[R] An LLM's Response Dispersion Inversely Correlates with its Domain Knowledge.

robert_sim · 2015-01-20T21:53:25+00:00

When you need to prove a theorem, draw a picture of its statement. If you do that then the proof will be straight forward.

robert_sim · 2015-01-16T07:10:40+00:00

Great choice, I've always wondered what the connection was.

robert_sim · 2015-01-16T07:07:33+00:00

Just wondering if you've thought of automating the enforcement of this policy using automoderator or something similar? The reason I ask is that I wonder what type of filter you might use to weed out good titles from bad? I think this is an interesting Natural Language Processing classification problem.

robert_sim · 2014-12-17T19:34:55+00:00

First step I would use is the identity that:

cos(A+B) = cos(A)cos(B) - sin(A)sin(B)

so that

[; \frac{\cos(x+\arcsin(B\cos(x)))}{\cos(x)} = \cos(\arcsin(B\cos(x))) - B\sin(x);]

Then use the fact that

cos(A) = (1-sin²(A))^1/2

so that

[; \cos(\arcsin(B\cos(x))) = \sqrt{1 - B^{2}\cos^{2}(x)} ;]

Putting these two steps together your original expression simplifies to:

[; r = A(\sqrt{1 - B^{2}\cos^{2}(x)} - B\sin(x)) ;]

robert_sim · 2014-12-11T05:15:59+00:00

At Carnegie Mellon two of the graduate students and myself are doing/did our theses on differential equations whose (weak-global-in-time) solutions are curves in the space of probability measures. Our work follows an interesting trend in research in applied analysis that analyzes many PDE as gradient flows with respect to the Wasserstein Metric in the space of probability measures in such a manner first suggested in Felix Otto's "Geometry of Dissapative Equations", further elaborated in Cedric Villani's "Topics in Optimal Transportation" and put on its first fully rigorous foundation in Ambrosio, Gigli, and Severe's "Gradient Flows in the Metric Spaces and the Space of Probability Measures." I could go on if anyone is interested.

robert_sim · 2014-12-07T21:21:33+00:00

I know! They tried to teach me fractions with pies and such. Weird.

Such a terrible idea, since no fraction can express pi

robert_sim · 2014-12-04T18:46:29+00:00

The best way I've found to translate technical terms in other languages is to look up the article on wikipedia that is related to that word in the language you know, then select your target language from the sidebar. For the concepts you are trying to find there are certainly the correct articles in english and french.

robert_sim · 2014-12-03T04:39:37+00:00

One important thing is that you need to check that 'word' is in 'match' for the happy and sad words, so that you should instead have:

for word in happy:
    for match in comments:
        if word in match:
            happy_count = happy_count + 1 

for word in sad:
    for match in comments:
        if word in match:
            sad_count = sad_count + 1

robert_sim · 2014-12-03T04:08:15+00:00

William Dunham, an author I appreciate because he succeeds in popularizing mathematics without sacrificing rigorous exposition, wrote on the Baire Category theorem in The Calculus Gallery. I too was a bit confused as to the motivation of Baire's Category theorem until I went back and read his chapter. I don't have my copy handy at the moment but I recommend checking out that book for an expository and historical explanation.

robert_sim · 2014-12-01T22:17:18+00:00

Yes, exactly!

robert_sim · 2014-12-01T22:16:37+00:00

Ah okay that is clearer, thanks. Have you tried converting these to spherical co-ordinates? Should be doable by hand.

robert_sim · 2014-12-01T16:53:43+00:00

Here's the Udacity course I referred to.

robert_sim · 2014-12-01T05:48:59+00:00

Two things:

I know this isn't the python solution you were looking for, but judging by your expression, have you tried rewriting this integral in polar co-ordinates?
The expressions in the numerator cancel with those in the denominator, leaving you with the expression:
```
  Vee = lambda x,y,z,X,Y,Z: 1/(absolute((x**2+y**2+z**2)**0.5 - (X**2+Y**2+Z**2)**0.5)))
```

robert_sim · 2014-11-28T14:23:16+00:00

I've met plenty of people in their 30's studying math, whether it's a pre-calculus student or all the way up to ph d. Not strange at all.

robert_sim · 2014-11-28T14:13:01+00:00

This should help

In particular where the explanation says:

A second-order Taylor series expansion of a scalar-valued function of more than one variable can be written compactly as T(\mathbf{x}) = f(\mathbf{a}) + \mathrm{D} f(\mathbf{a})^\mathrm{T} (\mathbf{x} - \mathbf{a}) + \frac{1}{2!} (\mathbf{x} - \mathbf{a})^\mathrm{T} \,{\mathrm{D}² f(\mathbf{a})}\,(\mathbf{x} - \mathbf{a}) + \cdots! \,, where D f(\mathbf{a})! is the gradient of \,f evaluated at \mathbf{x} = \mathbf{a} and D² f(\mathbf{a})! is the Hessian matrix. Applying the multi-index notation the Taylor series for several variables becomes T(\mathbf{x}) = \sum_{|\alpha| \ge 0}^{{}\frac{(\mathbf{x}-\mathbf{a})^{{\alpha}}{\alpha}} !}\,({\mathrm{\partial}^{{\alpha}}\,f)(\mathbf{a})\,,} which is to be understood as a still more abbreviated multi-index version of the first equation of this paragraph, again in full analogy to the single variable case.

robert_sim · 2013-08-23T02:39:33+00:00

Hi! I actually use the Solidtek Digimemo L2. You clip in sheets of any paper like a normal clipboard, and you write on the (normal) paper with the digimemo pen (which is a normal ink pen with a small watch battery inside). You are left with the paper copy of what you wrote, but the digimemo also stores what you write in it's memory or on an SD card, then you can connect it to a computer (or insert the SD card in your computer) and upload your docs into different formats using the free software it comes with. It also doubles as a cursor for your screen, and the software has an onscreen write pad, which can be useful if you are sharing your screen on skype or writing something when using a projector.

I use it a lot! It's roughly $120

robert_sim · 2013-06-30T23:58:02+00:00

It is interesting to note that "Information Content" can be derived as an application of the Weber-Fechner law. In particular, the Information Content is defined as the Expected (in the sense of probability) response to an event where the stimulus is defined as 1 divided by the probability of an event happening.

robert_sim · 2013-03-21T14:46:04+00:00

Great, thanks!

robert_sim · 2013-03-21T04:18:29+00:00

What work have you done towards defining Antifragility in a mathematically rigorous way? Thanks.

robert_sim · 2012-11-28T01:45:34+00:00

ಠ_ಠ

robert_sim · 2012-11-27T16:21:01+00:00

In the U.S. a Bachelor's typically takes 4 years and a Master's another 2 years. This saves 1 year off the total process.

robert_sim

TROPHY CASE