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# Encryption/ciphers/codes in Chinese

I am quite curious as to how you can perform simple encryption for the Chinese language.

Saw a similar question related to encryption/Chinese here: About cryptography in a character language, however the method of encryption appears to be quite complicated.

If I'm not mistaken, the method described in the answer above, requires something similar to a table which pre-maps certain characters to other characters; or the use of something like an One-time pad - both of which requires a fair amount of prior communication between both parties.

I was wondering if there is something simpler, what I have in mind is something like a Substitution cipher. That is, a way to encode the message easily, and also allowing the message to be decoded easily (if the secret key is known) or cracked given analysis or use of decoding techniques/knowledge.

For example, in English there are many ways to encrypt a message - some common/simple examples ROT13, Vigenere.

However, I can't seem to see how the concept of "pulling apart" a word can apply to Chinese characters.

For example, I can (fairly easily) encode the below using Vignere (key: chocolate), but how would I do so in Chinese?

I am learning Chinese --> K ha nslrgmpn Qjwyeli

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## migrated from chinese.stackexchange.comJan 31 '12 at 15:38

This question came from our site for students, teachers, and linguists wanting to discuss the finer points of the Chinese language.

I take your question to mean, how both historically and in the modern age one could construct a pen-and-paper cipher using the Chinese language.

As pointed out in the question, Chinese is a logographic langauge and therefore has a far greater number of characters than Phonetic systems. Historically this has cause chinese codes not to be based around the script.

The following claims are taken from a forum discussion and translation of ancient chinese codes for lack of a better source.

• Nüshu script may not have been intended for secrecy but it functions as such since it was almost exclusively used and readable by educated Chinese women. It was phonetic and had a set of 700 characters. This suggests that one could use the phonetic attributes of the chinese language as a basis for a reduced character set on top of which one could implement a code.

• In an earlier form of secret sharing, messages were cut into strips and delivered by different couriers.

The so called “阴书” was to write the document vertically and cut it into 3 sections. Sent 3 persons, and each person would hold one of the sections. They would depart in different times and using different paths. When the receiver received all 3 parts, he could get the whole thing of this secret document. If one of the messengers was captured by the enemies, the enemy would have difficulties to understand the secret document. As translated by the Chinese History Forum

• The technique of phrases is something I don't entirely understand I think the method is essentially to use the phonetic sound from ciphertext logographic characters to transmit a secret message. In english "eyesight hat very eight seashore create rat table" or "I ha-ve a se-cre-re-t"

“反切” (fan3 qie4) is a kind of phonetic system originated in ancient time to help document the pronunciation of Chinese language. The basic method for (fan3 qie4) is: Take the first word 上字 (shang4 zi4 - upper word) for its starting sound (or the consonant) and the second word (xia4 zi – lower word) for its ending sound (or the vowel). The tone would follow the ending sound. Therefore, a word is separated into two parts: 声母 (sheng mu3 – starting sound), 韵母 (yun4 mu3 – ending sound). Use the 声母 sheng mu adding a 韵母yun mu from another word to form the “反切” fan qie’s first word (or upper word). Use the 声母 sheng mu from another word adding a 韵母yun mu from this word to form the “反切” fan qie’s second word (or lower word). Use the lower word’s tone for the word’s tone. The first word’s starting sound and the second word’s ending sound is the pronunciation of the original word. As translated by the Chinese History Forum

• Code sticks were used in which each stick length represented a particular pre-agreed upon message. These stick lengths could be transmitted using signal fires without actually having to physically send the stick. More generally this technique is equivalent to code books which were also used by the ancient Chinese.

For example, one inch stick means victory. 9 inches stick means the army has broken the enemy army and captured the enemy generals. 8 inches stick means the enemy’s city (cities) has surrendered. 7 inches stick means successfully resisted the enemy’s army and the enemy’s army was gone. 6 inches stick means the army should be alert and defend the place diligently. As translated by the Chinese History Forum

• Grille ciphers have often been remarked as excellent pen and paper ciphers for chinese.

• While I can't find any historical reference to it, transposition ciphers seem completely compatible with the chinese language. Although one would have to choose the words carefully because some meaning would leak out as whole words are transposed rather than letters.

• A method of enciphering chinese characters similar to rot16 would be to write different characters on top of each other in different colors of ink. The key would state which color at each position was the correct character. For instance the key could be 'blue-red-red-black-green-blue'. One of the interesting features of such a scheme is that one could design the cipher text such that all possible keys encode an apparently valid and readable message. One advantage of this scheme would also be that it is secure against colorblind adversaries.

-

If you save the current page and examine the file with an hex editor, you will likely find that your example Chinese string is represented by the bytes

E6 88 91 E5 9C A8 E5 AD B8 E4 B8 AD E6 96 87

One option, very suitable for implementation by a machine, is to encipher the bytes representing the message in this (or other) format used by the machine. This will work well for a modern strong cipher, but quite poorly for a weak cipher like Vigenere. And it is very inappropriate for a hand cipher.

-

It seems I can't comment on answers because the question is no longer on the Chinese Q&A, but I wanted to support fgrieu's suggestion. Certain web services don't have much care for security, but they want to avoid containing keywords that are blocked by the Chinese Firewall. One I'm familiar with is PIMCloud, a cloud-supported IME, which does exactly what fgrieu suggested - reduces characters to the hexadecimal version of their unicode codepoint then performs a rot13-like substitution on these.

Obviously this is pretty difficult to do without a computer, but not impossible if you have a table of unicode codepoints (I know you rejected the 'great big substitution table' idea, but this was on the basis of requiring lots of communication rather than using something which is pretty easy for both sides to get hold of)

To use your example, 我在學中文 would first be changed to E68891E59CA8E5ADB8E4B8ADE69687.

Then this would be encrypted to 6E00196D14206D25306C30256E1E0F using a hexadecimal version of rot13 (rot8?)

To decode it, rot8 again to get back to E68891E59CA8E5ADB8E4B8ADE69687, then convert back to unicode*. A Vigenere cypher would also be possible, as long as the keyword was also hexadecimal, e.g. E5B7A7E5858BE58A9B instead of chocolate.

* by 'unicode' I mean UTF8.

-
Chinese computer users use standard keyboards. They construct the characters by typing latin letters (this system is called en.wikipedia.org/wiki/Hanyu_pinyin ), this process is reversible. (1). Write the chinese sentience in latin-alphabet using the Hanyu-Pinyin system, (2). apply rot13/vigenere, (3). type the result. It should be similar to your system but easier for users since it doesn't require doing UTF8 table look ups. –  Ethan Heilman Feb 1 '12 at 14:41
That wouldn't work very well - pinyin isn't actually reversible as multiple characters share the same pinyin - for example, 十 (ten) is pronounced the same way as 石 (stone). If you ignore the tones, it's even worse. In most cases it's possible to figure out that the wrong character has been used, but it's not lossless. –  Ironfrost Feb 6 '12 at 2:46
+1 Very interesting/good catch. I had just assumed that such a mapping would be reversible. I know this defeats the purpose of the exercise but what about translating a word into a phonetic alphabet (say english) and then using rot13. As a teenager me and some of my friends used online translation engines such as babel-fish as a form of code. –  Ethan Heilman Feb 6 '12 at 5:02
Yeah, unfortunately pinyin isn't a 1-1 mapping. Plus, in some Chinese speaking countries they don't learn pinyin, they learn zhuyin (en.wikipedia.org/wiki/Zhuyin). But same problem as pinyin - it isn't a 1-1 mapping. –  pyko Feb 6 '12 at 22:46


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## Pharyngulated!

November 24, 2008

Ha! Pure dumb luck has lead to me being linked to by PZ Myers! Now I’m the 95th fastest growing blog on WordPress. Gotta love pure dumb luck.

He’s tagged me with this meme.
1. Link to the person who tagged you.
2. Post the rules on your blog.
3. Write six random things about yourself.
4. Tag six people at the end of your post and link to them.
6. Let the tagger know when your entry is up.

Technically PeeZed hasn’t done number 5 but I’ll let him off because he has a proper job with fixed hours and yet seems to put it 10 hours solid blogging every day.

So, I’ve done 1 and 2. Now 3.

1. I have trouble pronouncing the letter “r” distinctly but only notice this when I hear recordings of my voice. I find it slightly embarrassing.
2. I am currently somewhat sleep-deprived and compensating with coffee. This may end badly.
3. I made the second round of University Challenge on BBC2 with the team from Nottingham. We lost the second round game to Leeds by the smallest possible margin. I contend that we was robbed.
4. I am the only person I’ve ever met who enjoyed the film “Velvet Goldmine”.
5. I don’t actually have to go work. Unlike postdocs in just about any other subject, who have to put in hours in labs or archives, as a mathematician I can work pretty much any schedule and anywhere provided I can occasionally convince people I’ve proven enough things. I don’t even live commuting distance from my office (mostly; I have digs down there).
6. I am yet to pass a driving test and haven’t taken any lessons in years. I also get claustrophobic on planes. If I could I would take the train everywhere.

Bonus fact: I know nearly no bloggers, even in a “people I know OL” sense.
Thus my esteemed collaborator toomuchcoffeeman gets a tag even though I know for a fact he’s way to busy, notedscholar gets tagged … just because, and the rest go to (more or less all) the people who’ve linked to my posts in the past and who let non-serious business on their blogs : Catsynth, mathmom, Blake Stacey and Reston Kid

## Just 2 England first team members still to get injured

November 19, 2008

This is getting silly. I fully expect to hear tomorrow morning that the bit of trouble John Terry was having with his foot has worsened to the point of losing a toe and that team doctors have ruled David James out of the game due to previously undiagnosed old age.

EDIT It’s Wednesday now!? I thought it was Tuesday all day. OK By “tomorrow morning” I meant “in the next 10 minutes”.
EDIT: No they were fine. And YAY England won.

## notedscholar- for real?

November 18, 2008

Before yesterday I had never heard of notedscholar but suddenly he’s commenting everywhere I look. First at Gower’s blog, then Pharyngula, then here. His blog Science Defeated is either the most subtle and brilliant satire of maths and science psychoceramics or it … isn’t.

It’s pretty eclectic stuff. One minute he’s supporting deutsche Physik. The next he’s quoting Noam Chomsky (whose worst put down of certain criticisms of “white male science” was that the term reminded him of “deutsche Physik”) as an infallible authority on physics. Then we have suggesting that the mathematicians of Asian civilizations smuggled phony negative numbers into mathematics because they had a “vested interest in the concept” but also attacking the idea that “colour of light” and “colour of a reflective object” are different uses of “colour” as colonialism.

My favourite is this on infinity.

According to math (and also its feisty sidekick, the English language), the number before infinity would be known as the “penultimate” in the series of all numbers. So in my opinion, the last number in the number line is the penultimate.

The author has clearly read at least a little about an awful lot and appears to have developed a fractally wrong understanding of it all. If we then add his rather self-assured assertion that “While the views expressed here are not always representative of academia at large, the views are nevertheless correct” it’s the most fascinatingly odd blog I’ve seen in ages.

So please, comment. Tell me if you think it’s real.

## Expat vs. Immigrant

November 17, 2008

I’m English and I live in Portugal. Since it’s very common for researchers to be working in countries other than there homeland, I would usually just define my status as “post doc”. Now, I was looking over things at Facebook (which I had more or less forgotten existed until they sent me an email yesterday) and I noticed they have a lot of expat groups. I have to confess that the word “expat” squicks me. It always brings up thoughts of Eldorado and of rich Brits in the Algarve who’ve lived there a decade and are proud that they have avoided learning any more Portuguese than “por favor” and “obrigado/a”. Since I have a Portuguese wife I don’t really relate to this. This isn’t actually very fair since I think a fair number of those (Brits, Germans, Americans…) who would self-identify as expats in Portugal don’t fit stereotypes of cultural arrogance or any other such nonsense but it’s what the word triggers in me.

My personal response to the word isn’t really the pint of this post though. Read the rest of this entry »

## Epic peer review fail

November 12, 2008

You’ve probably all seen this by now, but headesk. John “cousin of Joan” Baez describing how the editor in chief of Elsevier’s “Chaos, Solitons and Fractals” has been publishing a big pile of nonsense in his own journal.
This further strengthens my belief in the conjecture that for all $\epsilon >0$ the value that the big for-profit publishers add to a paper is less than $\epsilon$

## Lest we forget

November 11, 2008

For Armistice Day, some sad, beautiful songs about wars. Videos below the jump.
Read the rest of this entry »

## Pretty Möbius transform video is pretty

November 10, 2008

This is my favourite maths video ever.

## Songs for homesick Britons (part 1 of n for some n)

November 8, 2008

I’m feeling vaguely homesick today and trawling YouTube for music videos. I thought I ‘d share a couple

First are Blur who were pretty much the first band I really loved. They are playing “This Is a Low” which has lyrics based in part on the shipping forecast from Radio 4. Too few songs are based on the shipping forecast. It’s also quite startlingly lovely.

Second up, Billy Bragg singing Between the Wars. My elder sisters used to listen to Billy Bragg quite a lot when I was a kid. My dad seriously hated his voice, to the point were he just wouldn’t shut up about hating Billy Bragg’s voice. I usually start welling up around “Mine is a faith in my fellow man”.

## Gödel’s theorems on “In Our Time” by the BBC

November 5, 2008

Hat tip to Yemon Choi (via email) for this very interesting discussion of Gödel’s theorems on Radio 4. It features the aforementioned Marcus du Sautoy, John Barrow of Cambridge and Philip Welch of Bristol. It is pitched nicely with interest whether you are a professional mathematician or if you have no training in maths at all.

I was particularly glad to hear someone at least draw some attention to the philosophical trickiness of the usual popularization of the theorems which talks about “true statements that cannot be proved in the system”. This always erks me a bit, because it isn’t entirely clear that a statement in a formal system has a meaning that survives being taken out of the system (and if it does that is a pretty subtle thing for this level of discussion). Thus just hearing the warning (from Welch?) about the theorems and their proofs being basically syntactic rather than semantic was nice. (It was du Sautoy giving the usual “true statement” version with but I will forgive him since he does so much good work and most mathematicians seem to be happy with the truthiness).

Incidentally, I suspect my feelings of awkwardness towards the claim we can talk about “truth” outside of “proof in a given system” may be related to the sort of maths I work in. My “grand-supervisor” Garth Dales discusses here how those who work in abstract analysis (and in algebra) tend to view their work as essentially formal (although using “realistic pictures” to help us).

## Marcus du Sautoy FTW

November 1, 2008

The University of Oxford have appointed pure mathematician Marcus du Sautoy to the Simonyi Chair for Public Understanding of Science. This makes him Richard Dawkins’ successor, although I doubt Graun Unltd will be giving him his own category just yet. As well as being a very distinguished researcher, MdS is pure win as populizer. I loved Music of the Primes and his his Faraday Christmas lectures for kids were pitch perfect. Here he is with his Recreativo Hackney team mates and the infinity of primes:

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Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

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Introduction: Matthew Doty

edited March 2018 in Chat

Hi! I am a software engineer.

I program in Scala for work, and Haskell and Isabelle/HOL in my free time.

My interests are: computer assisted verification, probability, decision algorithms and mathematical logic.

• Options
1.

Sounds great! If you use Haskell and HOL you must already have some category theory flowing through your veins.

What's Isabelle, exactly?

Comment Source:Sounds great! If you use Haskell and HOL you must already have some category theory flowing through your veins. What's Isabelle, exactly?
• Options
2.

Isabelle/HOL is a dialect of HOL developed by the University of Cambridge and Technische Universität München. It’s original author is Laurence Paulson. It differs from HOL5 and HOL Light as it’s type system can express type classes. I use it because I prefer its automation tools.

Thank you so much for hosting this course. There’s always something to learn! This is a marvelous opertunity to get better at category theory

Comment Source:[Isabelle/HOL](https://isabelle.in.tum.de/) is a dialect of HOL developed by the University of Cambridge and Technische Universität München. It’s original author is Laurence Paulson. It differs from HOL5 and HOL Light as it’s type system can express type classes. I use it because I prefer its automation tools. Thank you so much for hosting this course. There’s always something to learn! This is a marvelous opertunity to get better at category theory
• Options
3.

Hi Matthew, do you get to explore any of your listed interests for work? If so, where do you work?

Comment Source:Hi Matthew, do you get to explore any of your listed interests for work? If so, where do you work?
• Options
4.

The Krein-Milman stuff is up.

This material is much easier than the length might imply. If you find this material interesting the fourth part has the definition of an extreme subregion. You may want to prove a couple of the statements. All but the algebraic one are easy.

Comment Source:The Krein-Milman stuff is up. This material is much easier than the length might imply. If you find this material interesting the fourth part has the definition of an extreme subregion. You may want to prove a couple of the statements. All but the algebraic one are easy.


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WIKI DEFINITION

# Solar Position

The position of the Sun in the sky varies continually during the day and also changes seasonally throughout the year. Sun position is also very location-dependant, so it is critical that you know the latitude and longitude of your development site before you begin any calculations.

Figure 1 - Animation showing both annual (left) and hourly (right) sun-path changes for the 21st day of each month for latitude -32

Despite our fundamental knowledge of solar position (experiencing it every day), calculating it at any specific date and time is not a trivial exercise. The off-axis rotation of the Earth and its elliptical orbit around the Sun add significant complexity to the equations required. For more information on this, see the Seasonal Variation topic.

Whilst an accurate manual calculation method is provided on this site, it is often much simpler and far quicker to read Sun positions directly from a table or a sun-path diagram. Such tables and diagrams are readily available for a range of locations.

You can use the on-line Solar Position Calculator to obtain the position at a specific time at 1/2 hourly values throughout the day.

## Solar Azimuth and Altitude

The position of the sun is generally given as an azimuth and altitude angle:
• Azimuth represents the horizontal angle of the sun relative to true north. This angle is always positive in a clockwise direction from north when viewed from above, and is usually given in the range -180° < azi < 180°.
• Altitude represents the vertical angle the sun makes with the horizontal ground plane. It is given as an angle in the range 0° < alt < 90°.

Figure 3 - Sun position in the sky is typically given as an azimuth and altitude angle.

## Local and Solar Time

In most locations, there will normally be a difference between solar and local time. Solar time is determined by the position of the Sun. At noon it is
directly overhead, with sunrise and sunset occurring at symmetrical times either side of noon. Local (or clock) time is determined by the local time zone and is taken at a reference longitude. For example, the local time zone for Perth is taken at a longitude of 120° (in the middle of Western Australia). The longitude of Perth, however, is 116°.

Figure 4 - World time zones coded by colour.

For each degree of difference in longitude between the actual and reference, there is a 4 minute time difference. Thus, to convert solar time to local time, use the following formula:

$\large T_{local} = T_{solar} + [(Longitude - Longitude_{ref}) \times 4]$

The reference longitude (Longituderef) refers to the longitude at which the time-zone is calculated. If thisw is not known, you can easily work it out from the time zone hourly offset. This is given as the decimal hour of the time zone offset multiplied by 15 degrees (TZ * 15). Thus, a time zone of +9.5 hours would have a reference longitude of 142.5° (9.5 * 15). Similarly, -5.0 hours would be 76°.

## Positional Characteristics

The most important characteristic of solar position is its seasonal variation. During summer in the southern hemisphere, the Sun rises slightly south of east and sets slightly south of west. In the northern hemisphere it rises slightly north of east and sets slightly north of west. In winter it rises slightly north of east and sets slightly north of west (again, opposite in the northern hemisphere).

In both hemispheres the Sun rises earlier and sets later in summer than in winter. The degree of this effect is greater the closer the site is to either pole.

### Sun-Path Selector

The following stereographic sun-path diagram clearly illustrates this pattern. For details on how to read these diagrams, see the sun-path diagram topic. Use the selector below the diagram to look at the characteristic patterns at a range of different latitudes. Notice the significant angular spread of the sun-path at higher latitudes.

<img src="http://naturalfrequency.com/files/nf/solar/stereo-30.gif" name="imageSunPath" id="imageSunPath" />

Select Site Latitude:
<select name='selectSunPath' onChange='imageSunPath.src="http://naturalfrequency.com/files/nf/solar/"+selectSunPath.options[selectSunPath.selectedIndex].value'>
90° (North Pole)
75° (Greenland)
60° (Norway)
45° (France)
30° (Isreal)
15° (Thailand)
0° (Equator)
-15° (Darwin)
<option value="stereo-30.gif" selected>-30° (Perth)
-45° (Wellington)
-60° (Antarctic Ocean)
-75° (Antarctica)
-90° (South Pole)

Figure 5 - Sun-path diagrams for different latitudes. Use the selector immediately above to compare sun-paths for a range of different latitudes. In some browsers you will need to hit the Enter key if you are selecting values using the keyboard.

### Important Dates

The aim of good shading design is to utilise the cyclical movement of the Sun through the sky to best advantage - usually for complete exclusion in summer and maximum exposure in winter. Given this cyclical nature, there are four important dates to remember when considering solar position:

Table 1 - Important dates relevant to solar position.
NAME Nth.Hem. Sth.Hem. DESCRIPTION
Summer Solstice 22 Jun. 22 Dec. Sun at its highest noon altitude
Autumn Equinox 21 Sep. 21 Mar. Sun rises due east, sets due west
Winter Solstice 21 Dec. 21 Jun. Sun at its lowest noon altitude
Spring Equinox 21 Mar. 21 Sep. Sun rises due east, sets due west

The altitude of the noon sun at the equinox is determined by the latitude of the site. At noon on the solstices, the altitude of the Sun is given as:

$\large \begin{tabular}{ r c l }
\mbox{Noon Mid-Summer Altitude} & = & 90^\circ - (|latitude| - 23.45^\circ)
\mbox{Noon Mid-Winter Altitude} & = & 90^\circ - (|latitude| + 23.45^\circ)
\end{tabular}
$

Where the vertical lines around the |latitude| denote its absolute value (ie: non-negative).

As a result, it is possible to represent the seasonal noon maximum and minimum altitudes as a function solely of site latitude. This is illustrated in Figure 6 below as a dynamic Flash animation. If you drag the slider on the left side up and down, the horizontal line represents the site latitude relative to the overlayed map of the world. The angular difference between the two solstices and the equinox always remains the same - only the overall rotational angle changes.

[swf:size=410x246&caption=Figure 6 - Noon sun angles at the equinox and seasonal extremes around the world. Drag the slider on the left hand side to change the latitude and see the resulting noon Sun altitudes.]solar/sun-angles.swf[/swf]

## Useful References

Other Solar Position Calculators:
http://www.cs.ucla.edu/~simonw/sunpos/
http://susdesign.com/sunangle/
Solar Radiation Data Manual for Buildings:
http://rredc.nrel.gov/solar/pubs/bluebook/bluebook_index.html
NASA Information on Sundials:

### Authors/Reviewers

View desktop or mobile version of site.


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# xyz < 0

Author Message
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Kudos [?]: 1119 [0], given: 5180

xyz < 0 [#permalink]  20 Oct 2017, 02:40
Expert's post
00:00

Question Stats:

75% (00:27) correct 25% (00:54) wrong based on 4 sessions

$$xyz < 0$$

 Quantity A Quantity B $$x + y + z$$ $$2x + 2y + 2z$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Kudos [?]: 343 [0], given: 66

Re: xyz < 0 [#permalink]  20 Oct 2017, 06:17
The fact that xyz < 0 does not give enough information about the unknowns to be able to compare the two quantities. We just know that two of them should be positive and the other negative but nothing more. Given that we can't compare the quantities answer is D!
Re: xyz < 0   [#permalink] 20 Oct 2017, 06:17
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text:
# naginterfaces.library.linsys.complex_posdef_tridiag_solve¶

naginterfaces.library.linsys.complex_posdef_tridiag_solve(d, e, b)[source]

complex_posdef_tridiag_solve computes the solution to a complex system of linear equations , where is an Hermitian positive definite tridiagonal matrix and and are matrices. An estimate of the condition number of and an error bound for the computed solution are also returned.

For full information please refer to the NAG Library document for f04cg

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f04/f04cgf.html

Parameters
dfloat, array-like, shape

Must contain the diagonal elements of the tridiagonal matrix .

ecomplex, array-like, shape

Must contain the subdiagonal elements of the tridiagonal matrix .

bcomplex, array-like, shape

The matrix of right-hand sides .

Returns
dfloat, ndarray, shape

If the function exits successfully or = + 1, is overwritten by the diagonal elements of the diagonal matrix from the factorization of .

ecomplex, ndarray, shape

If the function exits successfully or = + 1, is overwritten by the subdiagonal elements of the unit lower bidiagonal matrix from the factorization of . ( can also be regarded as the conjugate of the superdiagonal of the unit upper bidiagonal factor from the factorization of .)

bcomplex, ndarray, shape

If the function exits successfully or = + 1, the solution matrix .

rcondfloat

If the function exits successfully or = + 1, an estimate of the reciprocal of the condition number of the matrix , computed as .

errbndfloat

If the function exits successfully or = + 1, an estimate of the forward error bound for a computed solution , such that , where is a column of the computed solution returned in the array and is the corresponding column of the exact solution . If is less than machine precision, is returned as unity.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

The principal minor of order of the matrix is not positive definite. The factorization has not been completed and the solution could not be computed.

Warns
NagAlgorithmicWarning
(errno )

A solution has been computed, but is less than machine precision so that the matrix is numerically singular.

Notes

is factorized as , where is a unit lower bidiagonal matrix and is a real diagonal matrix, and the factored form of is then used to solve the system of equations.

References

Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug

Higham, N J, 2002, Accuracy and Stability of Numerical Algorithms, (2nd Edition), SIAM, Philadelphia


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# When the roulette has hit 5 reds why shouldn't I bet to black?

First some context, I'm not a mathematician, not even close (as you will soon see) I do grasp some things about it but in a need to know basis, so plain english answers are appreciated (too).

I can't figure out this one even though some have tried very hard to explain/convince me.

So let's say I'm on a roulette (let's leave out the zero, or make it a coin for that matter).

The roulette hits 5 (or any amount of) times red on a row.

My question is why should't I bet to black (or better said why it is the same the one I pick).

I DO UNDERSTAND THE BASIC PRINCIPLE, that there is a material reality which makes the ball randomly fall on any of the two colors (which gives the options a 50-50 chance).

But, I also understand that if you "say": I bet red will come out six times on a row, you do have a very low probability of that happening so:

How is it that if you have seen the ball fall 5 times on a row on red, and you bet on red, you are NOT betting on 6 times on a row on red (that does have lower probability).

I hope I was clear enough with my question, if not, please ask for any clarifications needed.

Sorry for the VERY plain English, feel free to modify or suggest a change to anything that may be misleading.

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This is my first question here and I could not find any other suitable tag, sorry! –  Trufa Dec 22 '10 at 17:27
A side remark: If you know that the roulette is fair, then it doesn't matter if you bet on red or black. However, if all that you have observed is that the ball has fallen on red five times in a row, then perhaps the most rational thing to do is to suspect that the roulette is biased towards red, and keep betting on red. –  Hans Lundmark Dec 22 '10 at 20:16
Meat for though: Question 1: Which of these sequence of six roulette balls is more probable: RRRRRR RRRRRB RBRBRB ? Answer: all are equally probable. Question 2: Which is more probable, that in six balls we get 3 red/3 black balls or that we get all 6 red? Answer: 3 red/3 black is much more probable. Think until you see no contradiction here. –  leonbloy Oct 1 '12 at 21:38
wheels are biased, so every wheel has a memory. –  user48195 Nov 4 '12 at 20:40

Lots of people have trouble with this. If you bet before any spins on six in a row, the chance of winning is 1/2^6=1/64. But having seen the five reds, as you say, the chances are 1/2 each on red and black for the next spin. It is also true for any specific series of six spins, at the start the chance of that series is 1/64. If you were to bet on RBBRRB, that is also 1/64. Now that you have seen five reds, there are only two series of six that are possible: RRRRRR and RRRRRB. They each started out 1/64 and are now each 1/2.

Hope this helps

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I can't believe it, you've made me seen the light!! :) no, but seriously you can't imagine how much "trouble" I had with this!! Thank you very much! I was missing a little piece of the puzzle, but it made it incomprehensible, I could understand that the probability was less (when betting to six) and the got bigger and bigger, which is actually a concept I (of course) undertand but could not apply it here. Bottom line, thanks a lot! –  Trufa Dec 22 '10 at 17:39
I'm more more of an old hand at probablilty than the OP, and this answer was enlightening to me (I'm slightly embarassed to admit). Very well put. I'd upvote twice if it were possible. Thanks! –  Todd Wilcox Dec 21 '12 at 8:30

There's an analogy that I like. Suppose I'm afraid to take planes as it's possible that some crazy terrorist brings a bomb onto the plane. Now it's really improbable that there are two bombs on the plane that I'm going to take. So I'll bring a bomb myself (which I of course won't detonate); then it's virtually impossible that anything happens. Well ...

I don't know, but maybe this helps.

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Ok I (sort of) see your point, but I already understood this. What I mean is I knew what what I was thinking was incorrect, I just wanted to understand why. Thanks :) –  Trufa Dec 22 '10 at 17:43

The events "given that the roulette hits $5$ reds, the next hit is red" and "the roulette hits $6$ reds" are different. The first has probability $\frac{1}{2}$ because different spins of the roulette are independent and the second has probability $\frac{1}{64}$ by the multiplication principle. (This is the same as the probability of "the roulette hits $5$ reds and a black," which is exactly the point of the first computation.)

For questions like these the general principle for getting to grips with how your intuition is failing is "when in doubt, list out all the possibilities."

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Thanks for the answer, but I sort of new that, I knew I was wrong to think the probability would be less than 1/2 but I needed to understand the why. I do understand now :) –  Trufa Dec 22 '10 at 17:48

The best explanation I have heard for this is: The roulette wheel has no memory. When you spin the wheel it does not know that there have been 5 reds in a row and it is due for a black. The odds are 1/2 each time.

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Exactly, so if you make a second bet with double money your odds are still the same. The only thing in your favour is that you are saying "I can't be wrong twice in a row so I will double my money" –  John Magnolia Mar 15 '13 at 17:00

Why is it so unlikely to get 6 reds in a row? Well, you have to cross your fingers and say "Hope the first one's red!" And if you get lucky and that one comes up red, then you have to cross your fingers and say "Hope the second one's red!" And if you get really lucky and that one also comes up red, then you have to cross your fingers and say "Hope the third one's red!" And so on.

On the other hand, if five reds already came up, all you have to do is cross your fingers and say "Hope this one's red!" a single time. In one case, you're hoping for "red red red red red red"; in the other, you don't care about the first five (they're already done with); you're just hoping to get "red" once.

To put it another way: would you rather go for six reds from scratch, or would you rather go for six reds after five have already come up red?

-

If the roulette is "fair" like China power said, no matter how many Red hit on a row it doesn't matter because the chance of hitting red/black is 50-50 and it's all pure luck when playing this game.

-

Why wouldn't a series have an increasingly lower probability of extending than a single event has of happening once?

Obviously, each unique spin has a probability of 50% (academically, by excluding the greens) for either color.

However, the overall proportion of total reds vs blacks should be 50%. So every time another of the same color is added to the group, the probability of the group/sample containing ONLY that one color decreases. Is there really a 50% probability that a sample size of 100 (e.g.) will contain 100 reds or blacks? When a person gambles on the roulette spin, he may be betting FOR a single spin, or AGAINST a series.

Isn't saying that the wheel has no memory like saying the wheel hasn't had a haircut in (x) weeks? A gambler isn't betting on the wheel, he's betting on the statistics. Past data would appear to be relevant due to the sampling.

The trick is to be in the right place at the right time: at what point will the group or sampling attempt to correct itself to ensure an equal distribution of reds and blacks? Because obviously it is inevitable.

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You have either not read or not understood the other answers. –  Rahul Aug 21 '12 at 1:12
«at what point will the group or sampling attempt to correct itself to ensure an equal distribution of reds and blacks? Because obviously it is inevitable.»: not really. Or to start from your premise of that there's no reason for «Why wouldn't a series have an increasingly lower probability of extending than a single event has of happening once?»: the series already happened. And while «the overall proportion of total reds vs blacks should be 50%», there's an infinite amount of plays to correct that, so any finite sequence of repeating blacks or reds is possible. –  JMCF125 Feb 5 at 11:37

It is correct that the different spuns are independent from each other when playing the roulette - however it is not entirely correct that roulette has no memory.

If the wheel was spun a million times you would see red and black occur the same amount of times.

If you have a case of five consecutive reds (and these are all your observations) the most rational choise would be to play black - HOWEVER - it is not the rationel choise because of the unlikely occurance of 6 reds in a row, but because you bet on the assumption that the roulette is out of its long term equilibrium.

6 reds in a row is no more unlikely to happen than five reds followed by a black - so that argument is not valid - both is 0,473^6 (47,3% chance of both black and red, and only one possible combination in both cases).

Now if you see five consecutive reds after ten consecutive blacks, and these are all your observations, the most rational choice would be to play red - all we know is that on the long term they will occur the same amount of times!...

You do not beat the roulette this way though ;)

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Did you really intend to write your second sentence? –  Rick Decker Sep 20 '12 at 14:47
This doesn't make any sense. You yourself said that the spins are independent of each other. Therefore, what has already happened has no affect on what will happen in the future. Even if there were 100 reds in a row, the odds of red and black are exactly the same on the next spin. So, there would be no inclination to choose one over the other. So, your sentences that say things like "... the most rational choice would be to play red ..." are not at all true. The fact that, over the long term, the number of reds and blacks should be even does not mean you can predict what comes next. –  Graphth Sep 21 '12 at 12:39

Dude no where in roulette history a colour has landed more thn 8 times in a row. But pay attention to this, im not talking about the real roullete on table where a attendent spins the ball but im talking about the rapid roullet's the one on the computer's. if u ever get a chance when a same colour has appeared 8 times in a row, you can definately bet on the othet colour with as much maximum amount you want but make sure you put some money on zero as well cos sometimes zero falls in after so many colours. Try this dude trust me iv made more thn 30000$in a year with this strategy. Its same like fishing you gotta be patient enough for the chance. - Dude, the chance that an American roulette wheel spun$9$times lands on the same color each time is$(36/38) * (18/38)^8 \approx .24012\%$. Thus it happens slightly more than$1$out of every$417$times. So your claim that it has never happened "in roulette history" is pure malarkey. – Pete L. Clark Feb 18 '13 at 8:44 The above probabilistic calculation does not disprove your claim that some virtual roulette game does not allow$9\$ consecutive instances of the same color. But this would have to be programmed in specifically, and then every once in a non-negligible while an opportunity would arise in which the expected value of betting on the other color would be positive (and indeed large). So you're claiming that someone specifically programmed a casino game so as to enable a strategy that enables the casino to lose money. That's wildly implausible as well. –  Pete L. Clark Feb 18 '13 at 8:53

## protected by Pete L. ClarkFeb 18 '13 at 9:00

Thank you for your interest in this question. Because it has attracted low-quality answers, posting an answer now requires 10 reputation on this site.


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## Sunday, November 14, 2021 ... //

### The absurdly pathetic "result" of COP26

Another summit of the climate psychopaths and their spineless collaborationists ended in Glasgow. The format was the same one that we remembered in dozens of previous summits: 30,000 parasites arrived by private jets and have bullšited about the evil of CO2 emissions for two weeks. The content of their talks was just nonsensical irrelevant gibberish, there was no agreement about anything, the talks had to go to overtime, like always, and some "result" was announced afterwards:

Nations including China and India agreed to say something about the "phaseout" of coal while all words that indicated some substance were deleted or softened to become completely ill-defined.
Even if some of these statements about the future were well-defined, it would still not imply that these statements will have anything to do with the truth. These statements are just would-be prophesies by idiots who think that they are about 1,000 times more important and powerful than they are.

I am sure you don't need to know anything else about this "event". Billions of dollars were wasted for another farce, the CO2 emissions created by these morons are obviously the least of the problems because there exists nothing such as a global problem with the climate, let alone one caused by CO2, and even if there were a problem, the subtraction of carbon dioxide's contribution, at most 0.01-0.02 °C, from the warming per year would clearly do nothing to avoid the problems. Do you really need to move 30,000 morons across the world and store them in hotels for 2 weeks if the only outcome is just another hateful remark about the fossil fuels which is completely detached from reality?

Jeremy Clarkson is the guy who should be getting a substantial portion of the money that was wasted for this farce. A week ago, he pointed out that Greta Thunberg was an uneducated arrogant moron and what she needed was a smacked bottom. But it has become politically incorrect to spank filthy bastards such as the Scandinavian dropout. Almost all the 30,000 participants of the farce need smacked bottoms, too. But the media landscapes in many countries are so fudged up that their members dare to disagree with Clarkson's self-evidently correct and important remark. In fact, if they could, they would make sure that Greta spanks Clarkson instead of the other way around!

The degeneration of the society has led to the birth of an entire extraordinarily annoying and idiotic parasitic class that believes that they are doing a very important work e.g. if they fly to a distant hotel for 2 weeks, babble nonsense that reveals their complete scientific illiteracy, and then they sign a hateful remark about King Coal, the 964,253rd such remark. Some of the "work" was probably all about the selection of the key word. "Phaseout" defeated "suppression" and even "ching-queng-kung-pao" (the "right" translation of the hostile verb to other languages surely consumed the work of hundreds of translators for many hours: Czech alarmists seem to have adopted "odklon" which could be back-translated as "deflection"). The word "phaseout" is the product of their work. They imagine that they are really controlling the world, they have eaten Solomon's excrement which promoted them to the smartest people in the room, and their choice of the word "phaseout" has the value of trillions of dollars that they deserve to be paid.

They are neither. Already much more modest green policies that have been imposed on nations so far have led to the meteoric rise of the fuel and electricity prices that is seen to be painful for billions of people and by billions of people. To make a truly significant impact on CO2 emissions – which would still have virtually no impact on the climate – they would need to increase these devastating policies by an order of magnitude or more. If that happened, the 30,000 parasites wouldn't be spanked, they would be eradicated. Their idea that they may command 8 billion people is breathtakingly arrogant but it is also dumb. Your own far left media have deceived you, aßholes, not only about all the science and economics but about your status, too. You are not the elites. You are braindead trash of mankind that will be eliminated by the bulk of the nations when it becomes really necessary and you are doing maximum you can to bring that moment closer. Your demise will almost directly follow from the basic laws of Nature, economics, and human psychology. It's too bad if you didn't bother to learn either of these laws.

The Czech name for the green deals

Czechia obviously belongs among the nations where some folks with common sense keep on controlling the key institutions, as the outgoing PM's talk exemplified. Incidentally, it is cool to observe that the climate skeptics' preferred translation of the "European Green Deal" seems to be winning in my homeland. We call it "Zelený úděl" while the EU's official term is "Zelená dohoda". It is a funny and not so delicate difference. As I learned after the years in the U.S., a "deal" is mainly just a small treaty, contract, something that you codify by a signature or a handshake. That is "dohoda" but the first backwards translation of "dohoda" would simply be a "treaty". Instead, we are using "úděl" for a "deal" which could be back-translated as a "fate", "destiny", and it has a rather negative content. Jesus had this "destiny" when he was force to carry his own cross. The Europeans are being forced into something similar that the Jews have imposed on Jesus Christ. It doesn't sound optimistic.

I was wondering why it is so that "Zelený úděl" was so widely accepted by the writers including the most influential mainstream media. One reason is that the climate realism is just way more widespread here, including in the media world and the important institutions. Another reason is historical but I only fully appreciated it a few days ago: Franklin Delano Roosevelt's "New Deal", i.e. the original one, has been translated mostly as "Nový úděl", the New Destiny, for almost a century (I am not 100% sure that it was the translation already in the 1930s, i.e. before the rise of the Czechoslovak communists, but I tend to believe so). And that makes a difference. Of course the Green Deal has to be an "úděl", too.

I think that you should back-translate our terminology and pick a more realistic phrase, perhaps Green Destiny, Green Fate, or something like that, to more correctly convey the fact that the Green Deals are fatally dangerous plans.


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# 5.2 Representing symbols by bits  (Page 2/2)

 Page 2 / 2

Let us assume that we represent a symbol ${x}_{n}$ , with probability ${p}_{n}$ , by ${l}_{n}$ bits. Then, the average number of bits spent per symbol will be

$\langle L\rangle =\sum_{n=1}^{N} {p}_{n}{l}_{n}$
We see that this equation is equal to the entropy if the code words are selected to have the lengths ${l}_{n}=-\lg {p}_{n}$ . Thus, if the source produces stochastically independent outcomes with probabilities ${p}_{n}$ , such that $\lg {p}_{n}$ is an integer, then we can easily find an optimal code as we show in the next example.

## Finding a minimal representation

A four-symbol alphabet produces stochastically independent outcomes with the following probabilities. $({x}_{1})=\frac{1}{2}$ $({x}_{2})=\frac{1}{4}$ $({x}_{3})=\frac{1}{8}$ $({x}_{4})=\frac{1}{8}$ and an entropy of 1.75 bits/symbol. Let's see if we can find a codebook for this four-letter alphabet that satisfies the Source CodingTheorem. The simplest code to try is known as the simple binary code : convert the symbol's index into a binary number and use the same number of bits for each symbol byincluding leading zeros where necessary.

$↔({x}_{1}, \mathrm{00})\text{}↔({x}_{2}, \mathrm{01})\text{}↔({x}_{3}, \mathrm{10})\text{}↔({x}_{4}, \mathrm{11})$
As all symbols are represented by 2 bits, obviously the average number of bits per symbol is 2.Because the entropy equals $1.75$ bits, the simple binary code is not a minimal representation according to the source coding theorem.If we chose a codebook with differing number of bits for the symbols, a smaller average number of bits can indeed be obtained. The idea is to use shorter bit sequences for the symbols that occur more often , i.e., symbols that have a higher probability. One codebook like this is
$↔({x}_{1}, 0)\text{}↔({x}_{2}, \mathrm{10})\text{}↔({x}_{3}, \mathrm{110})\text{}↔({x}_{4}, \mathrm{111})$
Now $\langle L()\rangle =1\frac{1}{2}+2\frac{1}{4}+3\frac{1}{8}+3\frac{1}{8}=1.75$ . We can reach the entropy limit! This should come as no surprise, as promised above, when $\lg {p}_{n}$ is an integer for all $n$ , the optimal code is easily found.

The simple binary code is, in this case, less efficient than theunequal-length code. Using the efficient code, we can transmit the symbolic-valued signal having this alphabet 12.5%faster. Furthermore, we know that no more efficient codebook can be found because of Shannon's source coding theorem.

## Optimality of the ascii code

Let us return to the ASCII codes presented in . Is the 7-bit ASCII code optimal, i.e., is it a minimal representation? The 7-bit ASCII code assign an equal length (7-bit) to all characters it represents. Thus, it would be optimal if all of the 128 characters wereequiprobable, that is each character should have a probability of $\frac{1}{128}$ . To find out whether the characters really are equiprobable an analysis of all English texts would be needed. Such an analysis is difficult to do. However, the letter "E" is more probable than the letter "Z", so the equiprobable assumption does not hold, and the ASCII codeis not optimal.

(A technical note: We should take into account that in English text subsequent outcomes are not stochastically independent. To see this, assume the first letter to be "b", then it is more probable that the next letter is "e", than "z". In the case where the outcomesare not stochastically independent, the formulation we have given of Shannon's source coding theorem is no longer valid, to fix this, we should replace the entropy with the entropy rate, but we will not pursue this here).

## Generating efficient codes

From Shannon's source coding theorem we know what the minimum average rate needed to represent a source is. But other than in the case when the logarithm of the probabilities gives an integer, we do not get any indications on how to obtain that rate. It is a large area of research to getclose to the Shannon entropy bound. One clever way to do encoding is the Huffman coding scheme.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
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LITNING
scanning tunneling microscope
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if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
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analytical skills graphene is prepared to kill any type viruses .
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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what is Nano technology ?
write examples of Nano molecule?
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The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
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yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
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biomolecules are e building blocks of every organics and inorganic materials.
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## G = D5×C34order 340 = 22·5·17

### Direct product of C34 and D5

Aliases: D5×C34, C10⋊C34, C1703C2, C854C22, C5⋊(C2×C34), SmallGroup(340,13)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C5 — D5×C34
 Chief series C1 — C5 — C85 — D5×C17 — D5×C34
 Lower central C5 — D5×C34
 Upper central C1 — C34

Generators and relations for D5×C34
G = < a,b,c | a34=b5=c2=1, ab=ba, ac=ca, cbc=b-1 >

Smallest permutation representation of D5×C34
On 170 points
Generators in S170
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34)(35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68)(69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102)(103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136)(137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170)
(1 161 53 99 119)(2 162 54 100 120)(3 163 55 101 121)(4 164 56 102 122)(5 165 57 69 123)(6 166 58 70 124)(7 167 59 71 125)(8 168 60 72 126)(9 169 61 73 127)(10 170 62 74 128)(11 137 63 75 129)(12 138 64 76 130)(13 139 65 77 131)(14 140 66 78 132)(15 141 67 79 133)(16 142 68 80 134)(17 143 35 81 135)(18 144 36 82 136)(19 145 37 83 103)(20 146 38 84 104)(21 147 39 85 105)(22 148 40 86 106)(23 149 41 87 107)(24 150 42 88 108)(25 151 43 89 109)(26 152 44 90 110)(27 153 45 91 111)(28 154 46 92 112)(29 155 47 93 113)(30 156 48 94 114)(31 157 49 95 115)(32 158 50 96 116)(33 159 51 97 117)(34 160 52 98 118)
(1 136)(2 103)(3 104)(4 105)(5 106)(6 107)(7 108)(8 109)(9 110)(10 111)(11 112)(12 113)(13 114)(14 115)(15 116)(16 117)(17 118)(18 119)(19 120)(20 121)(21 122)(22 123)(23 124)(24 125)(25 126)(26 127)(27 128)(28 129)(29 130)(30 131)(31 132)(32 133)(33 134)(34 135)(35 52)(36 53)(37 54)(38 55)(39 56)(40 57)(41 58)(42 59)(43 60)(44 61)(45 62)(46 63)(47 64)(48 65)(49 66)(50 67)(51 68)(69 148)(70 149)(71 150)(72 151)(73 152)(74 153)(75 154)(76 155)(77 156)(78 157)(79 158)(80 159)(81 160)(82 161)(83 162)(84 163)(85 164)(86 165)(87 166)(88 167)(89 168)(90 169)(91 170)(92 137)(93 138)(94 139)(95 140)(96 141)(97 142)(98 143)(99 144)(100 145)(101 146)(102 147)

G:=sub<Sym(170)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68)(69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102)(103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136)(137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170), (1,161,53,99,119)(2,162,54,100,120)(3,163,55,101,121)(4,164,56,102,122)(5,165,57,69,123)(6,166,58,70,124)(7,167,59,71,125)(8,168,60,72,126)(9,169,61,73,127)(10,170,62,74,128)(11,137,63,75,129)(12,138,64,76,130)(13,139,65,77,131)(14,140,66,78,132)(15,141,67,79,133)(16,142,68,80,134)(17,143,35,81,135)(18,144,36,82,136)(19,145,37,83,103)(20,146,38,84,104)(21,147,39,85,105)(22,148,40,86,106)(23,149,41,87,107)(24,150,42,88,108)(25,151,43,89,109)(26,152,44,90,110)(27,153,45,91,111)(28,154,46,92,112)(29,155,47,93,113)(30,156,48,94,114)(31,157,49,95,115)(32,158,50,96,116)(33,159,51,97,117)(34,160,52,98,118), (1,136)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,109)(9,110)(10,111)(11,112)(12,113)(13,114)(14,115)(15,116)(16,117)(17,118)(18,119)(19,120)(20,121)(21,122)(22,123)(23,124)(24,125)(25,126)(26,127)(27,128)(28,129)(29,130)(30,131)(31,132)(32,133)(33,134)(34,135)(35,52)(36,53)(37,54)(38,55)(39,56)(40,57)(41,58)(42,59)(43,60)(44,61)(45,62)(46,63)(47,64)(48,65)(49,66)(50,67)(51,68)(69,148)(70,149)(71,150)(72,151)(73,152)(74,153)(75,154)(76,155)(77,156)(78,157)(79,158)(80,159)(81,160)(82,161)(83,162)(84,163)(85,164)(86,165)(87,166)(88,167)(89,168)(90,169)(91,170)(92,137)(93,138)(94,139)(95,140)(96,141)(97,142)(98,143)(99,144)(100,145)(101,146)(102,147)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68)(69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102)(103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136)(137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170), (1,161,53,99,119)(2,162,54,100,120)(3,163,55,101,121)(4,164,56,102,122)(5,165,57,69,123)(6,166,58,70,124)(7,167,59,71,125)(8,168,60,72,126)(9,169,61,73,127)(10,170,62,74,128)(11,137,63,75,129)(12,138,64,76,130)(13,139,65,77,131)(14,140,66,78,132)(15,141,67,79,133)(16,142,68,80,134)(17,143,35,81,135)(18,144,36,82,136)(19,145,37,83,103)(20,146,38,84,104)(21,147,39,85,105)(22,148,40,86,106)(23,149,41,87,107)(24,150,42,88,108)(25,151,43,89,109)(26,152,44,90,110)(27,153,45,91,111)(28,154,46,92,112)(29,155,47,93,113)(30,156,48,94,114)(31,157,49,95,115)(32,158,50,96,116)(33,159,51,97,117)(34,160,52,98,118), (1,136)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,109)(9,110)(10,111)(11,112)(12,113)(13,114)(14,115)(15,116)(16,117)(17,118)(18,119)(19,120)(20,121)(21,122)(22,123)(23,124)(24,125)(25,126)(26,127)(27,128)(28,129)(29,130)(30,131)(31,132)(32,133)(33,134)(34,135)(35,52)(36,53)(37,54)(38,55)(39,56)(40,57)(41,58)(42,59)(43,60)(44,61)(45,62)(46,63)(47,64)(48,65)(49,66)(50,67)(51,68)(69,148)(70,149)(71,150)(72,151)(73,152)(74,153)(75,154)(76,155)(77,156)(78,157)(79,158)(80,159)(81,160)(82,161)(83,162)(84,163)(85,164)(86,165)(87,166)(88,167)(89,168)(90,169)(91,170)(92,137)(93,138)(94,139)(95,140)(96,141)(97,142)(98,143)(99,144)(100,145)(101,146)(102,147) );

G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34),(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68),(69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102),(103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136),(137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170)], [(1,161,53,99,119),(2,162,54,100,120),(3,163,55,101,121),(4,164,56,102,122),(5,165,57,69,123),(6,166,58,70,124),(7,167,59,71,125),(8,168,60,72,126),(9,169,61,73,127),(10,170,62,74,128),(11,137,63,75,129),(12,138,64,76,130),(13,139,65,77,131),(14,140,66,78,132),(15,141,67,79,133),(16,142,68,80,134),(17,143,35,81,135),(18,144,36,82,136),(19,145,37,83,103),(20,146,38,84,104),(21,147,39,85,105),(22,148,40,86,106),(23,149,41,87,107),(24,150,42,88,108),(25,151,43,89,109),(26,152,44,90,110),(27,153,45,91,111),(28,154,46,92,112),(29,155,47,93,113),(30,156,48,94,114),(31,157,49,95,115),(32,158,50,96,116),(33,159,51,97,117),(34,160,52,98,118)], [(1,136),(2,103),(3,104),(4,105),(5,106),(6,107),(7,108),(8,109),(9,110),(10,111),(11,112),(12,113),(13,114),(14,115),(15,116),(16,117),(17,118),(18,119),(19,120),(20,121),(21,122),(22,123),(23,124),(24,125),(25,126),(26,127),(27,128),(28,129),(29,130),(30,131),(31,132),(32,133),(33,134),(34,135),(35,52),(36,53),(37,54),(38,55),(39,56),(40,57),(41,58),(42,59),(43,60),(44,61),(45,62),(46,63),(47,64),(48,65),(49,66),(50,67),(51,68),(69,148),(70,149),(71,150),(72,151),(73,152),(74,153),(75,154),(76,155),(77,156),(78,157),(79,158),(80,159),(81,160),(82,161),(83,162),(84,163),(85,164),(86,165),(87,166),(88,167),(89,168),(90,169),(91,170),(92,137),(93,138),(94,139),(95,140),(96,141),(97,142),(98,143),(99,144),(100,145),(101,146),(102,147)]])

136 conjugacy classes

 class 1 2A 2B 2C 5A 5B 10A 10B 17A ··· 17P 34A ··· 34P 34Q ··· 34AV 85A ··· 85AF 170A ··· 170AF order 1 2 2 2 5 5 10 10 17 ··· 17 34 ··· 34 34 ··· 34 85 ··· 85 170 ··· 170 size 1 1 5 5 2 2 2 2 1 ··· 1 1 ··· 1 5 ··· 5 2 ··· 2 2 ··· 2

136 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 type + + + + + image C1 C2 C2 C17 C34 C34 D5 D10 D5×C17 D5×C34 kernel D5×C34 D5×C17 C170 D10 D5 C10 C34 C17 C2 C1 # reps 1 2 1 16 32 16 2 2 32 32

Matrix representation of D5×C34 in GL2(𝔽1021) generated by

 500 0 0 500
,
 0 1 1020 457
,
 0 1020 1020 0
G:=sub<GL(2,GF(1021))| [500,0,0,500],[0,1020,1,457],[0,1020,1020,0] >;

D5×C34 in GAP, Magma, Sage, TeX

D_5\times C_{34}
% in TeX

G:=Group("D5xC34");
// GroupNames label

G:=SmallGroup(340,13);
// by ID

G=gap.SmallGroup(340,13);
# by ID

G:=PCGroup([4,-2,-2,-17,-5,4355]);
// Polycyclic

G:=Group<a,b,c|a^34=b^5=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

׿
×
𝔽


text:
# All Questions

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text:
HOME  ›   pipelines

# Running cellranger aggr

## What is aggr?

Many experiments generate data for multiple samples. Depending on the experimental design, these could be replicates from the same set of cells, cells from different tissues or time points from the same individual, or cells from different individuals. Samples could be processed through different Gel Bead-in Emulsion (GEM) wells or multiplexed within the same GEM well on Chromium instruments. The cellranger aggr pipeline can be used to aggregate samples from these scenarios into a single feature-barcode matrix.

## Requirements

The first step is to run cellranger count or cellranger multi on each individual GEM well prepared using the 10x Genomics Chromium Controller or Chromium X Series.

For example, suppose you ran three count pipelines as follows:

$cd /opt/runs$ cellranger count --id=LV123 ...
... wait for pipeline to finish ...
$cellranger count --id=LB456 ... ... wait for pipeline to finish ...$ cellranger count --id=LP789 ...
... wait for pipeline to finish ...

These three runs can be aggregated with cellranger aggr to get a single feature-barcode matrix and secondary analysis outputs. In order to do so, next create an aggregation CSV file.

## Create aggregation CSV

Create a CSV file with a header line containing the following columns:

• sample_id: Unique identifier for this input GEM well. This will be used for labeling purposes only; it doesn't need to match any previous ID assigned to the GEM well.
• molecule_h5: Path to the molecule_info.h5 or sample_molecule_info.h5 file produced by cellranger count or multi. For example, if you processed your GEM well by calling cellranger count --id=ID in some directory /DIR, this path would be /DIR/ID/outs/molecule_info.h5.

Either make the CSV file in a text editor, or create it in Excel and save as a CSV file. Continuing with the example from the previous section, the Excel spreadsheet would look like this:

AB
1sample_idmolecule_h5
2LV123/opt/runs/LV123/outs/molecule_info.h5
3LB456/opt/runs/LB456/outs/molecule_info.h5
4LP789/opt/runs/LP789/outs/molecule_info.h5

When you save it as a CSV, the result would look like this:

sample_id,molecule_h5
LV123,/opt/runs/LV123/outs/molecule_info.h5
LB456,/opt/runs/LB456/outs/molecule_info.h5
LP789,/opt/runs/LP789/outs/molecule_info.h5

In addition to the CSV columns expected by cellranger aggr, you may optionally supply columns containing library metadata (e.g., lab or sample origin). These custom library annotations do not affect the analysis pipeline but can be visualized downstream in the Loupe Browser (see Categories section below). Note that unlike other CSV inputs to Cell Ranger, these custom columns may contain characters outside the ASCII range (e.g., non-Latin characters).

## Aggregating outputs from cellranger count

For large studies involving samples run on multiple GEM wells, run cellranger count on FASTQ data from each of the GEM wells individually, and then pool the results using cellranger aggr.

The cellranger aggr command takes an aggregation CSV file specifying the list of cellranger count output files (specifically the molecule_info.h5 from each run), and produces a single feature-barcode matrix containing all the data.

When combining multiple GEM wells, the barcode sequences for each channel are distinguished by a GEM well suffix appended to the barcode sequence (see GEM wells).

By default, reads from each GEM well are subsampled such that all GEM wells have the same effective sequencing depth, measured in terms of reads that are confidently mapped to the transcriptome or assigned to the feature IDs per cell. However, it is possible to change the depth normalization mode (see Depth Normalization).

### Aggregating Feature Barcode data

If Feature Barcode analysis is included, the input Feature Reference CSV file should be the same for each GEM well.

Starting from Cell Ranger v7.0, CRISPR Guide Capture libraries from multiple GEM wells can be aggregated with cellranger aggr. There are no changes to aggr inputs – the presence of CRISPR Guide Capture library information in the molecule_info.h5 input files enables CRISPR aggregation. Normalization is enabled by default for both Gene Expression and CRISPR Guide Capture libraries; changes to normalization parameters affect both libraries. Note that protospacer calling is performed again on the combined data included in the cellranger aggr run. CRISPR aggregation generates the crispr_analysis/ folder in the outs/ directory. The structure of the crispr_analysis folder is similar to the CRISPR outputs from cellranger count.

### Aggregating Targeted Gene Expression data

Targeted Gene Expression data is supported by cellranger aggr and can be aggregated with whole transcriptome Gene Expression data, provided that all GEM wells have matching chemistries and that the same target panel CSV file is used for all targeted samples.

## Aggregating outputs from cellranger multi

The cellranger aggr command takes an aggregation CSV file specifying the list of cellranger multi per sample sample_molecule_info.h5 files, and performs aggregation on any combination of Gene Expression and Feature Barcode (Antibody or CRISPR Guide Capture, Cell Multiplexing) data that are present in the individual sample outputs.

Consider two per sample datasets containing data from one 3' Cell Multiplexing experiment:

$cd /opt/runs$ cellranger multi --id=Run1 ...
... wait for pipeline to finish ...

To aggregate the datasets, you need to create a CSV containing the following columns:

Column NameDescription
sample_idUnique identifier for this sample. This will be used for labeling purposes only.
molecule_h5Path to the per sample sample_molecule_info.h5 file generated by the cellranger multi pipeline. For example, if you processed Cell Multiplexing data by calling cellranger multi --id=ID in some directory /DIR, and the sample was called Sample1, this path would be /DIR/ID/outs/per_sample_outs/Sample1/count/sample_molecule_info.h5

Apart from the change in the path to the per sample sample_molecule_info.h5 file, the documentation on additional columns for creating categories, depth normalization, and batch correction are the same.

Either make the CSV file in a text editor, or create it in Excel and save as a CSV file. The Excel spreadsheet might look like this:

AB
1sample_idmolecule_h5
2Sample1/opt/runs/Run1/outs/per_sample_outs/Sample1/count/sample_molecule_info.h5
3Sample2/opt/runs/Run1/outs/per_sample_outs/Sample2/count/sample_molecule_info.h5

The CSV file will look like this:

sample_id,molecule_h5
Sample1,/opt/runs/Run1/outs/per_sample_outs/Sample1/count/sample_molecule_info.h5
Sample2,/opt/runs/Run1/outs/per_sample_outs/Sample2/count/sample_molecule_info.h5

## Running aggr on the command line

These are the most common command line arguments (run cellranger aggr --help for a full list):

ArgumentDescription
--idRequired. A unique run ID string: e.g. AGG123
--csvRequired. Path to the aggregation CSV file containing the list of molecule_info.h5 files.
--normalizeOptional. String specifying how to normalize depth across the input libraries. Valid values: mapped (default) or none (see Depth Normalization).
--nosecondaryOptional. Add this flag to skip secondary analysis which includes dimensionality reduction, clustering, and visualization. This is applicable if you plan to use cellranger reanalyze or your own custom analysis.

After specifying these input arguments, run cellranger aggr:

cd /home/jdoe/runs
cellranger aggr --id=AGG123 \
--csv=AGG123_libraries.csv

The pipeline will begin to run, creating a new output folder named with the specified aggregation ID (e.g. /home/jdoe/runs/AGG123). If this folder already exists, Cell Ranger will assume it is an existing pipestance and attempt to resume running it.

## Pipeline outputs

The cellranger aggr pipeline generates output files that contain all of the data from the individual input runs, aggregated into single output files, for convenient multi-sample analysis. Refer to the Understanding Outputs section to learn about aggr output files.

## Categories

When combining multiple samples into a single dataset with the cellranger aggr pipeline, you can assign categories and values to individual samples by adding columns to the cellranger aggr input spreadsheet. These category assignments propagate into Loupe Browser, where you can view them in Categories Mode to help determine genes that are differentially expressed between samples. For example, the following spreadsheet was used to aggregate the acute myeloid leukemia (AML) tutorial dataset:

ABC
1sample_idmolecule_h5AMLStatus
2AMLNormal1/path/to/AMLNormal1/molecule_info.h5Normal
3AMLNormal2/path/to/AMLNormal2/molecule_info.h5Normal
4AMLPatient/path/to/AMLPatient/molecule_info.h5Patient

Any columns in addition to sample_id and molecule_h5 will be converted into categories, and the cells in each sample will be assigned to one of the values in that category.

## Aggregating libraries with different chemistry versions

If you are aggregating libraries generated by different chemistry versions of the Single Cell Gene Expression Reagents, you might observe systematic differences in gene expression profiles between libraries. The cellranger aggr pipeline incorporates batch effect correction (algorithm details) to overcome this. To enable batch correction, include the following column in your aggregation CSV file:

• batch: Optional. Unique identifier for the batch that this GEM well belongs to. Libraries with the same batch identifier are considered to be in the same batch.

For example, if the LV123 sample in the previous example is a v2 library and the LB456 and LP789 samples are v3 libraries, set up the aggregation CSV file like this:

sample_id,molecule_h5,batch
LV123,/opt/runs/LV123/outs/molecule_info.h5,v2_lib
LB456,/opt/runs/LB456/outs/molecule_info.h5,v3_lib
LP789,/opt/runs/LP789/outs/molecule_info.h5,v3_lib

The v2_lib and v3_lib identifiers are example identifiers. Every sample from a given batch must have the same batch identifier, but otherwise the identifier text itself is arbitrary.

• This Chemistry Batch Correction algorithm is specifically intended to correct for systematic variability in gene expression profiles caused by different versions of the Single Cell Gene Expression chemistry. 10x Genomics has tested and verified its effectiveness primarily on aggregating Single Cell Gene Expression v2 and v3 chemistry with well-matched input material. The algorithm may be useful in other scenarios, but will require careful validation of results.
• Chemistry batch correction affects the PCA, t-SNE, and UMAP visualization and clustering results. Values in the aggregated feature-barcode matrix are not adjusted by chemistry batch correction. Differential expression analysis is still performed on the feature-barcode count matrix.
• When chemistry batch correction is enabled, FBPCA is used to perform dimensionality reduction instead of IRLBA PCA.
• The batch effect score (described in algorithm details) is recommended to compare the performance before and after batch correction. Besides the batch effect, the score also depends on the composition of the cell populations across batches.
• The minimum System Requirements of 64GB RAM will allow batch correction on datasets with a total number of 128k cells.
• Libraries with different throughput but the same chemistry can be aggregated without chemistry batch correction. For example, Single Cell 3' Gene Expression v3.1 standard kit (SK), HT, and LT can be aggregated without batch correction, as can Single Cell 5’ Gene Expression SK and HT.

### Aggregating Single Cell 5' and 3' Gene Expression data

The cellranger aggr pipeline uses Chemistry Batch Correction when aggregating results from a combination of 5' and 3', or 3' v2 and 3' v3 Gene Expression data. Enabling Chemistry Batch Correction in this scenario improves the mixing of the batches in the t-SNE visualization and clustering results. We recommend using Chemistry Batch correction for these scenarios, however, residual batch effects may still be present and careful validation of the results is advised. In particular, for the V(D)J genes, the 5' Gene Expression assay will generally count the V gene segments of the immune receptor (e.g. TRBV12-1 or IGH4-2), while the 3' Gene Expression assay will count the C gene segments (e.g. TRBC or IGHA), which may pose additional analysis challenges.

### Aggregating Targeted Gene Expression data

The cellranger aggr pipeline can aggregate results that include Targeted Gene Expression analysis provided that the requirements above are met. Non-target genes are excluded from the feature-barcode matrices to conduct secondary analysis for all samples. Aggregated feature-barcode matrices follow the same convention as Targeted Gene Expression analysis: the filtered feature-barcode matrices exclude non-targeted genes, whereas the raw feature-barcode matrices include all genes.

## Aggregating Cell Multiplexing with non-Cell Multiplexing data

The cellranger aggr pipeline supports the aggregation of Cell Multiplexing v3.1 data with Single Cell 3’ Gene Expression v3.1 data (i.e. "non-Cell Multiplexing data").

To combine Cell Multiplexing with non-Cell Multiplexing data, cellranger aggr (v6.0 and later) requires identical references (including feature/CMO reference). Therefore, non-Cell Multiplexing data must be re-run with the CMO reference file that specified Cell Multiplexing tags (CMOs) for the Cell Multiplexing data. These datasets can be run with either cellranger count (v3.0 and later) or cellranger multi (v5.0 and later). We recommend using the same version of Cell Ranger to generate inputs for cellranger aggr.

• Option 1) For cellranger count, input the CMO reference with --feature-ref and use the --no-libraries option. The cellranger count pipeline will generate a molecule_info.h5, which can be used as input to the cellranger aggr pipeline. An example of the command is below (replace code in red with relevant file paths):
cellranger count --id=pbmc_1k_count \
--transcriptome=/path/to/transcriptome/GRCh38-2020-A \
--fastqs=/path/togex/fastqs/pbmc_1k_v3_fastqs/ \
--sample=pbmc_1k_v3 \
--feature-ref=/path/to/cmo-reference/cmo-ref.csv \
--no-libraries
• Option 2) For cellranger multi, input the CMO feature reference in the [feature] section of the multi config CSV file. An example of the config file is below (replace code in red with relevant file paths):
[gene-expression]
reference,/path/to/transcriptome/GRCh38-2020-A
[feature]
reference,/path/to/cmo-reference/cmo-ref.csv
[libraries]
fastq_id,fastqs,feature_types
pbmc_1k_v3,/path/togex/fastqs/pbmc_1k_v3_fastqs/,Gene Expression

The cellranger multi pipeline generates a per sample sample_molecule_info.h5 file which is equivalent to the molecule_info.h5 file from a cellranger count run. These files can be used as input to the cellranger aggr pipeline. An example of the multi pipeline command is below (replace code in red with relevant file paths):
cellranger multi --id=pbmc_1k_multi --csv=/path/to/config.csv

The Cell Multiplexing protocol has additional wash steps that may lead to depletion of more ambient mRNA from samples compared to non-Cell Multiplexing samples. This difference in mRNA may then introduce small batch effects between Cell Multiplexing and non-Cell Multiplexing datasets. However, observations from internal data show fairly small batch effects and batch effect correction is not needed in most cases. If the results for each sample reveals obvious differences between the Cell Multiplexing vs. non-Cell Multiplexing data, enabling chemistry batch correction may improve the mixing of the batches in the t-SNE visualization and clustering results.

If you are aggregating Single Cell 3' Gene Expression with Cell Multiplexing v3.1 samples with other chemistries (Single Cell 3’ v2, 5’ v2, etc.), the data can be treated similarly to Single Cell 3' v3.1 chemistry. For example, we recommend using chemistry batch correction when aggregating Single Cell 3’ v3.1 with v2 chemistry (see this article for more information about aggregating data from different chemistries).

## Depth normalization

When combining data from multiple GEM wells, the cellranger aggr pipeline automatically equalizes the average read depth per cell between groups before merging. This approach avoids artifacts that may be introduced due to differences in sequencing depth. It is possible to turn off normalization or change the way normalization is done. The none option may be appropriate if you want to maximize sensitivity and plan to handle depth normalization in a downstream step.

There are two normalization modes:

• none: Do not normalize at all.
• mapped (Default): For each library type, subsample reads from higher-depth GEM wells until they all have, on average, an equal number of reads per cell that are confidently mapped to the transcriptome (Gene Expression) or assigned to known features (Feature Barcode Technology). If Targeted Gene Expression libraries are included, then normalization is performed on the basis of average reads per cell mapped confidently to the targeted transcriptome. The subsampling rates for Targeted Gene Expression libraries are all multiplied by 2 (provided all samples can achieve that depth). This is consistent with sequencing depth recommendations and is also done to avoid removing large fractions of reads from targeted libraries whenever they are combined with whole transcriptome libraries.

## Understanding GEM wells

Each GEM well is a physically distinct set of GEM partitions, but draws barcode sequences randomly from the pool of valid barcodes, known as the barcode whitelist. To keep the barcodes unique when aggregating multiple libraries, we append a small integer identifying the GEM well to the barcode nucleotide sequence, and use that nucleotide sequence plus ID as the unique identifier in the feature-barcode matrix. For example, AGACCATTGAGACTTA-1 and AGACCATTGAGACTTA-2 are distinct cell barcodes from different GEM wells, despite having the same barcode nucleotide sequence.

This number, which indicates which GEM well the barcode sequence came from, is called the GEM well suffix. The numbering of the GEM wells will reflect the order that the GEM wells were provided in the Aggregation CSV.


text:
3.5.1.3.12 Bessel_j1

Definition:

$j1= bessel\_j1(x)$, evaluates an approximation to the Bessel function of the first kind $J_1(x)$ .

The function is based on Chebyshev expansions.


text:
### Home > GB8I > Chapter 2 Unit 2 > Lesson INT1: 2.2.2 > Problem2-65

2-65.

Calculate $f (−3)$ for each function below.

1. $f(x) = −2x + 3$

Substitute $−3$ for $x$ and then simplify.

1. $f(x) = 4^x$

Substitute $−3$ for $x$ and then simplify.

$f(-3)=4^{-3}$

$f(-3)=\frac{1}{4^{3}}$

1. $f(x) = x^{−2} + 1$

See Hint for part (a).

1. $f(x) = \frac{1}{2}x + 2$

See Hint for part (a).

$\frac{1}{2}$


text:
# Maxwell's equations and nonlinear media

Are there analytical methods to analyze electromagnetic fields or magnetic diffusion in materials which are not linear using (or starting from) Maxwell’s equations?

Nonlinear material could be described as $B=\mu(H)H$, where $B$ is the flux density, $\mu$ the permeability, and $H$ the magnetic field strength. But how to consider that in the Maxwell’s equations?

Furthermore, even for simple geometry (cube, cylinder, ...) and even for one dimensional problems, e.g, one dimensional diffusion equation, i would not know how to consider nonlinear behavior analytically.

To be more specific, consider the magnetic field governing PDE for a long rod with radius $\rho$ for the axial component of $H$. In polar coordinates it reads:

$\partial_{\rho}^2 H(\rho,t)+\frac{1}{\rho}\partial_{\rho}H(\rho,t)-\mu \kappa \partial_t H(\rho, t)=0$, with conductivity $\kappa$. Now insert $\mu(H)$:

$\partial_{\rho}^2 H(\rho,t)+\frac{1}{\rho}\partial_{\rho}H(\rho,t)-\mu(H)\kappa \partial_t H(\rho, t)=0$.

Now, $\mu(H)$ might be approximated by a polynomial in $H$. Even in this simple case, an analytical solution might be difficult to obtain. I am wondering if there is maybe a finite dimensional analytic approximation of ODEs to describe this problem. For linear PDEs a mode decomposition is often made, but clearly for nonlinear systems this doesn’t works. Are there other methods to analyze equations like that? Does Maxwell’s equations indeed allow to just replace the $\mu$ by a field dependent permeability?

Any hints, experience with that or references are appreciated.

• A very general approach is probably expanding around the current value of H using e.g. Taylor expansion or maybe in some subspace of the target space you choose, I think Krylov subspace method is something like that but I have never used it myself. Then iteratively try to find a solution B using a numerical method. Sorry missed the analytical part... But if you do it symbolically and take some limit of small mesh size in the end it is maybe analytical again. – Emil Mar 3 '18 at 8:33
• @Emil :thanks, can you please provide more details with the symbolic approach? Is this found in some reference? – Carlos Mar 3 '18 at 8:45
• Carlos: I don't understand your question. I just meant simulate the numerical outline I wrote symbolically. – Emil Mar 3 '18 at 8:50
• @Emil : sorry, i thought symbolically like symbolic calculations as in tools as Mathematica :) – Carlos Mar 3 '18 at 8:57
• Treating electromagnetism in nonlinear media is equivalent to solving nonlinear PDEs. Even over simple volumes, no analytic method exists. In fact, it's not clear that most nonlinear PDEs even have solutions to begin with. If you want analytic methods, you're going to have to specify the particular nonlinear function you're interested in. – probably_someone Mar 3 '18 at 21:41


text:
Short-term trading is a difficult task due to fluctuating demand and supply in the stock market. These demands and supply are reflected in stock prices. The stock prices may be predicted using technical indicators. Most of the existing literature considered the limited technical indicators to measure short-term prices. We have considered 82 different combinations of technical indicators to predict the stock prices. We evaluate DSW CAPITAL PLC prediction models with Modular Neural Network (Emotional Trigger/Responses Analysis) and Independent T-Test1,2,3,4 and conclude that the LON:DSW stock is predictable in the short/long term. According to price forecasts for (n+4 weeks) period: The dominant strategy among neural network is to Hold LON:DSW stock.

Keywords: LON:DSW, DSW CAPITAL PLC, stock forecast, machine learning based prediction, risk rating, buy-sell behaviour, stock analysis, target price analysis, options and futures.

## Key Points

1. Understanding Buy, Sell, and Hold Ratings
2. Nash Equilibria
3. Is it better to buy and sell or hold?

## LON:DSW Target Price Prediction Modeling Methodology

With the up-gradation of technology and exploration of new machine learning models, the stock market data analysis has gained attention as these models provide a platform for businessman and traders to choose more profitable stocks. As these data are in large volumes and highly complex so a need of more efficient machine learning model for daily predictions is always looked upon. We consider DSW CAPITAL PLC Stock Decision Process with Independent T-Test where A is the set of discrete actions of LON:DSW stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4

F(Independent T-Test)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Modular Neural Network (Emotional Trigger/Responses Analysis)) X S(n):→ (n+4 weeks) $∑ i = 1 n s i$

n:Time series to forecast

p:Price signals of LON:DSW stock

j:Nash equilibria

k:Dominated move

a:Best response for target price

For further technical information as per how our model work we invite you to visit the article below:

How do AC Investment Research machine learning (predictive) algorithms actually work?

## LON:DSW Stock Forecast (Buy or Sell) for (n+4 weeks)

Sample Set: Neural Network
Stock/Index: LON:DSW DSW CAPITAL PLC
Time series to forecast n: 12 Nov 2022 for (n+4 weeks)

According to price forecasts for (n+4 weeks) period: The dominant strategy among neural network is to Hold LON:DSW stock.

X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)

Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)

Z axis (Yellow to Green): *Technical Analysis%

## Adjusted IFRS* Prediction Methods for DSW CAPITAL PLC

1. For the avoidance of doubt, the effects of replacing the original counterparty with a clearing counterparty and making the associated changes as described in paragraph 6.5.6 shall be reflected in the measurement of the hedging instrument and therefore in the assessment of hedge effectiveness and the measurement of hedge effectiveness
2. Expected credit losses are a probability-weighted estimate of credit losses (ie the present value of all cash shortfalls) over the expected life of the financial instrument. A cash shortfall is the difference between the cash flows that are due to an entity in accordance with the contract and the cash flows that the entity expects to receive. Because expected credit losses consider the amount and timing of payments, a credit loss arises even if the entity expects to be paid in full but later than when contractually due.
3. For example, Entity A, whose functional currency is its local currency, has a firm commitment to pay FC150,000 for advertising expenses in nine months' time and a firm commitment to sell finished goods for FC150,000 in 15 months' time. Entity A enters into a foreign currency derivative that settles in nine months' time under which it receives FC100 and pays CU70. Entity A has no other exposures to FC. Entity A does not manage foreign currency risk on a net basis. Hence, Entity A cannot apply hedge accounting for a hedging relationship between the foreign currency derivative and a net position of FC100 (consisting of FC150,000 of the firm purchase commitment—ie advertising services—and FC149,900 (of the FC150,000) of the firm sale commitment) for a nine-month period.
4. However, depending on the nature of the financial instruments and the credit risk information available for particular groups of financial instruments, an entity may not be able to identify significant changes in credit risk for individual financial instruments before the financial instrument becomes past due. This may be the case for financial instruments such as retail loans for which there is little or no updated credit risk information that is routinely obtained and monitored on an individual instrument until a customer breaches the contractual terms. If changes in the credit risk for individual financial instruments are not captured before they become past due, a loss allowance based only on credit information at an individual financial instrument level would not faithfully represent the changes in credit risk since initial recognition.

*International Financial Reporting Standards (IFRS) are a set of accounting rules for the financial statements of public companies that are intended to make them consistent, transparent, and easily comparable around the world.

## Conclusions

DSW CAPITAL PLC assigned short-term Ba2 & long-term B1 forecasted stock rating. We evaluate the prediction models Modular Neural Network (Emotional Trigger/Responses Analysis) with Independent T-Test1,2,3,4 and conclude that the LON:DSW stock is predictable in the short/long term. According to price forecasts for (n+4 weeks) period: The dominant strategy among neural network is to Hold LON:DSW stock.

### Financial State Forecast for LON:DSW DSW CAPITAL PLC Stock Options & Futures

Rating Short-Term Long-Term Senior
Outlook*Ba2B1
Operational Risk 7282
Market Risk7636
Technical Analysis8441
Fundamental Analysis3844
Risk Unsystematic7978

### Prediction Confidence Score

Trust metric by Neural Network: 77 out of 100 with 872 signals.

## References

1. Knox SW. 2018. Machine Learning: A Concise Introduction. Hoboken, NJ: Wiley
2. Allen, P. G. (1994), "Economic forecasting in agriculture," International Journal of Forecasting, 10, 81–135.
3. J. Hu and M. P. Wellman. Nash q-learning for general-sum stochastic games. Journal of Machine Learning Research, 4:1039–1069, 2003.
4. Lai TL, Robbins H. 1985. Asymptotically efficient adaptive allocation rules. Adv. Appl. Math. 6:4–22
5. H. Kushner and G. Yin. Stochastic approximation algorithms and applications. Springer, 1997.
6. P. Artzner, F. Delbaen, J. Eber, and D. Heath. Coherent measures of risk. Journal of Mathematical Finance, 9(3):203–228, 1999
7. Chen, C. L. Liu (1993), "Joint estimation of model parameters and outlier effects in time series," Journal of the American Statistical Association, 88, 284–297.
Frequently Asked QuestionsQ: What is the prediction methodology for LON:DSW stock?
A: LON:DSW stock prediction methodology: We evaluate the prediction models Modular Neural Network (Emotional Trigger/Responses Analysis) and Independent T-Test
Q: Is LON:DSW stock a buy or sell?
A: The dominant strategy among neural network is to Hold LON:DSW Stock.
Q: Is DSW CAPITAL PLC stock a good investment?
A: The consensus rating for DSW CAPITAL PLC is Hold and assigned short-term Ba2 & long-term B1 forecasted stock rating.
Q: What is the consensus rating of LON:DSW stock?
A: The consensus rating for LON:DSW is Hold.
Q: What is the prediction period for LON:DSW stock?
A: The prediction period for LON:DSW is (n+4 weeks)