Name: Remco van der Hofstad - 複雜網絡的結構。無標度和小世界隨機圖形 (Remco van der Hofstad - The Structure of Complex Networks: Scale-Free and Small-World Random Graphs)
Uploaded: 2021-01-14T07:55:16.000Z
Duration: 1 h 1 min 54 s
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My pleasure to introduce to you professor Remco van der Hofstad.

情態副詞

But I heard about many of his great work.

Ramco is professor of probability at Eindhoven University.

He's doing a lot of work in the stochastic networks.

Among other, Prix Henri Poincare, 2003, and Rolo Davidson in 2007.

today he will be talking about structure of complex networks.

Small worth and scale-free random graphs.

Ramco, please. >> Thank you very much, and thank you for

So I'm a probabilist, working from the math department.

I'm interacting as well with engineers with various different backgrounds.

I'll be giving a talk that hopefully is at a relatively high level.

If there's anything that I'm saying that is unclear to you,

do ask because I'm giving this talk for you guys, and not for myself.

I'm supposed to know what I'm talking about.

And what I'll be talking about is structures of complex networks.

And this is very long line of research that we've been seeing all over the world.

Basically starting slightly before 2000, and

all of the empirical observation that have been found,

we'll discuss some of those as well, and then all of the efforts in modeling and

driving consequences of the observed phenomena.

And that's what I'll talking about today, all right.

Here are two examples, certainly the one on the left

is a very famous one from a paper of Balabassi and others.

the interactions that exist between proteins in a yeast cell.

So first of all, there is quite a few proteins as you can see.

And there's quite a few interactions between them as well.

And the interactions come in different forms.

It could be that two proteins together form a third protein.

But it could also be that certain proteins act as catalysts for

reactions that others are being involved in.

So the edges here can really signify lots of different biological interactions.

And you can imagine that producing a picture like this

is an enormous amount of work in biology, because you've gotta figure out what all

of the different reactions are that are taking place in one of these yeast cells.

And one of the things we see is that it's a fairly complex picture, and

that's my very informal definition of what a complex network is.

their many connections between them and it's pretty complex.

I don't think that there's any better definition of what a complex network is,

even though lots of people are using this terminology.

Now on the right, we see an artistic impression for

what the Internet Topology looks like in 2001.

I don't think that the artistic pictures are going to be changing a lot over time.

But again what you see is that, like here, we're on the outskirt,

you have things that are very loosely connected to the inside.

Which the inside being sort of a very highly connected bit,

sometimes called the core, certainly in Internet.

Here, the connections are so dense that you can't even visualize them.

Whereas on the outskirts here, you see lots routers,

as we're talking about Internet here, that are only connected through one or

Now, these networks come from completely different backgrounds.

And you can imagine that there's many more backgrounds to be observed.

Social networks, acquaintances, but also sexual relations, collaborations, etc.

Information networks, technological networks and biological networks.

So these networks come from various different backgrounds, so

it's actually quiet surprising that they share something.

And that's actually was one of the most profound empirical observations.

And many of these networks have things in common.

And that of course raises the question of whether these things that they

have in common are typical in such networks,

whether almost all of those networks have those properties, or

whether it is something very special, and if it's something very special,

what are the underlying principles that actually give rise to these properties?

So these are very broad questions in science.

I'm a humble mathematician, so we can certainly not answer all of those

questions for all of these different disciplines at the same time, but

it's just to indicate that network science is a very interdisciplinary field in which

lots of different communites look at their networks in their own different ways and

give rise to very interesting questions that are on the interplay with

And mathematicians can really say something sensible here and

we help these petitioners from different fields in answering their questions

What are we talking about when we're talking about a network?

Well, in general, we're just talking about graphs, and

graphs consist of entities that are connected to one another.

Sometimes nodes or sites, depending on the precise fuel that you're talking about.

And then you have connections between them.

And these are called edges, sometimes bonds, and

there's probably many more names for them.

And you should really think of these edges as being the building blocks of

They really indicate which vertices are interacting with which other vertex.

And you can think of an edge as being the building block of relational data.

Really think of an edge as indicating that there is some relation,

whatever the relation means, between the two vertices on the sides of the edge.

So that's what we are talking about here.

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Remco van der Hofstad - 複雜網絡的結構。無標度和小世界隨機圖形 (Remco van der Hofstad - The Structure of Complex Networks: Scale-Free and Small-World Random Graphs)

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