Sergey Malgin » Math (Математика)

An introduction to Category Theory for Software Engineers

Sergey — Wed, 21 Apr 2010 03:56:50 +0000

An introduction to Category Theory for
Software Engineers

Minus two fish

Sergey — Tue, 29 Dec 2009 02:41:14 +0000

I dedicate this post to Paul Adrien Maurice Dirac

Three fishermen come back from the sea, celebrating the catch of the day. They land their boat and set up camp. After much drinking (rum?), each collapses in their respective tent. Fisherman #1 wakes up and, after relieving himself, decides to get his share of the catch. He counts the fish, realizes it is not a number divisible by three, throws away one fish to the sea correcting the situation, and takes a third of the remaining fish into his tent. Fisherman #2 wakes up later, goes to pee too, and also decides he is going to get his share of the catch. Unaware that Fisherman #1 already took his part, Fisherman #2 wants a third of the fish he sees. It is not a multiple of three, but he throws away one fish and takes a third of the fish and goes to sleep. Fisherman #3 wakes up after, and does the same: he throws away one fish, takes a third of the fish, and goes into his tent.

What is the smallest number of fish for which this would happen?

Continuations

Sergey — Sat, 23 May 2009 02:57:47 +0000

Признаюсь в страшном:

Читать такой код

public IEnumerator GetEnumerator()
{
foreach (var element in _elements)
yield return new DynamicXml( element );
}

Я могу только с дикими тормозами. Мозг каждый раз визуализирует глобальную переменную __foo2d345fa5f, которая держит конкретное состояние конкретного объекта. Как только я визуализирую global state как некое бесформенное облако (можно в штанах) с торчащими из него yield return, жить станет легче. Но это ж как себя надо ломать!

Чувствую, пора дальше осваивать Scheme. Хочу stateless. Ну, максимум монады. Для души.

Notification strategies for social networks

Sergey — Tue, 05 May 2009 18:22:07 +0000

http://20bits.com/articles/notification-strategies-for-social-networks/

Простенькая вводная статья, иллюстрирующая проблему и дающая ссылку на хороший алгоритм.

Чтобы не забыть.

Множество Мандельброта в стиле Барокко

Sergey — Mon, 03 Nov 2008 05:58:55 +0000

Крышу сносит, голова после просмотра кружится :)

Пойду писать скринсейвер… :)

смотреть тут:

http://www.youtube.com/watch?v=WAJE35wX1nQ&fmt=18

PS так быстро на скринсейвере оно, конечно, считать не будетъ :) :)

PPS О! Я его на несколько машин распараллелю, у меня есть пяток. Заодно опробую VC2010 CTP :) А может даже через CCR … выбор есть короче. Еще мне Cilk++ рекламировали… :)

Derbyshire math puzzle and a solution

Sergey — Thu, 19 Apr 2007 00:36:00 +0000

http://elgordillo.blogspot.com/2004/09/another-derbyshire-maths-problem.html

Puzzle:

Consider the powers of two: 2, 4, 8, 16, 32, 64, 128… Their right-most digits follow a simple repetitive pattern: 2, 4, 8, 6, 2, 4, 8, 6, 2, 4, 8, 6… What about their left-most digits, though? Here are the first 40-odd [actually, it's the first 149 - Ed.]. (Read right to left, line by line. I’ve just jammed the digits together, leaving out the courtesy commas, to save space.)

24813612512481361251248136125

124813612512481371251249137125

124913712512491371361249137136

124913713612512481361251248136

125124813612512481361251248137…

There is a pattern there, but it keeps breaking down. When you get up into really big powers of 2, in fact, it breaks down altogether. For the ten powers of 2 from the 30th to the 39th, for instance, we have lead digits 1, 2, 4, 8, 1, 3, 6, 1, 2, 5. For the ten powers from the billionth to the 1,000,000,009th, by contrast, we have lead digits 4, 9, 1, 3, 7, 1, 2, 5, 1, 2. Every digit (except, of course, zero) shows up, though.

I am going to refer to this infinite sequence of digits as “the sequence.” Now I am going to ask the following two questions: In the first N digits of the sequence, how many occurrences of 3 shall I find? And how many occurrences of 4?

Call the first number U(N), the second V(N). The first few values of U(N) and V(N), for N from 1 to 15, look like this, as you can easily verify:

U(N) = 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2,…

V(N) = 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2,…

Show that for sufficiently large N, U(N) will always be bigger than V(N). Find the limit of the ratio U(N) to V(N) as N tends to infinity.

Индуктивная логика

Sergey — Wed, 24 Jan 2007 23:04:00 +0000

Читаю в стэнфордовской энциклопедии статью про индуктивную логику, набираюсь ума.

И нахожу там следующий абзац:

It is now generally held that the core idea of Bayesian logicism is fatally flawed—that syntactic logical structure cannot be the sole determiner of the degree to which premises inductively support conclusions. A crucial facet of the problem faced by Bayesian logicism involves how the logic is supposed to apply to scientific contexts where the conclusion sentence is some hypothesis or theory, and the premises are evidence claims. The difficulty is that in any probabilistic logic that satisfies the usual axioms for probabilities, the inductive support for a hypothesis must depend in part on its prior probability. This prior probability represents how plausible the hypothesis is supposed to be on its own, before the evidence is brought to bear. A Bayesian logicist must tell us how to assign values to these pre-evidential prior plausibilities for each hypothesis or theory under consideration, and must do so in a way that relies only on their syntactic logical structure, or on some measure of their syntactic simplicity. There are severe technical problems with getting this idea to work. Moreover, various counter-examples seem to show that such an approach must assign intuitively quite unreasonable prior probabilities to many hypotheses.

думаю – что-то мне это напоминает…

АААА!!! ВОТ!!!!

http://www.dilbert.com/comics/dilbert/archive/dilbert-20061231.html

PS
Не понимающим английского: увы и ах вам. Лениво переводить.

Data Mining, selected quotes

Sergey — Wed, 24 Jan 2007 22:42:00 +0000

A data mining system has the potential to generate thousands or even millions of patterns, or rules.

So, you may ask, are all of the patterns interesting? Typically not – only a small fraction of the patterns potentially generated would actually be of interest to any given user.

This raises some serious questions for data mining. You may wonder, What makes a pattern interesting? Can a data mining system generate all of the interesting patterns? Can a data mining system generate only interesting patterns?

To answer a first question, a pattern is interesting, if (1) it is easily understood by humans, (2) valid on new or test data with some degree of certainty, (3) potentially useful and (4) novel. A pattern is also interesting if it validates a hypothesis that the user sought to confirm. An interesting pattern represents knowledge.

Stanford School of Engineering – puzzle of the month

Sergey — Sun, 22 Jan 2006 07:27:00 +0000

http://soe.stanford.edu/alumni/puzzle.html

Quite easy, but neat :)

Mementos

Sergey — Thu, 08 Dec 2005 19:34:00 +0000

Usability and link design notes :)

http://www.designbyfire.com/deye_web/alertbox.htm

Nielsen Norman Group

http://www.nngroup.com/events/

Beginner’s guide to Search Engine Optimisation

http://www.seomoz.org/beginners.php

Numerical Recipes in C

http://www.library.cornell.edu/nr/bookcpdf.html

TODO: Find out what do they exactly do there:
“Case researchers discover methods to find ‘needles in haystack’ in data”
Create powerful statistical techniques to detect signals”

http://www.eurekalert.org/pub_releases/2005-12/cwru-crd120505.php