I'm partitioning a partitioned unit.

This is called fuel partitioning in the lingo.

In terms of equilibrium, there's 2 equilibrium points, the 9 9 and the 5 5.

Spectral partitioning, L1 minimization. This comes from the optimization community.

It does an equilibrium glide. Highly controlled.

But it's being balanced like that in equilibrium.

Now, the third concept is the concept of equilibrium.

It's sort of cool that Top K via partitioning as just described works.

The time it takes to run Top K via partitioning on one element.

It's a revolution in that it's a change in equilibrium.

The equilibrium point defines a pure strategy for each player.

It's kind of a partially sorted list, and we call this partitioning around V.

The first is, the system has to be in non equilibrium.

So, lets imagine there is some problem called graph partitioning which is a real problem.

What I want you is find the equilibrium point for this game.

There will be one equilibrium point. I want you to find it.

You must figure the tumult suddenly striking on the unstable equilibrium of old

Are they ever in equilibrium in the way that you see your work?

He says, the problem with thermal equilibrium is that we can't live there.

Every mammal on this planet instinctively develops an equilibrium with the surrounding environment.

Now, the partitioning algorithm is going to split this list L into a left and a right.

Do we know that graph partitioning is in NP, and therefore an exponential time solution would exist?

Now it's four apple cubes, and their behavior again moves towards the Nash equilibrium.

Economists talk about game theory, that every two person game has a Nash equilibrium.

And that equilibrium is not what the United States would like, but it's probably an equilibrium that the United States can live with, and that a lot of others can live with.

Let's go over now how we can actually solve the top K problem using this idea of partitioning.

Then tell me the outcome for the game for each player for that equilibrium point.

So Boltzmann says, look, you could start with a universe that was in thermal equilibrium.

dividing Guttermeg's principle of opposing forces in motion, and adjusting for the difference in equilibrium...

So when the fish control the urchin population, the ocean was restored to its natural equilibrium.

When we observe the world, what we're doing is we're taking the current belief state and partitioning it up into pieces.

level. Morally, the reason this is happening is because of a perfect equilibrium between two competing forces.

Right. Let's do an analysis of the time it takes for a Top K to do its work via this partitioning approach.

This is very similar to the K partitioning algorithm from the lectures, but returns a single value only, instead of a list.

Similarly, for the politicians, click on the right box for their strategy, which leads to the equilibrium point.

An equilibrium is a mathematical state in which everybody has figured out exactly what everyone else will do.

We would not be able to process information, metabolize, walk and talk, if we lived in thermal equilibrium.

This is Niles Eldredge. He was the co developer with Stephen Jay Gould of the theory of punctuated equilibrium.

That leads us to this Nash equilibrium point, and the values of that outcome are 3 for each party.

And as you can see, their behavior moves up in the direction of this change in the Nash equilibrium.

Multiplying these two together, the final virialized state of structured equilibrium, would be 180 times denser than surrounding background.

And like our relationship with the ecosystem we're always searching for equilibrium in how we divide ourselves across the planet.

From virial equilibrium that told him how much total mass there has to be in order to bind galaxies together.

Because picking a number that low is actually a bad choice if other people aren't doing equilibrium analysis as well.

When it's in the equilibrium state, the Virial theorem state, tells you kinetic energy will be 1 2 the potential .