Search found 527 matches

Sat May 02, 2015 1:29 pm UTC
Forum: Mathematics
Topic: Dice Probabilities in any order.
Replies: 7
Views: 1652

Re: Dice Probabilities in any order.

yes, P(aabbcc) is the same as P(dfefde)
Sat May 02, 2015 5:49 am UTC
Forum: Mathematics
Topic: Dice Probabilities in any order.
Replies: 7
Views: 1652

Re: Dice Probabilities in any order.

For your a, b, c, d, e, f scenario, you can say there are 6 ways to place the first letter, 5 ways for the second, 4 for the third... and so on. So you have 6*5*4*3*2*1 or 6! which equals 720 Then your probability is 720/46656 = 0.01543 ---- For your other scenarios it's helpful to know the combinat...
Fri May 01, 2015 11:52 pm UTC
Forum: Mathematics
Topic: Equations Like f(2x)=4f(x)
Replies: 8
Views: 5612

Re: Equations Like f(2x)=4f(x)

f(x) = 0 seems to work for a surprising number of these. I don't know if there's any general technique for solving these, but I suspect a lot of these have no solution. For example, take f(x^2)+f(2x)+f(1) = 0 We know f(1) is constant, so f(x^2)+f(2x) is also constant. this seems very unlikely for an...
Tue Apr 28, 2015 2:03 am UTC
Forum: Mathematics
Topic: A probability question (exploding dice with multipliers)
Replies: 9
Views: 1850

Re: A probability question (exploding dice with multipliers)

looks like it.
Fri Apr 24, 2015 10:54 pm UTC
Forum: Mathematics
Topic: "Random" sequences of binary strings?
Replies: 3
Views: 1282

Re: "Random" sequences of binary strings?

Yes i think i misinterpreted the sequence the first time. 11, 14, 35, 38, 41, 43, 44, 46, 50, 56, 58, 87, 93, 106, 117, 131, 134, 137, 139, 140, 142, 146, 152, 154, 161, 163, 164, 166, 169, 171, 172, 174, 176, 178, 184, 186, 194, 200, 202, 224, 226, 232, 234, 279, 285, 298, 309, 327, 333, 339, 342, ...
Fri Apr 24, 2015 1:16 pm UTC
Forum: Mathematics
Topic: "Random" sequences of binary strings?
Replies: 3
Views: 1282

Re: "Random" sequences of binary strings?

ignoring the first few terms, the sequence is basically just counting upwards in binary, modulo 1000, but skipping a few numbers. If you count up, you get: 000 001 010 011 100 101 110 111 000 ... this explains the pattern of 0s and 1s as 000 has less 1s than 111. your sequence jumps up by 0, 1, 2, o...
Fri Apr 24, 2015 10:42 am UTC
Forum: Mathematics
Topic: Real roots of polynomials with integer coefficients
Replies: 10
Views: 2685

Re: Real roots of polynomials with integer coefficients

This doesn't answer the question but you mentioned you don't like numpy or mpmath but have you tried sympy for root finding? It's all symbolic manipulation and answers come out in exact form.
Mon Apr 20, 2015 2:02 am UTC
Forum: Fictional Science
Topic: Tides on a perfectly spherical beach world.
Replies: 4
Views: 3977

Tides on a perfectly spherical beach world.

Suppose the world is a perfectly spherical stone, and covered in half a meter of water. An orbiting moon causes tides of one meter, so that during every tide (caused by rotation of the planet), a large portion of the planet becomes dry land and vice versa. Over time, erosion grinds the stone gradual...
Sat Apr 18, 2015 9:17 pm UTC
Forum: Mathematics
Topic: A probability question (exploding dice with multipliers)
Replies: 9
Views: 1850

Re: A probability question

Oh right, I miswrote the equation (which should be E(n,k) = k*(n+1)/2 + E(n,k+1)/n) So the coefficient on the (n+1)/2 term is k/(n^(k-1)), which can be rewritten as (w+1)/(n^w) = (w/n^w) + (1/n^w) the second term is the coefficient for the exploding dice with no multiplier, whose expected value is n...
Sat Apr 18, 2015 8:05 pm UTC
Forum: Mathematics
Topic: A probability question (exploding dice with multipliers)
Replies: 9
Views: 1850

Re: A probability question

That is true. You'll see that for every recursion in the equation, there is a 1/n multiplier.
Sat Apr 18, 2015 4:26 pm UTC
Forum: Mathematics
Topic: A probability question (exploding dice with multipliers)
Replies: 9
Views: 1850

Re: A probability question

E(n,k) = (n-1)/n * (n/2) + (1/n) * (n + k*E(n,k+1)) Where the first term is the expected value if the dice does not explode and the second term is the expected value if it does. k is the current multiplier. This simplifies to E(n,k) = (n+1)/2 + (k/n)*E(n,k+1) There is a k/n in front of the second te...
Mon Apr 13, 2015 3:06 am UTC
Forum: Mathematics
Topic: Why can't sine waves carry huge amounts of data?
Replies: 5
Views: 2074

Re: Why can't sine waves carry huge amounts of data?

I think the mistake is where your 2^(x*2) exponent comes in. With x cycles you can represent 2^(x*2) possible states, but you still only have x*2 bits, and x/4 bytes. So if you have 4 bits, you can count up to 2^4 = 16, and if you get another 4 bits, you can count up to 2^(4+4) = 256, but you still ...
Fri Apr 10, 2015 6:47 pm UTC
Forum: Mathematics
Topic: Löb's Theorem / Modal Logic
Replies: 9
Views: 2327

Re: Löb's Theorem / Modal Logic

Does it sort of make sense why people would want two different symbols for them? Yeah, that makes sense now I have actually never seen the square box notation before (nor studied formal logics), but if I understand what Tirian is saying here, then “◻” can be read as “it is a theorem (of the system ...
Thu Apr 09, 2015 9:48 pm UTC
Forum: Mathematics
Topic: Löb's Theorem / Modal Logic
Replies: 9
Views: 2327

Re: Löb's Theorem / Modal Logic

I see that ⊢A means "A is provable" (and hence it is a theorem). But then ⊢◻A means ◻A is provable, so "it is provable that A is a theorem", rather than "it is provable that A" The explanation given along with the rule is ambiguous about this -- have I interpreted it co...
Wed Apr 08, 2015 9:45 pm UTC
Forum: Mathematics
Topic: Löb's Theorem / Modal Logic
Replies: 9
Views: 2327

Löb's Theorem / Modal Logic

I'm trying to work my way through Wikipedia's proof of Löb's Theorem The first thing that confuses me is the difference between ⊢ and ◻, which both seem to mean "provable" or "it is provable". The first rule of modal inference given is ⊢A→ ⊢◻A "Informally, this says that if ...
Tue Apr 07, 2015 3:36 am UTC
Forum: Mathematics
Topic: Closed infinite intersection of open sets
Replies: 11
Views: 4316

Re: Closed infinite intersection of open sets

For infinite sets your argument doesn't work anymore, because induction only extends to natural numbers. You already see where your argument breaks down, because it is the word that you put quotations around. There is no smallest real open interval containing 0, just like there is no largest intege...
Mon Apr 06, 2015 11:09 pm UTC
Forum: Mathematics
Topic: Closed infinite intersection of open sets
Replies: 11
Views: 4316

Re: Closed infinite intersection of open sets

I see that the intersection appears to be {0}, but what breaks down with my reasoning when the intersection is infinite?
Mon Apr 06, 2015 9:56 pm UTC
Forum: Mathematics
Topic: Closed infinite intersection of open sets
Replies: 11
Views: 4316

Closed infinite intersection of open sets

I was told that the infinite intersection of the open sets (-1/1, 1,1), (-1/2, 1/2), (-1/3, 1/3), ... (-1/n, 1/n) as integer n -> infinity is just {0}, a closed set. However, I'm not sure this makes sense to me. Since for any two sets in the intersection, one is a proper subset of the other, the &qu...
Thu Mar 19, 2015 6:45 pm UTC
Forum: Science
Topic: Maxwell's demon -- consensus on disproofs?
Replies: 20
Views: 5200

Re: Maxwell's demon -- consensus on disproofs?

quantropy wrote:The sensor would be affected by thermodynamic fluctuations, either in its mechanism, or when the gas close to it has a higher pressure than the chamber as a whole. Thus most of the times it is triggered will be false alarms, which will cancel out any benefit

Thanks.

Ah well, entropy wins again
Tue Mar 17, 2015 10:53 pm UTC
Forum: Science
Topic: Maxwell's demon -- consensus on disproofs?
Replies: 20
Views: 5200

Maxwell's demon -- consensus on disproofs?

I was under the impression that the problem had long been solved, but the wikipedia page seems to show debate on the subject up into very recently and a paper from 2003 is linked. (http://arxiv.org/pdf/physics/0210005v2.pdf) Does this paper reflect scientific consensus? Also, how general are these d...
Wed Mar 11, 2015 9:22 pm UTC
Forum: Mathematics
Topic: A Set Packing problem; hopeless or just out of my depth?
Replies: 4
Views: 1326

Re: A grouping problem; hopeless or just out of my depth?

I'm not sure if any arrangement of teams meets your criteria. I have a hunch it's impossible. Actually, this seems like a form of the NP-complete set packing problem. https://en.wikipedia.org/wiki/Set_packing You want your quads to be unique. Basically, your universe U is all possible quads. Your su...
Wed Mar 11, 2015 12:50 pm UTC
Forum: Mathematics
Topic: A Set Packing problem; hopeless or just out of my depth?
Replies: 4
Views: 1326

Re: A grouping problem; hopeless or just out of my depth?

It's not immediately clear to me that your criteria for how many pair and triplets is the best we can do. If you want to minimize the similarity of teams, why not minimize the sum of the squares of the number of overlaps between any two teams. To clarify, when you say "pair of categories ... wi...
Fri Feb 27, 2015 2:13 am UTC
Forum: Mathematics
Topic: Calculating “fractional average” quantiles
Replies: 10
Views: 1943

Re: Calculating “fractional average” quantiles

Though now I look at it that way, I’m not even sure there’s a “nice” way to calculate the median , let alone the quantiles. It may well come down to iteration on the bounds of the integral until the target value is achieved. Medians don't seem too bad ∫ x<d f(x) dx = ∫ x>d f(x) dx Since f(x) must s...
Fri Feb 27, 2015 2:01 am UTC
Forum: Mathematics
Topic: Calculating “fractional average” quantiles
Replies: 10
Views: 1943

Re: Calculating “fractional average” quantiles

Why must the area of each side be 1/2? The mean isn't the same as the median. oh right, I somehow missed that. I guess then we'll need the area of a = m a and area of b = m b . The algebra should work out similarly though. Wait, are you saying that if I used ∫ x<k (k-x)²·f(x)·dx = q·∫ x>k (x-k)²·f(...
Fri Feb 27, 2015 1:49 am UTC
Forum: Mathematics
Topic: Calculating “fractional average” quantiles
Replies: 10
Views: 1943

Re: Calculating “fractional average” quantiles

I haven't solved it, but here's one idea: Assume for a moment that you were trying to find the point where the left side of the seesaw has q times the moment of inertia of the right side rather than the torque. Without loss of generality, have m = 0. Then, split the distribution, f(x), into two segm...
Mon Feb 16, 2015 5:09 pm UTC
Forum: Mathematics
Topic: Game Theory: Balancing Traits
Replies: 4
Views: 1425

Re: Game Theory: Balancing Traits

If you want a lot of strategies to be viable, one idea is to minimize the standard deviation of the number of strategies each strategy beats. Using brute force, the weights (1.83, 0.49, 0.36) lowers the standard deviation to 33 (versus 49 for (1, 1, 1)), and no strategy can beat all others / be beat...
Mon Feb 16, 2015 8:20 am UTC
Forum: Mathematics
Topic: Game Theory: Balancing Traits
Replies: 4
Views: 1425

Re: Game Theory: Balancing Traits

Am I correct to assume only integer points may be allocated? (10, 1, 21) or (10, 21, 1) or, for that matter, (10, x, 22-x), where x > 0, seems pretty optimal. Let strategy A be (10, x, 22-x) and assume that the best strategy against A must be of the form (10, y, 22-y). Call this B. There are three c...
Tue Feb 10, 2015 3:29 am UTC
Forum: Mathematics
Topic: computing the expected value of a function
Replies: 3
Views: 1490

Re: computing the expected value of a function

Thank you for the help. I did intend for c to be uniform from 0 to A+B I think it is possible for f(0) to be 1, when c > B, or have I misunderstood my own statement of the problem? https://i.imgur.com/XaAhNwo.png If it helps, I'm thinking of this as a traffic signal, where A is green light and B is ...
Sun Feb 08, 2015 2:00 am UTC
Forum: Mathematics
Topic: computing the expected value of a function
Replies: 3
Views: 1490

computing the expected value of a function

Let there be a periodic piecewise function f(x) = 1 if k(A+B) < x-c < k(A+B)+A and 0 if k(A+B)+A < x-c < (k+1)(A+B) for all integers k and unknown constants A, B, and c, where 0 < c < (A+B) (We can ignore the edge cases on the inequalities) Suppose I know V, the probability distribution of A, and W,...
Mon Feb 02, 2015 12:26 am UTC
Forum: Mathematics
Topic: Is it possible to convert a decimal matrix into a binary mat
Replies: 7
Views: 2466

Re: Is it possible to convert a decimal matrix into a binary

I think there are many ways, depending on the purpose. For example you could convert each of the 25 numbers into a 3-digit binary vector, then have a 25 by 3 or 3 by 25 matrix. In other words, let B_i,j be the j-th digit of A_(floor(i/5),(i%5). To reverse just flatten B back into a binary vector and...
Sun Feb 01, 2015 3:18 am UTC
Forum: Computer Science
Topic: an approximate algorithm for this optimization problem
Replies: 4
Views: 4311

Re: an approximate algorithm for this optimization problem

Oh I see what you mean now. That's a ingenious way of framing the problem. Thank you. After a bit of thinking, i also came up with a way to solve this problem on discrete functions (and continous ones) approximately with dynamic programming - let Q(x_i, y_i) be the minimum cost to move the car from ...
Fri Jan 30, 2015 9:31 pm UTC
Forum: Computer Science
Topic: an approximate algorithm for this optimization problem
Replies: 4
Views: 4311

Re: an approximate algorithm for this optimization problem

I'm not sure I completely understand what you mean by this non-continuous function from (lift location and target)^n to total cost. Can you explain that a bit further?
Thu Jan 29, 2015 6:14 pm UTC
Forum: Computer Science
Topic: an approximate algorithm for this optimization problem
Replies: 4
Views: 4311

an approximate algorithm for this optimization problem

Suppose there is a poorly designed car that must travel on a strip of road, represented by the function f(x), where f(x) is the altitude of the road at point x The car starts at x = 0 and must travel until x_f. The car is so poorly designed that it cannot travel across any surface which is not perfe...
Tue Jan 27, 2015 10:13 pm UTC
Forum: Mathematics
Topic: Problem equation mathematics
Replies: 2
Views: 1290

Re: Problem equation mathematics

Could it be that no such 4 positive integers exist which satisfy your equations? Where did you derive the original equation from, or did you just write it up?
Thu Jan 15, 2015 10:07 pm UTC
Forum: Mathematics
Topic: How to use Monte Carlo on a decision problem
Replies: 16
Views: 3588

Re: How to use Monte Carlo on a decision problem

Yes, I see now why recursion is necessary.

thanks!
Wed Jan 14, 2015 1:25 am UTC
Forum: Mathematics
Topic: How to use Monte Carlo on a decision problem
Replies: 16
Views: 3588

Re: How to use Monte Carlo on a decision problem

So the question is what should actually happen in step 2 in my earlier comment? It seems to be something like this:- Yes, I see what you mean. I don't think it would involve a large running time -- I don't see where recursion is necessary. Just do N simulated runs of opening up all the envelopes an...
Tue Jan 13, 2015 9:40 pm UTC
Forum: Mathematics
Topic: How to use Monte Carlo on a decision problem
Replies: 16
Views: 3588

Re: How to use Monte Carlo on a decision problem

Well suppose our probability functions are 'well-behaved' and not too skewed, and that i'm not gambling. Also suppose that the number of envelopes is low enough that my knowledge of the furthest envelopes isn't too murky. Or if Monte Carlo really isn't a good idea, are there any analytic solutions?
Tue Jan 13, 2015 1:45 am UTC
Forum: Mathematics
Topic: How to use Monte Carlo on a decision problem
Replies: 16
Views: 3588

Re: How to use Monte Carlo on a decision problem

Yes, you don't know the cost of opening an envelope until you open it.

You can get a better idea of the probability distribution of an envelope as you approach it.

and yes, you've got steps right. Though I would be using Monte Carlo to make the decision in step 2, not 1.

thanks!
Tue Jan 13, 2015 12:50 am UTC
Forum: Mathematics
Topic: How to use Monte Carlo on a decision problem
Replies: 16
Views: 3588

Re: How to use Monte Carlo on a decision problem

I'd like to ask for some clarification. Is the real number an amount of money you then get? It's how much it costs to open the envelope. But i suppose if you flipped all the signs you'd end up with the money you get so it goes either way. I'd like to ask for some clarification. Does that mean that ...
Mon Jan 12, 2015 11:49 pm UTC
Forum: Mathematics
Topic: How to use Monte Carlo on a decision problem
Replies: 16
Views: 3588

How to use Monte Carlo on a decision problem

There is a box filled with envelopes labeled 1, 2, .... n containing real numbers x_1, x_2, .... x_n respectively. It will cost me x_i dollars to open envelope i, and I cannot open envelope x_i before I have opened envelope x_i-1. I do not know the value of x_i until i open the envelope, but I do kn...

Go to advanced search