text: Use the Atom package manager and search for "latex", or run apm install latex from the command line.. Prerequisites TeX distribution. Does anyone know where it looks for files? If you use addpath within a local function, the path change persists after program control returns from the function. \item MATLAB resolves all path names containing '. MiKTeX executables can be found. That's where my .emacs was by default, at least. For a tutorial on how to use the EPS file inside LaTeX, search on Google: latex import graphics. The package documentation list the options width and height, as well as others.. Installing. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. It's pretty simple really, which is why its unsurprising that its so popular within the research community - whether you're a scientist or statistician, with LaTeX, you'll find it easy to present and communicate your work - it gives you full control of the documents you create, no matter how complex they might be. I started learning TeX today, so please correct me if I say something wrong. The environment variable PATH should reference the directory which contains the MiKTeX executables.. Windows, Linux. Ask Question Asked 8 years, 6 months ago. Using pdflatex several graphics formats are supported: pdf, png and jpg.Modern installations of LaTeX can use eps files as well, but indirectly. LaTeX package. You just have to think of a proper width for the images. in ~/bin, if you have installed MiKTeX for your private use; or in /usr/local/bin, if you have installed MiKTeX system-wide 2. In Kpathsea version 6.3.0 (released with TeX Live 2018), a new fallback search was implemented on Unix-like systems, including Macs: for each path element in turn, if no match is found by the normal search, and the path element allows for checking the filesystem, a second check is made for a case-insensitive match. LaTeX is both a word processor and a markup language. \itshape Italicizes the text which is inside curly braces with the command. TeX Live - Quick install. Some compilers (such as Microsoft Visual Studio) put symbol files in the same directory as the binary files. The folders provided with MATLAB and other MathWorks products, which are under matlabroot/toolbox, where matlabroot is the folder displayed when you run matlabroot in the Command Window 10/15/2020. LaTeX in dvi-mode supports only eps-files.. You can align the images in a matrix. Hello r/LaTeX!. The symbol path specifies locations where the Windows debuggers (WinDbg, KD, CDB, NTST) look for symbol files. 10/31/2020. If you don't want to bother reading the full install documentation and just want to install everything in TeX Live, on a Unix-like system, a minimal recipe follows.. Special considerations for Windows are described separately. RuntimeError: latex program is not installed. Just put this somewhere on your sys.path, and it'll add any directory under folder (from the current working directory), or under abspath: #using.py import sys, os.path def all_from(folder='', abspath=None): """add all dirs under folder to sys.path if any .py files are found. 10/29/2020. However, the individual shortcuts â including a command prompt â have a modified searchpath with TeX Live in front, so as long as you use TeX Live via the menu, you should be fine. Active 8 years, 6 months ago. As for LaTeX, sadly I can't help. Such as {\itshape This is in italics}. A further move-to operation in an existing path starts a new part of the path, which is not connected to the previous part of the path. The value of the make variable VPATH specifies a list of directories that make should search. ; For MacOSX (aka macOS), we recommend installing MacTeX, which contains all of TeX Live (and a few Mac-specific additions). For more information, see Add Folders to the MATLAB Search Path at Startup. Make sure to separate paths with a semicolon (;). You probably want to choose the first option. LaTeX is free software under the terms of the LaTeX Project Public License (LPPL).LaTeX is distributed through CTAN servers or comes as part of many easily installable and usable TeX distributions provided by the TeX User Group (TUG) or third parties. This setting is use by LaTeXTools to determine the PATH used for ... any LaTeX file with pdflatex -synctex=1 and opening the resulting PDF in SumatraPDF. Changed the let* in latex-help as follows (ugly, but seems to work). How to turn an Inkscape drawing into an editable LaTeX document. Database Administrators Stack Exchange is a question and answer site for database professionals who wish to improve their database skills and learn from others in the community. This means that to switch from one TeX to another, e.g., between TeX Live and MiKTeX if you have both installed, you must (at least) change the search path. Requires graphicx package. When the LaTeX compiler finds a reference to an external file in the base file, it will look for it in the same directory. The "Next Latex Error"and "Previous LaTeX Error" commands allow to get to the errors detected during compilation : 3.3 Synchronization source-pdf with Synctex If you add the "-synctex=1" option to the pdflatex command, the built-in pdf viewer will jump directly to the position in the PDF file that corresponds to the current line in the (La)TeX source file. A reasonably up-to â¦ Compare Products: Select up to 4 products. How can I write a path with LaTeX? The MATLAB userpath folder, which is added to the search path at startup, and is the default location for storing user files The folders defined as part of the MATLABPATH environment variable. This causes ltx-help to sometimes land on the top page, instead of the actual target node. 4.5.1 VPATH: Search Path for All Prerequisites. *Please select more than one item to compare Feedback appreciated. Search results for Latex beads at Sigma-Aldrich. However, you can in principle refer to any file on your system, using both absolute and relative paths. Matplotlib doesn't seem to find files in the current working directory when running latex. That setting might be configurable, but I've never cared enough to change it. administrator mode problem when using Miktex on Windows 10. 09/14/2020. \em is generally preferred since it allows nesting. ', '..', and symbolic links to their target location before adding them to the path.This ensures that each entry in the MATLAB path represents a unique folder location. An online LaTeX editor that's easy to use. The LaTeX export back-end can handle complex documents, incorporate standard or custom LaTeX document classes, generate documents using alternate LaTeX engines, and produce fully linked PDF files with indexes, bibliographies, and tables of contents, destined for interactive online viewing or high-quality print publication. To modify the search path programmatically at startup, use addpath statements in a startup.m file. Viewed 2k times 8. ... Inverse search is a feature where a mouse click in the DVI viewer can open an editor with the corresponding place in the ... Just edit the line beginning with TEXMFDIST and add the path of the packages you want to include. Algorithms. Matplotlib latex working directory / search path. It returns the path to the file. So I wrote a quick and dirty solution. Most often, the directories are expected to contain prerequisite files that are not in the current directory; however, make uses VPATH as a search list for both prerequisites and targets of rules. Surround some selected text with a LaTeX command using ctrl+l, ctrl+w (â+l, â+w on Mac). An absolute path is a full path- and filename with every From version 0.48, Inkscape has a special PDF+LaTeX output option. 13.10 LaTeX Export. The path might be different on your system, so see where Emacs takes you when you try to find a file and type ~/. User install of App-V MikTeX on non-persistent VM with shared package repo. Pdf and pdf viewer in Texstudio not update after compilation? To use it, we include the following line in the preamble: \usepackage{graphicx} The command \graphicspath{ {./images/} } tells L a T e X that the images are kept in a folder named images under the directory of the main document.. TinyTeX is a custom LaTeX distribution based on TeX Live that is small in size (about 61Mb on macOS/Linux, and 94Mb on Windows when (g)zipped), but functions well in â¦ For more see LaTex/Basics \includegraphics Inserts an image. kpsewhich will actually search for files only, not for packages. For more information about symbols and symbol files, see Symbols.. Latex can not manage images by itself, so we need to use the graphicx package. LaTeX log parser, with errors and warnings in LaTeX build automatically reported in VS Code. LaTeX is a markup language for describing a document. In this article. For more see LaTex/Basics. \includeonly \indent \input Used to read in LaTex files. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. Another change seems to be required in the latex-help function, since try-completion returns the actual match in case of a partial match, but only t in case of a perfect match. Linting; Snippets. A lot of LaTeX commands can be typed using snippets starting in \, then type part of the command to narrow the search. I want something like this: C:\\Program Files\\My Program\\my file.txt I have to use double slashes, not single ones. An online LaTeX editor that's easy to use. The PATH keyword that follows the SETX defines which set of values should be changed among the System Environment Variables possible values, and the %PATH% (the word PATH surrounded by the percent sign) inside the quotation marks, tells the OS to leave the existing PATH values as they are and add the following path (the one that follows the split sign ';') to the existing values. Compile LaTeX, knitr, literate Agda, literate Haskell, or Pweave documents from within Atom. Path of Exile is a free online-only action RPG under development by Grinding Gear Games in New Zealand. New MATLAB search path, specified as a character array or string array. 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# Tell me how to flop

As computer scientists, you're probably all familiar with the basic list operations of pop and push. These are simple operations that modify a list of elements. However, have you ever heard of the operation flop? (as in flip-flop)? It's pretty simple. Given a number n, reverse the first n elements of the list. Here's an example:

>>> a = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
>>> a.flop(4)
[4, 3, 2, 1, 5, 6, 7, 8, 9, 10]

The cool thing about the flop operation, is that you can use it do some cool things to a list, such as sorting it. We're going to do something similar with flops:

Given a list of integers, "Neighbor it". In other words, sort it so that every duplicate element appears consecutively.

This can be done with flops! For example, take the following list:

>>> a = [3, 2, 1, 4, 3, 3, 2]
>>> a.flop(4)
[4, 1, 2, 3, 3, 3, 2]
>>> a.flop(3)
[2, 1, 4, 3, 3, 3, 2]
>>> a.flop(6)
[3, 3, 3, 4, 1, 2, 2]

This leads us to the definition of today's challenge:

Given a list of integers, output any set of flops that will result in the list being neighbored.

Using the last list as an example, you should output:

4
3
6

because flopping the list by 4, then by 3, then by 6 will result in a neighbored list. Keep in mind that you do not need to print the shortest possible list of flops that neighbors a list. If you had printed:

4
4
4
3
1
1
6
2
2

instead, this would still be a valid output. However, you may not ever output a number larger than the length of the list. This is because for a list a = [1, 2, 3], calling a.flop(4) is nonsensical.

Here are some examples:

#Input:
[2, 6, 0, 3, 1, 5, 5, 0, 5, 1]

#Output
[3, 7, 8, 6, 9]

#Input
[1, 2]

#Output
<any list of integers under 3, including an empty list>

#Input
[2, 6, 0, 2, 1, 4, 5, 1, 3, 2, 1, 5, 6, 4, 4, 1, 4, 6, 6, 0]

#Output
[3, 19, 17, 7, 2, 4, 11, 15, 2, 7, 13, 4, 14, 2]

#Input
[1, 1, 1, 1, 2, 2, 2, -1, 4]

#Output
[]

#Input
[4, 4, 8, 8, 15, 16, 16, 23, 23, 42, 42, 15]

#Output
[12, 7]

Keep in mind that in each of these examples, the output given is just one potential valid output. As I said before, any set of flops that neighbors the given list is a valid output. You can use this python script to verify if a given list of flops correctly neighbors a list.

You may take input and output in any reasonable format. For example, function arguments/return value, STDIN/STDOUT, reading/writing a file etc. are all valid. As usual, this is , so make the shortest program you can, and have fun! :)

• I heard it as fl(oating point) op(eration). – Weijun Zhou Jan 31 '18 at 0:21
• @WeijunZhou That's a measure of computational speed, for counting operations carried out py a piece of hardware. en.wikipedia.org/wiki/FLOPS – iPhoenix Jan 31 '18 at 0:24
• Do submissions have to be deterministic or can I pseudo-randomly flop until the array is grouped? – Dennis Jan 31 '18 at 3:17
• Are zero flops allowed to appear in the output? – Laikoni Jan 31 '18 at 7:49
• Related. NB any answer to that question would be an answer to this one, but since being sorted is a stronger condition than being "neighboured" it may be possible to out-golf them so this might not be a duplicate (although the fact that the only answer so far sorts is not encouraging). – Peter Taylor Jan 31 '18 at 8:24

# Haskell, 98 71 bytes

h.r
h(x:s)|(a,b)<-span(/=x)s=l b:l s:h(b++r a)
h e=e
r=reverse
l=length

Try it online!

### Explanation

For a list of length n this method produces 2*n flops. It works by looking at the last element of the list, looking for the same element in the list before and flipping it to the second to last position. Then the list with the last element removed is recursively "neighboured".

For the list [1,2,3,1,2] the algorithm works like this:

[1,2,3,1,2]  flip longest prefix that ends in 2: flop 2
[2,1,3,1,2]  bring first element to second to last position: flop n-1 = flop 4
[1,3,1,2,2]  recursively work on n-1 list
[1,3,1,2]    there is no other 2: flop 0
[1,3,1,2]    flop n-1 = flop 3
[1,3,1,2]    recurse
[1,3,1]      flop 1
[1,3,1]      flop 2
[3,1,1]      recurse
[3,1]        flop 0
[3,1]        flop 1
...

All together this yields the flops [2,4,0,3,1,2,0,1,0,0] and the neighboured list [3,1,1,2,2].

# Wolfram Language (Mathematica), 71 bytes

If[(n=Tr[1^#])<1,{},{i=Last@Ordering@#,n,n-1,i-1}~Join~#0[#~Drop~{i}]]&

Try it online!

## How it works

Given an array of length n, outputs a sequence of 4n flops that sort the array in increasing order: in particular, putting duplicate elements next to each other.

The idea is that to sort an array, we move its largest element to the end, and then sort the first n-1 elements of the array. To avoid implementing the flop operation, we move the largest element to the end in a way which does not disturb the other elements:

{3, 2, 1, 5, 3, 3, 2}    starting array, with largest element in position 4
{5, 1, 2, 3, 3, 3, 2}    flop 4 to put the largest element at the beginning
{2, 3, 3, 3, 2, 1, 5}    flop 7 to put the largest element at the end
{1, 2, 3, 3, 3, 2, 5}    flop 6 (7-1) to reverse the effect of flop 7 on other elements
{3, 2, 1, 3, 3, 2, 5}    flop 3 (4-1) to reverse the effect of flop 4 on other elements

In general, if the largest element is in position i, the sequence of flops that moves it to the end is i, n, n-1, i-1.

• You can move the largest element to the end with just i, n. Why then do n-1, i-1? There's no need for a stable sort. – Peter Taylor Jan 31 '18 at 8:27
• @PeterTaylor I don't think the answer actually performs flops, rather, it removes the largest element each time, and outputs the equivalent of that operation in terms of flops. – Neil Jan 31 '18 at 9:38

# Python 2, 69 bytes

l=input()
while l:k=l.index(max(l));print-~k,len(l),;l=l[:k:-1]+l[:k]

Try it online!

# Jelly, 19 17 bytes

ỤỤạ‘Ḣ
ỤÇÐƤĖµUż’ṚF

Sorts the list.

Try it online!

• I think ỤŒ¿’Æ!‘ṚĖµUż’ṚF reverse sorts since Œ¿ is modulo L!. – Jonathan Allan Jan 31 '18 at 20:16
• For whatever reason, that doesn't work for the last test case, which probably means that my code will fail for some obscure edge case as well... – Dennis Jan 31 '18 at 20:30
• And it does indeed fail for input [4, 3, 2, 1, 3]. Bummer. – Dennis Jan 31 '18 at 20:38
• Oh, boo; that's a shame. – Jonathan Allan Jan 31 '18 at 21:00
• Ụ>Ṫ$ƤSạỤĖµUż’ṚF saving 2 bytes by replacing the helper link. – miles Feb 16 '18 at 15:59 # Clean, 88 bytes I think there's a possibly shorter one with guards, but I haven't found it yet. import StdEnv$[h:t]#(a,b)=span((<>)h)t
=map length[b,t]++ $(b++r a)$e=e
r=reverse

$o r  Try it online! As a function literal. Works the same way as Laikoni's Haskell answer, but golfed slightly differently, and of course also in a different language. # JavaScript, 150 bytes (a,f=n=>(a=[...a.slice(0, n).reverse(),...a.slice(n)],n),l=a.length,i=0)=>a.reduce(c=>[...c,f(a.indexOf(Math.max(...a.slice(0, l-i)))+1),f(l-i++)],[])  Try it online! # JavaScript, 151 bytes a=>{f=n=>(a=[...a.slice(0,n).reverse(),...a.slice(n)],n),r=[];for(i=a.length+1;--i>0;)r.push(f(a.indexOf(Math.max(...a.slice(0, i)))+1),f(i));return r}  Both basically sort the array by flipping the max number to the beginning and then flipping it to the back, repeating this with the remaining array. The first one uses reduce, the second one uses a for loop. ## Ungolfed: array => { let flop = n => { array = [...array.slice(0, n).reverse(), ...array.slice(n)]; return n; } let flops = []; for (let i = array.length + 1; --i > 0;) { let maxIndex = array.indexOf(Math.max(...array.slice(0, i))); flops.push(flop(maxIndex + 1), flop(i)); } return flops; }  # Perl 5.10 (or higher), 66 bytes Includes +3 for -n The use 5.10.0 to bring the language to level perl 5.10 is considered free #!/usr/bin/perl -n use 5.10.0;$'>=$&or$.=s/(\S+) \G(\S+)/$2$1/*say"$. 2$."while\$.++,/\S+ /g

Run with the input as one line on STDIN:

flop.pl <<< "1 8 3 -5 6"

Sorts the list by repeatedly finding any inversion, flopping it to the front then flopping the inversion and flopping everything back to its old position.

It was surprisingly hard to get in the same ballpark as python on this one :-)

# C (gcc), 165 160 bytes

m,j,t;f(A,l)int*A;{for(j=0;j+j<l;A[j]=A[l+~j],A[l+~j++]=t)t=A[j];}F(A,l)int*A;{for(;l;f(A,++m),printf("%d,%d,",m,l),f(A,l--))for(j=m=0;j<l;j++)m=A[j]>A[m]?j:m;}

• @ceilingcat Thank you. – Jonathan Frech Aug 6 at 19:55

format: plain


text:
### A Collection of My Fall 2020 Course Notes:

An * denotes a graduate level course, and a denotes a class I am a Course Assistant for.

Math 122: Theory of Groups and Vector Spaces
AC 209a: Data Science*
MIT 6.840: Theory of Computation*
MIT 6.006: Introduction to Algorithms
Stat 110: Introduction to Probability
Math 22a: Vector Calculus and Linear Algebra I

I am also taking Chinese 130xa: Pre-Advanced Modern Chinese for High-Proficiency Learners, which I have abstained from including above.


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# Is there any specific conditions for Neighbouring group participation?

I got to know about what neighboring group participation is, but does it always occur if there are lone pair donating groups in beta or delta positions. Or does it only occur in some kind of medium or is there any specific condition that is required?

For example, I have attached a picture below. I was solving some problems on this topic and came across this one.

The product I expected an epoxide(diazotization followed by attack of lone pair of oxygen) ,

But the answer given was a Ring contraction followed by formation of an aldehydic group,

So, to be clear, Why didn't Neighboring group participation take place, or in this case why an epoxide wasn't formed?

The mechanism I predicted:

• Can you draw out the mechanism for the epoxide formation? Jun 29 at 15:12
• @orthocresol I have added the mechanism I predicted that would take place. Can you please help me out? Jun 29 at 15:28
• The Tiffeneau rearrangement has been addressed here: chemistry.stackexchange.com/questions/116689/… Remember that the t-butyl group anchors the chair conformation. Jun 29 at 15:42
• Good work with the mechanism. Now, you've drawn what's basically an SN2 reaction. You remember that the nucleophile must approach from a certain angle in an SN2 reaction...? Jun 29 at 15:55
• You are right in saying that it must approach from the rear. Only that in your case, the $\ce{OH}$ group is not rear to $\ce{NH2}$ - both of them are faced to the right side. Since $\ce{NH2}$ is to pointing left, the attacking/migrating group from adjacent carbon must point to the right. The right pointing group is the alkyl part, which migrates causing ring contraction. It's always the opposite-side-pointing that matters - not up/down or cis/trans for the cyclohexane substituents.
– TRC
Jun 30 at 4:02

In the given compound the $$\ce{-OH}$$ group and the $$\ce{-NH2}$$ and later $$\ce{N2^+}$$ group are not in anti position with respect to each other. Equatorial positions in cyclohexane are not anti with respect to each other.
Below I have drawn newmann projection of the reactant which should help you visualise that a carbon (encircled) is instead in anti-relation to the leaving group, instead of $$\ce{-OH}$$. The cyclohexane cannot flip here either since $$\ce{t-Bu}$$ has locked the conformation would cause heavy steric repulsion in axial location making the ring unstable if it were to flip.
To show neighbouring group participation it is important that the lone pair donor be anti with respect to the leaving group. Hence here this is not availiable. Instead the anti-carbon attacks (undergoing ring contraction) because the resulting carbocation is stabilized by resonance with $$\ce{-OH}$$ as shown by this mechanism
Footnote:- The reaction does not involve hydride transfer to give ($$\ce{t-Bu}$$) substituted cyclohexanone as a major product because here $$S_n2$$ mechanism is faster than $$S_n1$$ (for most cases of secondary carbon in polar solvents and we can't have direct attack of hydrogen on $$\ce{N2+}$$ because it is not anti to leaving group) and there is not a great deal of difference in stability of 5 and 6 membered rings. However it still does occur to some extent.


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# Columbia 2013 (CBS) - Calling All Applicants

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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  05 Feb 2013, 13:22
3
KUDOS
I AM IN!

App: 9/30
Invite to interview: 10/28
Interview: 11/12
Feedback: 11/16
ED-Waitlist: 11/20
Accepted: 02/05

Good luck to all of you!

Posted from my mobile device
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  07 Feb 2013, 08:41
3
KUDOS
Dinged without interview. Submitted Jan 8. LatAm applicant.

Good luck to the remaining candidates.
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  12 Feb 2013, 09:43
3
KUDOS
aerien wrote:
Azn84 wrote:
just got dinged by Columbia... I'm kind of surprised because it was my safety school...

Applied Jan 9th..

Sorry to hear that but I don't think anyone can consider CBS their safety school (unless of course you're that one stellar guy who gets in to every top school). Good luck on your other apps. You have some great schools picked out and hopefully you hear good news soon.

Got dinged two hours ago. Had applied on 9th Jan.

This is what the email from Columbia says(Like really)

Dear Mr. Sticker Shock

In case you didn’t already know, you have been unsuccessful. We didn’t receive many applications, and even then, yours stood out as being the most mediocre. The hours you spent on the application would have been better spent in the pub. And you should also consider alternative career paths aside an MBA.

Kind Regards

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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  20 Feb 2013, 14:04
3
KUDOS
ACCEPTED!!! Got the call at 3PM today! And a fellowship!

Submitted: 01/02/13
Mid-Cycle Decision: 01/29/13 (27 days)
Interview: 02/07/13 (36 days)
Evaluation: 02/10/13 (39 days)
Final Decision: 02/20/13 (49 days)
_________________

-Onward, tomorrow.

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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  26 Feb 2013, 15:53
3
KUDOS
*warning* : digression from admissions related stuff (or not, if you are still searching for schools)

good friend souvik showed me this CBS follies video yesterday - Married But Available (MBA). Pretty funny.

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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  27 Feb 2013, 12:53
3
KUDOS

Call from Blocked/'Unknown' number.

Totally psyched. Almost certain I will accept, though have not yet received any info regarding a deposit timeline. Looking forward to potentially meeting some of you at the upcoming happy hour events.

Best of luck to all of you still waiting!

Last edited by 1234321 on 28 Feb 2013, 12:34, edited 1 time in total.
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  30 Mar 2013, 05:39
3
KUDOS
IN!!!!

Here is my timeline:
applied: 1/15
Invited to interview: 2/26
Interview: 3/14
Feedback: 3/17
accepted: 3/29
VP
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Re: Columbia 2013 - Calling All Applicants [#permalink]  14 Jun 2012, 17:46
2
KUDOS
crunchykapo wrote:
bozooo wrote:
considering to apply for the early decision, but i am confused with the merit based fellowship,

if i apply for the early decision, will my application be in the fellowship evaluation or not ?

wondering the same too...but im 70% sure I will apply ED this year...(if i dont decide to postpone application exercise..)

Yes ED applicants are considered for fellowships. The fellowship deadline is simply the latest date by which you can apply and still be considered for merit based fellowship, not a distinct round strictly for fellowship consideration. Remember CBS does not technically have rounds, but rather rolling admissions with key deadline dates (i.e. Early Decision, fellowship consideration, last call).
_________________

The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com

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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  27 Aug 2012, 18:43
2
KUDOS
A little bit of nostalgia and amusement while we wait:

I recently was digging through boxes in my basement, and found a 1999 copy of BusinessWeek's Guide to the Best Business Schools (6th edition) -- the year when Columbia's tuition broke (ohgosh) the $27,000 ceiling. Yes, that's right:$27,000/yr.

Some other incredible tidbits from a decade and change ago, to distract us from our communal freak-outs:

Corporate ranking: 4
Enrollment: 1284
Average age: 27
Applicants accepted: 12%

Average GMAT score: 680
Average GPA: 3.45
Average work experience: 4 years

Median starting pay: $125,000 Average starting pay:$146,400
Annual tuition and fees: $27,770 Room and board:$9918

Who else misses the 90's?
Current Student
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Schools: Columbia - Class of 2013
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  29 Aug 2012, 10:38
2
KUDOS
Bananas wrote:
akinakbiyik wrote:

One question: they send 3 names can we choose whom we contact first? anyone has any idea? because on the internet they said you can but in the status page it says:

"To schedule your interview, you should reach out via email to the first Ambassador on the above list. "

I received notification as well. I am going to start at the top of the list as the status page suggests.

I looked up the interviewers on LinkedIn and found one in my industry. It went well as we had a lot to talk about. I don't think that my interviewer was the first person on the list, however, but it didn't seem to be an issue. (I can't recall if that message about order was even there when I applied). Just a thought!
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  23 Sep 2012, 20:04
2
KUDOS
Thought I might do an interview debrief for those who are still watching and waiting, because I have nothing better to do and am already starting to get antsy. I hate that CBS' app status tracker this year doesn't actually show status changes -- so we have no way to know if the interviewer submitted the feedback form or not yet

Anyway, got my interview invite on 9/12. Got the names of my potential interviewers on 9/13 and emailed the first one on the list that day. She had already moved out of my area, and responded quickly, so I emailed the second interviewer also on Thursday. No response, so Monday night emailed the third person -- was getting really nervous at this point that no one would response. Thankfully the third person on my list responded, and we set the interview up for Saturday morning (9/23)

The interview itself was a LOT more formal than I expected from what I've read here on the boards. I know all interviewers have their own style, but mine was a very recent grad and asked to meet at a coffeeshop instead of a workplace, so I assumed it might be a little more relaxed. Nope - all in business attire, and had a portfolio spread out on the table with my resume and a notepad. Felt a lot like a job interview, actually. My interviewer was definitely cordial and spoke very passionately and positively about the community at CBS, but I'm not sure what to think overall because it pretty aloof and professional throughout.

Questions:
- tell me about yourself -- used this to launch into a very broad interview of my resume and how I got where I am. There weren't that many resume specific questions, though.
- why MBA, esp with my background
- why CBS?
- lots of CBS-specific questions: how much did I know about the core and flex-core, and how I wanted to use this to achieve my goals? Specific classes and clubs I was interested in? Other opportunities I might want to look into? This was definitely IMO the biggest chunk of the questions and where my interviewer dug in the most, and it matched up pretty well with Essay 1b (where they ask you to watch the diversity video). My advice to future interviewees: really get to know the CBS methodology, class structure, clubs, etc!
- tell me of a time you faced adversity, and follow-ups to this: what makes a good leader and why you are a good leader, how you might bring that to your studies and to your learning teams, etc.
This took somewhere around 35-40 minutes.

Then my interviewer let me ask questions about the various opportunities at CBS, clubs, etc. The emphasis was definitely on COMMUNITY, getting involved in clubs, learning from other people both in classes and in social settings, etc. The feeling I got was that he wasn't feeling me out so much in terms of why I wanted to get an MBA, but how I might be able to fit into the intellectual and esp. the social community of CBS. He really stressed that you go to CBS not for the hard skills as much as for the networking and soft skills and the people.

Total interview time - a little over an hour. Overall, I feel pretty ambivalent about it -- we talked a lot and my interviewer was friendly but so formal that I couldn't get any specific vibes off of him. Worries me, compared to some of the really enthusiastic interview debriefs I've read here and on other sites...

Anyway, hope this helps some of you out there preparing for your own interviews! For me, it's now just time to settle in, wait, and try to stop worrying either way.
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Interview Debrief from a J-term applicant [#permalink]  01 Oct 2012, 18:47
2
KUDOS
Just had my interview today, so I thought I'd share my experience with everyone.

Quick stats:
28/Male/American
GMAT 710, Q47, V41
UGPA 3.1 from top public university

Interview Location: Starbucks in Orange County, CA

My interview was with a CBS alumni, class of 2005. He had a background in Finance and worked and his first job out of CBS was at Citigroup. He then moved over to a hedgefund for a few years, and is currently working for one of the worlds largest bond companies. He was also an international alumni orginally from South America, so the international element definitely played into the interview.

Demeanor: Very laid-back and soft spoken, he wanted me to feel comfortable and simply have a conversation about Columbia with him. I walked him through my resume and shared my story of starting a company after college with him, and my various accomplishments. He definitely understood everything I was saying, but was not trying to "grill" me i.e. poke holes in my story, or stump me with random questions. He seemed very satisfied with my reasons for getting an MBA, and even told me that my reasoning was almost exactly the same as his when he applied.

The only mandatory question he said he had to ask me was "Tell me about a time in which you faced adversity" He told me this was the only question he was required to ask. He also told me that the school does not communicate with him about the interview, they just look at the interview sheet that he fills out.

All in all, it was much easier than I had prepared for it to be. My advice to those yet to interview, is go through the columbia interview boards, write down all the different questions that have been asked to past applicants, and prepare a response for each one. that's about 25 possible questions. If you do this, you will be ready for whatever comes your way, and even if they don't ask the questions you prepared for, you can work that information into the interview anyway.

I'm very happy with the interview, and even if things don't work out, I know for a fact that my interview won't be the reason I didn't get into Columbia.

Hope to get the call soon!!!!!
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  29 Oct 2012, 21:43
2
KUDOS
Hey guys,

My profile -

IT consultant, 23 y.o, female, Intl student, GMAT 700.

It took 3 weeks to get the interview invite, but got the call a week after my interviewer submitted his feedback.

I wish you guys all the best!

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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  05 Nov 2012, 12:09
2
KUDOS
Got the admit call about an hour ago. Good luck to the rest of you waiting to hear back, I know how stressful it is. By the way, any admits from the Toronto area on here?

Here's my stats & timeline:

Engineer / project manager, 3 years WE
75/100 GPA Engineering
760 GMAT (49Q, 44V)
Submitted 9/14, invited 10/5, interviewed 10/24, feedback received 10/25, admitted 11/5 ~2pm EST

Last edited by knik on 07 Mar 2013, 12:28, edited 1 time in total.
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  29 Nov 2012, 08:46
2
KUDOS
rjdunn03 wrote:
I also have a fairly low gpa (3.2), did you talk about yours in the optional essay or do anything in particular to take the sting off the gpa?

For what it's worth RJ, I have a 3.2 undergrad GPA as well and was admitted ED. I did not address my GPA in the optional essay - I chose not to write an optional essay at all.

I understand where you're coming from, because if you're like me you look at the 3.2 and know you could have done better, but if you ask me it is also not so bad as to warrant highlighting/explanation.

That said, my GPA was of my own making - no excuses. If you're in a different spot - i.e. extreme family commitments, or a taxing part time job while studying (something material that distracted you from your studies) you could mention/explain it. Otherwise I would leave it and let the best parts of your application speak for themselves. No need to highlight a weaker part of of your candidacy.

Your 3.2 should not keep you out. It didn't for me.

Hope that helps.
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  05 Dec 2012, 11:58
2
KUDOS
Submitted november 16th, got an invite on 23rd interviewed on 30th nov.. 3rd dec feedback submitted.. awaiting final result :-/
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  13 Dec 2012, 13:19
2
KUDOS
got the call for RD! I'm in
Applied early Oct. Got the interview invite on Nov 26. Interviewed Dec 4th. Feedback submitted Dec 6th. Got the call Dec 12th. 12/12/2012! lucky 12!
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  24 Dec 2012, 12:28
2
KUDOS
redpringles wrote:

By the way, does anyone know approximately what % of the applicants get interviewed, and what % of the interviewed applicants are given offers?

I forget the exact numbers but in past years it comes out to roughly 50% of interviewed applicants are accepted. So I think it was something like 28% are interviewed and 14% accepted or roughly in that region. So if you get the interview invite you have made it over the largest hurdle and are up to a 50% chance of success. This metric seems to hold roughly true at almost all of the Top 10 schools.
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  24 Jan 2013, 08:56
2
KUDOS
redpringles wrote:
TheFool wrote:
I got dinged by Columbia on Tuesday afternoon after an interview... have been moping around since and haven't wanted to post it on the forums. Sorry for the delay, and just for the record, here was my timeline:

Submitted: 11/26
Interview invite: 12/19
Interviewed: 1/11
Interview report submitted: 1/15
Decision: 1/22

I gotta say it really sucks. I'm currently 0-for-3, and feeling less and less optimistic about my chances of getting in anywhere. Especially after that interview at Columbia which was, frankly, unfriendly.

I'm sorry to hear that. It took 2 months after your interview feedback submission to get your decision? Wow...

Actually it wasn't two months -- I caught that right after I posted and it's been edited above. Sorry about that!! Timeline was:

Interviewed: 1/11
Interview report submitted: 1/15
Decision: 1/22

The first 50 minutes of the interview went fine. While the questions were tough ("give me a ballpark estimate of how many brand managers get hired every year" "Besides the six companies and three industries you mentioned that use brand management, what other companies recruit at Columbia for your desired field?").

Then he started lecturing me about the importance of seizing the advantage in networking, noted that I'm competing against my fellow students "including the guy with two years' of experience at McKinsey who is just interviewing for fun, but who looks better on paper."

He then asked me why I was applying so late and to so few schools. I replied that I had applied to five schools and submitted my application to Columbia on November 20. He said that was too late and to too few schools, and didn't seem optimistic about my chances of getting in.

Honestly, none of his advice was bad or unwelcome (though I still disagree about not following Columbia's instructions), but the tone of the conversation took a very negative turn near the end. I'm not sure if I was unlucky, if I said the wrong thing, if he was trying to push my buttons or that's just his manner.
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Re: Columbia 2013 (CBS) - Calling All Applicants [#permalink]  28 Jan 2013, 08:24
2
KUDOS
Just got in off the waitlist.

Got a call this morning, I'm in. Doing the Pre-MBA World Tour for 2 months for sure, who's down?
Re: Columbia 2013 (CBS) - Calling All Applicants   [#permalink] 28 Jan 2013, 08:24

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# Columbia 2013 (CBS) - Calling All Applicants

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## Impulse and Momentum

4.) The motion of an oscillating flywheel is defined by the relation   θ=θ0e-7πt/6sin(4πt) , where θ is expressed in radians and t in seconds. Knowing that θ0 = 0.4 rad, determine the angular coordinate, the angular velocity, and the angular acceleration of the flywheel when    (a) t = 0.125 s, (b) t = ∞.


text:
## Results (18 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
605.1-a1 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(4\phi-13\right){x}-1591\phi-1011$
605.1-a2 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(\phi-1\right){x}-\phi+2$
605.1-a3 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(\phi-6\right){x}+\phi-2$
605.1-a4 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(36\phi-91\right){x}+147\phi-322$
605.1-a5 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-34\phi-1\right){x}+83\phi+2$
605.1-a6 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(586\phi-1466\right){x}+10927\phi-22432$
605.1-b1 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\phi{x}{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-3\phi-10\right){x}+1581\phi-2595$
605.1-b2 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(35\phi-34\right){x}-84\phi+119$
605.1-b3 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}-4{x}-7\phi-2$
605.1-b4 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+{x}$
605.1-b5 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(-35\phi-54\right){x}-238\phi-211$
605.1-b6 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(-585\phi-879\right){x}-12393\phi-12091$
605.1-c1 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(48\phi-38\right){x}-1458\phi-1109$
605.1-c2 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$
605.1-c3 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}-4{x}+3$
605.1-c4 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$
605.1-c5 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}-59{x}+190$
605.1-c6 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-48\phi+9\right){x}+1410\phi-2558$


text:
# Seminário de Análise, Geometria e Sistemas Dinâmicos

18/07/2017, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Rachid El Harti, Univ. Hassan I

### C*-algebra valued numerical range for adjointable operators and some applications

Let $A$ be C*-algebra and $E$ a Hilbert C*-module over $A$. For an adjointable operator $T$ on $E$, we define an $A$-valued numerical range $W(T)$ of $T$. We derive properties of $W(T)$ which are the analogs of the classical numerical range for operators acting on Hilbert space, including the Toeplitz-Hausdorff theorem and the equality between the numerical radius and the operator norm for normal adjointable operators.


text:
# [NTG-context] ConTeXt Manual Errata

Marco Patzer lists at homerow.info
Sat Sep 21 19:15:01 CEST 2013

On 2013–09–18 Thangalin wrote:

Hi Dave,

> During a recent plane ride, I started to read the ConTeXt manual
> to get a better understanding:
> http://www.ctex.org/documents/context/cont-enp.pdf

A more recent manual can be found at

http://pmrb.free.fr/contextref.pdf

> If anyone has plans to revise it,

I assume everybody on this list had at some point plans to revise
the manual(s). Due to lack of time this has never happened.

> I have attached a file with corrections, specific comments, and

Thanks a lot for the corrections and suggestions.

> I did not have the ConTeXt manual source code on hand, so I could
> not directly modify it.

http://wiki.contextgarden.net/Improving_the_manuals

Do not count on someone else to fix it. Create an account and fix
what you think could be improved, especially the grammar and
spelling mistakes. If you're unsure about something, write a mail to
the manual mailing list¹ for questions about the manual (style,
layout, etc.) or this list for everything else.

Note: The manual has not been updated since a while and it's broken
at the moment. I'll prepare a fix soon, so it will compile with a
recent MkIV.

> Take the comments with a grain of salt:

Take the existing manuals with a grain of salt ;)

> ConTeXT Manual Errata & Suggestions
> ===================================
>
> Section 1.3.
> ------------
> The word "something" needs to be defined before it is used.
> For example, "\setupsomething" <- What does "something" mean?

A placeholder like foobar or whatever. I think it's clear from the
context, otherwise feel free to define it.

> The \defineenumeration[Question] creates a \Question command,
> but \definehead[Procedure][section] does not create \Procedure command?

It does:

\starttext
\Procedure{something}
\stoptext

However, I'd suggest to instead use:

\startProcedure [title=something]
…
\stopProcedure

> The \startnarrower requires an explanation on how it affects the
> resulting document. Likewise \startitemnize.

Feel free to add some info from the wiki.

http://wiki.contextgarden.net/Command/startnarrower
http://wiki.contextgarden.net/Enumerations

> What does the "of" in "\beginofAnswer" mean? Is it required?

It's not required. It's actually wrong.

> Where does it come from? Why is it not simply "\beginAnswer"?

MkII maybe?

> "Figure 1.1 is typeset this way" should include the page number.

That's more difficult than it seems to be. The manual is available
in different paper sizes and formats. This means the page number
can't be coded as \in{figure}[foo] on \at{page}[foo], since the
figure might end up on the same page. As far as I know ConTeXt does
not have a general mechanism for automatically placing the “on
page…” string if the reference is not on the current page. \atpage
comes close, though.

> Document processing is best done by TeXexec -- is this still true?

Well, your manual is from 2000.

> I thought the "context" program supercedes TeXexec?

yes

> Describe the relationship between TeX and ConTeXt. For example, why do the
> subsequent sections discuss TeX examples?

ConTeXt uses TeX and the following sections introduce some TeX
concepts that hold true for ConTeXt as well.

> Section 1.9.
> ------------
> Relatively empty page.

On purpose. The reader is invited to take a break and grab a coffee. ;)

> Section 2.2.
> ------------
> "It is advisable to type the document setups before the \start--command," --
> What start command? \starttext, perhaps?

\starttext, \startdocument, \startcomponent, etc.

Marco
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# ABCD

AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD

Result

DB =  20.999 cm
AD =  34.109 cm

#### Solution:

$DB=BD=20.9994589142 \doteq 20.9995 \doteq 20.999 \ \text{cm}$
$AD=34.1087752861 \doteq 34.1088=34.109 \ \text{cm}$

Try calculation via our triangle calculator.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

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text:
## Files in this item

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## Description

 Title: Generalized Kummer congruences and Iwasawa invariants Author(s): Gunaratne, Haputantirige Sunil Doctoral Committee Chair(s): Ullom, Stephen V. Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: We obtain the following generalization of the Kummer congruence: $$G\sb{c}(j,\chi,n) = -\left\lbrack{p\sp{-1}\Delta\sb{\rm c}\atop j}\right\rbrack {1\over n}(1 - \chi\omega\sp{-n}(p)\ p\sp{n-1}) B\sb{n,\chi\omega\sp{-n}}\in\doubz\sb{p}\lbrack\chi\rbrack ,$$where $B\sb{n,\chi}$ is the generalized Bernoulli number associated to the Dirichlet character $\chi,\ \Delta\sb{\rm c}$ is the difference operator$$\Delta\sb{\rm c} x\sb{n} = x\sb{n+c} - x\sb{n}\ {\rm and}\ \left\lbrack {p\sp{-1}\Delta\sb{\rm c}\atop j}\right\rbrack$$is a binomial coefficient operator.The classical generalization of the Kummer congruence is$$K\sb{c}(j,\chi,n) = -p\sp{-j}\Delta\sbsp{\rm c}{j}{1\over n}(1 - \chi\omega\sp{-n}(p)\ p\sp{n-1})\ B\sb{n,\chi\omega\sp{-n}}\in\doubz\sb{p}\lbrack \chi\rbrack .$$We show that this is periodic (mod p) in the sense that$$K\sb{c}(j,\omega\sp{m},n)\equiv K\sb{c} (j\sp\prime,\omega\sp{m},n\sp\prime) (mod\ p\doubz\sb{p})$$if $j\equiv j\sp\prime$ $(mod\ p-1),\ j,\ j\sp\prime > 0,$ and $n\equiv n\sp\prime$ $(mod\ p-1).$As a special case of a more general result on the $\mu$ and $\lambda$ invariants of a p-adic measure, we characterize the Iwasawa invariants $\mu(\chi)$ and $\lambda(\chi)$ as $\mu(\chi)$ = $min\{ord\sb\pi(G\sb{c}(j,\chi,n))\mid j\geq0\}$ and $\lambda(\chi) = min\{j\mid ord\sb\pi(G\sb{c}(j,\chi,n)) = \mu(\chi)\}$ provided that $(c,p) = 1,$ where $\pi$ is a local parameter of $\doubq\sb{\rm p}\lbrack\chi\rbrack.$The Iwasawa characterization of $\mu$ = 0 and a theorem of Kida on p-adic measures are obtained as by products of the method used. Issue Date: 1991 Type: Text Language: English URI: http://hdl.handle.net/2142/20942 Rights Information: Copyright 1991 Gunaratne, Haputantirige Sunil Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9210821 OCLC Identifier: (UMI)AAI9210821


text:
## Some elementary lessons from iterative fractal maps

The famous Sierpinski gasket was one of the first fractals we wrote code for when we got access to a computer. It impressed us enormously that an intricate object with self-similarity over all scales could be generated by a rather simple process:
1) Take three points that would define a triangle.
2) Take a fourth starting point.
3) Randomly pick one of the three vertices of the triangle. Plot the midpoint between the fourth starting point and the chosen vertex.
4) Repeat this process with that midpoint for a large number of iterations.
5) The points thus generated would converge to an attractor which is the Sierpinski gasket.

This process inspired us to use this procedure more extensively to develop other such fractal objects. We found an answer for this shortly thereafter in a book by the mathematician Barnsley precisely about this topic. In it Barnsley said something to the tune that we would stop looking objects in nature the same way once we see the fractals such as those for which he provided a recipe for construction. This had indeed already started happening to us with our encounter with the Sierpinski gasket. Notably, around that time we recorded a statement of Johannes Kepler (which we read somewhere), which was earlier expression of the same idea:
I believe the geometric proportion served the creator as an idea when he introduced the continuous generation of similar objects from similar objects.

The Hindu enacts such a concept when he performs śrauta rituals with complex rituals developing recursively with some modification from a simple “prakṛti”.

Coming back to Barnsley, he called these fractals Iterated Function Systems (IFS) and they are generated thus:
$\begin{bmatrix} x_{n+1} \\ y_{n+1} \end{bmatrix} = \begin{bmatrix} a & b\\ c & d\end{bmatrix}_i \begin{bmatrix} x_{n} \\ y_{n} \end{bmatrix} + \begin{bmatrix} e \\ f \end{bmatrix}_i; \; p_i$
where $i=1..n$

As one can see this map defines a set of affine transformations that are recursively applied to the starting coordinates $(x_n,y_n)$. However, there can be a set of n such of matrices $1..n$ any one of which $i$ can be applied to the point at a time with a probability of $p_i$. For each mapping of the point we have 7 numbers, 6 from the transformation matrices $(a..f)$ and the 7th being the probability with which it is applied $p_i$.

Barnsley’s most famous fractal map was the fern leaf. Several variants of this have been generated (some by us and others whose creators are either Barnsley himself or others not known to us).

Figure 1: the first one is Barnsley’s original fern leaf

Given that a relatively small number of values to can generate a rather complex object by this procedure, Barnsley developed this as a method for compression of images. To us the IFS immediately struck us as being a mechanism for illustrating evolution: In the simplest scenario, the values in the above matrices and the probability of its choice can be seen as ‘genes’ which are prone to mutations with quantitative effects on traits. Thus, one can allow the matrices to mutate while we act as the proxy for natural selection.

The same is quite well-illustrated by another of the IFS fractals the leaf. In this leaf we have 4 matrices which gives us a total of $24+4=28$ ‘genes’ which might be mutated. If we impose the conditions of continuity of the attractor region (a very real biological one) and reasonable bilateral symmetry then only 10 of those ‘genes’ can take mutations. Now, by letting them undergo mutation and selection we can see evolution occur in silico and spawn a variety of leaf forms close to what we actually see in nature.

Figure 2

One might learn two things from this:
1) If we give a person with no knowledge of how the matrices were constructed for generating a given shape, e.g. the leaf, he can mutate the ‘genes’ randomly and figure out how it works. After some mutagenesis he would soon discover that different ‘genes’ have different morphological roles and there is even a degree of hierarchy in terms of their effect on form. He would soon understand the difference between null mutations and change of function mutations. Thus, he can put together a developmental network for the role of the ‘genes’ in the development of the in silico leaf. In doing this on a very small scale he would have reproduced what geneticists have done to unravel the genetic networks for the development of real organisms like Caenorhabditis, Drosophila and the Danio (e.g. Nüsslein-Volhard and Wieschaus et al). Such efforts entirely dominated developmental biology and genetics for almost two decades.

2) Beyond doubt these efforts of the developmental geneticists contributed fundamentally to our understanding of biology. But in the end it spawned the field that is often irritatingly referred to as “evo-devo” — an attempt to marry the foundation of biology in the form of the evolutionary theory with developmental genetics. In our youth, even as we were discovering the beauty of IFS for ourselves, we were aligned towards a future as an evolutionary developmental geneticist. We even thought we should apprentice ourselves as a slave in one of those powerhouse developmental genetics labs, where we could bring our knowledge of evolution which was much ahead of theirs in those days. It was in this context the IFS experiments offered us an important negative lesson. We saw that the so-called evo-devo field was proceeding in a rather pedestrian direction. It was one where the protein or RNA products of the genes and were mostly faceless blobs (they would often literally be illustrated by researchers as such), with the primary expression of the studies being simple genome-demographic summaries from angle of genes they knew best and organism-specific variations of the maps of gene-interactions in development. To us this was not qualitatively telling us anything new about evolution of development beyond what we could glean from in silico experiments with systems such as IFS. Instead, we realized that we had to take a path that got directly to heart of what is unique to biology, i.e. the biochemistry of those gene products. This resonated with where we first began our science the chemistry of biological molecules. It was placing that within the framework of the evolutionary theory, which was to lead us closer to the foundations of biology than any of this other stuff.

In our childhood we had spent a lot of time simply gazing through the kaleidoscope. It brought home to us that one principle of aesthetics was symmetry. When we learned of IFS we saw how simple recursion was a second principle of aesthetics. We found that a very simple IFS could result objects of great beauty especially when combined with first principle symmetry. This led us to play with a simple map, namely one to generate the limit curve of a bifurcating tree. This can be done by choosing the below three matrices with equal probability:

$\begin{bmatrix} x_{n+1} \\ y_{n+1} \end{bmatrix} = \begin{bmatrix} s \cos(\theta) & -s\sin(\theta)\\ s \sin(\theta) & s \cos(\theta)\end{bmatrix} \begin{bmatrix} x_{n} \\ y_{n} \end{bmatrix} + \begin{bmatrix} 0 \\ 1 \end{bmatrix}; \; p_1=\frac{1}{3}$

$\begin{bmatrix} x_{n+1} \\ y_{n+1} \end{bmatrix} = \begin{bmatrix} s \cos(\theta) & s\sin(\theta)\\ -s \sin(\theta) & s \cos(\theta)\end{bmatrix} \begin{bmatrix} x_{n} \\ y_{n} \end{bmatrix} + \begin{bmatrix} 0 \\ 1 \end{bmatrix}; \; p_2=\frac{1}{3}$

$\begin{bmatrix} x_{n+1} \\ y_{n+1} \end{bmatrix} = \begin{bmatrix} 1 & 0\\ 0 & 1\end{bmatrix} \begin{bmatrix} x_{n} \\ y_{n} \end{bmatrix} + \begin{bmatrix} 0 \\ 0 \end{bmatrix}; \; p_3=\frac{1}{3}$

Here $s$ is the scaling factor whereas $\theta$ is the angle by which the branches of the bifurcating tree are rotated. Finally, we can rotate each fractal a fixed number of times to obtain a particular kaleidoscopic symmetry. In the first example below we have an overall symmetry of 6 with various $\theta$ values and $s=\frac{1}{\phi}$ the Golden ratio.

Figure 3

In the second example we have a symmetry of 4 with similar rotations and scaling as above. One may note that the first case in this figure where $\theta=\frac{\pi}{4}$ we get a structure that is immediately reminiscent of the floor plans towards which the central spire of the great Hindu temples (e.g. at Khajuraho) converged to before the coming down of the green curtain.

Figure 4

This entry was posted in art, Life, Scientific ramblings and tagged , , , , , , , , , , , . Bookmark the permalink.


text:
# Cauchy => bounded?

1. Jun 9, 2007

### pivoxa15

1. The problem statement, all variables and given/known data
Thm: If a sequence is Cauchy than that sequence is bounded.

However Take the partial sums of the series (sigma,n->infinity)(1/n). The partial sums form a series which is Cauchy. But the series diverges so the sequence of partial sums is unbounded.

Sequence of partial sums is Cauchy b/c d(1/x,1/(x+1))=1/(k(k+1)) -> 0 as k->infinity

Have I done something wrong?

Last edited: Jun 9, 2007
2. Jun 9, 2007

### matt grime

Why do you think the sequences of partial sums are cauchy? They aren't.

I cannot begin to decipher what b/c d(..... means.

If S_n means the sum to n terms, what makes you think that given e>0, there is an n(e) such that for all n,m>n(e) we have |S_n - S_m| < e?

It is easy to show this is impossible, using the same idea as to show that the series itself diverges. Remember that

1+1/2+1/3+1/4+1/5+... > 1+(1/2+1/2)+(1/4+1/4+1/4+1/4)+(1/8+1/8+1/8+...) > 1+1+1+1+...

Last edited: Jun 9, 2007
3. Jun 9, 2007

### siddharth

Is b/c d(.., "because" , the "distance" ...?

As matt suggested, I think you should be less cryptic in your notation.

4. Jun 9, 2007

### AKG

Yes, that's not the definition of Cauchy. A sequence a(n) is Cauchy if for all E > 0, there exist N natural such that for all m and n > N, |a(n) - a(m)| < E. All you've shown is that for all E > 0, there exists some natural N such that |a(N) - a(N+1)| < E, or something like that.

5. Jun 9, 2007

### pivoxa15

oh... I thought it was obvious. I actually used b/c in my exam recently to indicate 'because'. Although I used it in the middle of a sentence so hopefully might be less confusing than here.

6. Jun 10, 2007

### matt grime

If you'd've put a 'The' at the start of the sentence to actually make it into a sentence that might have helped. Anyway, have you understood the explanation of your mistake?

7. Jun 10, 2007

### pivoxa15

I think I have. Each term in the sequence is a series summed over a finite number of terms. However the larger the number of terms, the larger the sequence gets. Very much unlike Cauchy seqences where a recquirement is that each term in the seqence decreases in magnitude the further out the sequence gets.

8. Jun 10, 2007

### matt grime

it is perfectly possible to be strictly increasing and still bounded/cauchy

nope, there is nothing that states the terms have to decrease in magnitude. It is the difference between terms in the sequence that is important.


text:
# How to prove inverse direction for correlation coefficient?

To show: If |Cor(X,Y)| = 1, then there exists a, b ∈ R s.t Y = bX + a. Any ideas or hints to proceed?

Basically, I've to prove that if the absolute value of correlation b/w two random variables is 1, then they should be linearly related.

So far,

$$|cor(X, Y)| = 1$$

$$\frac{|Cov(X, Y)|}{|\sigma(X) \sigma(Y)|} = 1$$

$$|Cov(X, Y)| = |\sigma(X) \sigma(Y)|$$

How to proceed further?

• Hint: when is the Cauchy-Schwarz inequality actually an equality? – Watson Nov 17 '16 at 15:37
• Your statement is only almost sure: consider $X \sim N(0,1)$ and $Y=-X$ when $X$ is rational and $Y=+X$ when $X$ is irrational – Henry Nov 17 '16 at 15:40
• @Watson: Wiki says the equality holds when they are "linearly related". But I've to show/prove this formally and I don't know how to proceed. – rakudo Nov 17 '16 at 15:47


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# Which of the following equations is NOT equivalent to 10y^2=

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Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

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Updated on: 06 Aug 2012, 10:02
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Which of the following equations is NOT equivalent to 10y^2=(x+2)(x-2)?

A. 30y^2 = 3x^2 - 12
B. 20y^2 = (2x-4)(x+2)
C. 10y^2 + 4 = x^2
D. 5y^2 = x^2 - 2
E. y^2 = (x^2-4)/10

Trying to figure out how you guys would approach this problem:

it's PS: Q37 of OG13 - I searched for it on this forum but no result?

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Originally posted by DelSingh on 06 Aug 2012, 09:57.
Last edited by Bunuel on 06 Aug 2012, 10:02, edited 1 time in total.
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Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

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06 Aug 2012, 10:19
1
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DelSingh wrote:
Which of the following equations is NOT equivalent to 10y^2=(x+2)(x-2)?

A. 30y^2 = 3x^2 - 12
B. 20y^2 = (2x-4)(x+2)
C. 10y^2 + 4 = x^2
D. 5y^2 = x^2 - 2
E. y^2 = (x^2-4)/10

Trying to figure out how you guys would approach this problem:

it's PS: Q37 of OG13 - I searched for it on this forum but no result?

When $$x=2$$, then $$10y^2=(2+2)(2-2)=0$$ --> $$y=0$$.

Now, plug $$x=2$$ into the answer choices and look for the option which does not give $$y=0$$. Only option D gives the value of $$y$$ different from zero.

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Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

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06 Aug 2012, 11:27
1
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DelSingh wrote:
Which of the following equations is NOT equivalent to 10y^2=(x+2)(x-2)?

A. 30y^2 = 3x^2 - 12
B. 20y^2 = (2x-4)(x+2)
C. 10y^2 + 4 = x^2
D. 5y^2 = x^2 - 2
E. y^2 = (x^2-4)/10

Trying to figure out how you guys would approach this problem:

it's PS: Q37 of OG13 - I searched for it on this forum but no result?

To practice a little bit of algebra: equivalent equations are obtained by multiplying, dividing a given equation by a non-zero number, or adding, subtracting from both sides the same expression. In other words, after some algebraic manipulations, starting with one equation, we should exactly recover the other equation.
Equivalent equations have the same set of solutions, fact used in his solution by Bunuel. Meaning, for the same value of x, you must get the same value for y in both forms of the equation. Instead of 2, -2 could be used, it also gives y = 0 in the original equation but not in D. It's worth using the zeros of the expression, to avoid spending on computations.

So, the given equation is $$10y^2=(x+2)(x-2)$$ (a) or $$10y^2=x^2-4$$ (b)

A. $$30y^2 = 3x^2 - 12$$ can be obtained from the original equation (b) by multiplying both sides by 3. Therefore equivalent.
B. $$20y^2 = (2x-4)(x+2)=2(x-2)(x+2)$$, dividing through by 2 we obtain our original equation (a). Equivalent.
C. $$10y^2 + 4 = x^2$$, subtract 4 from both sides, recover the original equation (b). Equivalent.
D. $$5y^2 = x^2 - 2$$, multiply both sides by 2, we obtain $$10y^2 = 2x^2 - 4$$ and not $$10y^2=x^2-4$$. Not equivalent.
E. $$y^2 = (x^2-4)/10$$, multiply by 10 both sides, recover equation (b).

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Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

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Re: Which of the following equations is NOT equivalent to 10y^2= &nbs [#permalink] 29 Jul 2018, 10:57
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## Make Sharpness-Aware Minimization Stronger: A Sparsified Perturbation Approach

Abstract: Deep neural networks often suffer from poor generalization caused by complex and non-convex loss landscapes. One of the popular solutions is Sharpness-Aware Minimization (SAM), which smooths the loss landscape via minimizing the maximized change of training loss when adding a perturbation to the weight. However, we find the indiscriminate perturbation of SAM on all parameters is suboptimal, which also results in excessive computation,~\emph{i.e.}, double the overhead of common optimizers like Stochastic Gradient Descent~(SGD). In this paper, we propose an efficient and effective training scheme coined as Sparse SAM (SSAM), which achieves sparse perturbation by a binary mask. To obtain the sparse mask, we provide two solutions which are based on Fisher information and dynamic sparse training, respectively. In addition, we theoretically prove that SSAM can converge at the same rate as SAM,~\emph{i.e.}, $O(\log T/\sqrt{T})$. Sparse SAM not only has the potential for training acceleration but also smooths the loss landscape effectively. Extensive experimental results on CIFAR10, CIFAR100, and ImageNet-1K confirm the superior efficiency of our method to SAM, and the performance is preserved or even better with a perturbation of merely 50\% sparsity. Code is available at \url{https://github.com/Mi-Peng/Sparse-Sharpness-Aware-Minimization}.


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## FANDOM

436 Pages

 Sun > HD 149026b > Nemesis
"The sun a medium sized star, remain stable for approximately 10,000,000,000 years."
William Shatner, Universe

Sun
1st appearance: Big Bang
Status: Alive
Age: 5,000,000,000 year
Planets: 400 billion
Temperature: 9,941°F
Rotation: 23 hrs 56 mins 4 secs
Type: Medium star
Diameter: 900,000 mi
Gender: Female
Voice actor(s): Janis Cody
Death: Boiled alive (revived), exploded (revived again), died in explosion (revived), boiled alive in animated show (revived)
"The sun, with all those planets revolving around it and dependent on it, can still ripen a bunch of grapes as if it had nothing else in the universe to do. " --Galileo Galilei The Sun, (called Sol in Spanish), is the star at the center of our solar system. The Earth and other matter (including other planets, asteroids, meteoroids, comets and dust) orbit the Sun, which by itself accounts for more than 99% of the solar system's mass. It is the closest star to the earth. Because of it's luminosity, it dominates the sky during daylight hours. After it rises fully above the horizon no other stars are visible.
$M_\odot = 1.989\cdot 10^{30}\textrm{kg}$
Energy from the Sun—in the form of insulation from sunlight - supports almost all life on Earth via photosynthesis and drives the Earth's climate and weather. The Sun is a G-type main-sequence star (G2V) based on spectral class and it is informally referred to as a yellow dwarf. It formed approximately 4.567 billion[lower-alpha 1][1] years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into an orbiting disk that became the Solar System. The central mass became increasingly hot and dense, eventually initiating nuclear fusion in its core. It is thought that almost all stars form by this process. The Sun is roughly middle aged and has not changed dramatically for four billion[lower-alpha 1] years, and will remain fairly stable for another four billion years. However, after hydrogen fusion in its core has stopped, the Sun will undergo severe changes and become a red giant. It is calculated that the Sun will become sufficiently large to engulf the current orbits of Mercury, Venus, Earth, and possibly Mars. The enormous effect of the Sun on the Earth has been recognized since prehistoric times, and the Sun has been regarded by some cultures as a deity. Earth's movement around the Sun is the basis of the solar calendar, which is the predominant calendar in use today. Today the Sun pulls in close enough to engulf the current orbits of Nightmare Mercury, Nightmare Earth, Nightmare Mars, Nightmare Uranus, Nightmare Neptune, and most certainly Bad Saturn.

## NameEdit

• Sun
• Also know as The Sun or Sol

The Sun (in Greek: Helios, in Latin: SolTemplate:Efn) is the star at the center of the Solar System and is by far the most important source of energy for life on Earth. It is a nearly perfect spherical ball of hot plasma, The Sun is a G-type main-sequence star (G2V) based on spectral class and it is informally referred to as a yellow dwarf. It formed approximately 4.567 billion[lower-alpha 1][1] years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into an orbiting disk that became the Solar System. The central mass became increasingly hot and dense, eventually initiating nuclear fusion in its core. It is thought that almost all stars form by this process.

## The Red giant Sun's deathEdit

The Sun eventually uses up its Hydrogen (H2) gas and it expands to 400 times its present diameter in another ten billion years it will glow red hot, and it would get Theia baked in a heat that is 3,600°F, after it has already engulfed MarsEarth, Venus, and Mercury. The Sun completely fill the horizon on the fourth and a half planet of the Solar System, the seas would evaporate into gas, but Theia looks nothing like it use to. No signs indicate it would have ever sustained life. And then the final lack, The Sun's massive outer edges of its photosphere would begin to slow down Theia's orbit, the Martian planet would be a fireball, and starting to be burning up like a meteorite also it's going to be engulfed by our own star the red giant Sun and it's going to be toast, vapor literally. And our red giant would fall leaving behind a corpse of star called a white dwarf, over fifteen billion years the Sun would end its life as a black dwarf star. About 74% of the Sun's mass is hydrogen, 25% is helium, and the rest is made up of trace quantities of heavier elements. Each second, more than 4 million tons of matter are converted into energy within the Sun's core, producing neutrinos and solar radiation. In about 5 billion years, in is predicted that the Sun will evolve into a red giant and then a white dwarf, creating a planetary nebula in the process. The Sun is a magnetically active star; it supports a strong, changing magnetic field that varies year-to-year and reverses direction about every eleven years. The Sun's magnetic field gives rise to many effects that are collectively called solar activity, including sunspots on the surface of the Sun, solar flares, and variations in the solar wind that carry material through the solar system. The effects of solar activity on Earth include auroras at moderate to high latitudes, and the disruption of radio communications and electric power. Solar activity is thought to have played a large role in the formation and evolution of the solar system, and strongly affects the structure of Earth's outer atmosphere.

Although it is the nearest star to Earth and has been intensively studied by scientists, many questions about the Sun remain unanswered, such as why its outer atmosphere has a temperature of over a million Kelvin while its visible surface (the photosphere) has a temperature of just 6,000 K. Current topics of scientific inquiry include the sun's regular cycle of sunspot activity, the physics and origin of solar flares and prominences, the magnetic interaction between the chromosome and the corona, and the origin of the solar wind.

## Discovery dateEdit

• Has always been known to man.[2]

## DiscovererEdit

• Always been known by mankind.[2]

## About the starEdit

• G-type star.[2]
• Our own Sun is in fact white, but appears yellow through the Earth's atmosphere. [3]
• About one million Earths could fit inside the Sun.[4]
• At the core, the temperature is about 15 million °C (about 27 million °F), which is sufficient to sustain thermonuclear fusion.[4]
• The Sun is at its mid-life, and should keep its appearance for an other five (5) billion years.
• The density of the Sun is 1.4 g/cm3<\sup>[5]

## Voice ActorsEdit

• Janis Cody (UK/US; eighteenth - twentienth season)
• Amy Satras (UK/US; seventeenth - eighteenth season)
• Diana Radomski (UK/US; sixteenth - seventeenth season)
• Vanessa Porco (UK/US; fifteenth - sixteenth season)
• Fu Suzuki (Japan; fifteenth season onwards)

## ReferencesEdit

[[Category:Celestial Bodies known[[Category:G-type s[[Category:Fem [[Category:Revived Charact

Cite error: <ref> tags exist for a group named "lower-alpha", but no corresponding <references group="lower-alpha"/> tag was found.


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# Math Help - Canceling With Variables

1. ## Canceling With Variables

The Author of this book does not really explain the process very thoroughly, consequently I am lost.

$\frac{72x}{18xy}$

to solve:
$\frac{4}{y} * \frac{18x}{18x} = \frac{4}{y}$

I am completely stumped as to how the author gets $\frac{4}{y}$ and $\frac{18x}{18x}$, if someone could please clarify and tell me the process, and why its implemented it would be greatly appreciated.

When I look at it I dont see why you cant just cancel out the x in the numerator and denominator and get $\frac{72}{18y} = \frac{4}{y}$ I dont understand how she sets it up at all.

2. ## Hi

The author has done nothing special.

Since you have an expression $\frac{72x}{18xy}$ with just factors in it, you CAN definetely "just cancel out" the x.
The author has simply broken out the GCF (greatest common factor) from both the $72x \ \mbox{and the} \ 18xy$

So $\mbox{GCF}(72x,18xy) \ = 18x$

Now the $18x$ gets cancelled out, and we´re left with just
$\frac{4}{y}$

3. Ah many thanks. I learned GCF many years ago but this book, which is meant for beginners, jumps around from topic to topic. Even in the introduction of the book the author states she will build on previous material from chapter to chapter; however, GCF has not even been included this far. But at any rate many thanks for clarifying.

Also I know the same process must be going on here but how is the GCF of this expression 3x?

$\frac{6xy(2x-1)}{3x} = \frac{2y(2x-1)}{1} * \frac{3x}{3x} = 2y(2x-1)$

Looks like the 3 divides the 6 and the x just divides into the other x on the numerator.

4. ## hi

The GCF here is definetely $3x$.

You always try to "cancel out" as much as possible when simplifying expressions. The key thing not to forget is that you can only cancel out factors!