OpenLLM-France/wikimedia huggingface dataset:
# Next Generation Sequencing (NGS)/Genotyping by sequencing

Genotyping By Sequencing (GBS) is a method of cataloguing genetic variation between individuals on a common reference genome by using Next Generation Sequencing.

## Overview

Genetic variation between individuals is a key component of explaining phenotype, traits or characteristics. For this reason, cataloguing variations between individuals is an important step towards understanding, predicting, and ultimately engineering biology.
There are many methods of cataloguing variation between individuals. Genotyping By Sequencing (GBS) being a common method.
GBS relies on generating sequencing data for an individual which is aligned to the reference genome. Variations are then called on the reference using a variety of methods.

### Useful background

There are two key 'biological' concepts related to GBS, sequencing, alignment and genotyping.
From an informatics perspective, imputation.

### Objective

For a given individual, GBS produces a catalogue of variation for that individual. It is a relatively cheap and 'un-biased' method of discovering variations, not being limited to variations within genes, or transcripts, and without any prior expectation of polymorphic sites.

### Biological questions

Variation from GBS can be used to explain quantitative differences between individuals, better understand genetic relationships between groups of individuals, allow high density genetic maps to be constructed. GWAS.

## Inputs and outputs
### Inputs

* A reference genome
* Whole Genome Sequencing over one or more individuals.

### Outputs

* For each individual, a list of variant loci.
* Variations may include SNPs, InDels, or Structural Variations, depending on the sequencing technology used.

## Experimental design

There are two broad approaches to GBS, 1) relatively high depth of coverage over N individuals, or 2) relatively low level coverage of N groups of individuals (with relativly high coverage per group).
If only short read sequencing technology is used, then only SNPs and small InDels will be discovered. If longer reads and paired-end sequencing technology is used, larger InDels and structural variation may be discovered.

## Typical steps in the method
### Sample collection
#### Summary

    Brief bit of information.

### Sequencing
#### Summary

    Brief bit of information.

### QC and filtering
#### Summary

    Brief bit of information.

### Alignment
#### Summary

    Brief bit of information.

### Genotype calling
#### Summary

    Brief bit of information.

### Data submission
#### Summary

    Brief bit of information.

## Next steps

Depending on the type of experiment, GWAS, GSEA, Genetic Mapping.

## Workflows
### Example galaxy workflow

Link to an example galaxy workflow for for the method (including example datasets) on a given galaxy instance or to the XML document describing the workflow.

### Example command line workflow
## Discussion

POV discussion about the method.
Links to related discussion on BioStar: Genotyping By Sequencing on Biostars
# Macroeconomics/Aggregate Supply and Demand

Aggregate Demand - is the total of goods and services in an economy that people are willing and able to purchase at a given price over a period of time.
Aggregate Supply- is the total of goods and services in an economy that is produced at a given price over a period of time.
# Macroeconomics/Business Cycle
## Business Cycles

Business cycles or economic fluctuations are the upswings and downswings in aggregate economic activity. Business cycles are composed of two phases and two turning points.
The sequence from one peak to the next, or from one trough to the next, is a business cycle. The pattern of contraction–trough–expansion–peak occurs over and over again but not at regular, predictable intervals.
# Macroeconomics/Central Banks

Central banks are national banks that primarily control the monetary policy of the national economy, through changes in the interest rate. However, they also perform other duties, such as holding reserves of foreign currency, bankrolling government borrowing, and acting as the 'banker's bank', or the 'lender of last resort'.
There are two types of central bank, those that are state-controlled or at best quasi-independent, and those that are fully independent such as the US Federal Reserve and UK Bank of England (since 1997). Due to the potential for political interference in economic policy, with aims other than macroeconomic stability, the potential for infamous boom and bust cycles in an economy is greater for non-independent central banks.

## Further Reading

* Central Bank - recommended for further detail and clarification
# Functional Analysis/Harmonic Analysis
## Introduction

Harmonic Analysis is the study of the decomposition of representations of abstract algebraic structures acting on topological vector spaces.
Note: A table of the math symbols used below and their definitions is available in the Appendix.
* Foreword
* Old Introduction
* Manual of Style – How to read this wikibook
* The set theory notation and mathematical proofs, from the book Mathematical Proof
* The experience of working with calculus concepts, from the book Calculus
Part 1: General theory of Locally Compact Groups.

## Topological Groups

* Exercises
** Hints
** Answers
* Topological Group - Definition and elementary properties.

## Locally Compact Groups

* Locally Compact Groups - Definition and Elementary Properties

## Topic 1: Fell Bundles

Part 2 Reductive Groups:

## Appendices

Here, you will find a list of unsorted chapters. Some of them listed here are highly advanced topics, while others are tools to aid you on your mathematical journey. Since this is the last heading for the wikibook, the necessary book endings are also located here.
* List of Mathematical Symbols
* List of Theorems
* References
* Index
# Functional Analysis/Harmonic Analysis/Section 1 Exercises

1) Give as many examples as you can of topological groups which do not fall within any of the examples we gave in section Functional Analysis 9.1.
2) Prove that the inverse of an isomorphism.
3) show that for each $x\in G$ the maps $L_{x}(y)=xy$ and $R_{x}(y)=yx$ are topological group homomorphisms.
4)
# Functional Analysis/Harmonic Analysis/Locally Compact Groups
## Introduction

In this section we define the most well-known class of topological groups, namely locally compact groups. This class includes compact groups which in turn includes all finite groups, finite-dimensional Lie groups, etc.

## Exercises

* Exercises
** Hints
** Solutions

## Preliminaries

Definition 9.2.1: A locally compact group is a topological group whose underlying topological space is locally compact.
Examples:
* All compact, and therefore all finite groups are locally compact.
* A discrete group is always locally compact.
* Any finite-dimensional vector space is a locally compact group (equipped with addition).
The Hilbert space $l^{2}(\mathbb {N} )$ is not locally compact in the norm topology.
Proposition: An open subgroup of a locally compact group is always closed. A closed subgroup of a locally compact group is locally compact.
Proof: Indeed, let $H\subset G$ be an open subgroup of $G$. Choose a set $\{y_{j}\in G|\ j\in J\}$, one $y_{j}$ for each class in $G/H$, but choosing $e$ for the class of $H$. We then have the disjoint union $G=\sqcup _{j\in J}y_{j}H$. Since left multiplication by a given element $y_{j}$ is a homeomorphism between $H$ and $y_{j}H$, we have that each such set is open in $G$. Therefore the complement of $H=eH$ is open in $G$ and therefore $H$ is also closed.
If now $H\subset G$ be an closed subgroup of $G$, let $x\in H$. There exists a compact neighborhood $X$ of $x$ in $G$. But then the intersection $X\cap H$ is a compact neighborhood of $x$ in $H$. QED.
Combining the statements in the last proposition we conclude that an open subgroup of a locally compact group is also locally compact.
Proposition: Let $G$ be a topological group. In order for $G$ to be locally compact it is necessary and sufficient that the neutral element $e$ possesses a compact neighborhood.
Proof: Indeed, if $X$ is a compact neighborhood of $e$, then $Xx$ is a compact neighborhood of $x$ for any $x\in X$, since $Xx=R_{x}(X)$ is the image of a continuous map by exercise (ref) (left and right multiplication maps). QED.

## Appendices

Here, you will find a list of unsorted chapters. Some of them listed here are highly advanced topics, while others are tools to aid you on your mathematical journey. Since this is the last heading for the wikibook, the necessary book endings are also located here.
* List of Mathematical Symbols
* List of Theorems
* References
* Index
# Messier Index/M110

Messier 110 (also known as M110 and NGC 205) is a w:dwarf elliptical galaxy that is a satellite of the w:Andromeda Galaxy. M110 contains some dust and hints of recent star formation, which is unusual for dwarf elliptical galaxies in general.

## History

M110 was serendipitously discovered on August 10, 1773 by w:Charles Messier, who was making observations of the Andromeda Galaxy at the time. The galaxy was independently discovered by w:Caroline Herschel on August 27, 1783; her brother w:William Herschel described her discovery in 1785. Although the galaxy was not originally included in Messier's first catalogue, it was later added by w:Kenneth Glyn Jones in 1966. M110 remains the last object added to the Messier catalog.
In 1999, Johnson and Modjaz discovered a w:nova in M110.

## References

* ↑ McConnachie, A. W.; Irwin, M. J.; Ferguson, A. M. N.; Ibata, R. A.; Lewis, G. F.; Tanvir, N. (2005). "Distances and metallicities for 17 Local Group galaxies". Monthly Notices of the Royal Astronomical Society. 356 (4): 979–997. doi:10.1111/j.1365-2966.2004.08514.x.{{cite journal}}: CS1 maint: multiple names: authors list (link)
* ↑ R. W. Sinnott, editor (1988). The Complete New General Catalogue and Index Catalogue of Nebulae and Star Clusters by J. L. E. Dreyer. Sky Publishing Corporation and Cambridge University Press. ISBN 0-933-34651-4. {{cite book}}: |author= has generic name (help)
* 1 2 3 4 5 6 7 8 "NASA/IPAC Extragalactic Database". Results for NGC 205. Retrieved 2006-11-29.
* 1 2 A. Sandage, J. Bedke (1994). Carnegie Atlas of Galaxies. Washington, D.C.: Carnegie Institution of Washington. ISBN 0-87279-667-1.
* 1 2 3 K. G. Jones (1991). Messier's Nebulae and Star Clusters (2nd ed.). Cambridge: Cambridge University Press. ISBN 0-521-37079-5.
* ↑ Hartmut Frommert and Christine Kronberg (w:August 30, w:2007). "Messier Object 110". Students for the Exploration and Development of Space. Archived from the original on 1999-04-20. Retrieved 2007-10-14. {{cite web}}: Check date values in: |date= (help)
* ↑ van den Bergh, Sidney (April 2000), "Updated Information on the Local Group", The Publications of the Astronomical Society of the Pacific, 112 (770): 529–536, doi:10.1086/316548{{citation}}: CS1 maint: date and year (link)

## External links

* SEDS: Elliptical Galaxy M110
# Messier Index/M14

Messier 14 (also known as M14 or NGC 6402) is a w:globular cluster in the w:constellation w:Ophiuchus. It was discovered by w:Charles Messier in w:1764.
At a distance of about 30,000 light-years, M14 contains several hundreds of thousands of w:stars. At an w:apparent magnitude +7.6 it can be easily observed with w:binoculars. Medium-sized w:telescopes will show some hint of the individual stars of which the brightest is of magnitude +14.
The total w:luminosity of M14 is in the order of 400,000 times that of the w:Sun corresponding to an w:absolute magnitude of -9.12. The shape of the cluster is decidedly elongated. M14 is about 100 light-years across.
A respectable total of 70 w:variable stars is known in M14, many of the W Virginis variety common in globular clusters. In w:1938, a w:nova appeared although this was not discovered until w:photographic plates from that time were studied in w:1964. It is estimated that the nova reached a maximum brightness of magnitude +9.2, over five times brighter than the brightest 'normal' star in the cluster.
Slightly over 3° southwest of M14 lies the faint globular cluster NGC 6366.

## External links

* SEDS Messier pages on M14
* M14, Galactic Globular Clusters Database page

## References

* 1 2 3 4 "SIMBAD Astronomical Database". Results for NGC 6402. Retrieved 2006-11-15.
* ↑ distance × sin( diameter_angle / 2 ) = 50 ly. radius
# Messier Index/M13

Messier 13 or M13 (also designated NGC 6205 and sometimes called the Great Globular Cluster in Hercules or the Hercules Globular Cluster) is a w:globular cluster in the w:constellation of Hercules.

## Discovery and visibility

M13 was discovered by w:Edmond Halley in 1714, and catalogued by w:Charles Messier on June 1, 1764.
It is located at w:right ascension 16$^h$ 41.7$^m$ and w:declination +36° 28'. With an w:apparent magnitude of 5.8, it is barely visible with the w:naked eye on a very clear night. Its diameter is about 23 arc minutes and it is readily viewable in small telescopes. Nearby is w:NGC 6207, a 12th magnitude edge-on galaxy that lies 28 arc minutes directly north east. A small galaxy, IC 4617, lies halfway between NGC 6207 and M13, north-northeast of the large globular's center.

## Characteristics

M13 is about 145 light-years in w:diameter, and it is composed of several hundred thousand w:stars, the brightest of which is the w:variable star V11 with an apparent magnitude of 11.95. M13 is 25,100 light-years away from w:Earth.

## Arecibo message

The w:Arecibo message of 1974, designed to communicate the existence of human life to hypothetical extraterrestrials, was transmitted toward M13. The reason was that with a higher star density, the chances of a life harboring planet with intelligent life forms, were higher.

## Literary references

* The w:science fiction novellas "w:Sucker Bait" by w:Isaac Asimov and "w:Question and Answer" by w:Poul Anderson take place on Troas, a world within M13.
* In the science fiction series w:Perry Rhodan, M13 is the location of Arkon, the home world of the race of Arkonides.
* In author Dan Simmon's w:Hyperion Cantos the Hercules cluster is where Earth was secretly moved to after it was supposedly destroyed.
* In w:The Sirens of Titan, w:Kurt Vonnegut writes "Every passing hour brings the Solar System forty-three thousand miles closer to Globular Cluster M13 in Hercules -- and still there are some misfits who insist that there is no such thing as progress."

## External links

* Messier 13, SEDS Messier pages
* Messier 13, Galactic Globular Clusters Database page
* Messier 13, High-resolution LRGB image based on 2 hrs total exposure
* Messier 13, Image by Waid Observatory
* NightSkyInfo.com - M13, the Hercules Globular Cluster
* Photometric study of the V2 cepheid in M13
* Period, Amplitude and Light Curve of V38 in M13
* Great Globular Cluster in Hercules (Messier 13/NGC 6205)
* M13 images taken by Stargazer-Observatory
* M13

## References

* 1 2 3 4 "SIMBAD Astronomical Database". Results for NGC 6205. Retrieved 2006-11-15.
* ↑ Leonard, Peter J. T.; Richer, Harvey B.; Fahlman, Gregory G. "The mass and stellar content of the globular cluster M13".{{cite web}}: CS1 maint: multiple names: authors list (link)
* ↑ distance × sin( diameter_angle / 2 ) = 84 ly. radius
# Messier Index/M108

Messier 108 (also known as NGC 3556) is an edge-on w:spiral galaxy in the w:constellation Ursa Major. It was discovered by w:Pierre Méchain in 1781 or 1782.

## External links

* SEDS: Spiral Galaxy M108

## References

* ↑ R. W. Sinnott, editor (1988). The Complete New General Catalogue and Index Catalogue of Nebulae and Star Clusters by J. L. E. Dreyer. Sky Publishing Corporation and Cambridge University Press. ISBN 0-933-34651-4. {{cite book}}: |author= has generic name (help)
* 1 2 3 4 5 6 7 8 9 "NASA/IPAC Extragalactic Database". Results for NGC 3556. Retrieved 2007-06-21.
* ↑ Q. Daniel Wang et al., [http://arxiv.org/abs/astro-ph/0308150v1 Chandra Observation of the Edge-on Galaxy NGC 3556 (M 108): Violent Galactic Disk-halo Interaction Revealed]
* ↑ Kepple, George Robert (1998). The Night Sky Observer's Guide, Volume 2. Willmann-Bell, Inc. p. 399. ISBN 0-943396-60-3. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
# Messier Index/M106

Messier 106 (also known as NGC 4258) is a w:spiral galaxy in the w:constellation w:Canes Venatici. It was discovered by w:Pierre Méchain in w:1781. M106 is at a distance of about 22 to 25 million w:light-years away from w:Earth. It is also a Seyfert II galaxy, which means that due to w:x-rays and unusual w:emission lines detected, it is suspected that part of the galaxy is falling into a w:supermassive black hole in the center. w:NGC 4217 is a possible companion galaxy of Messier 106.

## Characteristics

M106 has a water vapor w:maser that is seen by the 22GHz line of ortho-H$_2$O that evidences dense and warm molecular gas. Water masers are useful to observe nuclear w:accretion disks in w:active galaxies. M106 has a slightly warped, thin, almost edge-on w:Keplerian disk which is on a subparsec scale. It surrounds a central area with mass four × 10$^7$M$_⊙$.

## External links

* Spiral Galaxy M106 @ SEDS Messier pages
* 4/10/07: M106 - Mystery Spiral Arms Explained? The X-ray/radio-visible extra spiral arms in M106/NGC 4258.
* Spiral Galaxy Messier 106 (NGC 4258) at the astro-photography site of Mr. Takayuki Yoshida.
* M106 image taken by Stargazer Observatory

## References

* 1 2 3 4 5 6 7 8 9 "NASA/IPAC Extragalactic Database". Results for Messier 106. Retrieved 2006-12-07.
* ↑ J. L. Tonry, A. Dressler, J. P. Blakeslee, E. A. Ajhar, A. B. Fletcher, G. A. Luppino, M. R. Metzger, C. B. Moore (2001). "The SBF Survey of Galaxy Distances. IV. SBF Magnitudes, Colors, and Distances". Astrophysical Journal. 546 (2): 681–693. doi:10.1086/318301.{{cite journal}}: CS1 maint: multiple names: authors list (link)
* ↑ Macri, L. M.; Stanek, K. Z.; Bersier, D.; Greenhill, L. J.; Reid, M. J. (2006). "A New Cepheid Distance to the Maser-Host Galaxy NGC 4258 and Its Implications for the Hubble Constant". The Astrophysical Journal. 652 (2): 1133–1149. doi:10.1086/508530.{{cite journal}}: CS1 maint: multiple names: authors list (link)
* ↑ Bonanos, Alceste Z. (2006). "Eclipsing Binaries: Tools for Calibrating the Extragalactic Distance Scale". Binary Stars as Critical Tools and Tests in Contemporary Astrophysics, International Astronomical Union. Symposium no. 240, held 22-25 August, 2006 in Prague, Czech Republic, S240, #008.
* ↑ Humphreys, E. M. L.; Greenhill, L. J.; Reid, M. J.; Argon, A. L.; Moran, J. M. (2004). "Improved Maser Distance to NGC 4258". American Astronomical Society Meeting 205, #73.01; Bulletin of the American Astronomical Society. 36: 1468.{{cite journal}}: CS1 maint: multiple names: authors list (link)
* 1 2 "SIMBAD Astronomical Database". Results for Messier 106. Retrieved 2006-12-07.
* ↑ "A spiral galaxy with a strange core".
* ↑ Henkel, C.; Peck, A. B.; Tarchi, A.; Nagar, N. M.; Braatz, J. A.; Castangia, P.; Moscadelli, L. (June 2005). "New H2O masers in Seyfert and FIR bright galaxies". Astronomy and Astrophysics. 436 (1): 75–90. doi:10.1051/0004-6361:20042175.{{cite journal}}: CS1 maint: multiple names: authors list (link)
# Messier Index/M11

The Wild Duck Cluster (also known as Messier 11, or NGC 6705) is an w:open cluster in the w:constellation w:Scutum. It was discovered by w:Gottfried Kirch in 1681. w:Charles Messier included it in his catalogue in 1764.
The Wild Duck Cluster is one of the richest and most compact of the known open clusters, containing about 2900 w:stars. Its age has been estimated to about 220 million years. Its name derives from the brighter stars forming a triangle which could represent a flying flock of w:ducks.

## External links

* Messier 11, SEDS Messier pages
* Messier 11 - LRGB result based on 2 hrs total data
# Messier Index/M15

Messier 15 or M15 (also designated NGC 7078) is a w:globular cluster in the w:constellation Pegasus. It was discovered by w:Jean-Dominique Maraldi in w:1746 and included in w:Charles Messier's catalogue of w:comet-like objects in w:1764. At an estimated 13.2 billion years old, it is one of the oldest known globular clusters.
M15 is about 33,600 w:light-years from w:Earth. It has an w:absolute magnitude of -9.2 which translates to a total w:luminosity of 360,000 times that of the w:Sun. Messier 15 is one of the most densely packed globulars known in the w:Milky Way galaxy. Its core has undergone a contraction known as 'w:core collapse' and it has a central density cusp with an enormous number of stars surrounding what may be a central black hole.
Messier 15 contains 112 w:variable stars, a rather high number. It also contains at least 8 w:pulsars, including one double w:neutron star system, M15 C. Moreover, M15 houses w:Pease 1, one of only four w:planetary nebulae known to reside within a globular cluster, which was discovered in w:1928.
To the amateur w:astronomer Messier 15 appears as a fuzzy star in the smallest of w:telescopes. Mid to large size telescopes (at least 6 in./150 mm diameter) will start to reveal individual stars, the brightest of which are of magnitude +12.6.
* The central square arcminute of M15 imaged using the w:lucky imaging technique
* Messier 15 Amateur Image Courtesy Hunter Wilson

## External links

* Messier 15, SEDS Messier pages
* Messier 15, Galactic Globular Clusters Database page
* Globular Cluster Photometry With the Hubble Space Telescope. V. WFPC Study of M15's Central density Cusp
* Wikisky.org SDSS image of M15

## References

* 1 2 3 "SIMBAD Astronomical Database". Results for NGC 7078. Retrieved 2006-11-16.
* ↑ distance × sin( diameter_angle / 2 ) = 88 ly. radius
# Messier Index/M107

Globular Cluster M107 (also known as w:Messier Object 107 or NGC 6171) is a very loose w:globular cluster in the w:constellation w:Ophiuchus. It was discovered by w:Pierre Méchain in April w:1782 and independently by w:William Herschel in w:1793. It wasn't until w:1947 that w:Helen Sawyer Hogg added it and three other objects discovered by Méchain to the list of Messier objects.
M107 is close to the w:galactic plane at a distance of about 20,900 w:light-years from w:Earth. There are 25 known w:variable stars in this cluster.

## External links

* SEDS Messier pages: Messier 107
* Messier 107, Galactic Globular Clusters Database page

## References

* 1 2 3 4 "SIMBAD Astronomical Database". Results for NGC 6171. Retrieved 2006-11-16.
* ↑ distance × sin( diameter_angle / 2 ) = 39.5 ly. radius
# Messier Index/M12

Messier 12 or M 12 (also designated NGC 6218) is a w:globular cluster in the w:constellation of w:Ophiuchus. It was discovered by w:Charles Messier on w:May 30, w:1764.
Located roughly 3° in the sky from the cluster M10, M12 is about 16,000 w:light-years from Earth and has a spatial diameter of about 75 light-years. The brightest stars of M12 are of 12th magnitude. It is rather loosely packed for a globular and was once thought to be a tightly concentrated w:open cluster. Thirteen w:variable stars have been recorded in this cluster.
A study published in w:2006 concluded that this cluster has an unusually low number of low mass stars. The authors surmise that they were stripped from the cluster by the gravitational influence of the w:Milky Way.
* M12 core by HST, 3.18′ view
* M12, courtesy Hunter Wilson
* The Central Part of Messier 12. Credit: w:ESO

## External links

* Messier 12, SEDS Messier pages
* Messier 12, Galactic Globular Clusters Database page
* 'Stolen' stars article at Universe Today

## References

* 1 2 3 4 "SIMBAD Astronomical Database". Results for NGC 6218. Retrieved 2006-11-15.
* ↑ distance × sin( diameter_angle / 2 ) = 37.2 ly. radius