/sci/ - Science & Math

>>5746832
Man please, read:

>>5746430
> Except you work with a finite field of course.

>>5746786
> Still infinitely many if you work in R.

Do you understand that you never specified what your restrictions are, and that when two other posters mentioned that, you didn't realize it? As >>5747047 said, you are probably working with positive integers, why aren't you realizing that this is not the same as R?

Beside, it is very improper to just talk about "matrices" without referring to matrices over a field, and if you have a "positive values" restriction somewhere, you aren't working on a field. If you use no linear-algebraic property of matrices and you consider these matrices on something that isn't a field, please don't call them matrices, call them something like 2D-arrays of integers, or tables, or whatever. If you say "matrices" and don't give any detail (even after being hinted at the lack of detail in your post), people will NOT think "positive integers".

>>5746726
Still infinitely many if you work in R. Take one such matrix <span class="math">M=(m_{ij})[/spoiler] and consider for all <span class="math">\alpha\in\mathbb{R}[/spoiler] the matrix <span class="math">M^{(\alpha)}=(m^{(\alpha)}_{ij})[/spoiler] defined by
i) <span class="math">m^{(\alpha)}_{ij}=m_{ij}+\alpha[/spoiler] if i=j=1 or i=j=2,
ii) <span class="math">m^{(\alpha)}_{ij}=m_{ij}-\alpha[/spoiler] if (i=1 and j=2) or (i=2 and j=1),
ii) <span class="math">m^{(\alpha)}_{ij}=m_{ij}[/spoiler] otherwise.

There are infinitely many such new matrices and they have the same sum on each row and on each column as M.

>>5707960
Looks a bit like the Euler totient graph. Not exactly, but somewhat.

I'm however assuming that it has a strong connection with the fact that we're in base 10, so whatever you do, if "10" or "2*5" don't appear clearly in your analysis, you've missed something.

>>5704976
Doesn't always work. For instance, I can be an ass and do that:
<span class="math">\def\a{\displaystyle \sum_{k=0}^n \frac{x^n}{n!}}[/spoiler]<span class="math">\a[/spoiler]<span class="math">\def\a{a}[/spoiler]

You can double-click it but you won't learn much.

>>5703406
This guy made \int do "OP is a fag".

>>5704814
That guy made \int do "Well played anon".

Now \int is going to be "I love sandwiches"<span class="math">\def\int{I~love~sandwiches}[/spoiler]

Have fun, anons. I've given too many clues already.

>>5704823
I don't think font management is such an issue.

What I think would change would be:
- The syntax. LaTeX is based on TeX, which induces a lot of issues. The symbols used in variable names are restricted (can't use numbers for instance). Overall TeX is extremely ugly and LaTeX partially inherits from that.
- Too many things require a double-compilation using the .aux file. Some "tricks" to balance the height of two objects that are created in parallel require you to more or less double-compile these objects by macroing them and reading the macro twice, once to check their height and once to actually output them (with the proper height). Compilation should be done in a different way to avoid that, for instance you could have it first output something in between LaTeX's abstraction and pdf/dvi's concreteness in which some things can be edited by future actions (like the height of some objects, when the height of nearby objects are computed, or references when they become available), and then that abstraction should fast-compile to dvi/pdf.

>>5703563
I like these kind of jokes in article titles, like
"Division by three" by Conway (from which I read only the "division by two" part but it was pretty cool and easy to understand for someone with little knowledge in that topic), or "On <span class="math">O_n[/spoiler]", etc.

>>5699331
> Divided by zero

>>5699187
You're welcome.

In general, when attempting to show that something can be written in terms of a given function (here in terms of <span class="math">\log_c x[/spoiler]), the strategy is:

- Check if it looks like it's possible on a trivial example (e.g. take a=b=1 and try to find c),
- In the above case, it's impossible. You can either figure it out and then try to prove it, or start proving it right away, because the same kind of idea is used:
- The idea is, <span class="math">\log_c(x)[/spoiler] only depends on a single parameter <span class="math">c[/spoiler]. In general, there could be a few parameters, but usually when you try to write something "in terms of" something, you don't have that many parameters (but you could have something like <span class="math">\lambda e^{\alpha x}[/spoiler] with two parameters).
- Because it depends on only one parameter, you don't have a lot of leeway for that parameter <span class="math">c[/spoiler] if you start fixing values of <span class="math">x[/spoiler]. If you choose your values that are "independent" in some sense, each value of <span class="math">x[/spoiler] that you observe gives you an equation on <span class="math">c[/spoiler]. Here I observed the value <span class="math">x=b[/spoiler], and it gave me <span class="math">\log_c b=0[/spoiler].
- Once you have more independent equations than you have parameters, you've usually won: all of them cannot be satisfied at once.

If I ask you why you can't write <span class="math">x^2[/spoiler] as <span class="math">ax+b[/spoiler],
1) x=0 gives <span class="math">0^2=a\times 0+b[/spoiler] so b=0,
2) x=1 gives <span class="math">1^2=a\times 1+b=a[/spoiler] so a=1 (using b=0),
2) x=-1 gives <span class="math">(-1)^2=a\times (-1)+b=-a[/spoiler] so a=-1, which is a contradiction.

Get the idea?

, <span class="math">x=1[/spoiler] and <span class="math">x=-1[/spoiler].

>>5690528
(((cont)))

And that's it. When it's published, it's published, you don't get the issue of the journal, you don't somehow get it for free online. If you want your article, you have to pay for it.

Also, publishing on a given topic means that you will get peer-review requests and end up working (for free) for IEEE to review the papers of your peers. You can of course decline all the review requests, but it is not going to help your carrier in the long run, because those that send the requests are working in your field too and they won't really like you if you don't contribute to the peer-review process.

Basically, IEEE exploits the researchers' need for high-quality editors in specific fields. You *have* to work with them, and they exploit it.

>>5690468
It's because they can. The worst part is the following:

I'm not sure if this applies to every field, but in my field, IEEE is the main editor and the main host for conferences. Basically everybody that I work with is an IEEE member for these reason (membership for students isn't too expensive, but it's more expensive for faculty, and it's really fucking expensive for engineers). You need to be an IEEE member to publish in their journals or conferences.

However, being an IEEE member doesn't mean that you get any of their papers for free. It only means that you can submit papers to their journals and conferences, and that you can access the most basic functions of their website (basically you can get the abstract and the .bib bibliography of any of their articles, but not the article itself). You still have to pay like $15 or something if you want to download the pdf of an article (the same as if you weren't a member).

So, okay, this is overcome by the fact that universities pay (a LOT) so that you have free access to most IEEE journals when you use their Internet. But wait, there's something else. Let's say you want to publish in an IEEE journal. You have written in pretty damn good article, but you're not an IEEE member. So you subscribe, of course (and cry at the yearly fee), and you submit your article. After several months, you get an answer telling you (in the best case scenario) that your article is accepted, and that you have minor revisions to make (you are forwarded with anonymous reviews, which can be pretty awesome and give a lot of insight when they are done well). So you make these changes, submit again, wait a few months again, and your paper is validated, they ask you to send yet another "Camera-ready" version, to sign a paper giving the exclusive copyright of your work to IEEE (*sigh*), and then you wait again until your article is finally published.

And that's it. When it's published, it's published, you don't (((comment too long)))

>>5690151
Damn, this made me sad... It's an entertaining thread involving problem solving, Caesar cyphers, and /sci/ works collaboratively to help OP. While it's not very deep scientifically or mathematically, the fact that it involves collaborative work makes it really good in my opinion.

Crowdsourcing is awesome and threads that involves a tangible amount of crowdsourcing are usually my favorite.

It appears that, it's just, like, my opinion man :/

>>5689904
Wohoooo, I had guessed Guadeloupe in >>5688161 based only on the triangle and the French language. What do I win? :>

Damn guys, we're getting close. I'm so excited right now. Best thread on /sci/ for a long while.

>>5689909
I think that it can work in a reasonable amount of memory and with a reasonable asymptotic complexity (only linearly more time than my current alg), by coming up with a map that transforms a solution into something small (maybe an integer is enough, I'm not sure), and using hash tables, search trees or whatever data structure gives a fast "insert(x)" time and fast "exists?(x)" time.

However, consider how little I work on each of my solution, I think it would multiply the time my program uses per solution by a pretty large factor (anywhere between 10 and 100 wouldn't surprise me), so it may take a long time.

I'll think about it tonight.

>>5689852
It rocks what you find is near Guadeloupe. It matches my wild guess from >>5688161

Coincidence or evidence?

>>5689874
Cool! Did you give a thought about how to get the number of non-congruent solutions?

>>5688853
Actually, it's 1111 or {foam} that isn't a proper subset. Proper subset of a set X are strictly included in X, meaning they are a subset of X which is different from X.

The rest is correct, the proof that there are 2^n subsets to a set of n element follows is exactly what you intuitively explained here.

>>5688746
Finished earlier than expected.

I found 3,835,119 patterns total.

Considering that cubes have 48 symmetries (http://en.wikipedia.org/wiki/Octahedral_symmetry)), that means that there are at least 79,899 non-congruent solutions (probably far more, but we know, assuming my algo is correct, that there are between 79,899 and 3,835,119 non-congruent solutions).

>>5688739
Okay, if the speed it roughly constant in the number of first shape, it should take roughly two hours.

>>5688293
jsmath lacks a lot of stuff. \mathrm is a better alternative than \text for inserting non-italicized letters which are not text, within an equation (and works in jsmath).

The other things missing are any convenient way to do tabulars / arrays, and the fact that if you write a very long formula without putting spaces in your code (for over 35 successive symbols), 4chan inserts a "you're allowed to linebreak here" special symbol in the middle of the formula before passing it to its server-side jsmath processor, which itself just replaces that symbol with a space, so you often end up with stuff like "\frac{1}{2}" being turned into "\fra c{1}{2}" and errors telling you that "\fra" isn't recognized.

>>5688492
Okay, I have a lot of duplicates. Need to figure out what went wrong.

>>5688493
> BTW are you currently counting the solutions you get by interchanging the red and green zones as distinct?
That's the only congruence I actually try to consider. (red,green,blue) and (red,blue,green) and (blue,red,green) and the other 3 permutations are counted as identical. Basically, I count the number of partitions of the set of blocks that work, and partitions are sets so the order in which I define the 3 shapes doesn't matter. Or well, considering that I still have kinda buggy results, maybe it does, but it's not supposed to.

Here are my 3504 shapes: http://pastebin.com/UyhBSVtN

I'll check for duplicates fast. It looks like they are valid in the sense that they are connected shapes which use the 27 different blocks by groups of 9.

Counting congruent shapes as different shapes (for now), my algo finds 3504 possibilities. I have to give it a fast check to make sure that what it returns is correct, though.

I considered a shape to be valid if it you can go from any block of the shape to any other block by traveling through contiguous faces (having common edges or vertices is not enough).

I basically count the number of ways one could take the 27 blocks and color them without moving them, as to define a red zone, a green zone and a blue zone, all containing 9 blocks, and all "valid" as detailed above.

Programming that. I'll let you know what I come up with.