us consider first a regular tetrahedron whose corners will have attached to them the TQFT symbols representing a TQF state in terms of so-called `j-symbols' as further detailed next. The vertices of the tetrahedron are located at the points $(a_{x},a_{y},a_{z})$, $(b_{x},b_{y},b_{z})$, $(c_{x},c_{y},c_{z})$, and $(d_{x},d_{y},d_{z})$, that will be labeled, respectively, as $1,2,3,4$.
A \htmladdnormallink{quantum field {http://planetphysics.us/encyclopedia/CosmologicalConstant.html} (QF) state} $\phi$ provides a total order denoted by $\leq _{\phi }$ on the vertices of the tetrahedron, and thus also assigns a `direction' to each edge of the tetrahedron--from the apparently `smaller' to the apparently `larger' vertices; a QF state also labels each edge $e=(i,j)$, by an element $\phi _{1}(e)$ of $B_{A}$, which is a distinguished basis of a fusion algebra Failed to parse (unknown function "\A"): {\displaystyle \A} , that is, a finite-dimensional, unital, involutive algebra over $\mathbb {C}$ --the field of complex numbers. Moreover, the QF state assigns an element ${\phi }^{2}(f)$ --called an intertwiner-- of a Hilbert space $\mathbb {H} _{\phi }(f)={\mathbb {H} ^{\phi _{1}(ik)}}_{\phi _{1}(jk),\phi _{1}(ij)}$ to each face $f=(ijk)$ of the tetrahedron, such that $i\prec _{\phi }j\prec _{\phi }k.$

### Remarks

A \htmladdnormallink{topological {http://planetphysics.us/encyclopedia/CoIntersections.html} quantum field theory} (TQFT ) is described as a mathematical approach to quantum field theory that allows the computation of topological invariants of quantum state spaces (QSS), usually for cases of lower dimensions encountered in certain condensed phases or strongly correlated (quantum) superfluid states. TQFT has some of its origins in theoretical physics as well as Michael Atiyah's research; this was followed by Edward Witten, Maxim Kontsevich, Jones and Donaldson, who all have been awarded Fields Medals for work related to topological quantum field theory; furthermore, Edward Witten and Maxim Kontsevich shared in 2008 the Crafoord prize for TQFT related work. As an example, Maxim Kontsevich introduced the concept of homological mirror (quantum) symmetry in relation to a mathematical conjecture in superstring theory.
# PlanetPhysics/Quantum Algebra

A quantum algebra over a field $k$ is defined as a triple $(A,\rho ,s)$ where $(A,\rho )$ is a Yang-Baxter algebra over the field $k$ and $s:A\to A^{op}$ is an algebra isomorphism, subject to the following two axioms:
* (QA.1) $\rho ^{-1}=(s\otimes 1_{A})(\rho )$
* (QA.2) $\rho =(s\otimes s)(\rho )$
Note also that(QA.1) and(QA.2) imply(QA.3):
(QA.3) $\rho ^{-1}=(1_{A}\otimes s^{-1})(\rho )$.
Remark Quasitriangular Hopf algebras are a basic source of quantum algebras.
# PlanetPhysics/Proper Generator Theorem

\begin{theorem} Any commutative ring is the endomorphism ring of a proper generator in a suitably chosen Grothendieck category. \end{theorem}
# PlanetPhysics/Proper Generator in a Grothendieck Category
### Introduction: family of generators and generator of a category

Let ${\mathcal {C}}$ be a category. A family of its objects $\left\{U_{i}\right\}_{i\in I}$ is said to be a family of generators of ${\mathcal {C}}$ if for every pair of distinct morphisms $\alpha ,\beta :A\to B$ there is a morphism $u:U_{i}\to A$ for some index $i\in I$ such that $\alpha u\neq \beta u$.
One notes that in an additive category, $\left\{U_{i}\right\}_{i\in I}$ is a family of generators if and only if for each nonzero morphism $\alpha$ in ${\mathcal {C}}$ there is a morphism $u:U_{i}\to A$ such that $\alpha u\neq 0$.
An object $U$ in ${\mathcal {C}}$ is called a generator for ${\mathcal {C}}$ if $U\in \left\{U_{i}\right\}_{i\in I}$ with $\left\{U_{i}\right\}_{i\in I}$ being a family of generators for ${\mathcal {C}}$.
Equivalently, (viz. Mitchell) $U$ is a generator for ${\mathcal {C}}$ if and only if the set-valued functor $H^{U}$ is an imbedding functor.

### Proper generator of a Grothendieck category

A proper generator $U_{p}$ of a Grothendieck category ${\mathcal {G}}$ is defined as a generator $U_{p}$ which has the property that a monomorphism $i:U'\to U_{p}$ induces an isomorphism $\iota$, $Hom_{\mathcal {G}}(U_{p},U_{p})\cong Hom_{\mathcal {G}}(U',U_{p}),$ if and only if $i$ is an isomorphism.
\begin{theorem} Any commutative ring is the endomorphism ring of a proper generator in a suitably chosen Grothendieck category. \end{theorem}
# PlanetPhysics/Quadratic Equation

The quadratic formula
   $x\;=\;{\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}$
can be used to find the solutions (roots) to a quadratic equation $ax^{2}+bc+c\;=\;0.$
# Neuroscience

Neuroscience
* Topic:Neuroscience
* Criticism
# Neurologist

This Medicine resource is a "stub". Learn how you can help Wikiversity to develop it.
Neurologists are physicians that are specialized neurology which includes nerves, brains, spinal cord and muscles. Neurologists have patients that have diseases or mental disorders.
The duty a neurologist performs is to perform surgery and diagnosing, treating, and managing brain and nervous system disorders. This may include disorders affecting a person's speech, memory, language, and cognitive abilities. Neurologists may specialize in research or clinical trials, generalized neurological patient care, or may receive additional training to become a neurosurgeon.
Knowledge on how to treat people that are afflicted by those diseases and disorders is taught during the studying period before becoming a neurologist. Diseases such as Parkinson’s disease and Alzheimer’s disease and schizophrenia, depression and autism are some of the main disorders and diseases the patients that come to the neurologist are afflicted with.
Neurologists are employed by hospitals and medical clinics. Some are self-employed, opening their own private practice offices. They could be either hired on a salaried basis by an institution such as a hospital, or they can bill the government for each medical service action they provide. Annual earnings vary depending on a number of factors, including experience, location, sub-specialty, and whether or not they are self-employed.
According to a report by the Canadian Institute for Health Information (CIHI), neurologists bill their local(sometimes higher in level) governments an average of about $237,000 a year for medical services provided to the public.
# Neuropsychology Forum

NEUROPSYCHE FORUM
By posting to this forum you agree to publishing your comments under the
CC-By-SA 3.0 (legal code) and the project license

## Topics of Interest

Put comments of interest here at the start to reduce viewer fatigue

### Lots of interesting stuff happening about NC of Attention

Have you seen the recent articles in Psyche ASSC's Ejournal?

### Differential Selection Theory

I have long felt that Dr. Edelman extended his TNGS theory to other parts of the brain, using mechanisms that are only really valid for the Cerebral Cortex. I however believe that other parts of the brain self-organize in a similar manner, so I have suggested the Differential Selection Theory, which states that self-organization in other parts of the brain depends on the architecture of those parts of the brain, and does not rely as heavily on reentry, and Neural Group Selection as it does in the cerebral cortex. As a result we need to look at each part of the brain separately to determine what the principles of self-organization might be for it.--Graeme E. Smith 17:54, 18 February 2009 (UTC)

## General Layout of Neuropsychology School

Who's stupid idea was it to put the School name on a Tab?
    In WikiVersity Schools are just a way of organizing information, there is no physical bricks and mortar to get uptight about, so we don't need all that much of an administration. When I suggested the idea of having a Dean of each School, I was told, that I had to propose it as a game. My proposed directorship didn't last a day, WikiVersity is a "Collaborative" effort and anyone can take on any role.--Graeme E. Smith 17:30, 2 February 2009 (UTC)
Who's stupid idea was it to name this school Neuropsychology?
    I'ts all my fault, at least so far, once we get going, I am hoping that others will want to change things up a little, but for now most of the work has been done by yours truly--Graeme E. Smith 17:30, 2 February 2009 (UTC)
# Neurology/Arteriovenous Malformation

Brain A.V.M. (Arterio Venous Malformation): a mass of extraneous blood vessels that forms in a being's brain at the first stages of that being's first stages of fetal development. An existent A.V.M., in an individual's brain, makes the experience of a hemorrhagic stroke much more likely; however, instead of having the stroke permanently affect the individual, he or she, after approximately 3-5 weeks of bed rest, can return to normal life, as though nothing happened.
After several strokes have occured, a Brain A.V.M. can be required to be treated, necessarily.

## See Also

* Wikipedia: Arteriovenous malformation
# Neurophilosophy

Welcome to the Wikiversity content development project for Neurophilosophy.

## Project scope

Neurophilosophy includes scientific studies that are related to philosophy of mind and philosophy that explores the implications of all aspects of neuroscience. This content development project is devoted to the creation and development of learning resources that help learners explore the mind from a biological perspective with special emphasis on philosophical implications of scientific study of consciousness. Learning resources that attempt to unify neuroscience, philosophy of mind and artificial intelligence research are also welcome.

## Learning resources

* Consciousness Studies - Exploration of the neuroscience and philosophy of consciousness.
* Topic:Neuroscience - General survey of neuroscience courses.
# Neuropharmacology

Neuropharmacology is the study of the effects of drugs on the nervous system, aiming to develop compounds to benefit humans with psychiatric and neurological disease.
Neuropharmacology is the study of the effects of drugs on the nervous system, with the goal of developing compounds that offer therapeutic benefit in humans with psychiatric and neurological disease. We believe that an understanding of a drug’s action requires an integrated knowledge of the cellular and molecular mechanisms by which the drug exerts its effects upon brain circuitry and ultimately human behaviour.
Neuropharmacology can be divided into:
* Experimental Neuropharmacology
* Neuronal circuit research
* Sinaptic Pharmacology
* Cellular and molecular Neuroscience
* Lysosomal and Sphingolipid Disorders
* Neuroanatomy and In Vitro Neurophysiology
The first consideration of neuropharmacology is to what degree a drug is able to cross the blood-brain barrier (BBB). Drugs that do not cross the BBB do not affect the brain, but do have interactions with the peripheral nervous system (PNS). For example, the second-generation antihistamine loratadine does not cause drowsiness (induced by CNS histamine receptors) but will still act on peripheral histamine receptors.
The mechanism of action of a drug describes how it interacts with the body to express its effects. Drugs work by interfering with the chemical transmission of neurotransmitters, which can in turn cause intracellular cascades to occur and gene expression to change. This interference is classified based on how they interact. Agonists mimic the action of a neurotransmitter by binding to receptors in the synapse. Antagonists inhibit the action of a neurotransmitter, usually by binding to postsynaptic receptors and disallowing action at that site. Reuptake inhibitors, like that of SSRIs, inhibit the reuptake of neurotransmitters by the presynaptic membrane transport proteins (SERT, DAT, etc). This increases extracellular concentration of the neurotransmitter.
# Numisid

The following project aims to provide a classification system for coins and other items of numismatic interest, generically and individually:
- to allow for exact identification of particular types of coins; - for the organisation of public and private collections; - to facilitate die studies and other research into coins; - to allow provenance of coins to be identified
The classification system; top level:
0.00.00... : ancient coins (manufactured before c. 500 AD)
1.00.00... : medieval coins (manufactured c. 500-1500 AD)
2.00.00... : modern coins (manufactured after c. 1500 AD)
3.00.00...: Islamic coins (generally pre-1900)
4.00.00... : tokens, tesserae, checks, passes
5.00.00... : historical and art medals
6.00.00... : civilian and military orders and decorations
7.00.00... : plaques
8.00.00... : miscellany
# Nursery rhymes and songs/Five Little Monkeys Jumping on the Bed

Five little monkeys jumping on the bed,
One fell down and bumped his head,
Mama called the doctor and the doctor said,
No more monkeys jumping on the bed!
Four little monkeys jumping on the bed,
One fell down and bumped his head,
Mama called the doctor and the doctor said,
No more monkeys jumping on the bed!
Three little monkeys jumping on the bed,
One fell down and bumped her head,
Mama called the doctor and the doctor said,
No more monkeys jumping on the bed!
Two little monkeys jumping on the bed,
One fell down and bumped his head,
Mama called the doctor and the doctor said,
No more monkeys jumping on the bed!
One little monkey jumping on the bed,
She fell down and bumped her head,
Mama called the doctor and the doctor said,
Put those monkeys back to bed!
Five Little Monkeys is a popular counting-out nursery rhyme, similar in nature to “Five Little Ducks” or Five Little Speckled Frogs.
Five Little Monkeys Finger Play
The song has an associated fingerplay, each verse being represented by an action. First the number of the monkeys left jumping on the bed is shown, followed by a hand falling and tapping one’s head (signifying a bump in the head). This is followed by a hand gesture mimicking a telephone call (calling the doctor) and wagging the finger during the last part (No more monkeys jumping on the bed).
# Numerical semigroup ring/3,4,5/Unitary operators/Exercise

Determine for the numerical semigroup ring $K[U^{3},U^{4},U^{5},\ldots ]$ unitary differential operators for the elements $U^{3},U^{4},U^{5}$.
# Nursery rhymes and songs

Nursery rhymes and songs help develop language skills as well as physical development and numeracy and are an essential part of pre-school education.

## Action songs and rhymes

Many songs and rhymes have a physical component.
* Wind the Bobbin Up
* Twinkle, Twinkle, Little Star
* I'm a Dingle Dangle Scarecrow
* If You're Happy and You Know it
* Sleeping Bunnies
* Ring around the Rosie
* Head, Shoulders, Knees and Toes
* Two Little Dickie Birds
* The Grand Old Duke of York
* Do the Hokey Pokey
* Trit Trot to Boston
* Tommy Thumb / Daddy Finger
* Wheels on the Bus
* Pat-a-Cake
* I'm a Little Teapot
* The Itsy Bitsy Spider
* One Potato, Two Potato, Three Potato, Four
* Round and Round the Garden
* What Do You Do With a Drunken Sailor

## Numeracy rhymes and counting

Many songs involve counting up and down. These songs can help your child become comfortable with counting.
* Five Little Monkeys Jumping on the Bed
* One, Two, Three, Four, Five, Once I Caught a Fish Alive
* Five Little Ducks Went Swimming One Day
* Five Fat Sausages Sizzling in a Pan
* Bell Horses
* Hickory Dickory Dock
* Zoom, Zoom, Zoom, We're Going to the Moon
* Five Little Speckled Frogs

## Other classic rhymes and songs

* Humpty Dumpty
* Yankee Doodle Went to Town
* Old McDonald Had a Farm
* Hey Diddle, Diddle
* My Bonnie Lies Over the Ocean
* You Are My Sunshine
# Materials Science and Engineering/Doctoral review questions/Oral Schedule

| Time | Student | O'Handley | Wuench | Kimerling | Thompson | Tuller | Gradecek | Ross | Stellacci | Fitz | Michel |
| 5th 9:30 am | LB | | LB | | LB | | LB | | | | |
| 5th 11 am | MB | MB | MB | | MB | | | | | | |
| 5th 1:30 pm | AC | | | | AC | | | AC | | | AC |
| 5th 3 pm | TC | | | | | | | TC | | TC | TC |
| 6th 9:30 am | JY | JY | | JY | | | JY | | | | |
| 6th 11 am | SK | SK | | SK | | | | | SK | | |
| 6th 1:30 pm | MS | MS | | | | | MS | | | MS | |
| 6th 3 pm | KV | | | KV | | KV | KV | | | | |
| 7th 10 am | GW | | | GW | | | | | | GW | GW |
| | ZR | | | | | | | | | | |
| 14th 12:30 pm | DG | | DG | | DG | | | DG | | | |
| 15th | JT | | JT | JT | | | | JT | | | |
# Materials Science and Engineering/Doctoral review questions/Micro and Nanoscale Processing

Overview of the History of the IC
Semiconductor and Device Physics
Thermodynamics
Kinetic Theory of Gases
Defect Chemistry
Bulk Crystal Growth
Microscopic Theory of Crystal Growth
Surfaces and Interfaces
Vapor Phase Epitaxial Film Growth
Evaporative Deposition
Chemical Vapor Deposition
Reactive Film Formation
Solution Growth
Rate Theory
# Materials Science and Engineering/Doctoral review questions/Thermodynamics

Partition Function
Solution Theory
Stirling Approximation
Solution theory
Entropy equations
Molar volume vs. composition plot
General heat capacity
Equilibrium condition with 1st and 2nd law
# Materials Science and Engineering/Doctoral review questions/Mechanics of Material

True stress / strain
Viscoelastic Response
Peach-Koehler
Stoney Formula
Mohr's Circle
Failure Criteria
$K_{I}$
$K_{IC}$
Methods of Creep
Deformation of single crystal
Finding modulus in arbitrary direction
Stiffness and compliance
Equibiaxial modulus
Strain energy
# Materials Science and Engineering/Equations/Electronic Materials
## Electrons
### Conductivity and Ohm's Law

    $U$: applied potential difference
    $L$: length
    $E$: electric field
    $\tau$: average time between collisions (mean free time, relaxation time, collision time)
    $v_{D}$: drift velocity
    $J$: electric current density
    $N_{e}$: multiply the drift velocity by the density of electrons
    $\sigma$: electrical conductivity