Talk:Andrey Markov

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Also the equation put up for which he won the gold medal seems too simple. The veracity needs to be checked. —Preceding unsigned comment added by Arjun.theone (talk • contribs) 12:56, 28 December 2007 (UTC)[reply]

No! You must not know too much about differential equations, and especially not about the differential equations of the 19th Century. That differential equation is quite complicated enough. Also, the complexity of the solution of a differential equation cannot be easily perceived just by glancing at it. Just look at the simple-looking differential equations of Bessel that cannot be solved in a "closed form", but rather they take exacting power series methods to solve them. Sometimes, those solutions define new functions. Furthermore, some other differential equations require Fourier series to solve them, and once again the answer cannot be expressed in a closed form.

In contrast, there are some differential equations that look really complicated, but their solutions work out simply because of the cancelation of a lot of terms in the solution. Please do go study differential equations for two semesters or more.
98.67.108.12 (talk) 15:00, 31 August 2012 (UTC)[reply]

In the article there is "Andreyevich" and "Andreevich" which presumably differ only in transliteration. Is there a standard transliteration for this? 67.101.45.65 (talk) 20:07, 28 June 2008 (UTC)[reply]

No, there are not standard transliterations from Russian into English, French, German, Spanish, etc. (If there were, we would probably use them.) Please see the article on Chebyshev to see the ten different ways that this name is transliterated into English.
98.67.108.12 (talk) 15:00, 31 August 2012 (UTC)[reply]

Good question. The Russian spelling should be Андреевич in both cases. I'm too ignorant of the transcription rules from Russian to English employed by en-wp to be able to decide which one of them is correct, though. JoergenB (talk) 19:52, 24 December 2011 (UTC)[reply]

I have seen the incorrect word "transcription" used several times. The real word is "transliteration". (Transcription is a much simpler process.)
98.67.108.12 (talk) 15:01, 31 August 2012 (UTC)[reply]

I suggest to rearrange articles on A. A. Markov and his son in the following way.

• - Andrey Markov will be a disambiguation page with three entries, Andrey Markov, Sr. (Russian mathematician, specialized in probability), Andrey Markov, Jr. (Soviet mathematician, specialized in logic), Andrei Markov (hockey player);
• - all pages like Andrei Markov, A .A. Markov, Andrey Andreyevich Markov are redirects to this disambiguation page;
• - real pages for A.A. Markovs will be placed at Andrey Markov, Sr. (mathematician) and Andrey Markov, Jr. (mathematician) and Andrei Markov (ice hockey)

Current situation leads to many confusions that are difficult to detect (see at "What links here" and look for logic or hockey-related articles). Of course, they can be linked properly, but such mistakes will emerge again almost surely, as any editor who make a link to A.A.Markov (meaning Jr.) can even test this link, read the first phrase of the article "A.A. Markov was a Russian mathematician..." and became satisfied.--92.39.161.221 (talk) 21:51, 4 May 2008 (UTC)[reply]

There was actually an Andrei Markov who was the father of Andrei Andreyovich Markov (Sr.) and the grandfather of Andrei Andreyovich Markov (Jr.) - but the grandfather was not a mathematician, physicist, etc. In any case, Andreyovich means "son of Andrei", and this implies that the grandfather was Andrei Markov. The one thing that I have been able to figure out about him is that his middle name was NOT Andreyovich.
98.67.108.12 (talk) 15:00, 31 August 2012 (UTC)[reply]

Hi all,

Hierarchical Hidden Markov Models, of great importance in machine learning in the recent years, apparently were pioneered by Markov himself. I have, however, not found primary sources on this.

According to the following, Markov himself and subsequently Norbert Wiener hypothesized models of hierarchical sequences of states:

"The Russian mathematician Andrei Andreyevich Markov (1856 - 1922) built a mathematical theory of hierarchical sequences of states. The model was based on the possibility of traversing the states in one chain, and if that was successful, triggering a state in the next higher level in the hierarchy. Sound familiar? Markov's model included probabilities of each state's successfully occurring. He went on to hypothesize a situation in which a system has such a hierarchy of linear sequences of states, but those are unable to be directly examined-- hence the name hidden Markov models. The lowest level of the hierarchy emits signals, which are all we are allowed to see. Markov provides sa mathematical technique to compute what the probabilities of each transition must be based on the observed output. The method was subsequently refined by Norbert Wiener in 1923. Wiener's refinement also provided a way to determine the connections in the Markov model; essentially any connection with too low a probability was considered not to exist. This is essentially how the human neocortex trims connections-- if they are rarely or never used, they are considered unlikely and are pruned away. In our case, " Source: How to create a mind, Ray Kurzweil.

I have so far located Markov's first paper on chains, his 1907 "Extension of the limit theorems of probability theory to a sum of variables connected in a chain". I have yet not found his hierarchical models.

Does anyone know more about this? Kurzweil himself claims to have pioneered the use of HHMMs in the 80s and 90s.