Not strictly academic geogebra app, more of visualisation onto how #bias and #variance in fact works.
Great visualisation for beginners, in my humble opinion.
Use sliders to change bias and variance of prediction of random dataset.
Geogebra applet with 4 datapoints, fitting line with best square distance (from point to line)
square here, as well as in variance concept – is because distance can well be negative, but we need to be able to sum it neatly somehow, therefore square is rational with MMSE and variance
Have met a concept of Bayes theorem, and would pretty much like to visualize it here. As per purpose of this blog, its studying diary, so pretty much – visualizations, and making of those – would give me myself broader understanding.
Not to mention, that keeping notes publicly does make wanders to being neat in thoughtful way, so – lets begin.
Suppose we hear the description of a man: “He is strong and with a loud strong but assuring voice”.
Who is this man, do we want to guess – is he a librarian or a military drill sergeant?
Добрый день. Раз пошла такая пьянка, нужен наверное сайт, куда удобно скидывать более постоянные артикли, которые можно редактировать.
Следуюший, вполне логичный шаг, после создание видео-вопроса.
См. следующую статью
Suppose we have two countably infinite sets, which means we can find injection (one-to-one) relation to natural numbers.
In other words, we could literally assign natural number indexes to only one of each member of the set.
So, we have with cardinality , and with cardinality
Then cartersian product (set of all possible pairs from A and from B) – is also infinite, but countable. I mean, for , we can assign single natural number for each member of P.
Lets prove it. Suppose we injections f and g, so that and
Lets define function this way:
Then for and , because of unique division into primes and f,g injectivity (a,b)=(c,d).
Therefore there is injection from p(a,b) to natural numbers, and cartesian product is infinitely countable.
About number construction
helmi 13
– Let us construct natural numbers (0,1,2,3..)
– Then from naturals, lets construct integer numbers (…,-2,-1,0,1,2…)
– Then from integers, lets construct rationals (…,-0.3,…,0,…,1/2,..,0.75,..)
– And finally from rationals – real numbers (…,-0.3,…,0,…,1/π,…,1/2,..,0.75,..,e,…,π,…)
Read the rest of this entry »
Lets consider linear cellular automata with Wolfram rule 90
Elementary cellular automata is essentially string of two symbols, lets call them 0 and 1, equipped with rules (and starting configuration, of course)
Rule takes symbol in the position, as well as left and right neighbors. Ie – when calculating symbol of the cell, we should consider 3 cells, cell to the left, cell itself and cell to the right.
Ie – suppose we have set of rules(*):111 - 0
110 - 1
101 - 0
100 - 1
011 - 1
010 - 0
001 - 1
000 - 0
Or graphically:

So if we have 10011 for starting configuration, calculation goes like this(from top to bottom):
1 | 0 | 0 | 1 | 1 |
(0) | 1 | 1 | 1 | (1) |
(1) | 1 | 0 | 0 | (1) |
(italics) means that we dont know which symbol is to the left and right to the starting configuration, for simplicity I consider here absent symbols to be 0s (ie …00000100110000…)
Now, what is 90, which is called Wolfram rule.
It is obvious, that 3 cells define state, and since we have two symbols, all possible combinations are , and since we have two possible symbols for each combination – rule of CA can be expressed as (0,2⁸=256) number.
90 in binary would be (*), which is enough to describe elementary ca behavior.
There were question in exam, which I understood very close to correct, thus absolutely wrong.

Roughly translated: “Define real axis ℝ Lebesque outermeasure on ℝ² surface“
Lets get into it. Bit intuitively first.. Suppose we have segment of a line (a,b)

segment (s) itself can be expressed as
Actually, lets forget about s, lets consider without segments, ie
Then outer measure can be expressed as union of open sets:
for all
Where intervals are:
Thus length of intervals are from one integer to another – ,.. all integers
Height of intervals are
Ie , where biggest height is , which is quater of epsilon.
Therefore
or shorter: and for all
It is obvious from here
This article was inspired by Margarita.
Opiskelu.org – reborn
helmi 7

I think I’d better come back to good old opiskelu.org, instead of spamming facebook page.
Oh yea, it all seems to work now.. kinda enjoy new editor for WordPress. So – here are plans for the future:
- Lebesque integral and measure, few notes regarding course and exam (english/finnish)
- Cellular Automata (english)
- Bitcoin shop with tor in mind (english)
- Немножко политики/russian politics (russian/english)
There. Lebesque integral notes&measure is coming today.
CA – on this weekend, based on university lecture.
Bitshop – next week.
Russian politics – when feel like it.