Markov was an atheist and he had no patience for people who were being unrigorous, something he considered Nekrasov to be, because in his eyes,
Markov had shattered Nekrasov's argument, and he knew it.
So Markov set out to prove that dependent events could also follow the law of large numbers, and that you can still do probability with dependent events.
Then Markov broke the string into overlapping pairs, that gave him four possible combinations, vowel-vowel, consonant-consonant,
So Markov had shown that the letters were dependent.
So Markov had built a dependent system, a literal chain of events, and he showed that it still followed the law of large numbers,
And Markov himself seemingly didn't care much about how it might be applied to practical events.
Harry Markopolos is a quant.
Harry Markopolos is a very, very smart hedge fund manager, and Harry Markopolos got a warning of a hedge fund run by a guy named Bernie Madoff.
Harry Markopolos learned that the hard way.
The Markowitz and its derivative equations lost investors' money about 40% of the time.
as Markov did like a 200 pound kid and they injected a similarly sized pallet of rice and it was the pig to see if it
this happened Marko was arrested.
- But to Markov, Nekrasov was delusional.
But when Markov actually counted, he found vowel-vowel pairs only show up 6% of the time, way less than if they were independent.
the exact split Markov had counted by hand.
With this Markov chain, as it came to be known, he found a way to do probability with dependent events.
By using Markov chains, Page and Brin had built a better search engine, and they called it PageRank.
He went back to Markov's original idea of predicting text, but instead of just using vowels and consonants, he focused on individual letters.
But the beautiful thing Markov and others found is that for many of these systems you can ignore almost all of that.
that's the Markowitz efficiency frontier.
And Harry Markowitz won the Nobel Prize for this.
He used Markov chains, Monte Carlo sampling techniques. Published it. Got no reaction at all. A year later, drops out of research and goes to teach at the University of British
and so it ends its Markov chain, or it can strike another uranium-235 atom, triggering a fission event and releasing two or three more neutrons
So now we can run this Markov chain and see what happens.
So there are some systems where Markov chains don't work, but for many other dependent systems, they offer a way of doing probability.
And if you read John Markoff's book, "What the Dormouse Saw," the early days were a bunch of people who were stoners, and trippers, and poets manque,
This program is written up by John Markoff in "The New York Times" this summer, "A Machine in the Co-pilot's Seat." There's a kind of prototype of it that Aurora has already made
rule on some derivatives of the Markowitz rule across 28 real-world data sets.
So we used something called Markov state models that was also developed at Standford mainly.
the international transparency movement is a guy named Marko Rakar, who several years ago he had a printing business, um, and ah, a tax auditor came to him and basically demanded
Um, and Marko is, is, uh, part of a generation of people in Croatia who are trying to move that country from being very much an authoritarian system to something that's more open and democratic.
- His intellectual nemesis on the socialist side was Andrey Markov, also known as Andrey The Furious.
And this was the idea that sparked Nekrasov and Markov's feud.
So to test this, Markov turned to a poem at the heart of Russian literature, "Eugene Onegin" by Alexander Pushkin.
Well, Markov knew that if you pick a random starting point, there is a 43% chance that it'll be a vowel.
Many of these processes could be modeled using Markov chains.
What von Neumann realized is that you needed a Markov chain.
And it wouldn't be the last time Markov chain based method changed the course of human affairs.
- And at the heart of this trillion dollar algorithm is a Markov chain, which only looks at the current state to predict what's going to happen next.
And it's this memoryless property that makes Markov chains so powerful because it's what allows you to take these extremely complex systems
So you can think of card shuffling as a Markov chain where each deck arrangement is a state, and then each shuffle is a step.
You can discover how large language models actually work from basic Markov chains to complex neural networks, or dig into the math behind this shuffling question.
So this is an equation written by a guy named Harry Markowitz to address on of the fundamental issues in finance, which is how you allocate your asset
I was one of the pioneers of hierarchical hidden Markov models in the '80s and '90s and used that for speech recognition, and today, that is the dominant technique in
No, that's Steve Markowski standing next to me, and I thin he was holding the basketball.
the Madoff case, Harry Markopolos, wrote extensively about this. And he provides some interesting quotes to explain what was going on in people's minds when they encountered Bernard Madoff.
remember the famous umbrella murder in 1978 where you Markov standing at a
There's Marko .
So what they realized is that we can model the web as a Markov chain.